FEATURE ARTICLE
Intracellular metabolite levels shape sulfur isotope
fractionation during microbial sulfate respiration
Boswell A. Winga,1,2 and Itay Halevyb,1,2
a
Department of Earth and Planetary Sciences and GEOTOP, McGill University, Montréal, QC, Canada H3A 0E8; and bDepartment of Earth and Planetary
Sciences, Weizmann Institute of Science, Rehovot 76100, Israel
This Feature Article is part of a series identified by the Editorial Board as reporting findings of exceptional significance.
dissimilatory sulfate reduction
flux–force relationship
| sulfur isotope fractionation |
D
issimilatory sulfate reduction is a respiratory process used by
some bacteria and archaea to generate energy under anaerobic conditions. Aqueous sulfate serves as the terminal electron
acceptor in this process, leading to the oxidation of organic carbon
compounds and sometimes hydrogen and to the production of
aqueous sulfide (1). Dissimilatory sulfate respiration was one of
the first microbial metabolisms to be isotopically characterized
through culture experiments (2), with 32S-bearing sulfate shown
to be consumed preferentially to 34S-bearing sulfate. Early
experiments identified two critical features of this dissimilatory
sulfur isotope fractionation: Its magnitude correlates inversely
with the sulfate reduction rate of an individual cell but correlates
directly with extracellular sulfate concentrations (3–5).
Through careful regulation of the environmental controls on
respiration, more recent experiments have precisely calibrated
these relationships and suggest that their particular form may
be strain specific (6–11). All experiments, however, show a nonlinear response, where sulfur isotope fractionation increases rapidly
with decreasing rate. At the low-rate limit, sulfur isotope fractionation appears to approach levels defined by thermodynamic equilibrium between aqueous sulfate and sulfide (8, 12), the initial
reactant and final waste product in the respiratory processing chain.
In parallel with experimental studies, theoretical work has
built a broad foundation for understanding the net sulfur isotope
fractionation expressed during sulfate respiration (13–17). These
efforts initially dealt with sulfur flow through simplified metabolic networks (13) (Fig. 1A) and have expanded to incorporate,
for example, electron supply to the reaction cycles of individual
respiratory enzymes (17). The reversibility of an individual enzymatic reaction is a central theoretical concept behind these
approaches, as it carries the isotopic memory of downstream
steps in the pathway (Fig. 1A). Net “back flux” of sulfur from
product sulfide to reactant sulfate was an early experimental
observation with pure cultures of sulfate-reducing bacteria (18),
www.pnas.org/cgi/doi/10.1073/pnas.1407502111
supported recently by a similar demonstration in a sulfatereducing coculture (19).
Here we describe a quantitative model for sulfur isotope
fractionation during microbial sulfate dissimilation that explicitly
links fractionation, reaction reversibility, and intracellular metabolite concentrations. Thermodynamic control over isotope
fractionation at the low-rate limit is a natural consequence of this
approach. It also leads to predictive relationships of fractionation with extracellular sulfate and sulfide concentrations, as well
as with intracellular sulfate reduction rates. These relationships
are observable characteristics of sulfate-respiring bacteria and
archaea, both in the laboratory and in nature. They are the basis
for interpreting fossil S-isotope fractionation patterns in the rock
record in terms of ancient organisms and their environmental
interactions (6, 11, 20). Both in concept and in application, then,
sulfur isotope fractionation is a phenotypic trait. Its relationships with environmental metabolites and reduction rate can be
thought of as a sulfur isotope phenotype. The approach we advocate here enables past and present variations of the sulfur
isotope phenotype to be linked to their physiological, enzymatic,
and environmental controls.
A Model for Dissimilatory Sulfur Isotope Fractionation
During the steady-state transformation of a sulfur-bearing reactant (r) to a sulfur-bearing product (p), the net fractionation of
Significance
Microbes can discriminate among metabolites that differ only
in the stable isotopes of the same element. This stable isotope
fractionation responds systematically to environmental variables like extracellular metabolite concentrations and to
physiological ones like cell-specific metabolic rates. These observable characteristics define a stable isotope phenotype,
as exemplified by the rich database of experimental sulfur
isotope fractionations from sulfate-respiring bacteria and
archaea. We developed a quantitative model for sulfur isotope
fractionation during sulfate respiration that incorporates only
experimentally accessible biochemical information. With this
approach, stable isotope phenotypes can be decomposed into
their physiological, enzymatic, and environmental parts, potentially illuminating the relative influences of these components in natural microbial populations today, as well as how
they may have varied in the deep past.
Author contributions: B.A.W. and I.H. designed research, performed research, contributed
new reagents/analytic tools, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1
B.A.W. and I.H. contributed equally to this work.
2
To whom correspondence may be addressed. Email: [email protected] or itay.halevy@
weizmann.ac.il.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
1073/pnas.1407502111/-/DCSupplemental.
PNAS Early Edition | 1 of 10
MICROBIOLOGY
We present a quantitative model for sulfur isotope fractionation
accompanying bacterial and archaeal dissimilatory sulfate respiration. By incorporating independently available biochemical data,
the model can reproduce a large number of recent experimental
fractionation measurements with only three free parameters: (i)
the sulfur isotope selectivity of sulfate uptake into the cytoplasm,
(ii) the ratio of reduced to oxidized electron carriers supporting the
respiration pathway, and (iii) the ratio of in vitro to in vivo levels of
respiratory enzyme activity. Fractionation is influenced by all steps
in the dissimilatory pathway, which means that environmental sulfate and sulfide levels control sulfur isotope fractionation through
the proximate influence of intracellular metabolites. Although sulfur isotope fractionation is a phenotypic trait that appears to be
strain specific, we show that it converges on near-thermodynamic
behavior, even at micromolar sulfate levels, as long as intracellular
sulfate reduction rates are low enough (<<1 fmol H2S·cell−1·d−1).
EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
Edited by Mark H. Thiemens, University of California, San Diego, La Jolla, CA, and approved September 30, 2014 (received for review April 28, 2014)
34
S from 32S in the reactant relative to the product can be
expressed by
αnet =
34 eq
αr; p
34 kin
− 34 αkin
r; p × fp;r + αr; p ;
[1]
34
S–32S
where 34 αeq
r;p is a fractionation factor characterizing the
ratio in the reactant relative to that in the product at equilibrium,
34 kin
αr;p is a kinetic fractionation factor that reflects the rate of
transformation of 34S-bearing reactant relative to 32S-bearing reactant in the absence of any product, and fp;r is the ratio of the
rate of formation of reactant from product relative to the rate of
product formation from reactant (SI Materials and Methods).
This ratio tracks the reversibility of the transformation and varies
from 0 for an irreversible transformation to 1 for equilibrium
between reactant and product (i.e., complete reversibility). The
flux–force relationship connects fp;r to the thermodynamic driving force for a chemical transformation,
fp;r = eΔGr =RT ;
where V + is a constant term that reflects the maximal rate capacity
of the reaction and κ is a term that incorporates fractional substrate and product saturation and, like fp;r , varies from 0 to 1 (SI
Materials and Methods) (23). From this decomposition, Eq. 1 can
be expressed as a function of the net rate of reaction (cf. ref. 24):
34
[2]
!
Q
mi
i ½pi + RT ln Q nj ;
j rj
[3]
where ΔGor is the free energy of the reaction at standard-state
conditions, mi is the stoichiometric coefficient for the ith product, and nj is the stoichiometric coefficient for the jth reactant.
The line of reasoning encapsulated in Eqs. 1–3 applies equally
well to enzymatically catalyzed biochemical transformations (19,
21–23), illustrating how the concentrations of all metabolic reactants and products ultimately control the net isotopic fractionations that accompany networks of enzymatic reactions.
SO42-
in
SO42-
out
PPi
ATP
2H+
SO42-
Sat
cell membrane
2H+
34 eq
αr;p
AMP
Apr
APS
MKred
− 34 αkin
r;p ×
J
:
V+ × κ
H2S
SO32-
APS
eETC
A
[5]
At the low-rate limit ðJ → 0Þ, 34 αnet will approach 34 αeq
r;p . When reaction rates are at maximal capacity ðJ = V + Þ, enzymes are saturated ðκ = 1Þ and αnet will be equal to 34 αkin
r;p (25). Importantly, if
34 eq
αr;p is greater than 34 αkin
r;p , as appears to be the case for individual
steps in the dissimilatory sulfate pathway, then the magnitude of the
net isotopic fractionation expressed during an enzymatic transformation will vary inversely with the rate of that transformation. We
note the variation of net fractionation between equilibrium and
kinetic end members (Eq. 5) is not exclusive to sulfur isotopes.
For linear series of reversible enzymatic transformations at steady
state, the net isotopic fractionation at any upstream step is given by
a recursive relationship that incorporates the net isotopic fractionations associated with all downstream enzymatic transformations
(SI Materials and Methods). As a result, the expression for the
overall isotopic fractionation associated with a catabolic pathway
like dissimilatory sulfate reduction will involve a product of the fp;r
values for every step in the pathway. The fp;r value for each step can
be related to the net rate of reaction for that step through expressions like Eq. 4. At steady state, however, the net rates of all steps
will be equal to the rate of the overall catabolic transformation ðJÞ.
Accordingly, the expression for the overall isotope effect will be
a nonlinear, polynomial function of J, with the polynomial degree
equal to the number of steps in the metabolic pathway.
The approach outlined here can, in principle, explain fundamental characteristics of dissimilatory sulfur isotope fractionation—
the inverse nonlinear relationship with cell-specific sulfate reduction
rate and the direct correlation with extracellular sulfate
where R is the gas constant, T is the temperature at which the
chemical transformation is taking place, and ΔGr is the actual
free energy change associated with the transformation of interest
(SI Materials and Methods) (19, 21, 22). This relationship means
that the back flux ratio and, in turn, the sulfur isotope fractionation expressed during a chemical transformation are a function
of product and reactant concentrations through
ΔGr = ΔGor
αnet = 34 αeq
r;p −
MKox
SO42-
SO32MKred
out
in
H2S
cytoplasm
dSiR
eETC
34
The kinetics of many reversible enzymatic reactions can be
represented with a Michaelis–Menten formalism. Here the net
rate of reaction (J) can be decomposed into
J = V + × κ × 1 − fp;r ;
[4]
H2S
MKox
H2S
cell envelope
B
SO42-
environment
H2S
Fig. 1. Two illustrations of the dissimilatory sulfate respiration network. (A) Sulfur-focused representation of S-isotope fractionation. Bidirectional arrows
represent reversible S transformations. In this framework the “back flux” on any one step is a phenomenological constraint. (B) Metabolite-focused representation used here to quantify back flux. Arrows indicate net flux through the individual steps of the pathway, with the ratio of backward to forward flux controlled
by the relative abundances of the reactants and products for each step as well as the kinetics of their associated enzymes. Sat is sulfate adenylyl transferase. Apr
is APS reductase. dSiR is dissimilatory sulfite reductase. MKred refers to the reduced form of menaquinone (menaquinol) and MKox refers to the oxidized form of
menaquinone. ETC stands for “electron transfer complex.” The likely identities of these complexes in sulfate-reducing microbes are discussed in the text.
2 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1407502111
Wing and Halevy
Wing and Halevy
Model Implementation
As outlined above, the backbone of the dissimilatory sulfate respiration pathway involves 13 substrates (Fig. 1). We assumed that
each of these substrates exists as a free metabolite rather than
a bound metabolic complex. In addition, we assumed that sulfate
and sulfide levels within the cell envelope were equal to their external concentrations and that cytoplasmic sulfide concentrations
were equal to external ones through efficient H2S permeation (i.e.,
[H2S]in = [H2S]out = [H2S]) (49) (Fig. 1). Accordingly, we end up
with 10 substrates linked by four separate biochemical transformations (Table S1), each of which is separately described by
equations like [1]–[3]. With standard-state ΔG values for each
substrate (Table S1), kinetic parameters for the transformations in
which they are involved (Table S2 and Dataset S1), and equilibrium
and kinetic fractionation factors for the isotopologues of each
S-bearing substrate (Table S3), we solved these linked equations
under the assumption of steady-state kinetics (Materials and Methods
and SI Materials and Methods). The relevant equilibrium fractionation factors are well constrained theoretically and experimentally
but the relevant kinetic fractionation factors are either inferred from
experiments with crude cell extracts or treated as a free parameter
(Materials and Methods). As such, the values we use for kinetic
fractionation factors should be viewed as “best guesses” to be
verified by fractionation experiments with purified enzymes.
We note that the standard-state free energy changes of reaction
ðΔGor Þ are positive for the final three steps in the sulfate reduction
pathway (Table S1). The activation of sulfate to APS, for example,
is widely recognized as endergonic under standard-state conditions, but sulfite reduction is typically considered to be exergonic
at standard state (35), in contrast to the results presented here.
This is a direct consequence of referencing the standard state to
the MKred =MKox redox pair, which has a much higher redox
potential than the H2/H+ couple that is conventionally used (35).
Like the majority of metabolically feasible biochemical reactions
(51), sulfite reduction is apparently reversible in vivo and depends
strongly on the physiological concentrations of metabolites (e.g.,
½MK red =½MKox ) to proceed in a net forward direction.
Our solution revealed a handful of important influences
on the net S-isotope fractionation (expressed as 34 «net ð‰Þ =
½34 αnet − 1 × 1;000) between the external sulfate consumed and
the external sulfide produced, during dissimilatory sulfate respiration (SI Materials and Methods). Two are environmental,
½SO2−
4 out and [H2S], and are fixed by the living conditions of a
particular sulfate-reducing population. The three others are intrinsic to the respiratory pathway: (i) the ratio of reduced to
oxidized menaquinone, ½MK red =½MK ox ; (ii) the kinetic fractionation factor associated with sulfate uptake, 34 αkin
uptake ; and (iii)
a scaling factor, uvivo−vitro , that reflects the concentration of active enzymes in whole cells in vivo relative to those in crude cell
extracts from in vitro enzyme assay experiments (SI Materials and
Methods). We calibrated these important parameters with a
PNAS Early Edition | 3 of 10
FEATURE ARTICLE
EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
Overview of Dissimilatory Sulfate Respiration
Dissimilatory sulfate reduction is a respiratory process based on
oxidative phosphorylation; substrate-level phosphorylation does
not appear to generate enough ATP for growth with hydrogen
or lactate as an electron donor (26). Careful accounting of sulfate accumulation within, and sulfate reduction by, dissimilatory
sulfate-reducing bacteria demonstrates that the enzymatic reactions leading from sulfate to sulfide occur within the cytoplasm
(27). Accordingly, the first step in dissimilatory sulfate reduction
is the transport of the sulfate anion from the extracellular environment into the cytoplasm. Microelectrode experiments reveal that the sulfate permeases that facilitate this process are
secondary transporters that symport protons or sodium ions with
sulfate rather than primary transporters that directly consume
ATP (28–30). The stoichiometry of symport is roughly two protons for every sulfate dianion (Fig. 1B and Table S1). Importantly,
the overall transport step appears to be reversible (Fig. S1), although the degree of reversibility has not been quantified (30).
Once in the cytoplasm, the ultimate reduction of the sulfate
anion to sulfide depends on the presence of ATP (31), indicating
that the sulfate needs to be activated into a higher energy form to
overcome the unfavorable energetics of a direct transformation
to sulfite (32). In the dissimilatory reduction network, adenosine5′-phosphosulfate (APS) is the free activated intermediate (33),
produced along with pyrophosphate (PPi) from ATP and sulfate
through the enzymatic activity of sulfate adenylyl transferase
(Fig. 1B and Table S1) (34). This reaction is endergonic at
standard-state conditions (Table S1) but a cytoplasmic pyrophosphatase “pulls” the reaction toward the products by efficiently hydrolyzing pyrophosphate to phosphate (35).
The enzyme APS reductase catalyzes the efficient reduction of
APS to AMP and sulfite, consuming two electrons in the process
(35). Sulfate reducers can grow on an energy source of H2 and
sulfate (36). However, APS reductase is located in the cytoplasm
of sulfate-reducing bacteria (Fig. 1B) (37), whereas hydrogenases
that catalyze H2 oxidation are located primarily within the cell
envelope (37, 38). This topography requires chemiosmotic energy conservation, in which electrons are partitioned through the
cell membrane (Fig. 1B) (37). A suite of quinone-interacting
membrane-bound oxidoreductase (Qmo) proteins makes up the
electron transfer complex that provides electrons to cytoplasmic
APS reductase in Desulfovibrio vulgaris (39, 40). The precise
mechanism of APS reduction via Qmo is complicated and may
ultimately involve electron bifurcation (41). However, menaquinones (MKox) are the most abundant electron carriers in
sulfate-reducing microbes (37), in line with suggestions that
membrane-bound menaquinols (MKred) are likely to be the
proximal source of electrons to the electron transport complex
that, in turn, supplies APS reductase (Fig. 1B and Table S1) (41).
Sulfite produced from APS reduction is the electron acceptor
for the final reductive step in the sulfate respiration pathway
(Fig. 1B). Dissimilatory sulfite reductase catalyzes the reduction
of sulfite to sulfide (42). Sulfate-reducing bacteria have been
shown to gain energy solely from sulfite and H2 (43). In light of
the disparate topography of their dissimilatory sulfite reductase
and hydrogenase enzymes (37), this means that a membranebound electron transfer complex (identified as DsrMKJOP) (44)
facilitates the exchange of reducing power. The reduction of
sulfite to sulfide likely proceeds through a pair of siroheme iron−
bound intermediates (SO2−
2 , SO ), consuming two electrons
during each of the three proposed conversions catalyzed by
dissimilatory sulfite reductase (45). During this reductive transformation, the DsrC protein appears to play a critical role in
cycling electrons between the membrane-bound DsrMKJOP
complex and cytoplasmic dissimilatory sulfite reductase (46, 47).
Within the cell membrane, the oxidation of menaquinol to
menaquinone is thought to be the ultimate source of electrons to
the transport complex that mediates this process (Fig. 1B and
Table S1) (41, 48).
At intracellular pH values, the sulfide produced during sulfite
reduction will exist as H2S and HS−. To compensate for the
energetic cost of symporting protons across the cell membrane,
however, sulfide efflux from the cytoplasm is likely to be as H2S
(Fig. 1B) (30). In line with these energetic arguments, limited
biophysical measurements indicate that microbial cell membranes
are freely permeable to H2S (49), whereas membrane-crossing
HS− ion channels have only a small probability of being open (50).
MICROBIOLOGY
concentrations —that have broad empirical support (2–11). To
do so, we next discuss the biochemistry of the sulfate respiration
pathway, with a focus on general characteristics that are shared
among most sulfate-reducing microbes. The discussion is not
exhaustive but attempts to provide enough common details to
enable us to take our approach from theory to practice.
Results and Discussion
Environmental Sulfate and Sulfide Levels Control S-Isotope Fractionation
Through the Proximate Influence of Intracellular Metabolites. Microbial
sulfate reduction can occur over a wide span of sulfate and sulfide concentrations. It is sustained at sulfate concentrations from
hundreds of millimolar, as found in some hypersaline soda lakes
(58), down to tens of micromolar, as shown by precise measurements of the sulfate affinity of actively growing sulfate reducers
(59). Sulfide concentrations much higher than tens of millimolar,
however, appear to inhibit microbial sulfate reduction (60). This
upper limit may be set by sulfide toxicity or by pathway energetics.
The lower limit set by physiological sulfide levels is poorly known,
with different estimates spanning millimolar (50) to micromolar
(61) concentrations. For a given csSRR and constant levels of
intracellular redox metabolites, these two environmental boundary conditions are the ultimate controls on sulfur isotope fractionation during dissimilatory sulfate reduction. They determine
intracellular metabolite concentrations (SI Materials and Methods
and Eqs. S22–S25), which in turn dictate reversibility (Eq. 2) (19)
and isotopic fractionations (Eq. 5) (62).
Predictions of intracellular metabolite concentrations show a
handful of different responses to these environmental conditions
(Fig. 2). First, internal sulfate concentrations are primarily controlled by external sulfate concentrations, relative to which they
are enriched by factors of ∼3–100 (Fig. 2A). Accumulation experiments show similar enrichments (30). Enrichments are more pronounced at lower external sulfate concentrations because relatively
high internal sulfate levels are required to make favorable the
energetics of sulfate activation to APS. Less pronounced intracellular sulfate enrichments at higher csSRR reflect the slower
kinetics of sulfate uptake relative to APS formation (Table S2).
On the other hand, intracellular sulfite levels illustrate another
control regime. They depend exclusively on sulfide concentrations, do not vary with respiration rate, and range from 0.1 mM
to 1 mM for typical environmental sulfide concentrations (Fig. 2D).
Maintenance of intracellular sulfite at essentially thermodynamic
levels results from the endergonic nature of sulfite reduction
at standard state when menaquinone is the electron carrier.
Comparison of the redox potentials of sulfite reduction and
menaquinol oxidation suggests that menaquinone must be almost completely reduced to reach thermodynamic equilibrium
(63). This condition is also inferred here (½MK red =½MK ox ≈ 100;
SI Materials and Methods) to maintain physiological levels of
respiratory metabolites. Intracellular sulfite concentrations have
4 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1407502111
[APS] (M)
B
[PPi] (M)
C
[SO32−] (M)
D
−1
−2
−3
−4
125
−3
−4
−5
−2
−7
−3
−8
−9
−4
−6
−8
−10
−4
−5
−2
−3
−4
−2
−5
−2
−3
−3
−4
−5
−4
−5
−2
E
ε (‰)
csSRR (fmol H2S cell–1 d–1)
5
25
1
−2
[H2S] (M)
[SO42−]in (M)
A
34
combination of physiological reasoning and well-characterized
experiments on S-isotope fractionation by sulfate-reducing microbes
(Materials and Methods and SI Materials and Methods).
An important result from the calibration exercise is that
uvivo−vitro appears to increase linearly with cell-specific sulfate
reduction rate (csSRR) (Fig. S2). As uvivo−vitro scales with relative
enzyme levels (SI Materials and Methods), this prediction can be
understood as a specific example of a long-observed physiological response: Overall intracellular protein levels correlate positively with growth rate (52). Other early experiments showed
that, under balanced growth, individual protein numbers (53)
increase with increasing growth rate as well. Although these
observations have theoretical backing (54, 55), supporting
proteomic comparisons between sulfate-reducing populations
maintained at different specific growth rates have not been
performed. We note, however, that there is a clear, coordinated
down-regulation of the genes within the sulfate reduction pathway
(Fig. 1B) in stationary-phase cultures of D. vulgaris compared with
exponentially growing cultures (56). Our results predict approximately fourfold differences in respiratory protein levels (Fig. S2),
variations that are well within the range estimated for other metabolic pathways (57) and that could be monitored with targeted
transcriptomic or proteomic experiments.
60
40
20
0
−3
−4
−5
−5
−4
−3
−2
−1 −5
−4
−3
−2
−1 −5
−4
−3
−2
−1 −5
−4
−3
−2
−1
[SO42−]out (M)
Fig. 2. Predicted metabolite concentrations and isotopic fractionation in
a model sulfate reducer. Shown are intracellular concentrations of sulfate
2−
(½SO2−
4 in , row A), APS ([APS], row B), PPi ([PPi], row C), and sulfite (½SO3 ,
row D) and the net isotopic fractionation between the substrate sulfate
and product sulfide (34 «, row E) as functions of extracellular sulfate (½SO2−
4 out ,
horizontal axis) and sulfide concentrations ([H2S], vertical axis). All concentrations are shown on logarithmic scales. Intracellular metabolite levels are
calculated from Eqs. S22–S25, whereas isotopic fractionation is calculated by
application of Eqs. 2 and 5. Regions where calculated PPi concentrations
(and associated fractionations) are physiologically unlikely are shown as gray
shaded fields (SI Materials and Methods) (rows C and E).
not been reported for sulfate reducers, but cytoplasmic sulfite levels
of ∼0.15 mM have been measured in the phototrophic sulfur oxidizer Chlorobaculum tepidum (64). Although the analogy is imperfect, this is a natural example where sulfite is an obligate metabolic
intermediate in a bacterium that inhabits anoxic environments.
More direct support for our predictions is provided by the reaction
rate between isolated siroheme (the inferred catalytic center for
dissimilatory sulfite reductase) and sulfite, which is maximized at
sulfite concentrations around 0.1 mM (65, 66). Targeted metabolomic studies are clearly needed to test these predictions.
Modeled APS and PPi concentrations show more complex
behaviors. At low respiration rates, APS levels are relatively low
and PPi levels are relatively high, whereas at high rates the
converse is true (Fig. 2 B and C). The negative covariance of
APS with PPi reflects the endergonic nature of sulfate activation,
which requires that the concentration product of both metabolic
products be kept low to sustain net forward reaction. Although
this concentration product has not been measured in sulfatereducing microbes, in vitro rates of APS reduction by APS reductase are ∼80% of measured maximums at APS concentrations of 1 μM (67) and estimates of cytosolic APS levels in
growing D. vulgaris are 0.25–5 μM (67). These estimates agree
well with the APS concentrations predicted here for high csSRR
(0.4–0.6 μM; Fig. 2B), which are required to support high rates
of sulfite production. The corresponding PPi concentrations fall
to the physiological limit of 1 nM at low external sulfate levels
(<10−5 M), indicated by the curved gray fields in Fig. 2D. We
note that PPi is an important intermediary in the energy metabolism of sulfate-respiring microbes. Given the multitude of
reactions that are likely responsible for maintaining cellular PPi
concentrations, the low PPi levels calculated here are best
interpreted as a consistency argument that is required for net
sulfate reduction to occur. Inorganic pyrophosphatase is an extremely efficient enzyme (68) and may sustain this condition
within the cell.
Wing and Halevy
A
B
0.516
Archaeoglobus fulgidus
2–
4
out
1
5
25
0.514
0.512
λ
0.2
ε (‰)
34
[SO ] (mM)
0.01
0.1
1
10
C
33
50
FEATURE ARTICLE
75
0.510
>25
0.508
0
75
D
E
0.506
0.516
DMSS-1
[SO42–]out = 21 mM
0.2
0.514
0.512
33
λ
1
0.510
25
5
0
75
125
G
H
0.2
Desulfovibrio vulgaris Hildenborough
ε (‰)
50
0.512
33
λ
5
0.510
25
25
0.508
125
0
0.01
I
0.514
[SO42–]out = 28 mM
1
0.506
0.516
EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
0.508
25
0.506
0.1
1
[SO42−]out (mM)
10
100 0
50
100
150
csSRR (fmol H2S day−1 cell−1)
0
25
ε (‰)
34
50
75
Fig. 3. Model calibration to experimental data. (A) Net isotopic fractionation ð34 «Þ by A. fulgidus grown at 80 °C at constant csSRR (6, 7) as a function of
34
« for different values of csSRR in fmol H2S·cell−1·d−1. The black curve
extracellular sulfate concentrations ð½SO2−
4 out Þ. Orange contours show the value of
shows 34 « for the harmonic mean of the csSRR values that were reported for some of the experiments (black squares). The csSRR values were not reported for
other experiments (white squares), resulting in the scatter around the black curve. (B) Predicted 34 « as a function of csSRR for ½SO2−
4 out between 10 μM and
34
33
100 mM. Experiments for which ½SO2−
« were all reported are also shown, color coded by ½SO2−
4 out , csSRR, and
4 out . (C) Predicted fractionation exponent ð λÞ
34
«-½SO2−
as a function of 34 « for the same ½SO2−
4 out as in B. Experiments for which minor isotope data exist are also shown (14). (D) Predicted
4 out relationship
34
for Desulfovibrio strain DMSS-1 grown at ∼20 °C, 21–14 mM ½SO2−
« vs.
4 out , and 2–7 mM sulfide (8–10). (E) Measured (white squares) and model (black curve)
csSRR for the experiments in D. These experiments were run in batch culture, so we assumed the average ½SO2−
4 out and external sulfide concentrations for the
interval over which 34 « vs. csSRRs were determined (SI Materials and Methods). (F) 33 λ vs. 34 « for the experiments in D. Error bars are 1σ reported in the
experiments. (G–I) Same as D–F, but for D. vulgaris Hildenborough, grown at 25 °C and with precisely controlled ½SO2−
4 out of 28 mM (11). Sulfide concentrations for the model curves were assumed to be 0.1 mM.
Taken together, these different metabolic responses combine
to produce relatively straightforward patterns of S-isotope fractionation. When net respiration is near zero, the magnitude of
net S-isotope fractionation is large and responds primarily to sulfide
concentrations (Fig. 2E). At a csSRR of 1 fmol H2S·cell−1·d−1,
for example, accessible 34 «net values increase with increasing
sulfide concentrations, approaching the thermodynamic S-isotope
fractionation between sulfate and sulfide (∼71‰ at 25 °C) at
millimolar levels of sulfide. With increasing sulfide concentrations, the energy yield of the reduction of sulfate to sulfide
decreases to zero; thermodynamic equilibrium demands complete reversibility ðfp;r → 0Þ and equilibrium S-isotope fractionation among all of the metabolic intermediates.
As respiration rate increases, external sulfate concentrations
become influential as well, with contours of equal 34 «net following systematic paths of decreasing external sulfate and increasing
sulfide concentrations at moderate csSRR (Fig. 2E). At a csSRR
of 125 fmol H2S·cell−1·d−1, accessible 34 «net values are small, only
Wing and Halevy
weakly sensitive to external sulfate, and insensitive to sulfide
(Fig. 2E). Together the fractionation characteristics at moderate
to high csSRR may explain why most batch experiments with
sulfate reducers return isotopic data consistent with a single value of
34
«net , despite changing sulfate and sulfide levels throughout the
course of the experiment. The insensitivity of 34 «net to csSRR at
high rates arises from our prediction that enhanced production of
respiratory enzymes will accompany enhanced csSRR (Fig. S2).
Because of this, the ratio of csSRR to uvivo−vitro becomes constant
at high csSRR, meaning that the concentrations of respiratory
metabolites (SI Materials and Methods and Eqs. S22–S25) and
34
«net stabilize as well.
S-Isotope Phenotypes Appear to Be Strain Specific. Recent culture
experiments have isolated the effects of single control parameters (csSRR, external sulfate concentration) on fractionation
of 33S–32S and 34S–32S (6–11, 14). The broad fractionation patterns in these experiments confirm inferences made from earlier
PNAS Early Edition | 5 of 10
MICROBIOLOGY
34
ε (‰)
50
34
F
work; 34 «net decreases with increasing rate and increases with
increasing external sulfate (Fig. 3). However, measured strainspecific fractionations are difficult to compare directly because
of limited overlap in the experimental conditions under which
they were determined. An initial attempt to address this issue
suggested that common fractionation behaviors might not accompany sulfate respiration by different strains (69), although, as
shown here, the environmental diversity in this important experiment complicates strain-by-strain comparisons. Starting from
the metabolic state defined by the model sulfate reducer illustrated in Fig. 2, we constrained a uvivo−vitro –csSRR relationship
for the two recent experiments that looked at the influence of
rate on fractionation by different bacterial strains of D. vulgaris
(DvH, DMSS-1) and another one that examined how sulfate affected fractionation by the sulfate-reducing archaeon Archaeoglobus
fulgidus (Fig. S2). Coupled with unique ½MK red =½MK ox and
34 kin
«uptake for each experiment, this exercise allowed us to extend
the strain-specific fractionations to other environmental conditions in a self-consistent fashion.
Once environmental biases are accounted for, it is clear that
the two bacterial strains have different fractionations when respiration rate is the control parameter and that their isotopic
responses to changing external sulfate concentrations differ also
(Fig. 3 D and G). The fundamental distinction is that DvH is
predicted to maintain a higher respiration rate at a given sulfate
concentration, giving rise to expanded access to the 34 «net –csSRR
field (Fig. 3G). The fivefold difference in the initial uvivo−vitro
value required by DvH and DMSS-1 to sustain minimal respiration, as well as the more profligate production of respiratory
enzymes by DvH with increasing csSRR, underlies this physiological response (Fig. S2 and Table S4). The scaling factor
between in vitro and in vivo reaction velocities incorporates
catalytic rate constants as well as enzyme levels (SI Materials and
Methods). Specific activities for individual sulfate respiration
enzymes vary nearly 100-fold (SI Materials and Methods), suggesting that the initial uvivo−vitro difference identified here may
have its roots in structural differences between DvH and
DMSS-1 respiratory enzymes. The clear tension between energy
yield and protein cost may be behind the distinct responses of
uvivo−vitro to increases in csSRR (Fig. S2) (57); DMSS-1 is a recently isolated strain that may be more economical in producing
proteins than the long-transferred, laboratory workhorse DvH.
Comparative predictions for DvH and the archaeal sulfate
reducer, A. fulgidus (Fig. 3), reveal S-isotope phenotypes that
differ in a number of ways as well. The most obvious difference
is at the low-rate limit, where the higher optimal growth temperatures of the archaeon lead to an equilibrium 34 «net that is ∼20‰
lower than that for DvH. In addition, the archaeal 34 «net −½SO2−
4 contours are more tightly spaced than those of DvH, representing the lower sensitivity of fractionation to increasing csSRR
in A. fulgidus. The domain-level physiological distinctions between these two strains are reflected in the kinetic performance
of their respective respiratory enzymes (Table S2), as well as in
the uvivo−vitro values required to reproduce the 34 «net –csSRR data
for DvH and the 34 «net −½SO2−
4 data for A. fulgidus (Fig. S2 and
Table S4). It appears that A. fulgidus needs to produce >10-fold
more respiratory enzymes than DvH to cause the same increase
in csSRR. Protein degradation rates are temperature sensitive,
potentially accounting for the higher predicted production rates
in A. fulgidus. For a given external sulfate concentration, this
feature leads to an unchanging archaeal 34 «net and, by inference,
a static respiratory metabollome, once csSRR surpasses ∼1 fmol
H2S·cell−1·d−1 (Fig. 3B). Our analysis supports the proposal
that the A. fulgidus experiments were run in a regime of SO2−
4
control rather than rate control (7).
2−
34
34
Unlike the «net –csSRR and the «net −½SO4 relationships, phenotypic variability in 34 λnet vs. 34 «net is less pronounced
among sulfate-reducing strains (Fig. 3 C, F, and I). This finding
6 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1407502111
is in marked contrast to the wide range of 33S–32S and 34S–32S
fractionations that are predicted by phenomenological models
of multiple S-isotope fractionation during microbial sulfate reduction (8, 14, 17). As explored below, this behavior has its roots
in the similar ½MK red =½MK ox and 34 «kin
uptake values assigned to the
sulfate reducers examined here.
Low Sulfate Concentrations Lead to Less Fractionation, but Not When
Coupled to Low Respiration Rates. Early experiments showed that
microbial sulfate respiration in barite-saturated solutions produced limited S-isotope fractionation (3). These observations
strongly influenced later interpretations of the geologic record
of microbial S-isotope fractionation, where limited variability in
whole-rock δ34 S values from ancient marine sediments was
linked to low levels of seawater sulfate at their time of deposition
(70). Later experiments examined respiratory S-isotope fractionation over a wider range of sulfate levels and with a variety of
populations of microbial sulfate reducers (6). The general fractionation pattern appeared bimodal, with 34 «net values near zero
below ∼200 μM ½SO2−
4 out but widely dispersed at higher concentrations. Recent experiments on microbial sulfate reduction
in low-sulfate euxinic lakes have expanded this relationship
and slightly blurred its apparent boundaries, with fractionation reported near the thermodynamic limit at ½SO2−
4 out =
1:1 2 mM (12) and shown to still be sizable (∼20‰) at
sulfate levels between ∼100 μM and 350 μM (71). In detail,
however, the low sulfate–high sulfate duality is not always obvious. A. fulgidus, for example, shows a positive log-linear relationship between 34 «net and extracellular ½SO2−
4 (7) (Fig. 3A).
The model described here naturally explains these disparate
observations. Whereas fractionation always decreases continuously with decreasing extracellular sulfate levels in a broadly loglinear fashion, the net respiration rate controls the range of
34
«net values that are accessible at a given ½SO2−
4 out . For example,
simple estimates of barite saturation at room temperature predict equal concentrations of Ba2+ and SO2−
4 near 50 μM (72). At
these extracellular sulfate levels, limited S-isotope fractionation
ð34 «net ≤ 5‰Þ is predicted for all strains when respiration rates
are greater than those typically seen in pure culture experiments
(≥25 fmol H2S·cell−1·d−1; Figs. 2E and 3 A, D, and G). For
a microbe respiring at 25 fmol H2S·cell−1·d−1 in media with
modern seawater ½SO2−
4 out (28 mM), however, strain-specific
behavior results in a wider range of possible fractionations (34 «net
up to ∼ 25‰; Fig. 3 A, D, and G). Consistent with fractionation
experiments conducted at near-seawater sulfate concentrations
(8), 34 «net can approach the thermodynamic limit between sulfate
and sulfide when net respiration rates decrease to <<1 fmol
H2S·cell−1·d−1 (Fig. 3 B, E, and H). In this region, any strainspecific behavior is trumped by the almost perfect two-way
metabolic communication between the initial reactant and ultimate product of the sulfate respiration pathway.
However, the most unexpected result of the new model is that
this near-thermodynamic reciprocity can be maintained down to
extremely low concentrations of external sulfate (Fig. 3 A, D, and
G). As anticipated by environmental incubations from sulfatepoor meromictic lakes (12), 34 «net values of 60–70‰ can occur
at sulfate concentrations down to tens of micromolar as long as
the right strains (e.g., DvH; Fig. 3G) maintain sluggish net respiration. The major features of published 34 «net −½SO2−
4 out
measurements can then be rationalized as follows. First, the
wide variation in 34 «net down to ∼200 μM extracellular ½SO2−
4 most likely represents unique strain-by-strain responses to external sulfate forcing [either in terms of well-known differences
in strain-specific sulfate affinities (59) or in terms of more speculative differences in the kinetic fractionation factor associated
with sulfate uptake; Table S3]. Second, the limited variability in
34
«net below ∼200 μM extracellular ½SO2−
4 is only superficial and
probably results from the experimental difficulty of sustaining
Wing and Halevy
50
2
34
ε (‰)
Reversibility (fp,r)
0
0.5
1
60
80
100
25
0
A
0
75
B
20
40
10−5
10−4
10−3
10−2
Uptake
Activation
Uptake
Activation
APS reduction
SO32– reduction
APS reduction
SO32– reduction
10−1
50
34
ε (‰)
25
0
75
50
25
0
0
20 40 60 80 100 0
20 40 60 80 100
csSRR (fmol H2S day−1 cell−1)
10−5 10−4 10−3 10−2 10−1 10−5 10−4 10−3 10−2 10−1
[SO42−]out (M)
Fig. 4. Sensitivity of 34 «–csSRR (A) and 34 «−½SO2−
4 (B) relationships to a halving (solid curves) and a doubling (broken curves) of the default [MKred]/[MKox]
(= 100) and [H2S] (= 0.1 mM) values. Fractionation resulting from the default
state is shown by the black curves. Shaded envelopes in A and B show the
reversibility of the steps in the sulfate reduction pathway resulting from
variation of [MKred]/[MKox] and [H2S] for a range of ½SO2−
4 and csSRRs. Values
of fp,r range from 0.45 to 0.99 for SO2−
4 uptake, 0.98 to ∼1 for activation, ∼0 to
0.98 for APS reduction, and 0.99 to ∼1 for SO2−
3 reduction.
viable cultures at respiration rates as low as those encountered in
natural environments. Rate-controlled chemostat experiments of
different strains of sulfate reducers at different sulfate concentrations will go a long way toward validating these predictions.
No Single Metabolic Step Controls Fractionation. Metabolic interpretations of isotope fractionation during sulfate respiration are
typically framed in terms of a “rate-limiting” step in the metabolic reaction network (3, 13, 15, 17, 73), with notable exceptions
(cf. ref. 62). The catalytic reduction of SO2−
3 to H2S is often
considered to be the rate bottleneck for respiration (73), leading
to the suggestion that larger S fractionations could result if this
constraint were released (15). Upstream steps have also been
proposed to fulfill the rate-limiting role. In early experiments, for
example, fractionation at low rates of respiratory reduction
(34 «net ∼ 25‰) was interpreted as the isotopic signature of the
conversion of APS to SO2−
3 (3). In contrast, a similar claim for
this step was drawn from the convergence of 34 «net on a value of
∼15‰ for six different strains of sulfate reducers in batch culture (74). Likewise the small respiratory fractionations observed
at low sulfate levels have been proposed to result from rate
limitation by sulfate uptake and the assumption of minor intrinsic fractionation during the uptake process (7, 13). Our
calculations support the hypothesis (62) that a fractionation
framework based on rate-limiting steps, although potentially
correct in theory, is often mistaken in practice. The holistic
approach described here acknowledges the relative isotopic
influence of each step in the respiratory pathway and reveals
their combined controls on fractionation limits.
There are three fractionation limits that bracket the 34 «net
patterns associated with sulfate respiration. The first limit occurs
where csSRR approaches zero (Fig. 4A). Here each internal
metabolite is in thermodynamic equilibrium with all others in the
reaction network, as ultimately dictated by environmental sulfate
and sulfide concentrations. As a result, the fp;r values for each
step are unity, resulting in an overall S-isotope fractionation
determined by the product of the equilibrium fractionation factors for each step. The other two limits occur at high respiration
rates and at low sulfate levels. Importantly fp;r values for sulfate
Wing and Halevy
activation and sulfite reduction are always near unity, even at
these limits, implying the 34 «kin values for these steps exert
minor influence on the isotope phenotype (Fig. S3). As csSRR
increases, the reduction of APS emerges early as the primary
bottleneck for the respiratory processing chain over a wide range
of metabolic states (Fig. 4A). As a result, fp;r for this step
approaches zero whereas csSRR is still much less than the
maximum achievable. The fractionation-free character of sulfate
activation to APS (Table S3) means that fractionation control is
switched to the sulfate uptake step at this point and, consequently, the drawn-out decay of 34 «net toward a low constant
value with increasing csSRR reflects the slow departure of sulfate uptake from equilibrium (Fig. 4A).
At variable extracellular sulfate levels, the distribution of
fractionation control depends on the initial metabolic state, with
the ratio of reduced to oxidized electron carriers and internal
sulfide concentrations playing key roles. In all cases, as external sulfate levels decrease, the reversibility of sulfate uptake
decreases (sulfate uptake departs from equilibrium; Fig. 4B).
Consequently, 34 «net slowly approaches a low constant value (Fig.
4B). The metabolic state modulates this behavior. For example,
at lower ½MK red =½MKox values or higher [H2S], reversibility in
the APS reduction step is relatively high (Fig. 4B) and sulfate
uptake exerts the primary control on fractionation changes at
low sulfate levels. The magnitude of 34 «net is still much larger
than that of 34 «kin
uptake , meaning that downstream steps continue to
exert an isotopic influence at extremely low sulfate levels (<10 μM;
Fig. 4B). At higher ½MK red =½MKox values or lower [H2S], the
path to low 34 «net is different, with the reduction of APS
approaching irreversibility ðfp;r → 0Þ over a wide range of sulfate concentrations (Fig. 4B). The overall fractionation is smaller
in this case, reflecting both the low reversibility in the APS reduction step and the decreasing reversibility of sulfate uptake
with decreasing sulfate levels (Fig. 4B). In both these cases,
however, extremely low sulfate concentrations (<10−6 M) appear
to be required before fp;r for sulfate uptake would approach zero.
This appears to rule out the hypothesis of a simple mass transfer
control on fractionation, where a low sulfate level confers a
small isotope effect (i.e., 34 «net = 34 «kin
uptake ) due to conservation
of mass. As the control of fractionation is distributed among
different enzymatic steps even at these limiting conditions, it
seems likely that S-isotope fractionation is never a sole function
of a single respiratory enzyme.
Minor Isotope Fractionations Are Uniquely Sensitive to Upstream
Steps in the Sulfate Respiration Pathway. Although the positive
correlation of 33 λnet with 34 «net has been experimentally validated,
the causation behind it is still opaque. One defining limit of the
relationship is clear. As the rate of sulfate respiration approaches
zero, 33 λnet and 34 «net will be pegged to their thermodynamic
counterparts regardless of the responsible sulfate respirer (Fig. 3 C,
F, and I). This characteristic suggests that comparative 33S–32S and
34 32
S– S fractionations will be most biologically informative in the
low fractionation limit. The experimental variation of 33 λnet seems to
increase as 34 «net decreases, lending some support to this inference
(Fig. 3 C, F, and I). Some of this variability may result from the
intracellular ratio of reduced to oxidized electron carriers for the
sulfate respiration pathway. Lower ½MKred =½MKox values produce
relatively steady declines in 33 λnet with 34 «net , whereas higher ratios
introduce cusps that separate fractionation regimes upstream and
downstream of APS reduction (Fig. 5). This redox control is also
seen in the 34 «net –csSRR behavior, where lower ½MK red =½MK ox values give rise to a more gradual decrease in fractionation with rate
whereas higher ratios show a more abrupt change in slope (Fig. 4A).
To reproduce the measured 33 λnet –34 «net patterns, we found
that an inverse isotope effect had to be associated with sulfate
uptake. For DvH, for example, 34 «kin
uptake is −7‰, whereas it is
−3‰ for DMSS-1 (Table S3). The isotope effects of transport
PNAS Early Edition | 7 of 10
FEATURE ARTICLE
0.5
EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
[MKred]/[MKox]
[H2S]
MICROBIOLOGY
75
0.516
33
λ
0.514
0.512
0.510
[MKred]/[MKox] 50
ε
34 kin
uptake
0.508
0
25
34
(‰) –15
ε (‰)
50
100 200
–5
+5
75
Fig. 5. Sensitivity of the 33 λ − 34 « relationship to the ratio of reduced to
oxidized menaquinone ([MKred]/[MKox], orange) and the kinetic isotope
fractionation during sulfate uptake (34 «kin
uptake , blue).
across cell membranes have been only rarely studied, but the one
isotope effect that has been directly observed for active transport
[∼14‰ for NH+4 uptake in Escherichia coli (75)] has a similar
absolute magnitude but opposite sign. Although inverse kinetic
isotope effects are unusual, we note that early experiments
assigned a fractionation of −3‰ to 34 «kin
uptake (3).
An inverse isotope effect is required for sulfate uptake
because 33 λnet decreases as 34 «net approaches zero. For the
equilibrium fractionations and temperatures considered here,
33 eq
λ is always close to 0.515 (Table S3). Under the Swain–
Schaad assumption, 33 λkin is very similar to 0.515 as well (Table
S3). As a result, when 34 «kin
uptake is positive, indicating a normal
kinetic isotope effect, 34 «net will always be positive and 33 λnet will
swing between 0.515 at both the high and low fractionation
limits, dipping slightly below 0.515 at intermediate fractionations
(Fig. 5) because of the nonlinear interaction of fractionation and
isotope mixing (14). On the other hand, when 34 «kin
uptake is negative,
34
«net will “cross over” from a positive value to a negative value;
this happens slightly before the sign change for 33 «net . Consequently, 33 λnet will go through a singularity, approaching negative
infinity from the right and positive infinity from the left (Fig. 5).
The 33 λnet –34 «net relationship for microbial sulfate respiration,
then, appears to be a natural example of the abnormal fractionation behavior first identified in a theoretical investigation of
the H-D-T system (76). (We stress that this behavior is not the
“mass-independent” S-isotope fractionation documented in ancient S-bearing minerals and in photolysis experiments with SO2.
The 33 λ values corresponding to these situations would require
vanishingly small values of 34 «, and the anomalous fractionation
would remain analytically undetectable as a result.) This inference, however, depends on the validity of the Swain–Schaad
relationship, particularly for the S-isotope effect associated with
sulfate uptake. Although it has been examined only in calculations for H isotopes, this relationship appears computationally
robust in the face of the complexity associated with enzyme kinetics (77), but may break down for secondary isotope effects,
especially when they become very small (78). It will take a welldesigned molecular and isotopic experiment (cf. ref. 75) to
determine whether these theoretical results apply to S-isotope
effects associated with sulfate uptake or activation.
Summary and Natural Extensions
In this contribution we predict the sulfur isotope phenotypes of
sulfate-respiring bacteria and archaea over a wide range of environmental sulfate and sulfide levels and at respiration rates
8 of 10 | www.pnas.org/cgi/doi/10.1073/pnas.1407502111
that range from those typical of laboratory cultivation down to
the much lower rates associated with natural populations (79).
One of our primary conclusions is that S-isotope fractionation
reflects the intracellular concentrations of all metabolites involved
in the respiratory pathway. Targeted metabolomic analyses should
be able to assess this result. Because of this dependence on
metabolite levels, it appears that the activity of a single enzyme is
unlikely to be the sole control over fractionation. Our approach
combines biochemical kinetics and thermodynamics and involves
only parameters that can, in principle, be experimentally determined. As it stands, we have been able to reproduce recent
S-isotope datasets (with more than 100 total measurements) from
three separate strains of sulfate reducers (two bacteria and one
archaeon) by considering variations in three model parameters:
(i) the ratio of reduced to oxidized membrane-bound menaquinone; (ii) S-isotope fractionation during sulfate uptake; and (iii)
a scaling factor, uvivo−vitro , that reflects the concentration of active
enzymes in whole cells relative to those in crude cell extracts.
The calculated S-isotope phenotypes associated with these
strains confirm some of the broad fractionation patterns inferred
from experimental work, while revealing that others might
be artifactual. The positive covariation of 33S–32S and 34S–32S fractionations is a robust isotopic feature, largely because of the thermodynamic anchor point provided at low respiration rates.
Sulfate-uptake–induced fractionation and intracellular redox
state create isotopic variability in this pattern when 34S– 32S
fractionations are small. Our results also clarify the long-observed
decrease in fractionation with increasing respiration rate. The
general grade is essentially preordained, given that equilibrium
fractionations in the sulfate respiration pathway have larger
magnitudes than their corresponding kinetic counterparts. Individual trajectories, however, are strain specific and reflect
primarily differences in the intracellular redox states and enzyme
levels of sulfate-reducing microbes. Although our results show
a monotonic increase in 34S–32S fractionations with increasing
sulfate levels for a given respiration rate, we never calculated
a threshold sulfate concentration above which fractionation was
expressed and below which it was repressed. Near thermodynamic fractionations appear to be accessible at extremely low
sulfate levels (<10 μM), as long as the average respiration rate of
a sulfate-reducing population is low enough (79). This feature
may neatly unite two conflicting views of S cycling on the
Archean earth: large intrasample variability in δ34 S values
(80, 81) in the face of low marine sulfate concentrations (6, 82).
Although sulfate respiration is particularly well investigated
from an isotopic point of view, other microbial metabolic pathways also exhibit the isotopic behaviors explicated here. For
example, biosynthetic carbon isotope fractionation is often contrasted as either an equilibrium or kinetic process (83). This
dilemma is captured in a pair of long-standing observations;
measured intermolecular C isotope fractionations in biosynthetic
products have been shown to correlate with fractionations estimated from the calculated intramolecular distribution of C isotopes at thermodynamic equilibrium (25, 84) while measured
intramolecular distributions of C isotopes in bacterial fatty acids
have been fully explained in terms of kinetic isotope effects (85).
These observations may not be incompatible, as physiological
state can bridge the divide between equilibrium and kinetic
fractionations (Eq. 5). Also consistent with the general principles
encompassed in Eq. 5, catabolic pathways with single processing
steps exhibit more linear relationships between «net and rate
[e.g., 34S–32S fractionation during dissimilatory S0 reduction
(86)] whereas longer processing chains show distinctly nonlinear
behavior [e.g., 13C–12C fractionation during methanogenesis (87)].
Nitrogen isotope fractionation during microbial denitrification,
however, exhibits a range of behaviors that are not so easily
classified. Recent work on respiratory nitrate reduction, for example, reveals a general pattern of increasing 15 «net with increasing
Wing and Halevy
Note Added in Proof. Experiments with pure cultures of Desulfobacterium
autotrophicum show a positive correlation between per-cell contents of dSiR
mRNA and csSRR (97). The slope of this correlation (≈fourfold change in dSiR
mRNA for every unit increase in csSRR) compares well with the predictions
made here (Fig. S2 and Table S4). We thank Alex Loy (University of Vienna)
for bringing this to our attention.
Isotopic Fractionation Factors. Published thermodynamic calculations provided equilibrium S-isotope fractionation factors for most individual steps
(95), whereas kinetic fractionation factors for 34S–32S were taken from
experiments with cell-free extracts where available (Table S3). Kinetic fractionation factors for 33S–32S were calculated from a fractionation exponent
based on the Swain–Schaad formalism (96), assuming that S–O bonds were
ACKNOWLEDGMENTS. The farsighted experiments of G. Shearer and D. Kohl
(Washington University) on catabolic N-isotope fractionation inspired this
work. Discussions with R. Milo (Weizmann Institute of Science) provided focus
at critical points in our development of the approach advocated here. We
thank W. Fischer (California Institute of Technology), D. Fike and W. Leavitt
(Washington University), and A. Pellerin (McGill University) for valuable discussions; D. Stahl and the Stahl research group (University of Washington) for
turning on to stable isotopes; J. Singh (McGill University) for finding two
important typos; and two anonymous reviewers for their criticism that improved this manuscript in substance and in style. J. Ferry (Johns Hopkins
University) made early suggestions that equilibrium thermodynamics might
partly account for microbial behavior. I.H. acknowledges funding from
a European Research Council Starting grant and from Israel Science Foundation Grant 1133/12. B.A.W. acknowledges support from a National Science and Engineering Research Council of Canada Discovery grant and the
Feinberg Foundation Visiting Faculty Program at the Weizmann Institute
of Science.
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Wing and Halevy
FEATURE ARTICLE
Additional Parameters. Intracellular concentrations of ATP, AMP, and total
MK have been measured in sulfate reducers (Table S4) and we maintained
these at constant levels in our calculations. Over the range of csSRR investigated here, we chose [MKred]/[MKox] such that intracellular metabolite
levels did not exceed 10 mM and were greater than the free physiological
limit of 1 nM. Because of the endergonic nature of reactions in the sulfate
reduction pathway at standard state (Table S1), the value of [MKred]/[MKox]
that fulfills these requirements is ∼100 (SI Materials and Methods).
PNAS Early Edition | 9 of 10
EARTH, ATMOSPHERIC,
AND PLANETARY SCIENCES
Materials and Methods
Reaction Thermodynamics and Kinetics. We constrained the free energies of
reaction at standard-state intracellular conditions (pH 7.0; ionic strength = 0.25;
Table S1), using an online biochemical calculator (http://equilibrator.weizmann.
ac.il) (93) that is based on an internally consistent database (51) and accounts for
speciation at intracellular pH values. The redox potential for [MKred]/[MKox] was
from ref. 35. Standard-state free energy values for sulfate uptake have not been
previously determined and we constrained these from membrane energetics
and sulfate accumulation experiments with sulfate-reducing bacteria (SI
Materials and Methods and Fig. S1). Velocities for the individual reactions
were taken from experiments with purified enzymes, whole-cell extracts,
and, in a few cases, cell suspensions (Table S2). Saturation constants were
taken from an online database (www.brenda-enzymes.info) (94) (Table S2).
broken (Table S3). We assumed equilibrium fractionation among external,
internal, and APS-bound sulfate is negligible. During APS production, S–O
bonds are not broken, and no bonds with S are made. Kinetic S-isotope
fractionation during this process would be characterized by a secondary
isotope effect, which we assumed was insignificant.
MICROBIOLOGY
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underpinning for these contrasting isotopic behaviors was sketched
out almost 30 y ago (90), the present contribution has the potential
to link them under a single quantitative framework. We hope that
our approach will enable stable isotope phenotypes like these, as
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Wing and Halevy
COMMENTARY
COMMENTARY
Predictive isotope model connects microbes
in culture and nature
Shuhei Onoa,1, Min Sub Simb, and Tanja Bosaka
a
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of
Technology, Cambridge, MA 02139; and bDivision of Geological and Planetary Sciences,
California Institute of Technology, Pasadena, CA 91125
In PNAS, Wing and Halevy (1) present a new
model that quantitatively describes the magnitude of sulfur isotope fractionation produced by dissimilatory microbial sulfate
reduction (MSR). MSR is a major player in
the global biogeochemical cycles and is responsible for the respiration of up to 30%
of organic matter in marine sediments (2).
This metabolism produces large isotope
effects, in which the product, sulfide, is depleted in the heavy isotopes (33S, 34S, and 36S)
relative to the most abundant isotope 32S (3),
enriching modern seawater sulfate in 34S by
about 21‰ (parts per thousand) compared
with mantle sulfur. Sedimentary sulfur minerals preserve a record of this effect and are
used to track changes in the sulfur isotope
composition of seawater and the biogeochemical sulfur, carbon, and oxygen cycles
through geologic time (4). Such reconstructions require an understanding of factors
that control the magnitude of sulfur isotope
effects and dictate the fractionation of sulfur
isotopes by sulfate reducers under a range of
growth conditions.
All models of sulfur isotope fractionation
during MSR, including that of Wing and
Halevy (1), attempt to describe the interpretations of sulfur isotope signals produced in
inherently complex natural systems and formalize trends bolstered by decades of observations and laboratory studies. Some of the
most prominent trends show that: (i) the
fractionation of S isotopes correlates inversely
with the cell-specific sulfate reduction rates
(csSRR) (Fig. 1), implying that the sluggish
flow of electrons toward the sulfate-reducing
pathway increases the magnitude of isotope
fractionation (34e) (3, 5–8); (ii) the magnitude
of isotope fractionation depends on the actual
electron transfer pathway and organism (Fig.
1) (9); and (iii) low fractionations are likely in
sulfate-limited environments (10, 11).
The new model by Wing and Halevy (1)
relies on these observations and interprets
some of the model parameters in the light
of organismal biochemistry to get around
www.pnas.org/cgi/doi/10.1073/pnas.1420670111
the microbe- or pathway-specific effects.
Conceptual origins of this work date back to
the model put forward by Rees (12) in the
early 1970s. Rees’ model (12) explained the
net observed sulfur isotope fractionations by
considering the following biochemical steps
involved in MSR: activation of sulfate as
adenosine-5′-phosphosulfate (APS), reduction of APS to sulfite, and further reduction
of sulfite to sulfide. The model assigned intrinsic isotope fractionation factors for the
two reduction steps and for the sulfate uptake, as do Wing and Halevy (1), and explored the range of reversibilities at each
step. A later study by Farquhar et al. (13)
added triple sulfur isotope systematics
(32S/33S/34S), whereas Brunner and Bernasconi (14) updated the fractionation factors
to explain large (>50‰) sulfur isotope fractionations observed in nature. These models
could explain the range of sulfur isotope fractionations seen in nature, but their output
was not related to environmental parameters,
such as the concentrations of sulfate and sulfide, limiting the predictive power. Experimental tests of the assumptions made by
these models have also proven difficult.
The Wing and Halevy model (1) is the
first to explicitly interpret some of its free
parameters using thermodynamics and the
influence of electron transfer to the sulfate-reducing pathway. The reversibility is
elegantly related to the free energy of reactions
and processes (also see ref. 15). The estimated
free energy of the reactions under standard
conditions (ΔG0) then allows the reversibility
to be quantified as a function of activities of
products and reactants. With reasonable
assumptions (e.g., fast equilibrium for H2S
inside and outside of the cell), the new model
predicts the net fractionation from only three
assumed parameters: (i) sulfur isotope effect
during the uptake of sulfate (other fractionation factors are fixed), (ii) overall redox potential of the cell, described as the ratios of
oxidized and reduced forms of menaquinone,
and (iii) a scaling factor, interpreted as the
Fig. 1. Relationship between cell specific sulfate reduction rates, growth rates, and isotope fractionation factors
for three different strains of sulfate-reducing bacteria. Data
from refs. 5–8.
ratio of in vivo enzyme activities to those
measured in in vitro crude cell extracts. One
of the main contributions of this model will
be to inspire future experimental tests of these
generalizations.
The Wing and Halevy model (1) uses the
results of recent culture studies (5, 6, 8, 13)
and produces some new, experimentally testable predictions and observations. As mentioned earlier, experimental studies show
a tight correlation between 34e and cell-specific sulfur reduction rate (csSRR), but the
exact relationship differs from one model microbe to another (Fig. 1). Wing and Halevy
Author contributions: S.O., M.S.S., and T.B. wrote the paper.
The authors declare no conflict of interest.
See companion article 10.1073/pnas.1407502111.
1
To whom correspondence should be addressed. Email: sono@mit.
edu.
PNAS Early Edition | 1 of 2
(1) attribute this difference to species-specific
properties: for example, differences in the
activities and abundances of respiratory
enzymes, with higher abundances expected
at higher growth rates (1). The authors propose proteomic tests for these predictions.
Proteomic studies of sulfate reducers are
few, but a study by Zhang et al. (16) showed
the same abundance of dissimilatory sulfite
reductase (Dsr) in cultures of Desulfovibrio
vulgaris grown on lactate and formate, despite different growth rates. This discrepancy encourages future proteomic analyses
of samples from continuous cultures and
measurements of Dsr abundances as a function of csSRR, rather than growth rate.
Assumptions about enzyme abundances,
activities, csSRRs, and growth rates intrinsic
to different microbes can also be investigated by mutagenesis experiments, comparative genomics, measurements of the
isotopic composition of intracellular inorganic sulfur species, and simple biochemical
assays that target the abundances of specific
redox-active components, such as ferredoxin,
NADH/NAD+, and cytochromes, all recognized players in the electron transfer toward
the sulfate-reducing pathway of different
sulfate-reducing bacteria (9, 17).
The new model by Wing and Halevy (1) is
also used to clarify the relationship between
the magnitude of isotope fractionation and
environmental sulfate levels, a key question
related to the cycling of sulfur on early Earth.
Because S isotope fractionations in the rocks
of Archean age (>2.5 billion years ago) are
typically small, low micromolar levels of seawater sulfate were assumed (10, 11), although
alternative explanations also existed (18).
Wing and Halevy (1) suggest that fractionations as large as 60–70‰ are possible in the
presence of micromolar sulfate, as long as
sluggish net respiration rates can be maintained. This theory is consistent with a recent
report of high fractionations from a low sulfate environment (10), but experimental verification of the model assumptions will be
truly challenging.
Wing and Halevy (1) predict that D. vulgaris reducing much less than 1 fmol of
2 of 2 | www.pnas.org/cgi/doi/10.1073/pnas.1420670111
sulfate per cell per day should produce longer experiments are ideal to ensure
34
e of 60‰. For DMSS-1, a recent ma- a complete reservoir exchange, which is
rine isolate different from D. vulgaris, the possible but not trivial. Furthermore, the
maintenance energy requirements may set
The Wing and Halevy
the low limit on the respiration rate attainmodel is the first to
able in chemostat experiments, such that
explicitly interpret some csSRRs much smaller than 0.5 fmol sulfate
per cell per day may not be attainable (20).
of its free parameters
The use of high-energy electron donors, such
using thermodynamics as glucose (5), may be one way to circumvent
the issue of maintenance energy, although
and the influence of
such donors are not commonly explored in
electron transfer to
experimental studies. Therefore, a fundathe sulfate-reducing
mental value of models, including the one by
pathway.
Wing and Halevy (1), is the ability to make
predictions under environmental conditions
predicted rate (csSRR) is smaller than
0.5 fmol sulfate per cell per day irrespective that elude culture experiments (10, 19).
Microbial sulfate reduction connects ecolof sulfate level (figure 3 in ref. 1). Note that
ogy,
biochemistry, geochemistry, physiology,
much slower csSSRs, from 0.1 to 0.0001 fmol
and
Earth
history. The predictive power of
per cell per day (19), are observed in nature.
In lactate-grown cultures, 0.5 fmol per cell the model by Wing and Halevy (1) improves
per day roughly corresponds to the growth our quantitative understanding of these
rate of 0.05 per day (Fig. 1). In continuous links and provides a new tool with which
cultures, this growth rate translates to the to explore the evolution of the sulfur cycle
turnover time of 20 days, and three-times from billions of years ago to today.
1 Wing BA, Halevy I (2014) Intracellular metabolite levels shape
sulfur isotope fractionation during microbial sulfate respiration. Proc
Natl Acad Sci USA, 10.1073/pnas.1407502111.
2 Bowles MW, Mogollón JM, Kasten S, Zabel M, Hinrichs K-U (2014)
Global rates of marine sulfate reduction and implications for sub-seafloor metabolic activities. Science 344(6186):889–891.
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6 Sim MS, Ono S, Donovan K, Templer SP, Bosak T (2011) Effect of
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Desulfovibrio sp. Geochim Cosmochim Acta 75(15):4244–4259.
7 Chambers L, Trudinger P (1979) Microbiological fractionation of
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249–293.
8 Leavitt WD, Halevy I, Bradley AS, Johnston DT (2013) Influence of
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Natl Acad Sci USA 110(28):11244–11249.
9 Sim MS, et al. (2013) Fractionation of sulfur isotopes by
Desulfovibrio vulgaris mutants lacking hydrogenases or type I
tetraheme cytochrome c3. Frontiers in Microbiology 4(June):1–10.
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13 Farquhar J, et al. (2003) Multiple sulphur isotopic interpretations
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14 Brunner B, Bernasconi SM (2005) A revised isotope fractionation
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Supporting Information
Wing and Halevy 10.1073/pnas.1407502111
SI Materials and Methods
Multireactant, Multiproduct Enzymatic Reactions. The net flux through a single, reversible, enzymatically catalyzed step in a metabolic
pathway can be expressed as (1)
+
−
J = J − J = ½E ×
k+cat
!
nj
Q j rj KMj
nj Q
×
× 1 − eΔGr =RT ;
Q mi
1 + j rj KMj + i ð½pi =KMi Þ
[S1]
where J is the net flux, and J + and J − are the forward and reverse fluxes, respectively. [E] is enzyme concentration, k+cat is the forward
catalytic rate constant, ½rj is the concentration of reactant j, KMj is the half-saturation constant of reactant j for the enzyme, and nj is
the stoichiometry of the reactant in the reaction. Likewise, ½pi is the concentration of product i, KMi is the half-saturation constant of
product i for the enzyme, and mi is the stoichiometry of the product in the reaction. ΔGr is the Gibbs free energy of the reaction, R is
the gas constant, and T is the temperature.
In what follows, we replace the term ½E × k+cat with a maximal metabolic rate capacity, V + . For brevity in derivation of the rate
equations for the specific reactions in the sulfate reduction pathway, we further omit the subscripts M from the half-saturation
constants and the subscript r from the Gibbs free energy of reaction:
!
Q nj
j rj K j
+
J =V
[S2]
1 − eΔG=RT :
Q
Q
nj
mi
1 + j rj Kj + i ð½pi =Ki Þ
The first term on the right-hand side of Eq. S2 (“kinetic term”) relates the forward flux to the reverse flux through the dependence on
enzyme kinetics, whereas the second term (“thermodynamic term”) relates these fluxes through the thermodynamic driving force or
the departure from thermodynamic equilibrium. In its simplified form, Eq. S2 is exactly equivalent to Eq. 4 in the main text.
Isotopic Fractionation in Linear, Reversible Metabolic Reaction Networks. Starting with the final pool (p) in the general reaction network,
ϕts
ϕsr
ϕrp
ϕst
ϕrs
ϕpr
t !
r !
p;
s !
where t, s, r, and p are metabolite pools, and ϕrp , for example, is the flux between pools r and p, we express the net flux of mass and
isotopes,
ϕnet = ϕrp − ϕpr ;
ϕnet Rp = ϕrp Rrp − ϕpr Rpr ;
[S3]
[S4]
where Rp , Rrp , and Rpr are the 34S/32S (or 33S/32S) ratios of p and the fluxes ϕrp and ϕpr , respectively. Noting that the isotopic
fractionation factor between any two pools a and b is αa;b ≡ Ra =Rb , and substituting the expression for ϕnet from Eq. S3 into Eq.
S4, we obtain
ϕrp − ϕpr Rp = ϕrp αrp;r Rr − ϕpr αpr; p Rp :
[S5]
Here αrp;r , the isotopic fractionation between the flux ϕrp and the pool r, is by definition the kinetic fractionation associated with
transformation from pool r to pool p. Rearranging to solve for Rr =Rp yields
Rr ϕrp − ϕpr + ϕpr αpr;p
=
:
Rp
ϕrp αrp;r
[S6]
We express the equilibrium fractionation factor between pools r and p, αeq
r;p , by considering the isotopic mass balance at equilibrium,
ϕrp αrp;r Rr = ϕpr αpr;p Rp (2), which yields Rr =Rp = αeq
=
α
=α
.
Defining
f
≡ ϕpr =ϕrp to be the ratio of the reverse to forward flux, we
pr;p
rp;r
p;r
r;p
obtain
eq
fp;r
Rr
1
=
−
+ fp;r αeq
r;p = αr;rp + fp;r αr;p − αr;rp :
Rp αrp;r αrp;r
[S7]
This expression for the fractionation factor between pools r and p is a function of the equilibrium fractionation factor, the kinetic
fractionation associated with the reaction, and the ratio of the reverse to forward rate, fp;r :
[S8]
αr;p = αeq
r;p − αr;rp × fp;r + αr;rp :
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This expression for the fractionation factor naturally yields the equilibrium fractionation factor when ϕrp = ϕpr (i.e., when fp;r = 1) and the
kinetic fractionation factor when ϕrp ϕpr (i.e., when fp;r → 0). It is exactly equivalent to Eq. 1 in the main text.
Constructing a similar mass budget for the reaction between pools s and r under the assumption of a steady state ðϕnet =
ϕrp − ϕpr = ϕsr − ϕrs Þ and recalling that Rr = αr;p Rp , we ultimately obtain a recursive expression for the fractionation between pools
s and p:
[S9]
αs;p = αeq
s;r × αr;p − αs;sr × fr;s + αs;sr :
That is, near equilibrium (ϕsr = ϕrs or fr;s = 1), the fractionation associated with the combination of the two reactions between s and r,
and between r and p, is the product of the equilibrium fractionation factor of the upstream step ðαeq
s;r Þ and the fractionation inherited
from the downstream step ðαr;p Þ. Far from equilibrium (ϕsr ϕrs or fr;s → 0), memory of the fractionation inherited from the
downstream reaction is lost, and the fractionation factor is simply the kinetic fractionation factor associated with the reaction of pool
s to form pool r.
Expanding this treatment to include also the reaction between pools t and s, we obtain a recursive expression for the fractionation
between the initial reactant (t) and the final product (p):
eq
αt;p = αt;s × αs;p − αt;ts × fs;t + αt;ts :
[S10]
This can be expanded to treat any linear network consisting an arbitrary number of reversible reactions. It then remains to obtain expressions for the ratios of the reverse to forward fluxes (which we hereafter generalize as fp;r ). This is done by dividing both sides of Eq. S1 by
the forward flux, J + , and rearranging to get
fp;r = eΔG=RT :
[S11]
Q
Q
Because ΔG = ΔGo + RT lnð i ½pi mi = j ½rj nj Þ, the value of fp;r is related to the energetics of the reaction at the standard state, the
temperature, and the metabolite concentrations:
Q
½pi mi
o
[S12]
fp;r = Qi nj eΔG =RT :
r
j j
Relating Sulfate Reduction Rate to Sulfur Isotope Fractionation. The reactions in the metabolic pathway for dissimilatory sulfate reduction
(Fig. 1 in main text) are shown in Table S1. Two assumptions are implicit in this list of reactions. First, free sulfur compounds of
intermediate oxidation state (e.g., thiosulfate, zero-valent sulfur) are assumed not to play a role in setting S-isotope fractionations.
The ability of the model to reproduce essentially all available experimental results lends confidence that this choice is not misguided.
Second, menaquinone is assumed to be the ultimate electron carrier used by sulfate reducers during respiration. This second choice
is justified by measurements of intracellular metabolite concentrations showing that menaquinone is by far the most abundant
electron carrier in sulfate reducers (3). We note that recent work, however, has discussed alternative conceptual hypotheses in
which both of these assumptions are released (4). The framework presented here could be used to quantitatively evaluate these
hypotheses.
Following conventional approaches to biochemical thermodynamics for reactions occurring at a constant, specific pH (5), we calculate
values of the transformed Gibbs free energy, ΔGo′ , for reactions B–D at pH 7 and an ionic strength of 0.25, which are reasonable
cytoplasmic values. For this purpose we use an online tool for biochemical thermodynamic analysis (http://equilibrator.weizmann.ac.il)
(6). Reduced menaquinone and oxidized menaquinone were not included in this database. Therefore, we convert the ΔGo′ of APS
reduction and sulfite reduction, using FAD/FADH2 as the electron carriers, which is included in the database, into the ΔGo′ of these
reactions with menaquinone as the electron carrier, using the redox potentials of FAD/FADH2 and menaquinone(ox)/menaquinone
(red) reported in ref. 7.
We calculate the Gibbs free energy (untransformed), ΔGo , of reaction A (sulfate uptake), using the results of sulfate uptake experiments in Desulfobulbus propionicus, which transport sulfate actively into the cell along with H+ ions to maintain charge balance (8).
In these experiments, the dependence of intracellular sulfate concentrations ð½SO2−
4 in Þ and the number of protons transported together with sulfate (n) on extracellular sulfate concentrations ð½SO2−
4 out Þ was recorded. The proton-motive force (PMF) was also
recorded in the experiments and found to be approximately constant with a value of −132 × 10−3 V. Using the measured values, we
calculate the membrane potential (Δψ in V) and ΔGoA ,
2− !
SO4 in z
n × PMF
+ log 2−
;
[S13]
Δψ =
2
SO4 out 2
ΔGoA =
Δψðn − 2ÞRT
;
z
[S14]
where z = 2:3RT=F, R is the gas constant, T is the temperature, and F is Faraday’s constant. The value of z is ∼59 mV at 25 °C. The
dependence of ΔGoA on extracellular sulfate concentrations is shown in Fig. S1. In addition, using the membrane potential calculated
above, we calculate the ratio of internal to external ½H+ indicated by the experimental results:
Wing and Halevy www.pnas.org/cgi/content/short/1407502111
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½H + in
= 10ðPMF−ΔψÞ=z :
½H + out
[S15]
We describe the rate of steps A–D in the sulfate reduction pathway with expressions in the form of Eq. S2:
!
!
2− 2− n
SO4 out KAs1
SO4 in ½H+ in ΔGo =RT
+
A
2− × 1 − 2− ;
JA = VA
n e
SO4 out ½H+ out
1 + SO2−
4 out KAs1 + SO4 in KAp1
!
2− !
SO4 in ½ATP KBs1 KBs2
½APS½PPi ΔGo′B RT
× 1 − 2− e
;
1 + SO2−
SO4 in ½ATP
4 in ½ATP KBs1 KBs2 + ½APS½PPi KBp1 KBp2
JB = VB+
JC = VC+
1 + ½APS½MK red ! 2− SO3 ½MK ox ½AMP ΔGo′ RT
½APS½MK red =ðKCs1 KCs2 Þ
C
2− × 1−
e
;
½APS½MK red KCs1 KCs2 + SO3 ½MK ox ½AMP KCp1 KCp2 KCp3
[S16]
[S17]
[S18]
0
1
2− !
3 3
SO
½MK
K
=
K
½H2 S½MK ox 3 ΔGo′D RT
Ds1
red
3
Ds2
A
e
:
JD = VD+ @
×
1
−
2− 3 3 3
3
SO3 ½MK red 3
1 + SO2−
3 ½MK red = KDs1 KDs2 + ½H2 S½MK ox = KDp1 KDp2
[S19]
The subscripts A, B, C, and D denote the reactions in Table S1. The subscripts s1 and s2 denote the first and second substrates in the
reaction, whereas p1–p3 denote the products. Note that the second parentheses in the right-hand sides of Eqs. S16–S19 are simply
ð1 − fp;r Þ for the reactions. We assume that the experimental determinations of enzyme activities were conducted at pH values similar
to those of the cell interior and do not require modification to account for pH differences. Additionally, [H+] does not appear in the
thermodynamic term of reaction D because we use the transformed Gibbs free energy, following common biochemical thermodynamics approaches (5). This approach also requires that all calculations are performed in units of mols L−1 (5).
Measurements of enzyme activity of crude cell extracts of pure cultures provide a basis for estimating V + . To account for differences
+
between these in vivo enzyme activities and those measured in vitro in the crude extract experiments (Vin vitro ; Table S2), we scaled the
in vitro activity measurements of the various reaction steps. This scaling factor uvivo−vitro is defined as
uvivo−vitro =
½Ein vivo × k+cat;in vivo
½Ein vitro × k+cat;in vitro
:
[S20]
Although specific activity may be affected by enzyme isolation and purification (9), we used experimental data from crude cell extracts
to minimize this effect. As a result, we assume that enzyme structure remains constant in the in vivo and in vitro experiments and
k+cat;in vivo ≈ k+cat; in vitro . This means that the “vivo–vitro” scaling factor reduces to a measure of the relative concentration of active
enzymes in whole cells vs. crude extracts,
uvivo−vitro ≈
½Ein vivo
:
½Ein vitro
[S21]
+
Given the regulation of respiratory gene transcription by the same regulon in many sulfate reducers (10), we scaled all values of Vin vitro
(Table S2) by the same uvivo−vitro , resulting in in vivo V + values for each step in the sulfate reduction pathway. The procedure we used
to calibrate uvivo−vitro is explained below.
By definition, at a steady state, JA = JB = JC = JD ≡ J, the overall rate of sulfate reduction. Under this constraint, we rearrange Eqs.
2−
S16–S19 to solve for the intracellular concentrations of SO2−
4 , APS, PPi, and SO3 :
SO2−
4 in
2− SO4 out KAs1 − J VA+ 1 + SO2−
4 out KAs1
= n o
;
J VA+ KAp1 + ½H + in ½H + out eΔGA =RT KAs1
i
h 2− o′
+ SO3 ½MK ox ½AMPeΔGC RT
J VC+ KCs1 KCs2 × 1 + SO2−
3 ½MK ox ½AMP KCp1 KCp2 KCp3
;
½APS =
½MK red 1 − J VC+
2− SO4 in ½ATP 1 − J VB+ − J VB+ KBs1 KBs2
½PPi =
h i;
o′
½APS J VB+ KBs1 KBs2 KBp1 KBp2 + eΔGB RT
i
h 3 3 ΔGo′
RT
+
3
3
D
K
K
+
½H
K
×
1
+
½H
S½MK
=
K
S½MK
e
J
V
Ds1 Ds2
2
ox
Dp1 Dp2
2
ox
2− D
h
i
SO3 =
:
½MK red 3 1 − J VD+
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[S22]
[S23]
[S24]
[S25]
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Net sulfate reduction implies J > 0, whereas the requirement for nonnegative intracellular metabolite concentrations places an upper
limit on J (a requirement that the numerators and denominators of Eqs. S22–S25 have the same sign). Once the equations are solved
for the intracellular metabolite concentrations, we calculate the free energy for each of the reactions in the network:
!
2− n
SO
½H+ ;
[S26]
ΔGA = ΔGoA + RT ln 2−4 in + in
n
SO4 out ½H out
ΔGB = ΔG′o′
B
ΔGC = ΔG′o′
C
!
½APS½PPi
+ RT ln 2− ;
SO4 in ½ATP
!
2− SO3 ½AMP½MK ox + RT ln
;
½APS½MK red !
½H2 S½MK ox 3
:
+
RT
ln
ΔGD = ΔG′o′
2− D
SO3 ½MK red 3
[S27]
[S28]
[S29]
We then use these values of the free energy to calculate the ratio of reverse to forward reaction rates ðfp;r Þ, as in Eq. S12, and from these
the fractionation between the initial substrate sulfate and ultimate product sulfide, using recursive expressions in the form of Eq. S10.
Model Calibration. The model parameters, required for solving Eqs. S22–S25, are listed in Tables S1–S4 along with constraints on their
values, where such constraints exist. Six parameters, to which the model results are sensitive, remain truly variable (½SO2−
4 out , ½H2 Sin ),
34 kin
poorly constrained (34 αkin
A , λA ), or both (½MK red =½MK ox , uvivo−vitro ). To calibrate the model we use a combination of constraints on
34
33
physiologically possible intracellular metabolite concentrations and experimental ½SO2−
4 out –csSRR– «– λ data.
Metabolomic compilations suggest that the majority of metabolite concentrations are less than 10 mM (11). Accordingly, we assume
that the concentrations of all metabolites except sulfate are less than 10 mM. In addition, cell volume places a hard lower limit on
metabolite concentrations from the requirement that at least one molecule of free metabolite exists in the cell. For a cell volume of
∼1 μL, typical of sulfate reducers, this hard lower limit on metabolite concentrations is ∼1 nM. The ½MK red =½MK ox values that yield
concentrations within these limits for all four metabolites and over relatively wide ranges of ½SO2−
4 out and [H2S]in depend on the kinetic
parameters of the enzymes involved in the metabolic pathway. For D. vulgaris enzyme kinetics (Table S2) the range is between ∼60 and
140 and we pick a default value of 100 for ½MK red =½MK ox for fitting the D. vulgaris data and for the model sulfate reducer. The
intracellular metabolite concentrations using this value and over a range of ½SO2−
4 out and [H2S]in are shown in Fig. 2 in the main text.
For A. fulgidus enzyme kinetics, which are ∼3–10 times slower than those of D. vulgaris (Table S2), the default value of ½MK red =½MK ox yielding metabolite concentrations within the physiological constraints is 40.
We note that the different redox potentials of other electron carrier pairs [e.g., reduced and oxidized cytochromec3 (12)] would
require a different ratio of reduced to oxidized electron carrier concentrations to satisfy the constraints on intracellular metabolite
concentrations. Different electron carrier redox ratios and different reaction stoichiometry would also be required if electron bifurcation supports sulfate reduction [e.g., through reduced and oxidized DsrC (13)]. With the ratio of reduced to oxidized electron
carrier concentrations as a free parameter, we are essentially quantifying the thermodynamic consequences of electron transfer for
successful sulfate reduction. Our approach can be adapted to the exact identity of the electron carrier pair, as long as the physiological
constraints on intracellular metabolite concentrations are met.
34
33
The value of the sulfate uptake kinetic fractionation factor ð34 αkin
A Þ is poorly constrained and strongly controls the «– λ relationship
of the full metabolic network (Fig. 5 in main text). We use experimentally observed 34 «–33 λ relationships to constrain the value of
34 kin
αA , which we allow to be strain specific. For recently published datasets (14–18), the best-fit values of 34 αkin
A are 0.997 and 0.993,
respectively. These values are consistent with early experiments, which assign a value of −3% to the fractionation associated with
sulfate uptake (19). For lack of experimental constraints, we use a value of 0.5146 for 33 λ, calculated using the Swain–Schaad formalism
(20). In calculations other than strain-specific fits to experimental data (model sulfate reducer and sensitivity analyses), we use default
33
values of 0.993 and 0.5146 for 34 αkin
λ, respectively.
A and
33
With ½MK red =½MK ox , 34 αkin
,
and
λ
constrained,
and with ½SO2−
4 out and ½H2 Sin as free model parameters (to be specified for
A
individual experimental or environmental conditions), we use the last remaining tunable parameter, uvivo−vitro to fit experimental
34
½SO2−
4 out –csSRR– « data (14–17, 21, 22). The extracellular sulfate and sulfide concentrations are reported for these experiments and
the latter must be related to the model parameter ½H2 Sin . Where extracellular concentrations of sulfide are not reported (e.g., in
N2-sparged experiments), we prescribe [H2S]in to be 0.1 mM. As suggested by sulfide accumulation experiments (23), membrane
resistance to H2S, although very low, may be enough to enable the buildup of intracellular H2S even when environmental sulfide levels
are small. Where csSRR values were not reported for some of the data in a set of experiments (21, 22), we assigned to those data the
harmonic mean of the csSRRs that were reported from that dataset.
We found that the value of uvivo−vitro required to fit the data of all three experimental studies depends linearly on the csSRR in the
specific experiment (Fig. S2). This can be understood as the up-regulation of enzyme levels to achieve a given increase in csSRR. We
used the coefficients of a least-squares linear fit to the uvivo−vitro –csSRR data (Fig. S2 and Table S4) to calculate csSRR-dependent
uvivo−vitro values for the model fits to the experimental data (black curves in Fig. 3 A, E, and H in main text).
Model Sensitivity Analysis. We tested the sensitivity of the model to the values of tunable parameters. The 34 «–csSRR and 34 « − ½SO2−
4 out
relationships are modestly sensitive to intracellular H2S concentrations and extremely sensitive to the ratio of oxidized to reduced
electron carriers (Fig. 4 in main text). The 33 λ–34 « relationship is also sensitive to these intracellular concentrations (Fig. 5 in main
Wing and Halevy www.pnas.org/cgi/content/short/1407502111
4 of 9
text). Additionally, this relationship is sensitive to the value chosen for the kinetic fractionation associated with sulfate uptake into the
34 kin
cell (34 αkin
A ; Fig. 5 in main text) and with reduction of APS ( αC ; Fig. S3). The latter of these fractionation factors is experimentally
constrained (24) and the sensitivity displayed is important for understanding limitations on sulfate reduction rate, but not for the
explanation of actual isotopic variability. These sensitivities are discussed fully in the main text. In addition to these, the results are
insensitive to modestly sensitive to a number of other parameter values (Fig. S3), but not in a way that qualitatively changes the results
34
33
of the model or its ability to explain experimental ½SO2−
4 out –csSRR– «– λ data.
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ΔGro for sulfate uptake (kJ mol−1)
4
3
2
1
0
−1
−2
−3
−6
10
−5
10
−4
−3
10
10
−2
10
−1
10
2−
4
[SO ] (M)
Fig. S1.
Gibbs free energy of reaction at standard state for sulfate uptake as a function of extracellular sulfate concentration calculated using Eqs. S13–S15.
Wing and Halevy www.pnas.org/cgi/content/short/1407502111
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Habicht et al. (2002; 2005)
7000
Sim et al. (2011a; 2011b; 2012)
200
180
450
6000
160
400
140
350
4000
uvit–viv
120
uvit–viv
uvit–viv
5000
100
3000
300
250
80
200
60
2000
150
40
1000
100
20
0
Leavitt et al. (2013)
500
0
50
100
150
200
csSRR (fmol H2S day−1 cell−1)
0
0
50
100
150
csSRR (fmol H2S day−1 cell−1)
200
50
0
50
100
150
200
csSRR (fmol H2S day−1 cell−1)
Fig. S2. The vivo–vitro scaling factor ðuvivo−vitro Þ required to fit 34 «–csSRR data as a function of csSRR (markers) and linear fits (lines) to the data (R2 = 0.97, 0.52,
and 0.82 for Left, Center, and Right plots, respectively).
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[H2S]in
20
34
ε (‰)
20
40
60
80
20
λ
0 10 20 30 40 50 60 70
34
ε (‰)
20
40
60
80
0.508
0.506
20
0 10 20 30 40 50 60 70
34
ε (‰)
0
0
100
0.512
0.510
40
0.508
0.506
33
33
0.510
0
0
100
20
40
60
80
0
100
20
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
csSRR (fmol H2S day−1 cell−1)
csSRR (fmol H2S day−1 cell−1)
csSRR (fmol H2S day−1 cell−1)
Uptake Vmax
Activation Vmax
APS red. Vmax
SO32– red. Vmax
20
0
20
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
csSRR (fmol H2S day−1 cell−1)
Uptake Km
Activation Km
0.516
0 10 20 30 40 50 60 70
34
ε (‰)
0
0 10 20 30 40 50 60 70
34
ε (‰)
60
80
100
20
40
60
80
csSRR (fmol H2S day−1 cell−1)
Uptake 34α
Activation 34α
0.506
20
0 10 20 30 40 50 60 70
ε (‰)
0
0.510
0.508
0.506
20
0 10 20 30 40 50 60 70
ε (‰)
34
0
0
20
40
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
60
80
20
40
0.508
0.506
20
100
60
80
100
csSRR (fmol H2S day−1 cell−1)
0 10 20 30 40 50 60 70
ε (‰)
34
0
20
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
APS red. 34α
SO32– red. 34α
0.516
0.514
0.512
1.032
1.022
1.012
0.510
40
0.508
0.506
20
0.514
60
0 10 20 30 40 50 60 70
ε (‰)
34
40
0.512
1.035
1.025
1.015
0.510
0.508
0.506
20
0 10 20 30 40 50 60 70
ε (‰)
34
0
0
0
0.512
csSRR (fmol H2S day−1 cell−1)
60
1.010
1.000
0.990
100
0.510
0.516
0.512
80
0
20
λ
λ
33
40
34
0 10 20 30 40 50 60 70
ε (‰)
ε (‰)
0.508
ε (‰)
0.510
34
λ
33
ε (‰)
40
1.005
0.995
0.985
60
0.514
40
34
0
0.514
60
0.512
0.510
0.508
0.516
0.514
60
40
0.516
0.512
0.506
100
csSRR (fmol H2S day−1 cell−1)
0.516
20
60
0
0
34
40
0
0.514
20
0
20
100
SO32– red. Km
40
0.508
20
80
APS red. Km
λ
0.512
0.506
60
csSRR (fmol H2S day−1 cell−1)
60
0.510
40
0.508
0
40
csSRR (fmol H2S day−1 cell−1)
ε (‰)
ε (‰)
0.510
20
33
λ
0.512
0.506
20
0.516
0.514
60
34
λ
33
ε (‰)
40
0
0
0.516
0.514
60
λ
0
0
ε (‰)
λ
100
0 10 20 30 40 50 60 70
34
33
80
0.506
20
λ
60
0.508
33
40
ε (‰)
34
33
20
34
0
ε (‰)
λ
ε (‰)
0 10 20 30 40 50 60 70
ε (‰)
0
34
0.506
34
20
0 10 20 30 40 50 60 70
0.508
0.512
0.510
40
34
ε (‰)
0.506
0.510
ε (‰)
34
0.508
0.512
34
0 10 20 30 40 50 60 70
40
0.514
60
33
20
0.510
40
0.508
0.512
0.516
0.514
60
ε (‰)
ε (‰)
0.510
0.506
33
λ
0.512
34
λ
33
ε (‰)
40
0.514
60
34
0.514
60
0.516
33
0.516
33
0.516
34
λ
ε (‰)
34
0
0
34
0 10 20 30 40 50 60 70
ε (‰)
0.506
0.514
60
0.512
40
0.508
20
0
34
ε (‰)
λ
0 10 20 30 40 50 60 70
[AMP]
0.516
0.514
60
0.512
0.510
40
0.508
0.506
33
ε (‰)
0.510
34
λ
33
ε (‰)
34
40
0.514
60
0.512
34
0.514
60
[ATP]
0.516
0.516
34
[SO42–]out
0.516
0
20
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
0
20
40
60
80
100
csSRR (fmol H2S day−1 cell−1)
Fig. S3. Sensitivity of model results to parameter values. The main plots show the 34 «–csSRR relationships and Insets show the 33 λ–34 « relationships. Black
curves are for default parameter values (Tables S2–S4). Blue and orange curves are for half and twice the default values, respectively, except for the sensitivity
analyses to the kinetic fractionation factors associated with each of the metabolic reactions (Bottom row), where the values of the fractionation factors are
shown in Insets.
Table S1. Metabolic reactions for dissimilatory sulfate reduction
Step
A
B
C
D
Reaction
+
SO2−
4 out + nHout
2−
SO4 in + ATP
+
⇌ SO2−
4 in + nHin
⇌ APS + PPi
APS + MKred
⇌ SO2−
3 + MKox + AMP
+
SO2−
3 + 3MKred + 2Hin ⇌ H2 S + 3MKox + 3H2 O
AMP, adenosine monophosphate; ATP, adenosine triphosphate; MKox,
menaquinone, oxidized; MK red , menaquinone, reduced; PPi, pyrophos−1
−1
o′
o′
phate; ΔGoA , see Fig. S1; ΔGo′
B = 55:9 kJ · mol ; ΔGC = 5:4 kJ · mol ; ΔGD =
31:2 kJ · mol−1 .
Wing and Halevy www.pnas.org/cgi/content/short/1407502111
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Table S2. In vitro enzyme kinetic parameters used in the model
Step
V+
Km
Notes
2−
+
+
A: SO2−
4 out + nHout ⇌ SO4 in + nHin
Archaeoglobus fulgidus
1.68 × 10−20
Desulfovibrio vulgaris
3.98 × 10−20
B: SO2−
4 in + ATP ⇌ APS + PPi
A. fulgidus
D. vulgaris
SO2−
4
0.01
1.71 × 10−19
3.24 × 10−19
SO2−
4
ATP
APS
PPi
10.00
0.10
0.17
0.13
C: APS + MKred ⇌ SO2−
3 + MKox + AMP
A. fulgidus
9.38 × 10−20
D. vulgaris
3.49 × 10−19
APS
MKred
0.02
0.10
MKox
SO2−
3
0.10
0.40
AMP
0.30
+
D: SO2−
3 + 3MKred + 2Hin ⇌ H2 S + 3MKox + 3H2 O
A. fulgidus
2.38 × 10−20
D. vulgaris
4.28 × 10−19
SO2−
3
MKred
MKox
H2S
0.05
0.02
0.02
0.01
Source or ref.
Harmonic mean of all data
Harmonic mean of D. vulgaris data
Approximate harmonic mean of D. vulgaris data
†
Internally consistent* harmonic mean of A. fulgidus data
Internally consistent* harmonic mean of D. vulgaris data
Estimate based on range of reported values and ½SO2−
4 Estimate based on range of reported values
Estimate based on A. fulgidus
Estimate based on A. fulgidus
†
Internally consistent* A. fulgidus data
Internally consistent* D. vulgaris data
Estimate based on D. vulgaris, A. fulgidus
Estimate based on Desulfobulbus propionicus,
Desulfovibrio gigas
Estimate based on D. propionicus, D. gigas
Estimate based on D. vulgaris, Desulfovibrio salexigens,
D. gigas, Desulfovibrio desulfuricans
Estimate based on D. vulgaris, D. salexigens,
D. desulfuricans
Internally consistent* A. fulgidus data
Internally consistent* D. vulgaris data
Estimate based on reported values for D. vulgaris
Estimate based on range of reported values
Estimate based on range of reported values
Estimate
†
†
†
(1)
(1)
(1)
(1)
†
†
(1)
(1)
(1)
(1)
(1)
†
†
(1)
(1)
(1)
The values for D. vulgaris were also used for the model sulfate reducer and as default values in the sensitivity analyses. The units of V+ are mol·cell−1·s−1.
The units of Km are mM for presentation purposes. The actual calculations require units of M.
*All values were taken from publications by the same research group to ensure similarity of methods (See Dataset S1).
†
Dataset S1.
1. Schomburg I, et al. (2013) BRENDA in 2013: Integrated reactions, kinetic data, enzyme function data, improved disease classification: New options and contents in BRENDA. Nucleic
Acids Res 41(Database issue):D764–D772.
Wing and Halevy www.pnas.org/cgi/content/short/1407502111
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Table S3. Equilibrium and kinetic fractionation factors and mass-dependent exponents used in
the model
Step
α
34 eq
λ
33 eq
α
Ref.
34 kin
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
T = 25 °C, for D. vulgaris experiments
A
1.000
0.5150
B
1.000
0.5150
C
1.006
0.5167
D
1.065
0.5147
T = 80 °C, for A. fulgidus experiments
A
1.000
0.5150
B
1.000
0.5150
C
1.004
0.5165
D
1.050
0.5149
λ
33 kin
*
Ref.
0.993–0.997†
1.000
1.022
1.025
0.5146
0.5146
0.5146
0.5146
(2)
NA
(3)
(4)
0.993–0.997†
1.000
1.022
1.025
0.5146
0.5146
0.5146
0.5146
(2)
NA
(3)
(4)
*The fractionation exponent was calculated with the Swain–Schaad formalism (5), where 33 αkin = ð34 αkin Þ λ .
†
The upper end of this range (0.997) was suggested by Harrison and Thode (2) and required to adequately fit the
33 34
λ– « datasets of Sim et al. (6–8). The lower end (0.993) was required to adequately fit the 33 λ–34 « datasets of
Habicht et al. (9, 10) and Leavitt et al. (11).
33 kin
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Otake T, Lasaga AC, Ohmoto H (2008) Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems. Chem Geol 249:357–376.
Harrison A, Thode H (1958) Mechanism of the bacterial reduction of sulphate from isotope fractionation studies. Trans Faraday Soc 54:84–92.
Kemp A, Thode H (1968) The mechanism of the bacterial reduction of sulphate and of sulphite from isotope fractionation studies. Geochim Cosmochim Acta 32(1):71–91.
Hoek J, Canfield D (2009) Controls on isotope fractionation during sulfate reduction. Geochim Cosmochim Acta 73:A538.
Swain CG, Stivers EC, Reuwer JF, Jr, Schaad LJ (1958) Use of hydrogen isotope effects to identify the attacking nucleophile in the enolization of ketones catalyzed by acetic acid1-3.
J Am Chem Soc 80:5885–5893.
Sim MS, Bosak T, Ono S (2011) Large sulfur isotope fractionation does not require disproportionation. Science 333(6038):74–77.
Sim M, Ono S, Donovan K, Templer S, Bosak T (2011) Effect of electron donors on the fractionation of sulfur isotopes by a marine Desulfovibrio sp. Geochim Cosmochim Acta
75:4244–4259.
Sim MS, Ono S, Bosak T (2012) Effects of iron and nitrogen limitation on sulfur isotope fractionation during microbial sulfate reduction. Appl Environ Microbiol 78(23):8368–8376.
Habicht KS, Gade M, Thamdrup B, Berg P, Canfield DE (2002) Calibration of sulfate levels in the archean ocean. Science 298(5602):2372–2374.
Habicht KS, Salling L, Thamdrup B, Canfield DE (2005) Effect of low sulfate concentrations on lactate oxidation and isotope fractionation during sulfate reduction by Archaeoglobus
fulgidus strain Z. Appl Environ Microbiol 71(7):3770–3777.
Leavitt WD, Halevy I, Bradley AS, Johnston DT (2013) Influence of sulfate reduction rates on the Phanerozoic sulfur isotope record. Proc Natl Acad Sci USA 110(28):11244–11249.
Table S4. Parameter values used in the model
Parameter
[ATP]
[AMP]
[MK]
½MKred =½MKox uvivo−vitro
Model sulfate reducer
Habicht et al. (4, 5)
Sim et al. (6–8)
Leavitt et al. (9)
Value
Source or ref.
Notes
2.6 mM
0.3 mM
0.6 mM
100 or 40*
(1, 2)
(1)
(3)
This study
For D. vulgaris
For D. vulgaris
For D. vulgaris Marburg
See Model Calibration
2.0 × csSRR + 70.0†
33.7 × csSRR + 70.1
0.9 × csSRR + 13.9
2.1 × csSRR + 70.0
This
This
This
This
study
study
study
study
See Fig. S2
See Fig. S2
See Fig. S2
*½MKred =½MKox of 100 was used for the model sulfate reducer, for the fits to the D. vulgaris data (6–9), and for
the sensitivity analyses. ½MKred =½MKox of 40 was used for the fit to the A. fulgidus data (4, 5).
†
The linear relationship between csSRR and uvivo−vitro in the model sulfate reducer was based on the fit to the
data of Leavitt et al. (9).
1.
2.
3.
4.
5.
6.
7.
8.
9.
Yagi T, Ogata M (1996) Catalytic properties of adenylylsulfate reductase from Desulfovibrio vulgaris Miyazaki. Biochimie 78(10):838–846.
Sekiguchi T, Noguchi A, Nosoh Y (1977) ATP and acetylene-reducing activity of a sulfate-reducing bacterium. Can J Microbiol 23(5):567–572.
Badziong W, Thauer R (1980) Vectorial electron transport in Desulfovibrio vulgaris (Marburg) growing on hydrogen plus sulfate as sole energy source. Arch Microbiol 125:167–174.
Habicht KS, Gade M, Thamdrup B, Berg P, Canfield DE (2002) Calibration of sulfate levels in the archean ocean. Science 298(5602):2372–2374.
Habicht KS, Salling L, Thamdrup B, Canfield DE (2005) Effect of low sulfate concentrations on lactate oxidation and isotope fractionation during sulfate reduction by Archaeoglobus
fulgidus strain Z. Appl Environ Microbiol 71(7):3770–3777.
Sim MS, Bosak T, Ono S (2011) Large sulfur isotope fractionation does not require disproportionation. Science 333(6038):74–77.
Sim M, Ono S, Donovan K, Templer S, Bosak T (2011) Effect of electron donors on the fractionation of sulfur isotopes by a marine Desulfovibrio sp. Geochim Cosmochim Acta
75:4244–4259.
Sim MS, Ono S, Bosak T (2012) Effects of iron and nitrogen limitation on sulfur isotope fractionation during microbial sulfate reduction. Appl Environ Microbiol 78(23):8368–8376.
Leavitt WD, Halevy I, Bradley AS, Johnston DT (2013) Influence of sulfate reduction rates on the Phanerozoic sulfur isotope record. Proc Natl Acad Sci USA 110(28):11244–11249.
Other Supporting Information Files
Dataset S1 (XLSX)
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