Kevin Lepot
email: kevin.lepot@univ-lille.fr

Kenneth H Williford

Pascal Philippot

Christophe Thomazo

Takayuki Ushikubo

Kouki Kitajima

Smaïl Mostefaoui

John W Valley

Extreme 13C-depletions and organic sulfur content argue

Keywords: Early life, SIMS, Carbon isotopes, Organic matter, Stromatolites, Sulfurization, Tumbiana Formation, Methanotrophy Acetyl-CoA: acetyl-coenzyme A. ANME: anaerobic methanotroph. AOM: anaerobic oxidation of methane. EDXS: energy-dispersive X-ray spectrometry. Ga: giga-annum microbial sulfate reduction/reducers. OM: organic matter. SEM: scanning electron microscopy. SD: standard deviation. SE: standard error. SIMS: secondary ion mass spectrometry. STXM: scanning transmission X-ray microscopy. XANES: X-ray absorption near-edge structure

come

Introduction

The low O2 concentration of the Archean atmosphere is indicated by mass independent fractionation of sulfur isotopes (MIF-S 1 , [START_REF] Farquhar | Atmospheric influence of Earth's earliest sulfur cycle[END_REF][START_REF] Pavlov | Mass-Independent Fractionation of Sulfur Isotopes in Archean Sediments: Strong Evidence for an Anoxic Archean Atmosphere[END_REF], which only disappeared after the Great Oxygenation Event, ca. 2.45-2.31 Ga ago [START_REF] Guo | Reconstructing Earth's surface oxidation across the Archean-Proterozoic transition[END_REF][START_REF] Luo | Rapid oxygenation of Earth's atmosphere 2.33 billion years ago[END_REF][START_REF] Philippot | Globally asynchronous sulphur isotope signals require re-definition of the Great Oxidation Event[END_REF]. The Neoarchean (ca. 2.8-2.5 Ga) has been distinguished from the earlier Archean by increase in MIF-S magnitude from |Δ 33 S|<3‰ between 3.2 and ca. 2.71 Ga to >3‰ and a change in the slope of Δ 36 S/Δ 33 S from -1.5 to -0.9 at ca. 2.71 Ga [START_REF] Kurzweil | Atmospheric sulfur rearrangement 2.7 billion years ago: Evidence for oxygenic photosynthesis[END_REF]. These changes have been interpreted as the result of increased biological oxygen and methane production [START_REF] Kurzweil | Atmospheric sulfur rearrangement 2.7 billion years ago: Evidence for oxygenic photosynthesis[END_REF]. Indeed, O2 production is proposed as early as 3.0-2.8 Ga ago based on Cr isotope ratios [START_REF] Frei | Fluctuations in Precambrian atmospheric oxygenation recorded by chromium isotopes[END_REF][START_REF] Crowe | Atmospheric oxygenation three billion years ago[END_REF], 2.95 Ga based on Mo isotope ratios [START_REF] Planavsky | Evidence for oxygenic photosynthesis half a billion years before the Great Oxidation Event[END_REF], 2.5 Ga based on Mo and Re abundance [START_REF] Anbar | A Whiff of Oxygen Before the Great Oxidation Event?[END_REF], on N isotope ratios [START_REF] Garvin | Isotopic Evidence for an Aerobic Nitrogen Cycle in the Latest Archean[END_REF], and on Se isotope ratios (Stüeken et al., 2015a). Moreover, the pronounced increase in abundance and diversity of stromatolitic carbonates also suggests a change in the evolution of the biosphere during the Neoarchean [START_REF] Hofmann | Archean Stromatolites as Microbial Archives[END_REF]. The accretion of stromatolites could derive (indirectly: [START_REF] Dupraz | Processes of carbonate precipitation in modern microbial mats[END_REF] from various autotrophic metabolisms such as oxygenic and anoxygenic photosynthesis (Fig. 1A; [START_REF] Bosak | The Meaning of Stromatolites[END_REF] or via anaerobic oxidation of methane (AOM) [START_REF] Greinert | Stromatolitic fabric of authigenic carbonate crusts: Result of anaerobic methane oxidation at cold seeps in 4,850 m water depth[END_REF]. Some Neoarchean stromatolites display fabrics strongly suggesting they formed in presence of photosynthetic bacteria. These fabrics include tufted mats similar to those formed by cyanobacteria [START_REF] Flannery | Archean tufted microbial mats and the Great Oxidation Event: New insights into an ancient problem[END_REF], clumps similar to those formed by filamentous cyanobacteria in response to O2 [START_REF] Sim | Oxygen-Dependent Morphogenesis of Modern Clumped Photosynthetic Mats and Implications for the Archean Stromatolite Record[END_REF], and palisade textures similar to those formed by vertically erected phototropic filaments [START_REF] Buick | The antiquity of oxygenic photosynthesis: evidence from stromatolites in sulphate-deficient Archaean lakes[END_REF].

The Fortescue Group of Western Australia records the largest negative excursion-the "Fortescue excursion"-in the organic carbon isotope (δ 13 Corg 1 ) record, with δ 13 Corg values as low as -60.9 ‰ (reviews of the data in Thomazo et al., 2009a;[START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF]. These extreme 13 C-depletions, as well as other values lower than ca. -40 ‰ commonly recorded in other Neoarchean rocks have been interpreted to be the result of methanotrophy (i.e. the oxidation of methane by prokaryotes)

1 Isotope ratios are given as δ deviations-in permil (‰) units-of the ratio of the isotope compositions of mass X to mass Y relative to the same ratio in a reference standard. The international reference standards are VPDB (Vienna Pee Dee Belemnite) for C isotopes, VCDT (Vienna Canyon Diablo Troilite) for S isotopes, and IRMM-014 for Fe isotopes. Deviations for S-, C and Fe-isotopes ratios reported or discussed here are calculated using: δ M S = 1000*[( M S/ 32 S) sample -( M S/ 32 S) VCDT ]/( M S/ 32 S) VCDT with M=33, 34 or 36, δ 13 C = 1000*[( 13 C/ 12 C) sample -( 13 C/ 12 C) VPDB ]/( 13 C/ 12 C) VPDB, and δ 56 Fe = 1000*[( 56 Fe/ 54 Fe) sample -( 56 Fe/ 54 Fe) IRMM- [START_REF] Schoell | Anomalous 13C depletion in early Precambrian graphites from Superior Province, Canada[END_REF][START_REF] Hayes | Global methanotrophy of the Archean-Proterozoic transition[END_REF]. Methanotrophy could have been performed aerobically (CH4 + 2O2 → CO2 + 2H2O, Fig. 1J) using photosynthetically produced O2 [START_REF] Hayes | Global methanotrophy of the Archean-Proterozoic transition[END_REF]. Molecules of 3-methylhopane found in Neoarchean rocks suggest aerobic methanotrophs [START_REF] Eigenbrode | Methylhopane biomarker hydrocarbons in Hamersley Province sediments provide evidence for Neoarchean aerobiosis[END_REF], although these molecules may have been produced by other bacteria [START_REF] Welander | Discovery, taxonomic distribution, and phenotypic characterization of a gene required for 3-methylhopanoid production[END_REF]. Moreover, the lack of these molecules in new samples from the same stratigraphic intervals recovered by ultraclean drilling methods shows that previously reported Archean biomarkers from Western Australia were the result of contamination during conventional drilling or curation [START_REF] French | Reappraisal of hydrocarbon biomarkers in Archean rocks[END_REF]. Alternatively, methanotrophy could have been performed anaerobically (AOM, Fig. 1K-L) using other oxidants such as sulfate, nitrite/nitrate, Fe 3+ -minerals, or Mn 4+ -minerals [START_REF] Raghoebarsing | A microbial consortium couples anaerobic methane oxidation to denitrification[END_REF][START_REF] Beal | Manganese-and Iron-Dependent Marine Methane Oxidation[END_REF][START_REF] Knittel | Anaerobic Oxidation of Methane: Progress with an Unknown Process[END_REF]). Today's most common AOM pathway uses sulfate (CH4 + SO4 2-→ HCO3 -+ HS -+ H2O) and, by extension, may explain the Fortescue δ 13 Corg excursion [START_REF] Hinrichs | Microbial fixation of methane carbon at 2.7 Ga: Was an anaerobic mechanism possible?[END_REF]. The sulfate fueling this type of AOM could have been produced through photolytic dissociation of SO2 in an anoxic atmosphere [START_REF] Farquhar | Observation of wavelength-sensitive mass-independent sulfur isotope effects during SO2 photolysis: Implications for the early atmosphere[END_REF] and/or chemotrophic or phototrophic S-oxidizing bacteria [START_REF] Konhauser | Introduction to Geomicrobiology[END_REF][START_REF] Ghosh | Biochemistry and molecular biology of lithotrophic sulfur oxidation by taxonomically and ecologically diverse bacteria and archaea[END_REF]. Isotope fractionations indicative of microbial sulfate reduction (MSR, Fig. 1D,1G) are indicated at ca. 3.5 Ga [START_REF] Philippot | Early Archaean microorganisms preferred reduced sulfur, not sulfate[END_REF][START_REF] Ueno | Quadruple sulfur isotope analysis of ca. 3.5 Ga Dresser Formation: New evidence for microbial sulfate reduction in the early Archean[END_REF]Shen et al., 2001[START_REF] Shen | Evaluating the role of microbial sulfate reduction in the early Archean using quadruple isotope systematics[END_REF], 2.7 Ga [START_REF] Thomazo | Multiple sulfur and carbon isotope composition of sediments from the Belingwe Greenstone Belt (Zimbabwe): A biogenic methane regulation on mass independent fractionation of sulfur during the Neoarchean? Geochim[END_REF], and 2.5 Ga [START_REF] Zhelezinskaia | Large sulfur isotope fractionations associated with Neoarchean microbial sulfate reduction[END_REF]. Bulk-rock δ 34 S values of pyrite between 2.7 and 3 Ga display a small range of values of ca. 0 ±8 ‰ (Thomazo et al., 2009a;Thomazo et al., 2009b;[START_REF] Johnston | Multiple sulfur isotopes and the evolution of Earth ' s surface sulfur cycle[END_REF], with one exception in the 2.7 Ga Manjeri Formation, Zimbabwe [START_REF] Grassineau | Stable isotopes in the Archaean Belingwe belt, Zimbabwe: evidence for a diverse microbial mat ecology[END_REF][START_REF] Thomazo | Multiple sulfur and carbon isotope composition of sediments from the Belingwe Greenstone Belt (Zimbabwe): A biogenic methane regulation on mass independent fractionation of sulfur during the Neoarchean? Geochim[END_REF]. This small range is indistinguishable from the range of values produced during abiotic processes (such as thermochemical sulfate reduction, e.g. [START_REF] Watanabe | Anomalous Fractionations of Sulfur Isotopes During Thermochemical Sulfate Reduction[END_REF] but is nevertheless consistent with small fractionations produced during MSR under low sulfate concentrations (Habicht et al. 2002) or mixing with sulfide derived (abiotically) from elemental S [START_REF] Farquhar | Pathways for Neoarchean pyrite formation constrained by mass-independent sulfur isotopes[END_REF]. In contrast, large ranges of positive and negative δ 34 S recorded at the microscale indicate MSR in lacustrine stromatolites of the Fortescue Group (Tumbiana Formation, [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF] and younger Neoarchean rocks [START_REF] Kamber | Micro-scale sulphur isotope evidence for sulphur cycling in the late Archean shallow ocean[END_REF][START_REF] Farquhar | Pathways for Neoarchean pyrite formation constrained by mass-independent sulfur isotopes[END_REF][START_REF] Fischer | SQUID-SIMS is a useful approach to uncover primary signals in the Archean sulfur cycle[END_REF] and show that sulfate was abundant enough to express Sisotope fractionations. Sulfate concentrations of less than 2.5 micromolar have been suggested for Archean seawater [START_REF] Crowe | Sulfate was a trace constituent of Archean seawater[END_REF]. Such low concentrations have been proposed to limit AOM [START_REF] Slotznick | Examining Archean methanotrophy[END_REF]. However, sulfate-dependent AOM has been shown to proceed at high rates even at such low concentrations [START_REF] Beal | High rates of anaerobic methanotrophy at low sulfate concentrations with implications for past and present methane levels[END_REF]. In modern sediments, AOM can reduce Fe 3+minerals in addition to, or instead of, sulfate [START_REF] Sivan | Iron oxides stimulate sulfate-driven anaerobic methane oxidation in seeps[END_REF][START_REF] Egger | Anaerobic oxidation of methane alters sediment records of sulfur, iron and phosphorus in the Black Sea[END_REF][START_REF] Bar-Or | Iron-Coupled Anaerobic Oxidation of Methane Performed by a Mixed Bacterial-Archaeal Community Based on Poorly Reactive Minerals[END_REF]. Minerals rich in Fe 3+ could have been produced throughout the Archean as the result of oxygenic and/or anoxygenic photosynthesis (Fig. 1A), as suggested by Fe-isotopes [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF][START_REF] Li | An anoxic, Fe(II)-rich, U-poor ocean 3.46 billion years ago[END_REF][START_REF] Dauphas | Iron Isotope Systematics[END_REF][START_REF] Busigny | Iron and sulfur isotope constraints on redox conditions associated with the 3.2 Ga barite deposits of the Mapepe Formation (Barberton Greenstone Belt, South Africa)[END_REF]. The coupling of 13 C-depleted kerogen and highly negative δ 56 Fe has been used to suggest AOM was coupled to microbial Fereduction during the deposition of the Fortescue Group [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF].

It has been proposed that Neoarchean methanotrophy was not compatible with the textures and isotopic composition of the carbonates associated with 13 C-depleted kerogen [START_REF] Slotznick | Examining Archean methanotrophy[END_REF], although this argument has been refuted [START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF][START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF], see also section 5.3). As an alternative to methanotrophy, extreme 13 C-depletions in OM could result from chemotrophic metabolisms using the acetyl-CoA (Wood-Ljungdahl) pathway [START_REF] Slotznick | Examining Archean methanotrophy[END_REF], e.g. Fig. 1C. One of the most controversial aspects of this model is that it allows formation of strongly 13 C-depleted kerogen without the need of cycling primary photosynthetic biomass through fermentation, methanogenesis and methanotrophy [START_REF] Slotznick | Examining Archean methanotrophy[END_REF], supporting the hypothesis that oxygenic photosynthesis appeared much later during the late Archean or Paleoproterozoic [START_REF] Kopp | The Paleoproterozoic snowball Earth: A climate disaster triggered by the evolution of oxygenic photosynthesis[END_REF][START_REF] Fischer | Evolution of Oxygenic Photosynthesis[END_REF].

It has been suggested that high concentrations of atmospheric methane could have led to the formation of organic aerosols with δ 13 Corg values as low as -65 ‰ without methanotrophic metabolism [START_REF] Pavlov | Organic haze in Earth's early atmosphere: Source of low-C-13 Late Archean kerogens?[END_REF]. However, the 13 C-depletions are more prominent in mudstones compared to stromatolites and silts at the same locality (Thomazo et al., 2009b), in lakes with a basaltic rather than felsic catchment [START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF], and in lacustrine and shallow marine compared to open marine deposits [START_REF] Eigenbrode | Late Archean rise of aerobic microbial ecosystems[END_REF][START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF]. These spatial heterogeneities support a local (i.e. sedimentary) rather than global (i.e. atmospheric) control on δ 13 Corg (Thomazo et al., 2009b;[START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF]. The apparent relationship between the larger Δ 33 S and the lowest δ 13 Corg in the 2.72 Ga Tumbiana Formation is also consistent with the hypothesis of methanotrophy under an atmosphere poor in organic aerosols (Thomazo et al., 2009b). Periodic changes in slope of Δ 36 S/Δ 33 S to values less than -1 linked with lower δ 13 Corg values after 2.71 Ga have been interpreted as the result of periodic organic aerosol haze caused by increased methanogenesis [START_REF] Zerkle | A bistable organic-rich atmosphere on the Neoarchaean Earth[END_REF][START_REF] Izon | Multiple oscillations in Neoarchaean atmospheric chemistry[END_REF][START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF][START_REF] Izon | Biological regulation of atmospheric chemistry en route to planetary oxygenation[END_REF], possibly concomitant with increased oxygenic photosynthesis [START_REF] Kurzweil | Atmospheric sulfur rearrangement 2.7 billion years ago: Evidence for oxygenic photosynthesis[END_REF]. This link is, however, not apparent in all >2.71 Ga units, possibly as the result of methanotrophy preventing organic haze formation (Thomazo et al., 2009b;[START_REF] Thomazo | Multiple sulfur and carbon isotope composition of sediments from the Belingwe Greenstone Belt (Zimbabwe): A biogenic methane regulation on mass independent fractionation of sulfur during the Neoarchean? Geochim[END_REF] or of variable effects of organic haze on Δ 36 S/Δ 33 S [START_REF] Izon | Biological regulation of atmospheric chemistry en route to planetary oxygenation[END_REF]. A better understanding of the origin of the extreme δ 13 Corg fractionations recorded during the Neoarchean could help tie microbial metabolism and the evolution of atmospheric chemistry during the prologue to atmospheric oxygenation.

Here, we investigate the organic matter (OM) from two lacustrine stromatolites of the Tumbiana Formation of the Fortescue Group, Western Australia, using a combination of X-ray spectroscopies, microscale analysis of organic carbon isotopes using Secondary Ion Mass Spectrometry (SIMS) and nanoanalyses of S/C with NanoSIMS. We document three distinct types of OM recognizable by their C-isotope compositions, petrographic contexts, and organic sulfur contents. Type-C OM is interpreted as migrated pyrobitumen and displays the highest δ 13 C values. Pronounced enrichments in organic sulfur are only found in Type-B OM, which displays the lowest δ 13 Corg values. We interpret this C-S relationship to reflect the operation of sulfur-dependent AOM. Type-A OM is poor in organic S but associated with Fe-minerals. This OM type is most parsimoniously interpreted as the product of sulfate-and/or Fe-dependent AOM.

Geological context and drillcores

The Tumbiana Formation is part of the Fortescue Group (Western Australia), which deposited over the granitoid-greenstone basement of the Pilbara Craton and which is overlain by the Hamersley Group [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF], Fig. 2. The Tumbiana Formation has been dated at 2724 ± 5 Ma using zircon U-Pb ages [START_REF] Blake | Geochronology of a Late Archaean flood basalt province in the Pilbara Craton, Australia: Constraints on basin evolution, volcanic and sedimentary accumulation, and continental drift rates[END_REF]. The lower part of the Tumbiana Formation is the Mingah Member, which features both primary and reworked mafic tuffs [START_REF] Lepot | Biogenic versus metamorphic origins of diverse microtubes in 2.7Gyr old volcanic ashes: Multi-scale investigations[END_REF]. This unit is overlain by the Meentheena Member, which comprises a suite of mudstones, siltstones, carbonate stromatolites and carbonate sandstones. Stromatolitic horizons of the Meentheena Member are 0.5-to 20-m thick and can be followed along strike for several kilometers [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF]. The Tumbiana Formation is overlain by subaerial basalts of the Maddina Formation.

The Fortescue Group experienced regional low-grade metamorphism [START_REF] Smith | Burial metamorphism in the Hamersley basin[END_REF] at about 2.2 Ga [START_REF] Rasmussen | Dating low-grade metamorphic events by SHRIMP U-Pb analysis of monazite in shales[END_REF]. The studied rocks come from the Meentheena locality [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF]Lepot et al., 2009a) in the metamorphism zone (II) of [START_REF] Smith | Burial metamorphism in the Hamersley basin[END_REF] shown in Fig. 2, which displays prehnite-pumpellyite facies with epidote. This metamorphic grade/facies together with the maturity of organic matter inferred with Raman spectroscopy indicate metamorphism temperatures no higher than 300°C [START_REF] Lepot | Microbially influenced formation of 2,724-million-year-old stromatolites[END_REF]. Regional metamorphism of the Fortescue Group was locally followed-as indicated by petrographic relationships-by heterogeneous metasomatism leading to transformation of primary volcanic minerals and clays (such as chlorite) into epidote [START_REF] White | Regional-scale Metasomatism in the Fortescue Group Volcanics, Hamersley Basin, Western Australia: Implications for Hydrothermal Ore Systems[END_REF], which was not observed in the basaltic flow overlying the studied sedimentary rocks.

Sediment facies and trace element compositions support deposition of the Meentheena Member stromatolites in a giant lake system [START_REF] Buick | The antiquity of oxygenic photosynthesis: evidence from stromatolites in sulphate-deficient Archaean lakes[END_REF][START_REF] Bolhar | A non-marine depositional setting for the northern Fortescue Group, Pilbara Craton, inferred from trace element geochemistry of stromatolitic carbonates[END_REF][START_REF] Awramik | A giant, Late Archean lake system: The Meentheena Member (Tumbiana Formation; Fortescue Group), Western Australia[END_REF][START_REF] Coffey | Sedimentology, stratigraphy and geochemistry of a stromatolite biofacies in the 2.72 Ga Tumbiana Formation, Fortescue Group, Western Australia[END_REF]. Shallow marine deposition has also been proposed for some parts of the Meentheena Member [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF][START_REF] Sakurai | Facies architecture and sequence-stratigraphic features of the Tumbiana Formation in the Pilbara Craton, northwestern Australia: Implications for depositional environments of oxygenic stromatolites during the Late Archean[END_REF], in particular based on herringbone cross-bedding at the Redmont/Knossos locality [START_REF] Sakurai | Facies architecture and sequence-stratigraphic features of the Tumbiana Formation in the Pilbara Craton, northwestern Australia: Implications for depositional environments of oxygenic stromatolites during the Late Archean[END_REF], but these could not be found by subsequent studies and have been re-interpreted as trough cross-bedding [START_REF] Awramik | A giant, Late Archean lake system: The Meentheena Member (Tumbiana Formation; Fortescue Group), Western Australia[END_REF][START_REF] Coffey | Sedimentology, stratigraphy and geochemistry of a stromatolite biofacies in the 2.72 Ga Tumbiana Formation, Fortescue Group, Western Australia[END_REF][START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF].

Here we study samples of the PDP1 drill core recovered from the Meentheena locality at 21°18'15"S and 120°24'40"E [START_REF] Philippot | Early traces of life investigations in drilling Archean hydrothermal and sedimentary rocks of the Pilbara Craton, Western Australia and Barberton Greenstone Belt, South Africa[END_REF]Van Kranendonk et al., 2006, Fig. 2). The top 42.7 m of the core comprise metabasalts of the Maddina Formation. The Meentheena Member of the Tumbiana Formation was intersected between 42.7 and ~92m, followed by the Mingah Member until core end at 104 m [START_REF] Philippot | Early traces of life investigations in drilling Archean hydrothermal and sedimentary rocks of the Pilbara Craton, Western Australia and Barberton Greenstone Belt, South Africa[END_REF]. This study focuses on the two stromatolite samples described in Lepot et al. (2009a) and whose bulk chemistry is described in Thomazo et al. (2009b[START_REF] Thomazo | Extreme15N-enrichments in 2.72-Gyr-old sediments: Evidence for a turning point in the nitrogen cycle[END_REF]. Our thin sections KGI68.2 and KGI68.2' come from the same core depth (68.2 m), and the thin section 69.2a comes from 1 m deeper. These samples come from below the modern water table and appeared pristine of recent meteoric alteration [START_REF] Lepot | Microbially influenced formation of 2,724-million-year-old stromatolites[END_REF]. Nano-pyrites with δ 34 S values from -33.7 to +64.4 ‰ indicate MSR in individual microscopic layers of organic matter enclosed in a domical stromatolite from 68.9 m in the same drillcore [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. Arsenic enrichments in specific layers of the stromatolite sample from 69.7 m core depth suggest that arsenite might have been oxidized by microorganisms and in turn might have been available for chemoautotrophic and/or heterotrophic aresenate reducers [START_REF] Sforna | Evidence for arsenic metabolism and cycling by microorganisms 2.7 billion years ago[END_REF][START_REF] Sforna | Patterns of metal distribution in hypersaline microbialites during early diagenesis: Implications for the fossil record[END_REF].

Methods

Scanning Transmission X-ray Microscopy

Scanning transmission X-ray microscopy (STXM) was used to perform X-ray Absorption Near-edge spectroscopy (XANES) at the sulfur L-edge (in the energy range 155-190 eV) to evaluate the speciation of sulfur atoms. Ultrathin sections (~140 nm) were prepared for STXM using Focused ion beam milling (Lepot et al., 2009a). Beamline 10ID-1 (SM beamline) of the Canadian Light Source synchrotron [START_REF] Kaznatcheev | Soft X-ray spectromicroscopy beamline at the CLS: Commissioning results[END_REF] was used to perform STXM. The instrument chamber was pumped down to 100 mTorr and filled with He prior to analyses. Sulfur L-edge XANES spectra were extracted from hyperspectral stacks of energy-filtered images [START_REF] Jacobsen | Soft X-ray spectroscopy from image sequences with sub-100 nm spatial resolution[END_REF] recorded with a spectral resolution of 0.5 eV between 155-161 eV, 0.15 eV between 161-175 eV, and 0.5 eV between 175-190 eV. The spatial resolution was about 25 nm and counting times were a few milliseconds or less per pixel. Data were processed using AXis2000 (hyperspectral data reconstruction and spatial shift alignment), available on http://unicorn.mcmaster.ca/aXis2000.html.

Sample preparation and SEM

Samples were prepared for SEM and SIMS as detailed in [START_REF] Lepot | Texture-specific isotopic compositions in 3.4 Gyr old organic matter support selective preservation in cell-like structures[END_REF]. In brief, doubly polished thin sections ca. 100-µm-thick were unglued in acetone and broken into millimetric fragments. The later were deposited face-down onto double-sided tape and embedded in epoxy mounts (i.e. epoxy did not flow on the surface of interest in contact with tape). The surface of each mount was polished with Al 2 O 3 suspensions and mounts were cleaned in ethanol. Targets were located with optical microscopy in reflected and transmitted light. After coating mounts with 5 nm of gold, SEM was used to image the targets prior to SIMS. Secondary and backscattered electron images and EDXS (Energy Dispersive X-ray Spectrometer) elemental maps were recorded using a Thermo Electron detector on a Hitachi S3400 SEM (at University of Wisconsin -Madison) at a working distance of 10 mm and 10 kV (EDXS spectra/maps) or 15 kV (imaging). Using EDXS spectra, an approximation of relative variations in S/C in OM (henceforth termed "S/C proxy") was derived from the ratios of the heights of single peaks (pulses) at 0.27 (carbon) and 2.33 (sulfur) keV. The "S/C proxy" is proportional to true S/C concentrations but true quantification cannot be made because quantification of organic C is not possible using EDXS due to large bias on light elements. Additional SEM analyses were performed using a FEI Quanta 200 SEM equipped with a Bruker Quantax EDXS (at Université de Lille). The SEM operated at a working distance of 10 mm and 10 kV (EDXS spectra) or 20 kV (EDXS maps, imaging). After SIMS analyses, SEM was performed after removal (polishing) of the 35 nm gold coating used for SIMS, and deposition of ~5 nm of gold, which leaves remains of the thicker gold coating in the topographic lows.

NanoSIMS

Quantitative imaging of 12 C and 32 S was performed using a NanoSIMS 50 at MNHN, IMPMC laboratory, Paris. Stacks of ion images of 12 C -, 28 Si -and 32 S -were obtained by rastering a Cs + beam of ~150 nm as detailed in Supplementary Table 1. OpenMIMS v3.0.4 (National Resource for Imaging Mass Spectrometry) was used to align automatically the image stacks, apply a 44 nanosecond electron-multiplier dead-time correction, and extract 12 C -and 32 S -counts in regions of interest of the quantitative image stacks. Regions of interest were drawn to avoid nanopyrites with intense S signal and weak C signal. Since elements present different ionization efficiencies during NanoSIMS analysis, standard analysis is required to determine relative sensitivity factors to derive 32 S/ 12 C ratios from measured 32 S -/ 12 C -intensity ratios. The LGIS-A1 anthracite standard (Supplementary Table 2) was used to yield atomic S/C ratios. External precision of two standard deviations (2SD) of three analyses of LGIS-A1 yielded 1.14x10 -4 on the atomic S/C. Internal precision on the atomic S/C is reported as two standard errors (2SE) calculated from multiple measurement cycles within each analysis. Internal precision is an order of magnitude higher than external precision, and henceforth only the former is reported. We note that a more accurate quantification of S/C could be made using a set of standards with variable S/C (see [START_REF] Thomen | Determination of the nitrogen abundance in organic materials by NanoSIMS quantitative imaging[END_REF] for N/C).

SIMS

Secondary ion mass spectrometry analyses of carbon isotope ratios were carried out using a CAMECA IMS 1280 at the WiscSIMS laboratory, University of Wisconsin-Madison [START_REF] Valley | In situ oxygen isotope geochemistry by ion microprobe[END_REF] during three different sessions. In general, we followed techniques described previously [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF], and specific analytical parameters for the three different sessions are given in Supplementary Table 1. About 30 nm of gold coating was added after SEM imaging and samples were degassed for 48 h at 10 -9 torr in the SIMS sample chamber prior to analysis. A primary focused beam of 133 Cs + was used to sputter superficial zones ca. 6 µm, 3 µm and 1 µm in diameter. Collection of 12 C -, 13 C -and 13 CH -ions was simultaneous. Before analysis, targets of interest were pre-sputtered with Cs + ions to locally remove gold coating and possible surface contamination, and secondary ions were centered in the field aperture. To target micrometer to sub-micrometer size organic particles using the 1-µm spot condition, 10 µm x 10 µm 13 C -ion images were generated prior to analysis (Supplementary Images), and the target area was positioned with repeated X-Y translations during continuous ion imaging, which allows sub-micrometric lateral accuracy in spite of the ~1-µm accuracy of the sample stage motors.

Carbon isotope ratios are shown in standard delta notation with respect to VPDB 1 . Correction for instrumental mass fractionation was achieved as follows. We bracketed each series of samples with unknown δ 13 C with 8 (4+4) measures of δ 13 C meas on anthracite standards UWLA-1 and/or LGIS-A1 (Supplementary Tables 2345678) mounted together with unknown samples, hence allowing evaluations of electron multiplier (EM) aging and other machine drifts. The α bias correction factor is calculated using equation (1) from the δ 13 C true of these anthracites measured using bulk δ 13 C org analyses [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF] and the uncorrected δ 13 C meas value measured with SIMS. The gain of the EM was monitored between analyses of anthracite standards and its drift, if any, was compensated by adjusting the high voltage setting [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF].

(1) 𝜶 = (𝟏𝟎𝟎𝟎 + 𝜹 13 𝑪 𝒎𝒆𝒂𝒔 ) ÷ (𝟏𝟎𝟎𝟎 + 𝜹 13 𝑪 𝒕𝒓𝒖𝒆 )

The bias correction factor may vary with chemical compositions. Bias caused by differences in H/C ratios (or apparent H/C ratios measured as 13 CH -/ 13 C -ions) between unknown samples and standards may need correction [START_REF] Sangély | Microanalysis of carbon isotope composition in organic matter by secondary ion mass spectrometry[END_REF][START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. This bias, α*, is derived from the determination of α on a series of carbonaceous matter standards (ambers, coals, anthracites, shungite), each displaying spatially homogeneous 13 CH -/ 13 C -ratios and δ 13 C values, and selected to cover the broadest possible range of 13 CH - / 13 C -ratios [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. Their δ 13 C org compositions were measured in bulk [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF] and Supplementary Table 2). The α* value of each of these standards is derived from its α value divided by the α of the bracketing standard UWLA-1, hence correcting for the machine instrumental fractionation caused by physical properties other than the difference in structure and composition of the carbonaceous standards.

For each instrumental session, α* of the carbonaceous standards plotted linearly with R H meas = 13 CH -/ 13 C - (Supplementary Tables 345678). Therefore, the linear relationship was used to derive a general expression of α* that can be used to correct instrumental mass fractionation linked with varying apparent H/C of unknown samples as defined in equation ( 2), with α* = -0.043491 × R H + 1.002305 (R² = 0.93) for 6-µm spot analyses, α* = -0.037833 × R H + 1.002324 (R² = 0.90) for 3-µm spot analyses, and α* = -0.069964 × R H + 1.003831 (R² = 0.90) for 1-µm spot analyses (Supplementary Tables 4,6, and 8).

(2)

𝜶 * = 𝜶 𝒔𝒕𝒅 𝜶 𝑼𝑾𝑳𝑨-𝟏 = 𝒂 × 𝑹 𝒎𝒆𝒂𝒔 𝑯 + 𝒃
However, we note that this correction was determined for each session using settings that may be specific to these analyses and WiscSIMS Lab. These α* values should not be applied to other measurements without analytical verification. Altogether, the organic carbon isotope ratio of unknown samples is derived from equation ( 3), where α is the value measured on bracketing anthracite standards and α* is derived from equation (2) using the R H ratio measured on the unknown sample together with δ 13 C meas . In addition, an additional correction factor α' was needed to apply a cross-calibration between the standards UWLA-1 and LGIS-A1. α' is equal to 1 when the bracketing standard is UWLA-1, and to the α* of LGIS-A1 when LGIS-A1 is the bracketing standard.

(3) 𝜹 13 𝑪 𝒐𝒓𝒈 = 𝜹 13 𝑪 𝒎𝒆𝒂𝒔 +𝟏𝟎𝟎𝟎

𝜶×𝜶 * × 𝜶 ′ -𝟏𝟎𝟎𝟎
Bias is defined as the mean α of the bracketing standard analyses, and external precision is defined as two standard deviations (2SD) of these bracketing analyses. Internal precision is defined as two standard errors (2SE) of the multiple measurements (cycles) of each analysis. [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF] have shown that the accuracy of SIMS data recorded at low 12 C -count rate in mixed phases can be significantly degraded. Additional bias arising from the presence of chlorite and/or calcite in the analyzed volume are evaluated below together with their effect on internal precision. Both 2SD and 2SE are reported in Supplementary Tables 345678910. The total range of 2SD is 0.08-1.33‰, whereas 2SE values display a larger range of 0.44-8‰ reflecting data recorded at lower count rates. The filtering of data with low count rates relative to that of pure OM standard restrains the range of 2SE to 0.44-1.6. For data filtered as detailed below the mean of 2SD values-weighed by the number of filtered analyses for each bracket-is 0.72, smaller than the mean of 2SE of 0.99. Accordingly, we report 2SE values as error bars in figures 8-11. Only for the data of figure 4 we report errors as the larger 2SD values instead of 2SE. Finally, statistical analyses of SIMS data (Kernel density plots, Welsh two sample t-test, Mann-Whitney U test) were conducted using the software R version 3.4.2.

Bulk-rock elemental analyses

Bulk rock elemental analyses of Fe, Mn and As were performed after fusion in LiBO 2 and dissolution in a HNO 3 -H 2 O 2 -glycerol mixture (at CRPG-SARM) as detailed in [START_REF] Carignan | Routine Analyses of Trace Elements in Geological Samples using Flow Injection and Low Pressure On-Line Liquid Chromatography Coupled to ICP-MS: A Study of Geochemical Reference Materials BR, DR-N, UB-N, AN[END_REF]. All Fe has been converted to Fe 2 O 3 and is thus reported in wt.% Fe 2 O 3 . Similarly, Mn is reported as wt.% MnO. As is reported in ppm. Fe and Mn were measured by inductively coupled plasma optical emission spectrometry, whereas As was measured by inductively coupled mass spectrometry [START_REF] Carignan | Routine Analyses of Trace Elements in Geological Samples using Flow Injection and Low Pressure On-Line Liquid Chromatography Coupled to ICP-MS: A Study of Geochemical Reference Materials BR, DR-N, UB-N, AN[END_REF]. Detection limits on blanks were 0.04 wt.% for Fe 2 O 3 , 0.001 wt.% for MnO, and 1.6 ppm for As. The uncertainties measured on geochemical reference materials [START_REF] Carignan | Routine Analyses of Trace Elements in Geological Samples using Flow Injection and Low Pressure On-Line Liquid Chromatography Coupled to ICP-MS: A Study of Geochemical Reference Materials BR, DR-N, UB-N, AN[END_REF] were <2% (Fe 2 O 3 ), <5% (MnO) and <15% (As).

Results

Petrographic observations and variations in organic S/C distinguish three types of organic matter in the two studied stromatolites. Organic carbon isotope microanalyses are grouped by OM type in Supplementary Tables 9 and10. The Supplementary Images file displays the precise localization of each SIMS analysis target.

Petrography of the stromatolites

Stromatolite samples KGI68.2 and 69.2a comprise the same three main mineral assemblages (Fig. 3 and [START_REF] Lepot | Microbially influenced formation of 2,724-million-year-old stromatolites[END_REF]Lepot et al. , 2009a)). First, the light-coloured layers are predominantly composed of micritic to microsparritic calcite, with minor quartz, chlorite, muscovite, pyrite and anatase. Second, the black mud-type layers are poor in calcite but rich in quartz, chlorite, muscovite, and also display variable amounts of pyrite and anatase. Third, clastic grains are interspersed and sometimes dominate in calcite-rich layers (Fig. 3C). These clastic grains are often similar in composition (chloritic and/or Ti-rich) and shape to the volcanoclastic material of the Mingah Member [START_REF] Lepot | Biogenic versus metamorphic origins of diverse microtubes in 2.7Gyr old volcanic ashes: Multi-scale investigations[END_REF]. Calcite pseudomorphs after cubic halite crystals occur embedded in stromatolitic layers of both samples (e.g. Fig. 3B), some displaying diagnostic hopper growth structures [START_REF] Philippot | Early traces of life investigations in drilling Archean hydrothermal and sedimentary rocks of the Pilbara Craton, Western Australia and Barberton Greenstone Belt, South Africa[END_REF].

Two main types (A and B) of OM have previously been identified in these samples (Lepot et al., 2009a), and an additional type (C) is described below. Type-A OM is distributed in seams and clusters at the grain boundaries of quartz and/or finely layered chlorite. Seams of Type-A OM occur only in mud-type layers and are variably interspersed with chlorite and pyrite (Fig. 3E). Chloritic clusters of Type-A OM occur both in mud-type layer and carbonate-dominated layers (Fig. 3D-E). Type-B OM comprises clusters of sub-rounded globules smaller than 2 µm in diameter embedded in calcite crystals of carbonate-dominated layers (Fig. 3D). Chloritic clusters of intergranular Type-A OM are sometimes found at the center of clusters of Type-B globules in calcite-the largest example of this distribution is shown in Fig. 3D. Type-C OM consists of an elongated ca. 50x80-µm nodule that is mostly composed of OM. This nodule is surrounded by quartz, calcite, chlorite and muscovite (Fig. 4) and cut across by chlorite+muscovite veinlets, and interspersed with pyrite, chalcopyrite, chlorite, muscovite, quartz and U-rich microcrystals. A large hole (Fig. 4A) has a size and central disposition reminding of that of U-rich crystals commonly found in bitumen nodules [START_REF] Rasmussen | Evidence for pervasive petroleum generation and migration in 3.2 and 2.63 Ga shales[END_REF][START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. Such a crystal might have been dissolved or torn away during polishing. This nodule is located in a layer rich in volcanoclastic material of sample 69.2a. Two similarly-shaped nodules with diffuse OM and abundant pyrite, chlorite and muscovite occur in another layer rich in (volcano)clastic material of the same sample (fig. 7 of Lepot et al., 2009a).

Semi-quantification of organic sulfur using SEM-EDXS of sulfide-free zones indicated that Type-A and -C OMs are poor in organic S (S/C proxy of 0.01-0.08, mean 0.04), whereas Type-B OM is variably enriched in organic S (S/C proxy of 0.01-0.38, mean 0.16), consistent with previous transmission electron microscopy (Lepot et al., 2009a). NanoSIMS analyses revealed atomic S/C of 0.003-0.004 in Type-A OM in a chlorite cluster and atomic S/C of 0.031-0.042 in Type-B OM in adjacent calcite (Fig. 5). The thiophenic nature of organic S suggested by C K-edge XANES (Lepot et al., 2009a) was confirmed with the S L-edge XANES spectrum of Type-B organic globules (Fig. 6). The latter display two main bands at 166.6 eV and 173.5 eV that correspond respectively to the 2p→σ*(C-S) transition and S3d orbitals of (poly)thiophenes [START_REF] Tourillon | Electronic structure and orientation studies of undoped poly-3-alkyl thiophenes electrochemically deposited on Pt as studied by NEXAFS[END_REF][START_REF] Riboulleau | Pyrolytic and spectroscopic study of a sulphur-rich kerogen from the "Kashpir oil shales" (Upper Jurassic, Russian platform)[END_REF] and that are absent in S-bearing minerals [START_REF] Fleet | XANES spectroscopy of sulfur in Earth materials[END_REF].

Finally, bulk-rock analyses of samples KGI68.2 and 69.2a yielded 3.64 and 3.92 wt.% Fe2O3, respectively, 0.30 and 0.37 wt.% MnO, respectively and 3.02 and 4.12 ppm As, respectively.

δ 13 C of Type-A OM associated with quartz

Two distinct seams of Type-A OM, where the only mineral matrix is quartz, were analyzed multiple times to evaluate microscale homogeneity and matrix effects with SIMS using 3-µm spot size. The δ 13 Corg values measured in Type-A OM associated with quartz range between -56.1 and -54.1 ‰ (n=7, mean -55 ‰) ± 2SE of 0.5 to 1.6 ‰ (mean ± 1 ‰). In each seam, all δ 13 Corg values are similar within 2SE error (Fig. 7A-C) supporting intra-seam isotopic homogeneity. The 13 CH -/ 13 C -ratios of these OM seams range between 0.075-0.085, with the exception of one low count rate outlier with 13 CH -/ 13 C -ratio of 0.094 (Fig. 7C). Similar δ 13 Corg values are found irrespective of the 13 CH -/ 13 C - ratios. Moreover, the quartz to OM concentration ratio in each SIMS spot is proportional to the ratio of the 12 C -signal in the measured spot to the 12 C -signal of a pure anthracite standard. Variable quartz concentrations do not appear to bias the δ 13 C signal (Fig. 7D).

δ 13 C of Type-A OM associated with chlorite

A wide range of 13 CH -/ 13 C -ratios between 0.078 and 0.158 was measured in chlorite-rich clusters of Type-A OM (Supplementary Table 9). Two chlorite-rich clusters were measured repeatedly with 3and 1-µm spot sizes to sample zones with variable OM to chlorite (± minor quartz) concentration ratios (Figs. 89). In each cluster, the δ 13 Corg values were negatively correlated with 13 CH -/ 13 C -ratios (Fig. 8D,9A). In a cluster (q5chip1 in Fig. 8), a 4.6 ‰ (± 0.5-0.9 ‰ 2SE) decrease in δ 13 Corg values was observed over a 13 CH -/ 13 C -ratio range of 0.079-0.103. In a second cluster (c14 in Fig. 8), a 3.9 ‰ (± 0.5-0.9 ‰ 2SE) decrease in δ 13 Corg values was observed over a 13 CH -/ 13 C -ratio range of 0.079-0.098. Bias imparted (to the δ 13 C values) by variable apparent H/C ratios ( 13 CH -/ 13 C -) in OM can be calculated using the α* correction expressed in δ notation (see Supplementary Table 6, IMF δ = -37.833 × 13 CH -/ 13 C -+ 2.3236), leading to a bias <1 ‰ over the 0.079-0.103 range of 13 CH -/ 13 C - ratios. Hence, variable apparent H/C ratios in OM may not alone account for the observed range of δ 13 Corg values (up to 4.6 ‰ variation) in these two chlorite clusters. Importantly, the 13 CH -/ 13 C -ratios were found to increase with increasing chlorite/OM concentration ratios (Fig. 8E). Therefore, a large bias occurs on the measurements of δ 13 Corg and 13 CH -/ 13 C -ratios of OM in presence of chlorite. We interpret this bias as the result of the recombination of OM-derived C ions with H ions [START_REF] Spool | Interpretation of static secondary ion spectra[END_REF] derived from chlorite [START_REF] Deloule | D/H analysis of minerals by ion probe[END_REF] in Supplementary Discussion 1, where we suggest implications for SIMS measurement of δD [START_REF] Deloule | Interstellar water in meteorites? Geochim[END_REF].

We could not derive an accurate correction curve to correct this matrix bias in chlorite-rich domains using the present data because we could not determine the H content in chlorite and derive endmembers to use simple mass balance equations. However, the δ 13 Corg values recorded in chlorite-poor zones where 13 CH -/ 13 C -ratios lie in the same range as in the H-free quartz (<0.085) should be close to those of chlorite-free OM within 2SE error. Only some of the analyses in OM+chlorite zones performed with 1-and 3-µm spots satisfy this criterion. Chloritic zones in sample KGI68.2 and KGI68.2' that satisfy the filtering criterion 13 CH -/ 13 C -< 0.085 display δ 13 Corg values ranging between -55.4 and -50.6 ‰ (± 0.4 to 0.9 ‰ 2SE) and averaging at -52.5 ‰ (n = 11). In sample 69.2a, none of the SIMS measurements in chloritic zones satisfy this filtering criterion as all the targets had low OM/chlorite relative abundances.

The range of δ 13 Corg in Type-A OM analyzed near quartz in the absence of chlorite is small and overlaps with the δ 13 Corg values recorded with no/minimal interference of chlorite (at 13 CH -/ 13 C - <0.085; Supplementary Table 9). All Type-A OM filtered with 13 CH -/ 13 C -<0.085 were recorded at 12 Cmeas -/ 12 Canthracite ->0.22, thus providing acceptable count rates (>0.1: [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. After filtering out analytical spots in which chlorite was evidenced by coupled SEM-EDXS detection and increased 13 CH -/ 13 C ->0.085, we expect that the δ 13 Corg values recorded in the vicinity of chlorite are accurate within 2SE error. Henceforth, all Type-A OM (associated with quartz and/or chlorite) will be grouped, yielding a range of δ 13 Corg between -56.1 to -50.6 ‰ ±0.4-1.6 ‰ (2SE), with a mean value of -53.5 ‰.

δ 13 C of Type-B OM in carbonates

The Type-B globules of OM in carbonates are generally smaller than the SIMS sampling size. Although carbonates only yield 1.7 to 2.3 % of the 12 C -count rate relative to the anthracite OM standard (Supplementary Table 10), the volume of sputtered carbonate may not be negligible compared to the volume of OM globules. The total 12 C -count rates measured on OM globules in carbonates ( 12 Cmeas -, see equation 4, with 12 Ccarb -and 12 Corg -the ion count rates from carbonates and OM, respectively) relative to that of pure anthracite ( 12 Canthracite -) were, using 6-µm spot: 4.4-12.2 % (mean 8.4 %, SD=2.7 %), using 3-µm spot: 12.7-29.6 % (mean 21 %, SD=5.2 %), and using 1-µm spot 3.8-35.2 % (mean 14.4 %, SD=10.1 %).

(4) 12 𝑪 𝒎𝒆𝒂𝒔 -= 12 𝑪 𝒄𝒂𝒓𝒃 -+ 12 𝑪 𝒐𝒓𝒈 -An interference of Ccarb is possible in the measurement of δ 13 Cmeas in micrometric organic globules because of the low OM volume and the large difference in δ 13 Cmeas between pure carbonate and organic-rich targets. However, knowing the relative fractions of carbonate Ccarb and organic Corg and the uncorrected SIMS-measured δ 13 Cmeas(pure-carb) of pure carbonate spots (-36.8 ±14.5 ‰ 2SE, -34.2 ±5.9 ‰ and -40.7 ±7.2 ‰ with 6-, 3-and 1-µm spots respectively), can help estimate the δ 13 Corg of micrometric globules using mass balance. Homogeneous bulk δ 13 Ccarb values of 0.4 and 0.9 ‰ were recorded in bulk carbonate of KGI68.2 and 69.2a, respectively (Thomazo et al., 2009b). In addition, δ 13 Ccarb values of micro-drilled Tumbiana stromatolites display <1 ‰ variation [START_REF] Slotznick | Examining Archean methanotrophy[END_REF]. Hence, we assume that the δ 13 Cmeas(pure-carb) value is constant in our samples for each SIMS analytical setup (i.e. at constant instrumental mass fractionation).

To make this mass-balance estimation, we define the fraction f of 12 Corg -ions from OM in the total measured 12 C -count rate ( 12 Cmeas -, see equation 4) using equation ( 5).

(5) 12 𝑪 𝒐𝒓𝒈 -(𝒇) = 𝒇 × 12 𝑪 𝒎𝒆𝒂𝒔 -At any value of f, the flux of 12 C -ions generated by carbonates is defined using equation ( 6).

(6) 12 𝑪 𝒄𝒂𝒓𝒃 -(𝒇) = (𝟏 -𝒇) × 12 𝑪 𝒎𝒆𝒂𝒔 -

The known limit conditions to equations (5-6) are given in ( 7) and ( 8), and can be applied to yield equation ( 9). A negative correlation is observed between δ 13 Corg (eq. 3) and f values using both 1-and 6-µm spot analyses of Type-B globules in calcite (Fig. 10A). Therefore, although intrinsic heterogeneities may occur in the isotopic composition of organic globules, a mixture trend could be demonstrated between carbonate Ccarb and organic Corg in the analyzed spots. Accordingly, the raw δ 13 Cmeas(org+carb) measured on mixed OM+carbonate can be used to derive the raw (not yet corrected from α and α* bias) isotopic composition of the organic fraction (δ 13 C*meas) in each spot, corrected from carbonate interference, using equation ( 11).

(11) 𝜹 13 𝑪 𝒎𝒆𝒂𝒔 * = 𝜹 13 𝑪 𝒎𝒆𝒂𝒔(𝒐𝒓𝒈+𝒄𝒂𝒓𝒃) 𝒇 + (𝟏 -𝒇) × 𝜹 13 𝑪 𝒎𝒆𝒂𝒔(𝒑𝒖𝒓𝒆-𝒄𝒂𝒓𝒃)

In turn, the obtained δ 13 C*meas value has to be corrected from α and α* bias (and cross-calibrated with α', see above). However, α* derives from R H meas = 13 CH -/ 13 C -, which is expected to decrease in presence of H-free carbonate. Accordingly, the R H of organic matter (R H org) is corrected by subtracting the carbonate interference (non-zero R H carb) to R H meas using equation 13 (following eq. 12). The correction factor α2* can then be calculated from equation (2) using R H org derived from equation ( 13) instead of R H meas. Finally, the isotopic composition of organic globules corrected from carbonate interference, apparent H/C bias and matrix effects can be reported against VPDB as δ 13 C*org according to equation ( 14).

(

) 𝜹 13 𝑪 𝒐𝒓𝒈 * = 𝜹 13 𝑪 𝒎𝒆𝒂𝒔 * +𝟏𝟎𝟎𝟎 𝜶×𝜶 𝟐 * ×𝜶 ′ -𝟏𝟎𝟎𝟎 14
The measurements of δ 13 Cmeas(pure-carb) we used to derive δ 13 C*org values have low counting statistics (±5-7 ‰ 2SE using 1-and 3-µm spots, ±14-15 ‰ using 6-µm spot). This uncertainty must be propagated to the estimation of the 2SE of δ 13 C*org using equation ( 15).

(15) Composite error: 2SE*(𝜹 13 𝑪 𝒐𝒓𝒈 * ) = 𝟐𝑺𝑬(𝜹 13 𝑪 𝒎𝒆𝒂𝒔 ) 𝒇 + (𝟏 -𝒇) × 𝟐𝑺𝑬(𝜹 13 𝑪 𝒎𝒆𝒂𝒔(𝒑𝒖𝒓𝒆-𝒄𝒂𝒓𝒃) )

Unfiltered δ 13 C*org values (Fig. 10B) range between -75.8 and -48.1 ‰ (mean -59.3 ‰) with a poor precision of ±1.3-12 ‰ 2SE* (mean 2.5 ‰). All Type-B OM spots with f>0.9 were recorded with count rate ratios 12 Cmeas -/ 12 Canthracite ->0.15, which are high enough (>0.1) to allow accurate measurements [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. The accuracy of the correction yielding δ 13 C*org values is estimated by 2SE* (eq. 15). At f>0.9, 2SE* becomes acceptable (<2.2 ‰). Using the data filtering criterion of f>0.9, which applies only to OM in carbonates and that is equivalent to 2SE*<2.2 ‰, (see eq. 15), δ 13 C*org values recorded in Type-B globules range between -65.2 and -52.5 ‰ (mean -58.8 ‰) ± 1.3-2.2 ‰ 2SE*. These δ 13 C*org values filtered with f>0.9 correspond to a range of δ 13 Corg values (uncorrected from carbonate interference) of -61.5 to -49.1 (mean -55.6 ‰) ± 1-1.5 ‰ 2SE. We note that δ 13 C*org values filtered with the criterion f>0.7 show a similar range (-65.2 to -52.5 ‰). At f>0.7, the mean δ 13 C*org is -58.2 ‰ for 1and 3-µm spots with 2SE* of 1-3.5 ‰ and -57.9 ‰ (with 2SE* increasing up to 6 ‰) when including 6-µm spots, hence similar to the mean with f>0.9 (Fig. 10B). This indicates that the lower precision of the δ 13 Cmeas(pure-carb) measurement influences little the correction of equation 14 when f is sufficiently high (>0.7). In contrast, at f<0.7 δ 13 C*org values deviate significantly.

δ 13 C of Type-C OM

In the nodule of Type-C OM of sample 69.2a, targets were large enough to avoid chlorites, as confirmed with SEM-EDXS mapping (Fig. 4). In this nodule, the 13 CH -/ 13 C -ratios range between 0.079 and 0.089 (mean 0.083) and values were not correlated with δ 13 C, consistent with measurements unbiased by chloritic H. The δ 13 Corg values range between -48.0 and -39.1 ‰ (± 1.33 ‰ 2SD) and average at -44.2 ‰ (n = 10, SD ±2.6 ‰). The spatial distribution of δ 13 Corg values is zoned with the lower values in the lower left and upper right extremities of the nodule, and with higher values in the central part.

Data assessment and summary

Evaluation of bias correction methods and data filtering criteria is required to address the significance of the isotopic heterogeneities described.

The correction of the bias on δ 13 Corg values induced by variable apparent H/C contents in OM [START_REF] Sangély | Microanalysis of carbon isotope composition in organic matter by secondary ion mass spectrometry[END_REF][START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]) yielded a range of correction factors (expressed as 1000.log(α*)) of -0.92 ‰ to 0.27 ‰ (mean -0.3 ‰) in the measured range of 13 CH -/ 13 C -ratios (excluding chloritic regions with 13 CH -/ 13 C ->0.085). This narrow range cannot explain the observed isotopic heterogeneities.

The values of δ 13 C*org and δ 13 Corg do not correlate to variations in S/C ratios (R²=0.2 for a linear fit of all data in Fig. 11,R²=0.01 for a linear fit of δ 13 C*org in Type-B globules only versus S/C proxy). This observation is consistent with the observation that SIMS measurements of S isotope ratios in OM are not correlated with S/C [START_REF] Bontognali | Sulfur isotopes of organic matter preserved in 3.45-billion-year-old stromatolites reveal microbial metabolism[END_REF]. In S-rich kerogens and in kerogen residues after thermal decomposition, S-C bonds are generally at least an order of magnitude less abundant than H-C bonds [START_REF] Riboulleau | Pyrolytic and spectroscopic study of a sulphur-rich kerogen from the "Kashpir oil shales" (Upper Jurassic, Russian platform)[END_REF]. Kerogen of the Tumbiana stromatolites display bulk atomic H/C of ~0.3 [START_REF] Strauss | Abundances and Isotopic compositions of Carbon and Sulfur species in Whole rock and Kerogen samples[END_REF] whereas the atomic S/C in S-rich globules only reached ~0.042 (Fig. 5). In turn, assuming that the isotopic fractionation associated with S-C bond breakup has the same magnitude as that associated with H-C breakup (<5 ‰, Supplementary Tables 4, 6 and8), the former would be smaller than our 2SE* analytical precision of ca. 1.3-2.2 ‰.

Statistical analyses of the C isotope data, filtered according to above criteria (f>0.9, 13 CH -/ 13 C - <0.085), is shown in Supplementary Table 11. The Wilcoxon-Mann-Whitney test indicates that the filtered but uncorrected δ 13 Corg values recorded in Type-B globules are significantly (p=2.5 %) lower (mean -55.6 ‰, -61.5 to -49.1 ‰ ±1-1.6 ‰ 2SE, Supplementary Table 10) than δ 13 Corg values recorded in Type-A OM (mean -53.5 ‰ ±1.8 ‰ SD, -56.1 to -50.6 ‰ ±0.4-1.6 ‰ 2SE). Although their mean values are close within error, uncorrected Type-B OM displayed a group of δ 13 Corg values that are significantly lower within error (down to -61.5 ‰). More importantly, corrected (δ 13 C*org) values of Type-B OM (-65.2 to -52.5 ‰ ± 1.3-2.2 ‰ 2SE*, mean -58.8 ‰ ±3.6 ‰ SD) are significantly lower than δ 13 Corg values of Type-A OM, passing the Wilcoxon-Mann-Whitney test with p=0.0022 %. Finally, the δ 13 Corg values of Type-C OM occurring only in sample 69.2a (-48.0 to -39.1 ‰ ± 1.3 ‰ 2SD) do not overlap with the values recorded in all Type-A and -B OM.

Discussion

OM migration

Large pyrobitumen nodules associated with radioactive grains are common in the Fortescue Group, including in ~2.75 Ga old fluviolacustrine deposits of the Hardey Formation [START_REF] Buick | Archean Oil: Evidence for Extensive Hydrocarbon Generation and Migration 2.5-3.5 Ga 1[END_REF][START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF][START_REF] Rasmussen | Evidence for microbial life in synsedimentary cavities from 2.75 Ga terrestrial environments[END_REF] and 2.63 Ga old shales of the Jeerinah Formation [START_REF] Rasmussen | Evidence for pervasive petroleum generation and migration in 3.2 and 2.63 Ga shales[END_REF]. The presence of U-rich grains, of chalcopyrite and the zonation in δ 13 Corg values observed in the nodular Type-C OM (Fig. 4) are also consistent with formation as pyrobitumen [START_REF] Rasmussen | Evidence for pervasive petroleum generation and migration in 3.2 and 2.63 Ga shales[END_REF][START_REF] Sangély | Micrometer scale carbon isotopic study of bitumen associated with Athabasca uranium deposits: Constraints on the genetic relationship with petroleum sourcerocks and the abiogenic origin hypothesis[END_REF]. The δ 13 Corg zonation could be the product of abiotic synthesis of the pyrobitumen through catalytic hydrogenation of CO2 or radiolytic alteration of biomass-sourced oil that segregated onto U-minerals [START_REF] Sangély | Micrometer scale carbon isotopic study of bitumen associated with Athabasca uranium deposits: Constraints on the genetic relationship with petroleum sourcerocks and the abiogenic origin hypothesis[END_REF]. The apparent absence of link between H/C ratio and δ 13 Corg values in the nodule (Supplementary Table 9) favors the biogenic interpretation [START_REF] Sangély | Micrometer scale carbon isotopic study of bitumen associated with Athabasca uranium deposits: Constraints on the genetic relationship with petroleum sourcerocks and the abiogenic origin hypothesis[END_REF]. This pyrobitumen nodule features δ 13 Corg values that are 3-12 ‰ higher than those determined from both Type-A and Type-B OM. Similarly, U-associated pyrobitumen nodules in the ~2.5 Ga Mount McRae Shale feature 2-8 ‰ 13 C-enrichments compared to co-occurring kerogen [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. The 3-12 ‰ 13 C-enrichment in Type-C compared to Type-A OM may be explained by a combination of isotope fractionations associated with bitumen mobilization (up to +3.8 ‰: Des [START_REF] Marais | Isotopic evolution of the biogeochemical carbon cycle during the Precambrian[END_REF][START_REF] Close | Inverse carbon isotope patterns of lipids and kerogen record heterogeneous primary biomass[END_REF] and radiolysis (up to about +8 ‰: [START_REF] Leventhal | Carbon-13/Carbon-12 Isotope Fractionation of Organic Matter Associated with Uranium Ores Induced by Alpha Irradiation[END_REF][START_REF] Sangély | Micrometer scale carbon isotopic study of bitumen associated with Athabasca uranium deposits: Constraints on the genetic relationship with petroleum sourcerocks and the abiogenic origin hypothesis[END_REF].

Alternatively, Type-C OM may have migrated through the Tumbiana Formation from an exogenous source. It has been shown that the most 13 C-depleted kerogens of the Fortescue Group occur in association with shallow lakes with mafic catchments, such as the studied stromatolites [START_REF] Eigenbrode | Late Archean rise of aerobic microbial ecosystems[END_REF][START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF][START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. In contrast, lakes with felsic catchments and open sea deposits typically display higher δ 13 Corg values between -50 and -20 ‰ [START_REF] Eigenbrode | Late Archean rise of aerobic microbial ecosystems[END_REF][START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF][START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. Moreover, the siltstones of the Tumbiana Formation at the studied locality display δ 13 Corg values between -44.9 and -23.8 ‰, except for sample GIS88.8 (Thomazo et al., 2009b) that we latter re-evaluated as an interbedded carbonate/mudstone (not shown). By analogy with the Phanerozoic, these siltstones including the millimetric siltstone layer hosting the nodule of Type-C OM (Fig. 3C) were likely more prone to Archean oil sequestration than the mudstones and possibly (depending on porosity) than the stromatolites of the Tumbiana Formation. The grains in the volcanoclastic siltstones interbedded within the mudstones/carbonates deposits of the Meentheena Member and the underlying Mingah Member are coated with organic films [START_REF] Lepot | Biogenic versus metamorphic origins of diverse microtubes in 2.7Gyr old volcanic ashes: Multi-scale investigations[END_REF]. In addition, OM was also found in vesicles of the overlying Maddina basalts at the studied locality (Lepot et al., 2009b). Together, these observations suggest that, similar to Type-C pyrobitumen, OM with δ 13 Corg values exceeding -48 ‰ may have migrated from elsewhere, originating from marine or felsic-housed lacustrine systems. Alternatively, the OM in the siltstones, particularly that within the Mingah Member may have originated from the primary biomass that decomposed into CO2 and/or CH4 (Thomazo et al., 2009b). These carbon compounds could have been reprocessed by either Acetyl-CoA-dependent metabolisms and/or methanotrophs. The respective importance of each of these metabolism is discussed below.

Acetyl-CoA pathways

The acetyl-CoA pathway can form acetate autotrophically using H2 (Fig. 1C), and imparts 13 Cdepletions of -50 to -60 ‰ to the acetate relative to parent CO2 and of -12.9 to -20.6 ‰ to the biomass relative to parent CO2 [START_REF] Gelwicks | Carbon isotope effects associated with autotrophic acetogenesis[END_REF][START_REF] Preuß | Carbon Isotope Fractionation by Autotrophic Bacteria with Three Different CO2 Fixation Pathways[END_REF][START_REF] Blaser | Carbon isotope fractionation of 11 acetogenic strains grown on H2 and CO2[END_REF][START_REF] Freude | Carbon isotope fractionation during catabolism and anabolism in acetogenic bacteria growing on different substrates[END_REF]. This 13 C-depleted acetate could, in principle, have been used by heterotrophs, transferring its 13 C-depleted signature to the sedimentary OM reservoir [START_REF] Slotznick | Examining Archean methanotrophy[END_REF]. Indeed, the ratio of acetate to biomass carbon produced by hydrogenotrophic acetogenesis is more than nine to one [START_REF] Balch | Acetobacterium, a New Genus of Hydrogen-Oxidizing, Carbon Dioxide-Reducing, Anaerobic Bacteria[END_REF][START_REF] Gelwicks | Carbon isotope effects associated with autotrophic acetogenesis[END_REF][START_REF] Freude | Carbon isotope fractionation during catabolism and anabolism in acetogenic bacteria growing on different substrates[END_REF]. Thus, assuming the only autotrophic producers were acetogens, 90% of the organic matter available for heterotrophs would have been 13 C-depleted acetate. The H2 demand of acetogenesis may be fueled by fermentation of biomass (Fig. 1B), hydrothermal activity associated with ultramafic rocks [START_REF] Mével | Serpentinization of abyssal peridotites at mid-ocean ridges[END_REF][START_REF] Mccollom | Serpentinites, hydrogen, and life[END_REF][START_REF] Konn | The Production of Methane, Hydrogen, and Organic Compounds in Ultramafic-Hosted Hydrothermal Vents of the Mid-Atlantic Ridge[END_REF], or possibly via atmospheric H2 supply [START_REF] Tian | A Hydrogen-Rich Early Earth Atmosphere[END_REF][START_REF] Catling | Comment on "A Hydrogen-Rich Early Earth Atmosphere[END_REF].

Ultramafic lavas could possibly have produced H2 abiotically via low temperature serpentinization [START_REF] Konn | The Production of Methane, Hydrogen, and Organic Compounds in Ultramafic-Hosted Hydrothermal Vents of the Mid-Atlantic Ridge[END_REF]. Ultramafic (komatiitic) lavas, however, are only found in the Pyradie Formation [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF]. In contrast, other lavas of the Fortescue Group, including the Kylena Formation subaerial lavas underlying the Tumbiana Formation, are generally of basaltic-andesitic composition resulting from crustal contamination of an initially komatiitic magma [START_REF] Thorne | Geology of the Fortescue Group, Pilbara Craton, Western Australia[END_REF][START_REF] Mole | The Archean Fortescue large igneous province: A result of komatiite contamination by a distinct Eo-Paleoarchean crust[END_REF]. Consequently, the igneous rocks in proximity to the deposition center were not prone to serpentinization. Local metasomatism of basaltic flow tops occurred only after regional metamorphism of the Fortescue Group [START_REF] White | Regional-scale Metasomatism in the Fortescue Group Volcanics, Hamersley Basin, Western Australia: Implications for Hydrothermal Ore Systems[END_REF]. In the absence of a vein system similar to that observed in Paleoarchean rocks [START_REF] Ueno | Carbon isotopes and petrography of kerogens in ~3.5-Ga hydrothermal silica dikes in theNorth Pole area, Western Australia[END_REF], and in the absence of distinct hydrothermally-derived Fe/S mineralization [START_REF] Buick | The antiquity of oxygenic photosynthesis: evidence from stromatolites in sulphate-deficient Archaean lakes[END_REF], no fluid conduits that could have delivered H2-rich fluids to the Tumbiana lake system are recognized/identified. Hydrogenotrophic microbial reduction of sulfate (Fig. 1D; Londry and Des Marais, 2003) and of Fe 3+ -minerals (Fig. 1E; [START_REF] Etique | Magnetite as a precursor for green rust through the hydrogenotrophic activity of the iron-reducing bacteria Shewanella putrefaciens[END_REF] outcompete acetogenesis for H2 [START_REF] Hoehler | Thermodynamic control on hydrogen concentrations in anoxic sediments[END_REF]fig. 3.9 in Madigan et al., 2009) just like sulfate-and iron-reducing bacteria outcompete methanogens for OM (Fig. 1G-I;[START_REF] Konhauser | Introduction to Geomicrobiology[END_REF]. The sulfur isotope systematics of the Tumbiana stromatolites display evidence for microbial sulfate reduction [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. In addition, the Feisotope signatures of some mudstones from the Tumbiana Formation require microbial Fe-reduction [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF]. Furthermore, microbial reduction of arsenate with H2 [START_REF] Chung | Bio-reduction of arsenate using a hydrogen-based membrane biofilm reactor[END_REF] may also have occurred as suggested by As-enrichments in specific laminae of the Tumbiana stromatolites [START_REF] Sforna | Evidence for arsenic metabolism and cycling by microorganisms 2.7 billion years ago[END_REF]. Methanogenesis also outcompetes acetogenesis for H2, except in special conditions such as low temperatures and/or low pH [START_REF] Drake | Acetogenic Prokaryotes[END_REF][START_REF] Heuer | Experimental studies on the stable carbon isotope biogeochemistry of acetate in lake sediments[END_REF]. Nitrogen isotope ratios rather suggest that the Tumbiana lakes were alkaline (Stüeken et al., 2015b). Thus, microbial sulfate reducers, methanogens, and Fe-reducing bacteria, likely consumed a large fraction of the available H2, limiting the potential to form 13 C-depleted acetate. Interestingly, a Tumbiana mudstone displayed two closely associated types of kerogen, with δ 13 Corg of -52 ‰ and -34 ‰ that were interpreted as OM from the biomasses of methanotrophs and primary producers, respectively [START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF]. Although the lower δ 13 Corg values of -52 ‰ may have formed through assimilation of hydrogenotrophic acetate, the δ 13 Corg values of -34 ‰ recorded by the co-existent kerogen is too low to reconcile with the biomass of acetogens alone [START_REF] Preuß | Carbon Isotope Fractionation by Autotrophic Bacteria with Three Different CO2 Fixation Pathways[END_REF][START_REF] House | Carbon isotopic fractionation by Archaeans and other thermophilic prokaryotes[END_REF]. Rather, this later value is best interpreted as the product of other primary producers such as photosynthesizers [START_REF] House | Carbon isotopic composition of individual Precambrian microfossils[END_REF][START_REF] Kaufman | High CO2 levels in the Proterozoic atmosphere estimated from analyses of individual microfossils[END_REF][START_REF] Williford | Preservation and detection of microstructural and taxonomic correlations in the carbon isotopic compositions of individual Precambrian microfossils[END_REF] or hydrogenotrophic MSR using the acetyl Co-A pathway [START_REF] Preuß | Carbon Isotope Fractionation by Autotrophic Bacteria with Three Different CO2 Fixation Pathways[END_REF]. Moreover, Type-A and -B OM are both sulfurized and commonly associated with swarms of nano-pyrites (Fig. 5;Lepot et al., 2009a;[START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. This observation of a strong coupling between sulfur cycling and OM is at odds with the inferred situation whereby production of hydrogenotrophic acetate required a termination of the more competitive MSR.

Alternatively, using analogy to modern settings, hydrogenotrophic acetogenesis can be fueled by the H2 and CO2 products of fermentation (Fig. 1B) of primary biomass with 13 C-depleted CO2. However, in this case, the isotopic fractionation of hydrogenotrophic acetogenesis will be dampened in bulk and at the microscopic scale of kerogen formation by that of acetate and other molecules produced by fermentation metabolisms [START_REF] Heuer | The stable carbon isotope biogeochemistry of acetate and other dissolved carbon species in deep subseafloor sediments at the northern Cascadia Margin[END_REF][START_REF] Heuer | Experimental studies on the stable carbon isotope biogeochemistry of acetate in lake sediments[END_REF][START_REF] Conrad | Stable carbon isotope biogeochemistry of propionate and acetate in methanogenic soils and lake sediments[END_REF], as well as by abiotic condensation of labile molecules [START_REF] Vandenbroucke | Kerogen origin, evolution and structure[END_REF] inherited from the primary biomass. In this case, the kerogen would likely not depart by more than ±10 ‰ from the composition of the primary biomass (δ 13 C ≥ -39.3 ‰, Figs. 1A, 1C-F), as developed in Supplementary Discussion 2. Importantly, to our knowledge, the formation of biomass with δ 13 Corg values lower than -50 ‰ through the consumption of hydrogenotrophic acetate has never been observed directly, for example with the SIMS techniques coupled to fluorescence in situ hybridization used to reveal the isotopic composition of methanotrophic biomass [START_REF] Orphan | Methane-consuming archaea revealed by directly coupled isotopic and phylogenetic analysis[END_REF].

Thus it appears difficult to attribute bulk OM δ 13 Corg values lower than -50 ‰ as well as microscale δ 13 Corg as low as -65.2‰ in Type-B OM to heterotrophic consumption of acetate that was generated through fermentation and/or using fermentative H2. In contrast, methanotrophic cells have been directly observed to carry the signature of parent methane as they displayed δ 13 Ccell values usually much lower than -50 ‰ and even as low as -96 ‰ [START_REF] Orphan | Methane-consuming archaea revealed by directly coupled isotopic and phylogenetic analysis[END_REF][START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF]. The fact that 13 C-depletions imparted by production (Fig. 1F,1I) and consumption (Figs. 1J-K) of methane can be, once cumulated, much larger than those imparted by hydrogenotrophic acetogenesis alone (Fig. 1C), favors the production of biomass with the most extreme 13 C depletions. For instance, the biomass of methane seeps can be dominated by methanotrophic consortia and display bulk δ 13 Corg values as low as -72.2 ‰ [START_REF] Michaelis | Microbial reefs in the black sea fueled by anaerobic oxidation of methane[END_REF]. Extreme δ 13 Corg values such as those associated with Type-B OM, going down to -65.2 ‰-and likely about 2 ‰ lower before thermal alteration [START_REF] Hayes | Precambrian organic geochemistry, preservation of the record[END_REF]-are thus best interpreted as the signature of methanotrophy in agreement with traditional inferences [START_REF] Hayes | Global methanotrophy of the Archean-Proterozoic transition[END_REF][START_REF] Hinrichs | Microbial fixation of methane carbon at 2.7 Ga: Was an anaerobic mechanism possible?[END_REF].

Record of methanotrophy in carbonates?

Oxidation of methane can occur aerobically [START_REF] Hanson | Methanotrophic bacteria[END_REF], or anaerobically (AOM) using SO4 2- [START_REF] Knittel | Anaerobic Oxidation of Methane: Progress with an Unknown Process[END_REF], Fe 3+ -oxides and Mn 4+ -oxides [START_REF] Beal | Manganese-and Iron-Dependent Marine Methane Oxidation[END_REF][START_REF] Norði | Anaerobic oxidation of methane in an iron-rich Danish freshwater lake sediment[END_REF][START_REF] Sivan | Iron oxides stimulate sulfate-driven anaerobic methane oxidation in seeps[END_REF], and NO3 -or NO2 - [START_REF] Raghoebarsing | A microbial consortium couples anaerobic methane oxidation to denitrification[END_REF][START_REF] Haroon | Anaerobic oxidation of methane coupled to nitrate reduction in a novel archaeal lineage[END_REF]. While aerobic methanotrophy promotes calcite dissolution [START_REF] Krause | Enhanced Calcite Dissolution in the Presence of the Aerobic Methanotroph Methylosinus trichosporium[END_REF], AOM promotes calcite precipitation (e.g., [START_REF] Michaelis | Microbial reefs in the black sea fueled by anaerobic oxidation of methane[END_REF] and may have contributed to the formation of the Tumbiana carbonates. Slotznick and Fisher (2016), however, argued that the texture and isotopic composition of carbonates in the Tumbiana Formation were incompatible with methanotrophy. On the basis of geochemical modelling they argued that δ 13 C values of carbonates produced by AOM in Archean environments should range between -2 and -30 ‰ [START_REF] Slotznick | Examining Archean methanotrophy[END_REF]. Thus, the range of δ 13 Ccarbonates values (-0.9 to 1.2 ‰) reported by Slotznick and Fisher (2016) appeared too high to support AOM. Other studies, however, have reported a wider range of δ 13 Ccarbonates values (-10.9 to +1.9 ‰) that are more consistent with a methanotrophic origin [START_REF] Eigenbrode | Late Archean rise of aerobic microbial ecosystems[END_REF]Thomazo et al., 2009b;[START_REF] Coffey | Sedimentology, stratigraphy and geochemistry of a stromatolite biofacies in the 2.72 Ga Tumbiana Formation, Fortescue Group, Western Australia[END_REF][START_REF] Williford | Carbon and sulfur isotopic signatures of ancient life and environment at the microbial scale: Neoarchean shales and carbonates[END_REF][START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF].

Importantly, the model of [START_REF] Slotznick | Examining Archean methanotrophy[END_REF] neglects to account for other generations of carbonates not related to AOM whose higher δ 13 C values would mute the AOM-derived δ 13 C signal [START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF][START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. The consortia responsible for AOM may thrive as endolithic communities in the pore-spaces of older, low-permeability seafloor carbonates (Marlow et al., 2014). Although, in the latter case, the seafloor carbonates likely formed through methanotrophy in the past [START_REF] Greinert | Stromatolitic fabric of authigenic carbonate crusts: Result of anaerobic methane oxidation at cold seeps in 4,850 m water depth[END_REF], such endolithic AOM may similarly thrive in shallow water stromatolites. Consistent with this view, sulfate-dependent AOM is suggested by δ 13 Corg values ranging between -55.4 and -43. 3 ‰ and δ 34 Spyrite ranging between -8.5 and +19 ‰ in millimeter-scale synsedimentary cavities of fluviolacustrine stromatolites of the 2.75 Ga Hardey Formation (Fortescue Group, Australia) [START_REF] Rasmussen | Evidence for microbial life in synsedimentary cavities from 2.75 Ga terrestrial environments[END_REF]. A large fraction of stromatolitic carbonates could have been produced by photosynthesis, as suggested by stromatolitic textures including tufts [START_REF] Flannery | Archean tufted microbial mats and the Great Oxidation Event: New insights into an ancient problem[END_REF], clumps [START_REF] Sim | Oxygen-Dependent Morphogenesis of Modern Clumped Photosynthetic Mats and Implications for the Archean Stromatolite Record[END_REF], and palisades [START_REF] Buick | The antiquity of oxygenic photosynthesis: evidence from stromatolites in sulphate-deficient Archaean lakes[END_REF]. Photosynthesis associated with respiration can produce stromatolitic carbonates with δ 13 C values of up to +4 ‰ [START_REF] Andres | Isotopic fingerprints of microbial respiration in aragonite from Bahamian stromatolites[END_REF]. In addition, fixation of methanogenic CO2 by phototrophs can produce stromatolitic carbonates with strongly positive (up to +16 ‰) δ 13 C values [START_REF] Birgel | Methanogenesis produces strong 13 C enrichment in stromatolites of Lagoa Salgada, Brazil: A modern analogue for Palaeo-/Neoproterozoic stromatolites?[END_REF]. Altogether, the δ 13 Ccarbonate signature of methanotrophy may have been diluted by other metabolic reactions active during the deposition of the Tumbiana Formation. We turn to SIMS analyses of δ 13 Corg coupled to petrography to further address the metabolic signatures in the Tumbiana stromatolites.

Methanotrophy as a source of 13 C-depleted OM

The Precambrian kerogen sample with the lowest bulk δ 13 Corg values (-60.9 ‰) originates from the Tumbiana Formation (Strauss et al., 1992). Here we report δ 13 C * org values down to -65.2 ‰ associated with Type-B OM, which currently represent the lowest δ 13 Corg values known in ancient, deeply-buried OM [START_REF] Eigenbrode | Late Archean rise of aerobic microbial ecosystems[END_REF]Thomazo et al., 2009a;[START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF]. As discussed above, such extremely low δ 13 Corg values may hypothetically originate from hydrogenotrophic acetogenesis, but are more commonly reconciled with methanotrophy.

The δ 13 Corg values in our samples are dependent on OM type, with Type-A OM being enriched in 13 C compared to Type-B OM. A variety of interpretations can explain these isotopic differences. For example, aceticlastic, hydrogenotrophic, and methylotrophic pathways can generate CH4 with distinct δ 13 C values (Fig. 1F, 1I;[START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. Similarly, differences in pathways for aceticlastic methanogenesis by Methanosaeta and Methanosarcina genera may also explain such heterogeneities (Fig. 1I), although Methanosarcina may not have evolved until the late-Permian [START_REF] Rothman | Methanogenic burst in the end-Permian carbon cycle[END_REF]. Differences in methanogenic pathways have been invoked to explain environmentally-dependent (ocean versus alkaline lakes) variations in bulk-rock δ 13 Corg values [START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. In addition, variations in methane flux may also have impacted the isotopic fractionation of AOM communities [START_REF] Hinrichs | Molecular and isotopic analysis of anaerobic methane-oxidizing communities in marine sediments[END_REF]. While variable sources/flux of methane are viable at the bulksediment scale, they are more difficult to reconcile with the sub-millimeter-scale heterogeneities identified here (Figs. 3,5) and would require that Type-A and Type-B OM formed at different times. The only type of OM found in mud-type laminae was Type-A, whereas in calcitic laminae Type-A OM was only found within clusters of Type-B OM (Fig. 3). This intimate association of Type-A and Type-B OM suggests they have been co-genetic.

Excluding variations in methane sources, the higher δ 13 Corg values in Type-A OM may reflect aerobic methanotrophy, while the lower δ 13 Corg values of Type-B OM could relate to AOM. Biomass from aerobic methanotrophs may display smaller 12 C-enrichment than that of their anaerobic counterparts (Fig. 1J-K; [START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF][START_REF] Templeton | Variable carbon isotope fractionation expressed by aerobic CH4-oxidizing bacteria[END_REF]. Stromatolite textures [START_REF] Buick | The antiquity of oxygenic photosynthesis: evidence from stromatolites in sulphate-deficient Archaean lakes[END_REF][START_REF] Flannery | Archean tufted microbial mats and the Great Oxidation Event: New insights into an ancient problem[END_REF][START_REF] Sim | Oxygen-Dependent Morphogenesis of Modern Clumped Photosynthetic Mats and Implications for the Archean Stromatolite Record[END_REF] and Mo isotope ratios are consistent with production of O2 within the Tumbiana Lake system [START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF]. Contrastingly, Fe-isotope ratios indicate only partial oxidation of iron in an oxygen-limited environment [START_REF] Nishizawa | Grain-scale iron isotopic distribution of pyrite from Precambrian shallow marine carbonate revealed by a femtosecond laser ablation multicollector ICP-MS technique: Possible proxy for the redox state of ancient seawater[END_REF][START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF]. Aqueous Fe 2+ was most likely produced by alteration of basaltic volcanic ash [START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF] that occurs throughout the stromatolites (Lepot et al., 2009a;[START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF] and in the thick underlying Mingah tuffs [START_REF] Lepot | Biogenic versus metamorphic origins of diverse microtubes in 2.7Gyr old volcanic ashes: Multi-scale investigations[END_REF]. This Fe 2+ could have served as a buffer, limiting oxygen availability in the sediment and potentially even in the water column, in turn limiting the role of aerobic methanotrophy in forming the observed δ 13 Corg heterogeneities.

Sulfate-dependent methanotrophy

In the sulfate-permeated region of recent seafloor sediments, nearly all the methane flux is used up by AOM [START_REF] Knittel | Anaerobic Oxidation of Methane: Progress with an Unknown Process[END_REF]. Sulfate, possibly of atmospheric origin [START_REF] Farquhar | Atmospheric influence of Earth's earliest sulfur cycle[END_REF], was reduced by microorganisms in the Tumbiana Lake water and/or sediments [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. A significant fraction of this MSR could have proceeded through sulfate-dependent AOM pathways [START_REF] Hinrichs | Microbial fixation of methane carbon at 2.7 Ga: Was an anaerobic mechanism possible?[END_REF]. Unlike Type-A and Type-C OM, Type-B OM commonly displays enrichments in organic sulfur (Figs. 5, 11;Lepot et al., 2009a). Organic sulfur typically forms through polymerization of reduced sulfur species, including polysulfides (HSx -, Sx 2-), HS -, and/or elemental sulfur [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF]. In contemporary settings, these reduced species are provided by MSR [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF]. Heterotrophic MSR (Fig. 1G) is an important possible pathway for sulfurization [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF], but it has recently been proposed that sulfate-dependent AOM (Fig. 1K,L) can also drive OM sulfurization [START_REF] Quijada | Organic matter sulfurization on protracted diagenetic timescales: The possible role of anaerobic oxidation of methane[END_REF]. Sulfate-dependent AOM can be conducted by syntrophic consortia of anaerobic methanotrophic (ANME) archaea and MSR (Fig. 1K; [START_REF] Boetius | A marine microbial consortium apparently mediating anaerobic oxidation of methane[END_REF][START_REF] Orphan | Methane-consuming archaea revealed by directly coupled isotopic and phylogenetic analysis[END_REF]. Sulfate-dependent AOM, however, can also be performed independently by ANME group 2 (ANME-2) archaea (Fig. 1L;[START_REF] Milucka | Zero-valent sulphur is a key intermediate in marine methane oxidation[END_REF]. Here, the ANME-2 archaea oxidize CH4 and reduce sulfate to elemental S (intracellular S8 polysulfides). This elemental S can diffuse outside ANME-2 to react with HS -and form polysulfides such as HS2 - [START_REF] Milucka | Zero-valent sulphur is a key intermediate in marine methane oxidation[END_REF]. Associated bacteria, instead, are responsible for disproportionating the product polysulfide HS2 -into HS -and sulfate [START_REF] Milucka | Zero-valent sulphur is a key intermediate in marine methane oxidation[END_REF]. Interestingly, the polysulfides such as HS2 -produced by these specific ANME-2 archaea are highly potent toward OM sulfurization [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF]. Furthermore, ANME-2 are known to produce larger 13 C-depletions in biomass relative to those produced by ANME-1 methanotrophs (Fig. 1K; [START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF][START_REF] Treude | Consumption of methane and CO2 by methanotrophic microbial mats from gas seeps of the anoxic Black Sea[END_REF]. Accordingly, the high organic S content and extreme 13 C-depletion observed in Type-B OM support an origin tied to sulfate-dependent AOM, possibly carried out by polysulfide-producing ANME-2 (Fig. 1L). If the ANME-2 produced S° and HS2 -independently, OM sulfurization could have proceeded without sulfate-reducing bacteria. In addition, intracellular polysulfides in ANME-2 could have been preserved in OM for several thousand years (e.g., [START_REF] Lepot | Organic and mineral imprints in fossil photosynthetic mats of an East Antarctic lake[END_REF]. Later during diagenesis, polysulfides could have implanted large amounts of organic S locally in Type-B OM. In this scenario, the sulfurization of biomass other than that of ANME-2, such as that of Sdisproportionating bacteria, may be limited.

The large isotopic heterogeneity observed in Type-B OM can be explained via the admixture of MSR or S-disproportionating microbial biomass that can also produce highly 13 C-depleted biomass by consuming the 13 C-depleted CO2 liberated from methanotrophy (Fig. 1K, Hinrichs et al., 2000;[START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF]. Similarly, the higher δ 13 Corg values and lower organic S abundance in Type-A OM relative to Type-B OM can be explained by biomass of MSR and/or S-disproportionating bacteria. Alternatively, Type-A OM may also be the product of sulfate-dependent ANME-1 in consortia with MSR. Microscale investigation of modern sediments/biofilms have demonstrated that the biomass of ANME-1 is less 13 C-depleted than that of ANME-2 (Fig. 1K, [START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF][START_REF] Treude | Consumption of methane and CO2 by methanotrophic microbial mats from gas seeps of the anoxic Black Sea[END_REF]. Their production of HS -, rather than S8 or HS2 -, would presumably be less efficient at promoting OM sulfurization [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF], resulting in S-poorer OM. Consistent with this, we note the small concentration of organic sulfur associated with Type-A OM (Figs. 5,11). Moreover, in another stromatolite from 68.9 m core depth, OM corresponding to textural Type A (in seams with chlorite and quartz) was observed in association with nanopyrites bearing the S-isotope signature of MSR [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. Together these observations are consistent with the hypothesis that Type-A OM also had a genetic history linked to sulfur-dependent AOM.

Nitrate/nitrite-dependent AOM

Among the other environmentally relevant chemical species that may have fueled AOM are nitrate and nitrite [START_REF] Raghoebarsing | A microbial consortium couples anaerobic methane oxidation to denitrification[END_REF]. Recent investigations indicate that NO2/3 --dependent methanotrophs are bacteria operating without partner archaea [START_REF] Ettwig | Denitrifying bacteria anaerobically oxidize methane in the absence of Archaea[END_REF]. Unfortunately, to our knowledge, the C-isotope fractionations of the biomass of NO2/3 --dependent methanotrophs has yet to be measured. The available isotope fractionations measured on methane did not allow to clearly distinguish the various forms of methanotrophy [START_REF] Rasigraf | Carbon and hydrogen isotope fractionation during nitrite-dependent anaerobic methane oxidation by Methylomirabilis oxyfera[END_REF]. Nitrate availability within the Tumbiana system has been proposed based on the extreme δ 15 N values it records [START_REF] Thomazo | Extreme15N-enrichments in 2.72-Gyr-old sediments: Evidence for a turning point in the nitrogen cycle[END_REF]. These extreme δ 15 N values have, however, been alternatively explained via NH3 volatilization processes (Stüeken et al., 2015b). Moreover, the availability of nitrate and nitrite during the Archean may have been limited in oxygen-poor environments by their reduction through denitrification and anaerobic ammonium oxidation [START_REF] Zerkle | The geobiological nitrogen cycle: From microbes to the mantle[END_REF]Zerkle et al., 2017;[START_REF] Luo | Nitrogen fixation sustained productivity in the wake of the Palaeoproterozoic Great Oxygenation Event[END_REF] and possibly though microbial oxidation of Fe 2+ [START_REF] Miot | Iron biomineralization by anaerobic neutrophilic iron-oxidizing bacteria[END_REF][START_REF] Klueglein | Potential role of nitrite for abiotic Fe(II) oxidation and cell encrustation during nitrate reduction by denitrifying bacteria[END_REF]. Therefore, similar to O2, N-oxyanions may not have been readily accessible for methanotrophs.

Fe-, Mn-, As-dependent AOM

Perhaps more relevant than methanotrophy using O2 or NO2/3 -in an anoxic Archean setting are Fe-/Mn-dependent AOM metabolisms (Fig. 1K; [START_REF] Beal | Manganese-and Iron-Dependent Marine Methane Oxidation[END_REF]. Arsenate reduction [START_REF] Sforna | Evidence for arsenic metabolism and cycling by microorganisms 2.7 billion years ago[END_REF] may also have potentially fueled AOM, although to the best of our knowledge, As-dependent AOM has not been documented in recent settings, and even if it was proven to be viable, the low As concentrations (≤4.12 ppm) likely render it unimportant in our samples.

Genetic studies of methane seep sediments associated with active Fe-and Mn-coupled AOM demonstrated that ANME-1 genes were significantly more abundant than those of ANME-2 (Beal et al., 2009). Accordingly, Fe-and/or Mn-coupled AOM would be expected to produce less negative δ 13 Corg values [START_REF] Orphan | Multiple archaeal groups mediate methane oxidation in anoxic cold seep sediments[END_REF][START_REF] Treude | Consumption of methane and CO2 by methanotrophic microbial mats from gas seeps of the anoxic Black Sea[END_REF], which could explain the higher δ 13 Corg values of Type-A OM relative to Type-B OM. The studied stromatolites (KGI68.2 and 69.2a) display Mn concentrations of 0.30 and 0.37 wt.% MnO and Fe-concentrations of 3.64 and 3.92 wt.% Fe2O3, respectively, that is atomic Fe/Mn ratios of about 10. Although Fe is much more abundant, AOM requires two times less Mn than Fe per mole of CH4 oxidized [START_REF] Beal | Manganese-and Iron-Dependent Marine Methane Oxidation[END_REF]. Possibly more relevant than the relative Fe/Mn concentrations in distinguishing the possible importance of these AOM pathways was the initial availability of Fe 3+ and/or Mn 4+ . Although abiotic Mn 2+ oxidation by O2 is slow, aerobic microbial oxidation favors Mn 2+ over Fe 2+ [START_REF] Konhauser | Introduction to Geomicrobiology[END_REF]. In contrast, anaerobic photosynthetic oxidation of Fe 2+ is possible [START_REF] Konhauser | Introduction to Geomicrobiology[END_REF], whereas anoxygenic photosynthetic oxidation of Mn has yet to be discovered [START_REF] Jones | No evidence for manganese-oxidizing photosynthesis[END_REF].

Molybdenum isotope fractionations recorded in the Tumbiana Formation [START_REF] Stüeken | Environmental niches and metabolic diversity in Neoarchean lakes[END_REF] could have been produced by adsorption of Mo onto Mn 4+ -oxides, Fe 3+ -(oxyhydr)oxides, and sequestration into sulfide minerals [START_REF] Kendall | The stable isotope geochemistry of Molybdenum[END_REF]. Furthermore, Mn was not detected with SEM EDXS in the mineral assemblage associated with Type-A OM (i.e. chlorite), and instead Mn is essentially found as a minor Mn 2+ component included in calcite [START_REF] Lepot | Microbially influenced formation of 2,724-million-year-old stromatolites[END_REF]Lepot et al., 2009a). Thus far, we lack petrographic and isotopic evidence that oxidized Mn participated in AOM.

In contrast, Type-A OM is intimately associated with Fe-bearing phases. Type-A OM and siliceous layers that exclusively host Type-A OM are also enriched in pyrite compared to calcitic layers that include Type-B OM (Lepot et al., 2009a;Thomazo et al., 2009b;[START_REF] Nishizawa | Grain-scale iron isotopic distribution of pyrite from Precambrian shallow marine carbonate revealed by a femtosecond laser ablation multicollector ICP-MS technique: Possible proxy for the redox state of ancient seawater[END_REF][START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. Moreover, the intimate association of Fe-and Mg-rich chlorites with Type-A OM (Figs. 3,5,8) suggests that some of these Fe-silicates could have formed as authigenic rather than clastic minerals, as seen in modern stromatolites (Lepot et al., 2009a;[START_REF] Burne | Stevensite in the modern thrombolites of Lake Clifton, Western Australia: A missing link in microbialite mineralization?[END_REF][START_REF] Zeyen | Formation of low-T hydrated silicates in modern microbialites from Mexico and implications for microbial fossilization[END_REF][START_REF] Pace | Microbial and diagenetic steps leading to the mineralisation of Great Salt Lake microbialites[END_REF]. Formation of authigenic Fe 2+ -silicates may have been linked with microbial reduction of Fe 3+ -minerals (Percak-Dennett et al., 2011). In addition, consortia of ANME and MSR have been shown to facilitate biomineralization of siliceous minerals, some of which contained minor Fe [START_REF] Chen | Biomineralization mediated by anaerobic methaneconsuming cell consortia[END_REF]. These authigenic siliceous Fe 2+ -minerals may represent the precursors to chlorite and/or quartz associated with Type-A OM. Furthermore, sulfide ions would have been able to react with Fe 2+ sequestered in minerals such as Fe-phosphates, Fe-carbonates [START_REF] Egger | Anaerobic oxidation of methane alters sediment records of sulfur, iron and phosphorus in the Black Sea[END_REF], or reactive Fe-silicates [START_REF] Canfield | The reactivity of sedimentary iron minerals toward sulfide[END_REF]. In turn, the low abundance of organic sulfur in Type-A OM may be explained by preferential reaction of sulfide ions with soluble and/or mineral iron rather than with OM [START_REF] Werne | Organic sulfur biogeochemistry: Recent advances and future research directions[END_REF]Lepot et al., 2009a). In the microenvironments associated with Type-A OM, after depletion of sulfate [START_REF] Sivan | Geochemical evidence for iron-mediated anaerobic oxidation of methane[END_REF][START_REF] Egger | Anaerobic oxidation of methane alters sediment records of sulfur, iron and phosphorus in the Black Sea[END_REF], Fe 3+ -minerals may have promoted Fe-dependent AOM both directly and indirectly. The reduction of Fe 3+ -minerals can fuel Fe-dependent AOM without S [START_REF] Beal | Manganese-and Iron-Dependent Marine Methane Oxidation[END_REF][START_REF] Egger | Iron-mediated anaerobic oxidation of methane in brackish coastal sediments[END_REF][START_REF] Bar-Or | Iron-Coupled Anaerobic Oxidation of Methane Performed by a Mixed Bacterial-Archaeal Community Based on Poorly Reactive Minerals[END_REF]. Additionally, a "cryptic sulfur cycle" whereby the abiotic reaction between Fe 3+ -minerals and HS -forms S 0 (Fig. 1M) can fuel sulfur-dependent AOM after the direct oxidation of the product S 0 by MSR or after disproportionation of S 0 into HS -and sulfate [START_REF] Sivan | Iron oxides stimulate sulfate-driven anaerobic methane oxidation in seeps[END_REF][START_REF] Hansel | Dominance of sulfur-fueled iron oxide reduction in low-sulfate freshwater sediments[END_REF].

Fe-isotope analyses are consistent with intense biogeochemical cycling, indicating that at least some of the pyrite in the Tumbiana stromatolites was formed following the reduction of ferric (oxyhydro)oxides [START_REF] Nishizawa | Grain-scale iron isotopic distribution of pyrite from Precambrian shallow marine carbonate revealed by a femtosecond laser ablation multicollector ICP-MS technique: Possible proxy for the redox state of ancient seawater[END_REF][START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF]. The association of pyrite with δ 56 Fe values lower than -3.1 ‰ and OM with δ 13 Corg values ranging between -51.8 and -40 ‰ has been also used to argue for Fe-dependent AOM in mudstones of the Tumbiana Formation [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF]. Similarly, the pyrites in the Tumbiana stromatolites also feature negative δ 56 Fe values [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF] that may represent either abiotic [START_REF] Guilbaud | Abiotic pyrite formation produces a large Fe isotope fractionation[END_REF] or microbial [START_REF] Czaja | Comment on "Abiotic pyrite formation produces a large Fe isotope fractionation[END_REF] Fe-reduction processes. The bulk δ 34 S values of pyrites are equally equivocal, displaying relatively muted fractionations (δ 34 S = -5.7 to 2.7 ‰) that can be explained by either abiotic processes or MSR at low sulfate concentrations (Thomazo et al., 2009b). Microscale δ 34 S values, however, display a wide range (-33.7 to +50 ‰) suggesting that sulfate may have been abundant at least in microscale niches [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. In summary, the available geochemical evidence suggests that Fe-dependent AOM with or without a "cryptic S-cycle", as well as sulfate-dependent AOM, could have been responsible for the Type-A OM preserved in the Tumbiana stromatolites.

Conclusions

In the studied stromatolites, indigenous-Type-A and -B-kerogen displayed δ 13 Corg values ranging between -65.2 and -50.6 ‰ whereas only pyrobitumen, which is likely exogenous, displayed higher values (-48 to -39.1 ‰). With such low δ 13 Corg values, neither Type-A and -B OM can be directly related to primary photosynthetic or chemoautotrophic biomass. These OM include a significant fraction of carbon that was fixed through consumption of 13 C-depleted methane and/or acetate.

Reviewing known biogeochemical pathways and their combinations reveals that δ 13 Corg values lower than -50 ‰ are difficult to reconcile with acetogenesis fueled only by fermentation. Acetogenesis fueled by abiotic H2 in addition to fermentative H2 may theoretically yield lower δ 13 C values. However, thermodynamics dictate that H2 will be consumed preferentially by microbial reductions of Fe 3+ and sulfate [START_REF] Hoehler | Thermodynamic control on hydrogen concentrations in anoxic sediments[END_REF][START_REF] Madigan | Brock biology of Microorganisms[END_REF]. These oxidized species were present during the deposition of the Tumbiana stromatolites [START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF][START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF]. The activity of hydrogenotrophic acetogens would thus have required complete termination of MSR and microbial Fe-reduction. However, we show that the two main types of highly 13 C-depleted OM are intimately associated with pyrite and/or organic sulfur, which rather point to a strong coupling between sulfur cycling and OM production. In addition, we still lack evidence for abiotic H2 sources in the Tumbiana Lake system.

Alternatively, the association of extreme 13 C-depletion (δ 13 C*org = -65.2 to -52.5 ‰) in Type-B globules with organic sulfur enrichments strongly argues that this OM was derived from biomass produced by sulfate-dependent AOM. Indeed, some of the ANME-2 produce the most extreme 13 Cdepletions by reducing sulfate to elemental sulfur and polysulfides, which are highly prone to organic matter sulfurization. The less extreme δ 13 Corg values (-56.1 to -50.6 ‰) recorded in Type-A OM are most parsimoniously interpreted as the result of AOM using various oxidants. Observation of strongly 32 S-enriched nanopyrites in Type-A organic matter in another Tumbiana stromatolite [START_REF] Marin-Carbonne | Sulfur isotope's signal of nanopyrites enclosed in 2.7 Ga stromatolitic organic remains reveal microbial sulfate reduction[END_REF] suggests that AOM coupled to sulfate reduction may similarly have proceeded in micro-environments where Fe 2+ was available to outcompete OM for sulfur (Lepot et al., 2009a). Type-A OM is frequently associated with Fe-silicates. The latter could have resulted from Fe 3+reduction (like some Tumbiana pyrites: [START_REF] Nishizawa | Grain-scale iron isotopic distribution of pyrite from Precambrian shallow marine carbonate revealed by a femtosecond laser ablation multicollector ICP-MS technique: Possible proxy for the redox state of ancient seawater[END_REF][START_REF] Yoshiya | In situ iron isotope analyses of pyrite and organic carbon isotope ratios in the Fortescue Group: Metabolic variations of a Late Archean ecosystem[END_REF], which could have sustained AOM. Future microanalyses of δ 13 Corg, δ 34 S and δ 56 Fe targeting all the OM-types and associated minerals described herein are anticipated to provide a more comprehensive perspective on the complex and cryptic redox cycles that apparently fueled methanotrophy.

The most extreme bulk-OM δ 13 Corg values lower than -50.2 ‰ are restricted between 2.8 and 2.7 Ga during the Precambrian, and are apparently unique to lacustrine deposits [START_REF] Flannery | Lacustrine facies dependence of highly 13C-depleted organic matter during the global age of methanotrophy[END_REF]. In the conical stromatolites of the Tumbiana Formation, bulk δ 13 Corg values as high as -15 ‰ are best interpreted as reflecting photosynthetic primary production [START_REF] Coffey | Sedimentology, stratigraphy and geochemistry of a stromatolite biofacies in the 2.72 Ga Tumbiana Formation, Fortescue Group, Western Australia[END_REF]. In the fluvial-lacustrine Tumbiana system, oxygenic and/or anoxygenic photosynthesis could have produced S°/sulfate and Fe 3+ -minerals. These, together with the photochemical sulfur aerosols (e.g., [START_REF] Zerkle | A bistable organic-rich atmosphere on the Neoarchaean Earth[END_REF] may have been concentrated by the drainage basins and evaporation of the Tumbiana Lake system. These oxidized S and Fe species could have fueled anaerobic respiration of OM, as well as S-and possibly Fe-dependent methanotrophy. The impact of lacustrine methanotrophy on Neoarchean atmospheric methane concentrations (Thomazo et al., 2009b;[START_REF] Izon | Multiple oscillations in Neoarchaean atmospheric chemistry[END_REF] is difficult to address. The δ 13 Corg > -50.2 ‰ of Neoarchean and Paleoproterozoic marine deposits may record a more limited methanotrophic biomass. Today's (non-anthropogenic) net release of methane to the atmosphere is mostly contributed by continental ecosystems [START_REF] Reeburgh | Oceanic Methane Biogeochemistry[END_REF], and is limited in marine context thanks to sulfate-dependent AOM [START_REF] Knittel | Anaerobic Oxidation of Methane: Progress with an Unknown Process[END_REF]. Our study suggests that some Archean lacustrine ecosystems may have consumed methane using sulfate, and possibly, Fe 3+ . In contrast, methanotrophy may have been less efficient and/or active in marine, ca. 2.7 Ga sediments, which appeared less depleted in 13 C (Flannery et al., 2016). Continental ecosystems may have been widespread at about 2.7 Ga [START_REF] Thomazo | Possible nitrogen fertilization of the early Earth Ocean by microbial continental ecosystems[END_REF], which is the time of the formation of the first supercontinent [START_REF] Condie | Episodic zircon age spectra of orogenic granitoids: The supercontinent connection and continental growth[END_REF]. In addition, the Tumbiana Formation deposited between two major episodes of eruption of subaerial large igneous provinces [START_REF] Kump | Increased subaerial volcanism and the rise of atmospheric oxygen 2.5 billion years ago[END_REF], the weathering of which could have sustained luxuriant photosynthesis in soil and fluviolacustrine ecosystems [START_REF] Lalonde | Benthic perspective on Earth's oldest evidence for oxygenic photosynthesis[END_REF]. Ensuing methane production during OM remineralization may have fueled persistent AOM in these newly-formed and possibly widespread types of Archean ecosystems until the protracted Neoarchean rise in oxygen confined these anaerobic metabolisms to a more restricted ecological importance.

  𝟏) = 12 𝑪 𝒂𝒏𝒕𝒉𝒓𝒂𝒄𝒊𝒕𝒆 -, i.e. the count rate measured on pure OM (8) 12 𝑪 𝒎𝒆𝒂𝒔 -(𝒇 = 𝟎) = 12 𝑪 𝒑𝒖𝒓𝒆-𝒄𝒂𝒓𝒃 -, i.e. the count rate measured on pure (OM-free) carbonate can be expressed in direct relationship with measured values using equation (10).

FIGURESFig. 1 .

 1 FIGURES

Fig. 3 .

 3 Fig. 3. Petrography of studied stromatolites. (A-C) Photomicrographs of samples KGI 68.2' (A) and 69.2a (B-C). (C) Zoom on the boxed zone in (B). Light grey layers in (A-C, box 1 in C) are dominated by micritic to microsparitic calcite. Calcite pseudomorphs after cubic halite are highlighted with arrowheads in B. Clusters of organic matter globules occur in these layers (center of box 1 in C). Black « mud-type » layers in (A-C) and box 2 in (C) are dominated by clay minerals and quartz. (Volcano)clastic grains are interspersed with micritic/microsparitic layers, and sometimes dominate these layers (e.g. box 3 in C). A large organic matter nodule appears in black in box 3 in (C). (D-E) SEM BSE images showing organic matter (black; Type A: white arrowheads, Type B: black arrowheads), quartz (Q, dark grey), muscovite (Mu, medium-dark grey), calcite (Ca, medium grey), chlorite (Ch, light grey) and pyrite (Py, white, red arrows). (D) Shows a cluster of OM embedded in

Fig. 4 .

 4 Fig. 4. Type-C organic matter nodule in sample 69.2a. (A) SEM-BSE image of a Type-C organic matter nodule in sample 69.2a located by box 3 in Fig. 3C. SIMS δ 13 Corg values recorded on zones circled in red range between -39.1 and -48 ‰ ± 1.33 ‰ 2SD in this nodule and are spatially zoned. (B). SEM-EDXS map. The organic matter (pink) in the nodule is interspersed with pyrite and chalcopyrite (white) and cut across by chlorite (yellow) and muscovite (blue) microveins. (C). SEM-EDXS map of the left and central part of the nodule showing a micrometric U-rich crystal (cyan) and a hole (now filled with gold coating, purple-blue) that could correspond to a U-rich crystal removed during polishing.

Fig. 5 .

 5 Fig. 5. NanoSIMS maps and S/C quantification in sample KGI68.2 (zone F3). (A-C) Single cycle maps of 12 C -(A), 32 S -(B) and 28 Si -(C). The upper half of the mapped area displays Type-A OM associated with chlorite, whereas the lower half displays Type-B organic globules embedded in calcite. (D) Overlay of (A+B), where regions of interest outlined in white are associated with their atomic S/C ratios (±2SE). In (D), OM rich in organic S appears in mottled white/cyan/magenta (S: cyan + C: magenta), whereas nanopyrites appear as cyan hotspots.

Fig. 6 .

 6 Fig. 6. Sulfur L-edge XANES spectrum of a Type-B organic globule. The sample analyzed was the globule #2 of fig. 8C of Lepot et al. (2009). Dashed lines indicate bands of thiophene groups at 166.6 and 173.5 eV (see text for interpretation).

Fig. 7 .

 7 Fig. 7. SIMS analyses (3-µm spot) of Type-A organic matter in quartz. SEM BSE images of zones c11d (in A) and c11b (in B) of sample KGI68.2'. SIMS targets (circled) were chosen in order to sample zones with variable OM (in black) to quartz (in grey) concentration ratios. With the exception of one spot (yellow circle), SIMS analyses avoided crystals of muscovite (Ms, yellow) and chlorite (Ch, green) and targeted OM in quartz-only matrices. (C) In the quartz matrices (red and blue targets in A-B), the 13 CH -/ 13 C -ratios remain consistent with nearly all values between 0.075-0.085. The outlier has a low count rate as indicated by large 2SE error bars. (D) The δ 13 Corg values are consistent and independent of the organic matter to quartz concentration ratios, which is represented here by the 12 C -count rate in % relative to the count rate recorded on the pure anthracite bracketing standard. Error bars in (C-D) are 2SE.

Fig. 8

 8 Fig. 8 SIMS analyses (3-µm spot) of Type-A organic matter in contact with chlorite±quartz. (A-B) SEM BSE images of zones q5chip1 (A) and c14 (B) of sample KGI68.2'. SIMS targets (circled in A-C) were chosen in order to sample zones with variable OM (in black) to chlorite (light grey to white) ± quartz (medium grey) concentrations ratios. (C) SEM-EDXS map of Si (pink, from quartz and chlorite), Al (cyan, from chlorite), and C (yellow, from OM) in the zone of (B). (D) The 13 CH - / 13 C -ratios display large variations compared to those recorded in quartz as shown in Fig. 7. Linear

Fig. 10 .

 10 Fig. 10. SIMS analyses of micrometric Type-B organic globules in calcite crystals recorded with SIMS spot size of 1, 3 and 6 µm. (A) Plot of δ 13 Corg (2SE error bars) against f (the fraction of organic C in total 12 C -signal, see equation 10) values. The analytical sessions with 1-and 6-µm spots display a wide range of f where δ 13 Corg decreases with increasing f, indicating that at low OM concentrations (low f), the signal contains a mixture of carbonate and organic carbons (see text). (B) Mass balance calculation (using equations 11-15) provide δ 13 C*org values (2SE* error bars) corrected of interference of carbonate. The red box indicates the values that satisfy the filtering criterion f>0.9 (see text).

]/( 56 Fe/ 54 Fe) IRMM-014 . Mass-independent fractionations of S isotopes (MIF-S) are defined as non-zero values of the capital-delta deviations Δ 33 S = δ 33 S -1000*[(1+ δ 34 S/1000) 0.515 -1] and Δ 36 S = δ 36 S -1000*[(1+ δ 34 S/1000) 1.9 -1].

AKNOWLEDGEMENTS

We thank Noriko Kita and Jim Kern (WiscSIMS, UW-Madison) for assistance with SIMS analyses, and Brian Hess (UW-Madison) for expert SIMS mount preparation and polishing. P.P. thanks the Institut de Physique du Globe de Paris, the Institut des Sciences de l'Univers and the Geological Survey of Western Australia for supporting the PDP. Jian Wang (Canadian Light Source) is thanked for help with STXM analyses. P. Recourt (LOG) is thanked for help with SEM. M. Ader (IPGP) is thanked for providing the LGIS-1A standard. M. Delattre (LOG) is thanked for performing elemental analyses of standards. We thank Drs. A. Zerkle (associate editor), G. Izon, and two anonymous reviewers for their constructive comments that helped improve this manuscript significantly. NanoSIMS analyses were performed at the MNHN-INSU-IMPMC national facility in Paris. K.H.W. acknowledges a grant from the National Aeronautics and Space Agency for work performed at the Jet Propulsion Laboratory, California Institute of Technology. Funding was provided by the NASA Astrobiology Institute (NNA13AA94A), the Agence Nationale de la Recherche (ANR eLife2: ANR-10-BLAN-0602 to P.P.), the São Paulo Research Foundation (FAPESP grant 2015/16235-2 to P.P.), and the Agence Nationale de la Recherche (ANR M6fossils: ANR-15-CE31-0003-01 to K.L.). The WiscSIMS Lab is funded by the National Science Foundation, Division of Earth Sciences (1053466, 1355590, 1658823) and the University of Wisconsin-Madison.

regressions are provided for SIMS measurements made in the same seam/cluster of organic matter. Points grouped under "other zones" are dispersed through the sample. In a given seam/cluster, δ 13 Corg values decrease with increasing 13 CH -/ 13 C -ratios. Error bars are 2SE. (E) The 13 CH -/ 13 C -ratios increase at lower 12 C -count rates that is when the organic matter to chlorite±quartz ratios decrease. The 12 C -count rate is represented in % relative to the count rate recorded on the pure anthracite bracketing standard. 13 CH -/ 13 C -ratios and δ 13 Corg values (2SE error bars) display large variations comparable to those shown in Fig. 8. Linear regressions are provided for SIMS measurements made in the same seam/cluster of organic matter. Points grouped under "other zones" are dispersed through the sample. In a given seam/cluster, δ 13 Corg values decreases with increasing 13 CH -/ 13 C -ratios. (B) In zones N1z4 and N1z5a, δ 13 Corg values decreases at lower 12 C - count rates (in % relative to the 12 C -count rate recorded on the pure anthracite bracketing standard) that is when the organic matter to chlorite±quartz ratio decreases. In contrast, in zones F3 and 2-g10 where calcite occurred in the SIMS spots, δ 13 Corg values increase with decreasing 12 C -count rates consistent with mixing with a carbonate phase of high δ 13 Cmeas and low ionization yield (see text). The red box in (A) indicates analyses filtered with the criterion 13 CH -/ 13 C -<0.085 (see text) and not affected by carbonate interference; these analyses were recorded at high 12 C -count rates as shown in B, hence the small error bars.