Gravity-cores from eight different geographic locations were retrieved for this study during 2012–2014. When possible, the gravity-cores were supplemented with either box-cores or Rumohr cores from the same site. Two additional datasets were retrieved from the databases of the Ocean Drilling Program (ODP) Leg 201 and Integrated Ocean Drilling Program (IODP) Leg 323. The goal of the site selection was to access samples from an extensive range of well-constrained sediment ages within the sulfatic sediment zone. In addition, the sedimentary and geochemical settings were selected such that the rate of dissimilatory sulfate reduction could be determined with good accuracy. The sampling sites can be found in Table 1, in Supplementary Figure S1, and at https://drive.google.com/open?id=1rYE3drQ6eSkWIjRFQtpxwL265bM&usp=sharing.

Gravity-cores were retrieved specifically for the study and the greatest care was taken to avoid oxygen exposure and heating. Thus, the cores were sectioned into 1-meter sections immediately after core recovery and the full core sections were capped and placed horizontally near in situ temperature. Rumohr cores were capped with overlying water and stored vertically until processing. All cores were taken at high latitudes, which helped to avoid elevated temperatures in the upper water column and on deck.

Extraction of pore water and solid-phase sampling were completed within 4–48 h after sediment recovery. Pore-water was extracted with Rhizon soil-moisture samplers (Rhizosphere Research Products, Wageningen, Netherlands) through 4 mm holes drilled through the plastic core-liners every 10–25 cm within the top 1 m of the gravity-cores and Rumohr Lot cores. Below 1 m, the sample resolution in the gravity-cores was 20 to 25 cm. The first milliliter of extracted pore water was discarded, and the rest of the pore water was collected in evacuated Exetainers (Labco) before distribution for further analyses. Solid phase samples were collected with sterile plastic syringes with cut-off tip through windows cut into the core liner with a vibrating saw (Røy et al., 2014), after the outer sediment in contact with the liner had been removed. The solid-phase samples were taken from the same depths as the pore water and care was taken to only sample one side of the core (working half of the core). For selected cores, the archive-half was scanned by an ITRAX x-ray diffraction core scanner (Croudace et al., 2006).

The loss of sediment from the top of the gravity-cores, due to the core catcher and the violent penetration of the sediment surface, was estimated by matching the pore water profiles of NH₄⁺, SO₄²⁻, and δ¹³C_DIC. The estimated sediment loss was then used to extend the age-models of the cores all the way to the sediment–water interface (see section 3.4 for analytical details). The matched pore water profiles can be found in the cited literature for each individual cores.

The average age of the upper 5 few cm of sediment in Little Belt core (SKA14-05-B25) was estimated based on correlation to IODP expedition 347 site M0059 (Andrén et al., 2015), which was retrieved at the same location.

The age of the rapidly accumulating sediment in the Glacier Fjord (core SA13-ST8-47G) was analyzed via short-lived natural gamma emitters (²¹⁰Pb and ²²⁶Ra). The sedimentation rate was estimated from the least-squares fit to the natural log of excess ²¹⁰Pb in the core and the output of a one-dimensional two-layer advection–diffusion model that accounted for both biomixing and compaction with depth (Lavelle et al., 1985; Kuzyk et al., 2015). The data and the procedures are described in detail in Pelikan et al. (2019).

Calcareous mollusk shells and organic worm-tubes were collected in the Greenland Continental Shelf (core SA13-ST3-20G), Main Fjord of Nuuk Kangerlua (also known as Nuuk Fjord or Godthåbsfjord; SA13-ST5-30G), Side Fjord Kapisillit Kangerluat of Nuup Kangerlua (SA13-ST6-40G), Iceland Basin (DA12-11-ST1-GC01), and Faroe Bank (DA12-11-ST2-GC03) sediment cores for ¹⁴C age determination by Accelerator Mass Spectrometry at Aarhus AMS Centre, Aarhus University. The ¹⁴C ages were calibrated using the Marine13 radiocarbon calibration curve (Reimer et al., 2013) with no further regional reservoir correction (ΔR = 0). The age models were reported as calibrated ¹⁴C years BP (Before Present, where present = AD 1950). For the analysis of the organic matter reactivity here, however, the ages were calculated to years before collection (AD 2013) to relate to mineralization age. The procedures and data are described in detail in Petro et al. (2019).

The age-depth model of the South Azores core (DA14-ST1-GC01) was developed from the sediment description and from calcium (Ca) and iron (Fe) measurements using an ITRAX x-ray fluorescence (XRF) core scanner (Croudace et al., 2006). The profile of Ca/Fe, which may here be considered a proxy for marine productivity, was aligned with marine isotope stages and the age of the stages was determined according to LR04 Benthic Stack (Lisiecki and Raymo, 2005).

The age-depth model of the Bering Sea site (IODP Exp323, Hole U1342B) was retrieved from Knudson and Ravelo (2015), who based their age model on calcite δ¹⁸O of benthic foraminifera, which they too correlated to the LR04 Benthic Stack (Lisiecki and Raymo, 2005). The depths were converted into ages using a linear interpolation between the measurements. Below 35 mbsf (meters below seafloor), there was a shift in stratigraphic unit (Unit II), where the age versus depth was not clearly resolved (Expedition 323 Scientists, 2011). Therefore, data below this depth were excluded from our study.

The age-depth model for the Eastern Equatorial Pacific core (ODP Leg 201, Hole 1,226-B) was based on one unique ¹⁴C measurement and six biostratigraphic boundaries from the Pleistocene to the Middle Miocene (Shipboard Scientific Party, 2003; D'Hondt et al., 2004), previously assessed at site 846 of ODP Leg 138 (Shipboard Scientific Party, 1992). The depths were converted into ages using a linear interpolation between the seven age points. Below 388 mbsf, the age model was interpolated linearly, based on a basement age of 16.5 million years at the base of the core.

The reactivity of the sedimentary organic matter was assessed in each sediment sample from the momentary first-order rate constant of its decay (k, in y⁻¹):

where C_{ox rate} is the rate of organic carbon mineralization based on SRR or NH₄⁺ production rates (nmol C cm⁻³ y⁻¹) and TOC is the measured concentration of total organic carbon (nmol C cm⁻³) at the same depth. The relation between k and sediment age was then derived by fitting a non-biased linear model to log–log transformed data and transposing this relation back to linear space according to Flury et al. (2016).

The mean cell-specific carbon oxidation rates were calculated by dividing the volume-specific carbon oxidation rates by the total cell abundance at the same depth. Similarly, the mean cell-specific sulfate reduction rates were assessed by dividing the volume-specific sulfate reduction rates by the number of sulfate-reducing cells. The latter was estimated by multiplying the relative abundance of dsrB genes (in %) by the total cell abundance at each depth.

Complex sedimentary organic matter was represented by the net-formula C₂₇H₂₈O₇ (LaRowe and Amend, 2015a), which has a nominal oxidation state of carbon (NOSC) of −0.52.

Since the standard free energy of organic matter is closely linked to the mean oxidation state of carbon, we can assess ΔG⁰_ox of the half reaction from C₂₇H₂₈O₇ to CO₂ per carbon atom via the relationship presented by LaRowe and Van Cappellen (2011) at 25°C and 1 bar:

We summed ΔG⁰_ox and the standard free energy of the sulfate reduction half-reaction (ΔG⁰_red) calculated from tabulated Gibbs energy of formation for HS⁻, SO₄²⁻ and H⁺ (Kulik and Harff, 1993). The total Gibbs energy of the reaction (ΔG_r) was then calculated from ΔG⁰ and the pore water concentrations of HS⁻, SO₄²⁻, HCO₃⁻ and H⁺:

where R is the gas constant (0.00831 kJ mol ⁻¹ K⁻¹), and T is the temperature (K).

∏ i a i ν i = ( ∏ i a ( p r o d u c t ) ν i ∏ i a ( s u b s t r a t e ) ν i ) is the mass action expression where a_i is the activity of the i^th component of the reaction, and vi is its stoichiometric ratio.

We used activity coefficients: 0.172 for SO₄²⁻, 0.6592 for HS⁻, 0.6843 for HCO₃⁻, retrieved from (Kulik and Harff, 1993) at an ionic strength of 0.647. Organic matter as a solid has an activity of 1 regardless of its concentration. We assumed a pH of 7, which influenced the activity of HCO₃⁻ based on DIC concentration and HS⁻ based on total H₂S concentration. For simplicity, the calculation was done at 25°C (298 K).

Likewise, ΔG_r of acetate (CH₃COO⁻) oxidation to CO₂ with sulfate as electron acceptor was calculated from Eq. 12, using the following stoichiometry:

For acetate, we used the same activity coefficient as HCO₃⁻ and assumed pH = 7. Acetate concentrations in the Greenland cores were available from Glombitza et al. (2015), but such data are rare because acetate is difficult to measure in saline water at the relevant concentrations (Glombitza et al., 2014). But the most complete datasets indicate that the acetate concentrations in cold marine sediments are remarkedly constant due to thermodynamic constraints (Glombitza et al., 2019; Beulig et al., 2022). We therefore use the mean value of the acetate concentration in the Greenlandic cores (5.96 μM ± 1.6) in the calculation of ΔG_r for the Eastern Equatorial Pacific sediments where no measurements were available. To estimate the Gibbs energy liberated by fermentation, we subtracted ΔG_r from oxidation of acetate to CO₂ via sulfate reduction from the total ΔG_r from C₂₇H₂₈O₇ all the way to CO₂.

The data from ODP Leg 201, site 1226, in the Eastern Equatorial Pacific were retrieved from the Janus Web Database.¹ Pore-water NH₄⁺ concentration and porosity were obtained from Hole 1226-B and the porosity measurements were interpolated to the same depth resolution as NH₄⁺. Cell counts from Hole 1226-B were retrieved from Parkes et al. (2005), who used direct counts with acridine orange, fluorescent dye, without cell extraction. TOC data (weight %) were retrieved from Janus web database and recalculated to nmol cm⁻³. Note that most TOC concentrations were measured in hole 1226-E.

Data from IODP expedition 323, site U1342, in the Bering Sea were retrieved from the Janus database and from published studies. The depth-matching between parameters (porosity from Hole C, pore water from Hole B) was done via the corrected composite depth scale (CCSF-A) in meter core composite depth below seafloor. This depth scale was constructed by Expedition 323 Scientists (2011) based on multiple drillings holes, A–D, and was calculated by adding a specific cumulative offset to the CSF-A depth scale of each core. We used ammonium concentration as our reference sample resolution. Porosity was matched to this resolution using linear interpolation between measurements, except for the top and bottom depths, where we used the closest porosity data point. D_s was calculated from porosity based on Eq. 4, as the data quality of the measured formation factors was low. After matching the parameter depths, the CCSF-B scale (mbsf) was used for the modeling, which corrected CCSF-A for the core expansion during drilling by dividing the CCSF-A-depth by 1.06 (Expedition 323 Scientists, 2011). Cell count samples were retrieved from the Hole U1342B, published in Kallmeyer et al. (2012) and derived via cell extraction based on Kallmeyer et al. (2008) and SYBR Green I dye. If the samples were counted multiple times, we used the mean value. TOC data (weight %) were retrieved from the LIMS database and transformed into nmol C cm⁻³.

The Little Belt core (SKA14-05-B25) was co-located with IODP expedition 347 site M0059. Samples from the same site and day were designated SKA05-B25 by Deng et al. (2020), who describes the link between bioturbation and the microbial community. Information on benthic infauna and mineralization pathways can be found in Kristensen et al. (2018). The site was situated in a local depression prone to seasonal anoxia and, at the time of sampling, the bottom water had just barely re-oxygenated. Thus, the sediment was still thoroughly reduced and devoid of fauna (Kristensen et al., 2018). The sedimentation rate was 5 to 7 mm yr⁻¹, based on the preliminary age-model of IODP Expedition 347 site M0059 retrieved from the same site (Andrén et al., 2015); paleoclimatic and paleoenvironmental data from the site are presented by Kotthoff et al. (2017). SKA14-05-B25 provided the youngest sulfate-reducing sediment available (average age ca 10 years), when sampling the upper 3.5 cm with cut-off syringes directly through the sediment–water interface in a box-core.

Greenland Glacier Fjord core SA13-ST8-47G was sampled in the innermost part of Nuup Kangerlua (Godthåbsfjord), close to the marine-terminating glaciers Narsap Sermia and Kangilinnguata Sermia [see Glombitza et al. (2015) and Pelikan et al. (2019) for details on all Greenland cores, including age models and geochemistry]. The glacier at the head of the fjord delivered large amounts of clastic material to the seabed, giving a mean sedimentation rate 2.9 cm yr⁻¹ (95% confidence interval 2.2–4.1 cm yr⁻¹ based on excess ²¹⁰Pb activity) (Pelikan et al., 2019; Supplementary Figure S2), Thus, the 6-m long core provided samples with ages in the range of 0–200 years.

Greenland Main Fjord core (SA13-ST5-30G) was sampled in Nuup Kangerlua in the path of the ice-flow from the glaciers, but more distant from the glacier front, resulting in lower sedimentation rates and higher ages than the Glacier Fjord Core (SA13-ST8-47G). One bivalve shell was found at 39 cmbsf (cm below seafloor) and dated to 265 ± 42 cal yrs BP, a second at 553 cmbsf was dated to 457 ± 26 cal yrs BP. This dating could be ascribed to a dramatic change in sedimentation rate occurring sometime between the upper 39 cm (0.15 cm yr⁻¹) and the rest of the core below (2.68 cm yr⁻¹). A more likely explanation is that the shell found at 39 cmbsf was redeposited from an older deposit. Thus, the sediment accumulation rate was estimated to 1.2 cm yr⁻¹ from linear extrapolation between the sediment surface and the age of the deepest shell (Supplementary Figure S2). According to this, the site provided samples in the age range from 80 to 600 years.

Greenland Side Fjord core (SA13-ST6-40G) was sampled in a side-fjord (Kapisillit Kangerluat) of Nuup Kangerlua; this side fjord is currently not connected to the Greenland ice-cap at its head. Matching of Rumohr cores and Gravity-cores indicated a loss of 10 cm from the top of the gravity-core. The core was dated to 4.6 ka cal. BP at 270 cmbsf, which implied an accumulation rate of 0.6 mm yr⁻¹ (Supplementary Table S1). The surface sediment was heavily bioturbated and burrows were observed down to 43 cmbsf. The sediment was homogeneous in structure down 340 cmbsf, where the material changed from silty-clay to mud with an abundance of small ice-rafted pebbles. Data from below the deepest datable fossil at 270 cmbsf was rejected due to unknown age. The site provided usable sediment in the range from 200 to 4,600 years old (Supplementary Figure S2).

Iceland Basin gravity-core (DA12-11/1-GC01) and a box-core from the same site were collected from 2021 m deep water in the North Atlantic. The age model, the paleo-climate, and the paleo-circulation are described in Van Nieuwenhove et al. (2018), Orme et al. (2018), and Braun et al. (2017). Matching of pore-water profiles between gravity-core and box-core indicated a loss of 14 cm from the top of the gravity-core. The sediment was rich in carbonates and contained four distinct horizons of volcanic ash. Sulfate reduction rates were measured in the upper parts of the core with radiotracer, at sediment ages of 100–380 years. The sulfate reduction rates in the deeper parts of the core were below our level of quantification, but the ammonium profile in the entire core could be modelled (Figure 1E). Discarding the modelled rates of mineralization in the shallowest and deepest intervals left data with good confidence in the age-interval from 4,000 to 8,200 years (Supplementary Figure S2).

Greenland Continental Shelf core (SA13-ST3-20G) and a Rumohr Lot core (SA13-ST3-17R) were both retrieved at the same site on the West Greenlandic Shelf in the Labrador Sea. Matching of the two cores indicated that the upper 18 cm was lost from the top of the gravity-core. The sediment accumulation rate was on average 0.48 mm yr⁻¹, with a higher sedimentation rate during the recent 2,000 years (0.86 mm yr⁻¹, 0–163.5 cmbsf, Supplementary Figure S2). From 253 to 568 cmbsf the core was weakly laminated, changing to millimeter-thick laminations (silty-sand) from 568 cmbsf to the bottom of the core, indicative of permanent ice cover during the Weichelian ice age (see Allan et al., 2021, for age model, stratigraphic and paleoenvironmental details). The core provided sulfate reduction rates at sediment ages ranging from 300 to 10,000 years and useful modeled rates based on pore water profiles of ammonium in the overlapping age range from 1,000 to 8,000 years old (Supplementary Figure S2; Figure 2).

Faroe Bank core (DA12-11-ST2-GC03) and a box-core were collected from 742 m deep water SW of the Faroe Islands. The sediments were carbonaceous with more than 14 cm of accumulated foraminiferal tests at the surface. Matching of Rumohr and gravity-cores indicated a loss of 18 cm from the top of the gravity-core. The sediment was too old for reliable determination of sulfate reduction rates with radiotracer but provided useful rates of carbon mineralization modeled from ammonium profiles in an age range from 22,000 to 35,000 years (Supplementary Figure S2, age model published in Braun et al., 2017).

South Azores core (DA14-ST1-GC01) was collected from 2,500 m deep water between the Azores Archipelago and the East Azores Fracture zone. The sediment consisted of calcareous deep-sea ooze covering the past 300,000 years. No attempts were made to measure reduction of ³⁵S tracer as the younger layers of sediment, where tracer-incubations could have been feasible, were assumed not to be sulfate reducing. The model could not resolve more than one reaction zone from the ammonium profile. The calculated rate of mineralization was, therefore, only associated with the central third of the core where the age ranged from 100,000 to 200,0000 years (Supplementary Figures S2, S3).

Bering Sea IODP Leg 323 Bower Ridge Site U1342 was drilled in the southern Bering Sea under the Integrated Ocean Drilling Program (IODP). The data were retrieved from IODP LIMS Online Report http://web.iodp.tamu.edu/LORE/. The temperature at the seafloor was 1.9°C and increased by 0.0977°C m⁻¹ down-core (Takahashi et al., 2011). The core covered the past 1,000,000 years, and mineralization of organic matter could be modelled with good confidence in the age-range from 400.000 to 700.000 years (Supplementary Figure S2).

Eastern Equatorial Pacific IODP Leg 201 Site 1,226 was drilled 300 km south of the Galapagos Islands. The temperature at the seafloor was 1.74°C and increased by 0.0572°C m⁻¹ down-core (Shipboard Scientific Party, 2003; Wang et al., 2008). The core penetrated the 417 m thick sediment column all the way to the basaltic basement and covered the past 15,600,000 years. The core had an unusual geochemical profile due to diffusion of oxygen, nitrate, and sulfate from the basaltic basement (Jørgensen et al., 2006). Therefore, the core lacked a methanic zone and instead had a very deep penetration of sulfate. This unique core provided rates of carbon mineralization modelled from ammonium production in the sulfatic sediment in an age interval of 2–3.75 million years, after discarding data from the upper and lower reaction zones from PROFILE (Supplementary Figure S2).

The content of organic carbon differed between sites but did not decrease systematically with increasing sediment age in the individual cores (Figure 3). The lowest carbon content was found near the glaciers in the Greenlandic fjord (site DA13-ST8-47G), where the organic matter was diluted by a large influx of glacially-derived clastic material, and in old deep-water deposits (ODP Leg 201/1226-B from the Eastern Equatorial Pacific). A continuous loss of organic material over time was partly balanced by compaction, when expressed in the volume-specific unit applied here, and the trajectory down-core was mostly determined by the depositional history. This is for example seen in the core from the Greenlandic continental shelf (SA13-ST3-20G), where the content of organic matter decreased abruptly in the early Holocene 6,000–10,000 years ago, when ocean circulation and climate changed dramatically after the Last Glaciation (the Weichselian; Figure 3). The total variation in organic matter content in the entire dataset was mostly between 2 × 10⁵ and 2 × 10⁶ nmol C cm⁻³.

In sharp contrast to the low variability of organic carbon concentrations, the volume-specific carbon oxidation rates spanned 8 orders of magnitude from 7 × 10² to 8 × 10⁻⁶ nmol C cm⁻³ day⁻¹ (Figures 1A–I, 4A). The highest rates of mineralization of organic matter were found in the youngest sediments using ³⁵S-radiotracer measurements. Conversely, the lowest rates of mineralization were determined in the oldest sediments using modeling of ammonium profiles. Fortunately, the geochemical settings on the Greenlandic shelf (SA13-ST3-20G) allowed both methods to be used on the same age interval (Figure 2). As expected, the modeled rates of ammonium production could not resolve the steep decrease in sulfate reduction in the upper meters, and the average rates given by the model systematically underestimated the measured rate of carbon mineralization in the top of the sediment and overestimated the rate in the lower half of the upper reaction zone. Deeper in the core, where the sulfate reduction rate changed more gradually, the two methods dropped in parallel, although with up to one order of magnitude discrepancy.

The reactivity of the organic matter, quantified as the momentary first order rate constant (k), decreased systematically with increasing age. There was no offset in the trend between data derived from incubations with radiotracer and data derived from modeling of ammonium profiles (Figure 4C). The best power-law fit to the relationship between k and sediment age was:

The exponent of −1.11 in the power function signified that the reactivity of organic carbon decreased by 1.11 order of magnitude each time the age increased by one order of magnitude. The exponent in the fit to the rate constant vs. depth (−1.11, Figure 5) was less negative than exponent in the fit to the sulfate reduction rate vs. depth (−1.23, Figure 4A). The faster drop in the rate of sulfate reduction compared to the rate constant was caused by a relatively fast initial drop in carbon concentration, and because loss of pore-space at depth concentrated the remaining volumetric carbon content.

The total cell abundance decreased with increasing sediment age, but only by three orders of magnitude, from 3.9 × 10⁹ to 1.9 × 10⁶ cells cm⁻³ (Figures 1A–I, 4B). The corresponding exponent of the fitted power function was −0.63. As the cell counts decreased relatively less than the volume-specific organic carbon oxidation rates (Figure 4A Figure 4B), the mean cell-specific carbon oxidation rate decreased continuously with sediment depth and age over ~5 orders of magnitude from 1.8 × 10⁻¹ to 1.4 × 10⁻⁶ fmol C cell⁻¹ day⁻¹, with no indication that the decrease was tapering off in the oldest sediment (Figure 4D).

The relative proportion of dsrB vs. 16S rRNA gene copies, and thus the proportion of potentially sulfate-reducing microorganisms within the total microbial community, was up to 40% in the youngest sediments but decreased rapidly with increasing sediment age (Figure 5). In sediments older than 10,000–100,000 years, the abundance of dsrB gene copies fell below the limit of quantification (10⁴ cm⁻³). The decreasing proportion of sulfate-reducing microorganisms did not follow a common function with increasing age, but if the individual cores were treated separately, then the decrease followed power functions with exponents of −0.77 to −0.86 (Figure 5). We disregard the calculated exponent from the Iceland Basin here because the surface of this deep-sea core was most likely iron-reducing rather than sulfate reducing, and because the high calculated percentages of sulfate-reducing cells deep in the sediment were interspersed with samples below the level of quantification which skewed the fit.

The cell numbers decreased with an exponent of −0.63 and the proportion of sulfate-reducing cells decreased with an exponent of −0.82. Combined, this caused the number of sulfate-reducing cells to decrease with an exponent of −1.45, which is closely matched by the rate at which the mineralization of organic carbon decreased (exponent of −1.36). Thus, the combined effect of decreasing cell numbers and decreasing proportion of sulfate-reducing cells caused the quantified abundance of sulfate-reducing cells to decrease as steeply as the rate of carbon mineralization over sediment ages from 10¹ and at least to 10⁴ years old. Accordingly, the sulfate reduction rates per sulfate-reducing cell remained surprisingly constant in the order of 10⁻² fmol sulfate cell⁻¹ day⁻¹, although the overall cell-specific community metabolism decreased by 4 orders of magnitude. We could not resolve how the sulfate reduction rate per sulfate-reducing cell developed in even older sediments ranging from 10⁴ up to 10⁷ years because our methods were not sensitive enough to quantify the number of dsrB gene copies.

The careful selection of sites and methods allowed us to determine the rate of mineralization of organic matter in sulfatic sediments (Canfield and Thamdrup, 2009; Jørgensen, 2021) with ages from 10 years to 3,750,000 years. The data extended the power law of organic matter decay constants, first presented by Middelburg (1989), to even older sediments and overcame the original need for a site-specific “initial age,” possibly because our data were more uniform with respect to temperature and geochemical zone. In contrast to previous data syntheses [e.g., Middelburg (1989) and Katsev and Crowe (2015)], our approach did not rely on a measurable decrease in the concentration of organic matter with increasing depth and age of the sediment. In fact, we found little correlation between depth in the sediment column and the concentration of organic matter (Figure 3). Our correlation predicted a slightly faster loss of reactivity with k = 0.180 × sediment age^-1.11 (Eq. 13), compared to models based on, or verified from, vertical profiles of organic carbon, which have exponents ranging from −0.8 to −1 (Shang, 2023). Power-law models with exponents close to −1 demonstrate that the overwhelming factor responsible for decreasing rates of microbial catabolism in ageing sediments is not so much the loss of organic carbon, but rather the loss of organic carbon reactivity (Figures 3, 4D). Conceptually, this corresponds well with the increasing molecular complexity of degrading organic matter (e.g., Estes et al., 2019; Hach et al., 2020), but poorly with models that assume concurrent degradation of multiple pools of organic matter with individual degradability (Jørgensen, 1978b; Shang, 2023). Note, however, that the two types of models provide equally good fits to empirical data (Arndt et al., 2013).

Cell numbers decreased as a function of sediment depth and age, as seen in several previous studies (Whitman et al., 1998; Kallmeyer et al., 2012). The decrease in total cell abundance with increasing age of the sediment was much slower than the decrease in carbon oxidation rates (Figure 4A vs. Figure 4B), which implied a large drop in the mean cell-specific rates of catabolism (Figure 4D). The degradation of organic matter in sulfatic marine sediments is, however, divided between two major guilds of cells, one guild that hydrolyses and ferments complex organic matter to volatile fatty acids and hydrogen, and a second guild that oxidizes these fermentation products to CO₂ and water while reducing sulfate to sulfide. The rate-limiting step in mineralization of complex organic matter is the initial hydrolysis (Beulig et al., 2018) and the fermenters will take up the resulting monomers so efficiently that their concentrations are mostly too low to even detect. The community that oxidizes the fermentation products via anaerobic respiration is equally efficient, and fermentation products do not normally accumulate above a few μM (Postma and Jakobsen, 1996; Wang et al., 2010; Glombitza et al., 2015). The metabolic guild that has the most energetic respiratory metabolism will deplete the fermentation products to such low concentrations that energy conservation via proton translocation across the cell membrane is only barely possible. This excludes energy conservation from respiration with less energetic electron acceptors and causes the characteristic geochemical redox-zonation with limited overlap between utilization of different external electron acceptors (Postma and Jakobsen, 1996). We can, therefore, assume a tight link between fermentation and sulfate reduction regardless of which specific fermentation processes that were active: The fermenters oxidize some organic carbon to CO₂, while concurrently producing more reduced carbon or H₂ in the process. When these electron-rich substrates are then used by the sulfate reducers, it balances the stoichiometric ratio between sulfate consumption and total CO₂ production to the same value as if the sulfate reducer had mineralized the original organic matter with no fermentation involved (Eq. 2). This way, the electrons from complex organic matter must pass through both fermentation and sulfate reduction for the carbon to be funneled fully to CO₂, and the rate of sulfate reduction is a measure of the flow of carbon and electrons through both processes. Even syntrophic interactions with direct electron transfer do not change the overall stoichiometry between mineralized organic carbon/CO₂ and sulfate.

The fermentation product acetate is instrumental in the transfer of reducing equivalents from fermentation to sulfate reduction, and oxidation of acetate accounts for 30–65% of the sulfate reduction rate in sulfatic sediments (Christensen and Blackburn, 1982; Finke et al., 2007; Beulig et al., 2018). We specifically selected sediments for the study where all other electron accepters than sulfate and CO₂ had already been depleted. Under these conditions, sulfate reduction is the primary terminal electron accepting process, and all known prokaryotes that respire via sulfate use the dsrB gene. The gene is also used in sulfide oxidation, but the sediment strata that we analyzed did not contain suitable electron accepters for this process. We therefore assumed that all cells that contained the dsrB gene were potential sulfate reducers, and as they were found in sulfate-reducing sediment, we assumed that all potential sulfate reducers were active. This allowed us to calculate the per-cell sulfate reduction rate. We found elevated rates of per-cell sulfate reduction in upper centimeters of sediment with active bioturbation. But when both the decreasing cell numbers and the decreasing proportion of sulfate reducers were considered, the cell-specific carbon oxidation rate by sulfate-reducing microorganisms in the subsurface stayed remarkably constant on the order of 10⁻² fmol C cell⁻¹ day⁻¹, despite increasing depth and a drop in sulfate reduction rates of four orders of magnitude (Figure 5).

Previous studies have shown relatively high cell-specific rates of sulfate reduction in the very surface of coastal sediments, gradually decreasing to an organic carbon oxidation rate of 10⁻³ to 10⁻² fmol C cell⁻¹ day⁻¹ between 30 and 100 cm below seafloor (Hoehler and Jørgensen, 2013; Petro et al., 2019). Interpretation of the data deeper in the sediment from these coastal sites is difficult because of the transition from the sulfatic zone and into the methanic zone, and because the early qPCR protocols and primers used (Leloup et al., 2007, 2009) lacked the necessary resolution. In an attempt to predict the cell specific rates of sulfate reduction deeper in the sediment, Lever et al. (2015) extended the estimate of Hoehler and Jørgensen (2013) into deeply buried sediments of the Peru Margin by assuming that sulfate reducers constituted 10% of the total microbial community regardless of sediment depth and age. This assumption resulted in calculation of constantly decreasing per-cell rates of sulfate reduction in deeper sediment, but later studies have not confirmed the proportion of sulfate reducers to be constant (Webster et al., 2006; Petro et al., 2019). Thus, the constant cell specific sulfate reduction rates across depth and age up to 20,000 years seen in our study do not contradict the more recent studies and might imply that the size of the sulfate-reducing community is indeed controlled by a fixed minimum energy requirement of these microorganisms, as hypothesized by Hoehler and Jørgensen, (2013). Further, this minimum metabolic rate of sulfate reducers in deeply buried marine sediments might not be far from that seen below the depth of bioturbation in sediment that is buried only 30 cm deep and is only 300 years old (Petro et al., 2019).

Our attempt to detect sulfate-reducing prokaryotes in sediments older than 26,000 years was not successful as the dsrB gene copy numbers fell below our limit of quantification of ~10⁴ gene copies cm⁻³. Thus, it awaits more sensitive experimental methods to see if the proportion of sulfate reducers continue to drop with increasing sediment age beyond 26,000 years, which is necessary for the cell specific sulfate reduction rates to stay at the constant level of 10⁻² fmol C cell⁻¹ day⁻¹ that we observed down to this depth. There are, however, indications that this could indeed be the case: Studies have revealed (a) low abundance of functional genes related to sulfate reduction (dsrAB genes) or methanogenesis (methyl-coenzyme M reductase, mcr genes) in deep sediments (<1% of total community, Schippers and Neretin, 2006; Lever, 2013), (b) fermentation-related genes that were much more abundant than dsr or mcr genes in metagenomes (Kirchman et al., 2014; Gaboyer et al., 2015), and (c) apparent virtual absence of genes related to sulfate reduction in metagenomes from deep sulfatic sediments of the Bering Sea (Biddle et al., 2008). The apparent difficulty in detection and quantification of dsr genes in the diverse pool of DNA extracted form sediment from deep below the sea floor on the Peru Margin indicate that terminal-oxidizing prokaryotes are present at low abundance (Webster et al., 2006), while the consistent detection of mRNA transcript of dsr (Orsi et al., 2013, 2016) indicate that sulfate reduction play a larger role in community activity than the low proportion of sulfate-reducing prokaryotes suggests.

To assess the division of Gibbs free energy (ΔG_r) between fermenters and sulfate reducers, we calculated the Gibbs free energy (ΔG_r) by complete oxidation of organic matter to CO₂ via Eqs 11, 12 according to LaRowe and Van Cappellen (2011). We also calculated ΔG_r for oxidation of acetate to CO₂ with sulfate as electron acceptor based on measured concentrations of reactants and products (Eqs 12, 13). By subtracting the energy yield of this terminal oxidation from the total energy yield, we could estimate the energy yield of fermentation under in situ conditions without needing to know the molecular identity or the concentrations of fermentation substrates (i.e., the products of hydrolysis). This is a rather crude approximation, as fermentation processes produce other products than acetate, and sulfate reducers oxidize H₂ and other volatile fatty acids, such as formate or propionate, in addition to acetate (Glombitza et al., 2015). Moreover, this calculation overestimates the energy available for the fermenters, as the free energy from extracellular hydrolysis cannot be coupled to energy conservation (i.e., to ATP). Note also that our operational definition of “fermenters” includes all organisms involved in production of acetate regardless of the actual biochemical pathway. Thus, the purpose was not to calculate the accurate ΔG_r of the processes or to compare energy yields close to thermodynamic thresholds. But to test if the overwhelming dominance of fermenting cells could be explained by an inequal sharing of energy between fermentation and sulfate reduction. Thus, we calculated the division of energy between fermentation and sulfate reduction on the four Greenland cores and in the oldest core from the Eastern Equatorial Pacific, where we had the most complete data on pore water chemistry that is needed.

In the core from the Greenland Continental Shelf (SA13-ST3-20G), the ΔG_r liberated by fermentation 1 m below seafloor was −43 kJ (mol C)⁻¹, while the ΔG_r liberated by acetate oxidation was −24 kJ (mol C)⁻¹. At 5.9 meters below seafloor, the values changed only slightly to −42 kJ (mol C)⁻¹ and − 18 kJ (mol C)⁻¹, respectively. The remaining Greenlandic cores (SA13-ST5-30G, SA13-ST6-40G, SA13-ST8-47G) were in the same range, with even less variation down-core. In the core from the Eastern Equatorial Pacific (ODP Leg 201, Hole 1,226-B), the fermenters and the terminal oxidizers shared the energy in a similar manner with −42 to −43 kJ (mol C)⁻¹ for the fermenters and − 35 to −26 kJ (mol C)⁻¹ for the sulfate reducers. Similar values of −42.9 ± 2.7 kJ mol acetate⁻¹ have previously been reported for sulfate reduction coupled to acetate oxidation for most of the sediment column at ODP Site 1226 (Wang et al., 2010), and − 32 kJ mol C⁻¹ for global marine sediments in general (Bradley et al., 2020).

The assumptions and approximations in the thermodynamic calculations above were coarse. Most notably the assumed temperature of 25°C, while the effects of the pressure between one bar and in situ were negligible (Helgeson, 1969). But effects of pressure and temperature on thermodynamic calculations are much less severe than the effects on kinetics (Jannasch, 1997), and even the temperature effect does not influence the conclusions drawn here: The standard Gibbs energy of sulfate reduction per mole acetate, for example, only change from −48.1 to −44.5 kJ (mol acetate)⁻¹ between reference temperature and pressure (25°C, 1 bar) and in situ conditions (2°C, 50 bar) at the Greenlandic sites. Thus, the coarse calculations still allow us to conclude that ΔG_r from mineralization of organic carbon to CO₂ was shared between the guilds of fermenters and terminal oxidizers in a ratio of roughly 1:1 regardless of site and sediment age. Since the fermentation products do not accumulate in the sediment, there must be a balance between fermentation and sulfate reduction, whereby rates of fermentation limit and control the rates of sulfate reduction (Jørgensen, 2021). Thus, the carbon flow through fermentation must be similar to the carbon flow through sulfate reduction. As non-sulfate-reducing bacteria outnumbered the sulfate reducers by >100-fold, the energy dissipation (i.e., power) available to the individual fermenters was much lower than the power available to the individual sulfate reducers.

Volume-specific power of reactions in the sediment (Watt cm⁻³ or Joule s⁻¹ cm⁻³) was calculated by multiplying ΔG_r of the reaction (J mol⁻¹\C) by the rates of reaction (mol C cm⁻³ s⁻¹). The mean cell-specific sulfate reduction rates in the Greenland cores were in the order of 10⁻² fmol C cell⁻¹ day⁻¹, which was not far outside the range from 10⁻¹ to 10¹ fmol C cell⁻¹ day⁻¹ seen in cultures of mesophilic and psychrophilic sulfate-reducing bacteria (Canfield et al., 2000). The 10⁻² fmol C cell⁻¹ day⁻¹ translates to a power dissipation of 10⁻¹⁷ W cell⁻¹ if we assume an energetic yield of −42 kJ (mol C)⁻¹ (see above and note that J/s equals W). This rate of energy dissipation is similar to the value calculated for coastal surface sediments by Lever et al. (2015), and similar to the per-cell power dissipation in slow-growing axenic cultures of Desulfotomaculum putei (Davidson et al., 2009). It is also similar to the power dissipation of extremely low-light adapted green sulfur bacteria in the Black Sea (1.9 × 10⁻¹⁷ W cell⁻¹; Marschall et al., 2010). Conversely, the values are far above the per-cell power dissipation calculated for deeply buried sulfate reducers on the Peru Margin by Lever et al. (2015), even though our estimation of the carbon oxidation rates in the same deep Pacific sediment based on NH₄⁺ agrees well with calculations based on sulfate (Wang et al., 2008). The difference between our relatively high and invariant estimate of power dissipation by deeply buried sulfate reducers, and the low and age-dependent power dissipation reported by Lever et al. (2015) is that these authors assumed a constant 10% proportion of sulfate-reducing microorganisms (see above). The fact that the power dissipation we calculated per sulfate-reducing cell did not continue to drop with depth and age in the sediment, is because the estimated number of sulfate reducers decreased in near perfect balance with the decrease in sulfate reduction rates. This could indicate that 10⁻¹⁷ W cell⁻¹ approaches a minimum power requirement of sulfate reducers in deeply buried sediments. As the same range of power dissipation can be observed only 30 cm below the sediment–water interface in eutrophic coastal sediments and in axenic cultures, this suggests that the sulfate reducers in the deep biosphere do not necessarily have any unique physiological adaptations to low energy availability.

The cell-specific power dissipation of extremely old oxic sediments has been calculated to 5 × 10⁻¹⁸ W cell⁻¹ in the North Pacific Gyre, and within the range from 3.5 × 10⁻¹⁸ down to 4.9 × 10⁻²⁰ in the South Pacific Gyre (LaRowe and Amend, 2015a). These calculations assume an energetic yield of −443 kJ (mol C)⁻¹ for aerobic oxidation of organic matter all the way to CO₂ in a single step (Lever et al., 2015). The low values from the SPG were calculated based on an assumed constant rate of carbon burial across the 75 million years and is, most likely, less accurate than the data from the North Pacific Gyre (NPG) that was based directly on modelled oxygen consumption rates (Røy et al., 2012). Thus, the apparent maintenance power of aerobic and anaerobic respiration come within one order of magnitude of each other. And in contrast to the per cell power dissipation of the “fermenters” (or the total carbon oxidation per total cells), both aerobic and anaerobic respiration appears to converge at fixed rates of per cell power dissipation rather than dropping continuously with increasing sediment age. The difference in the two levels is not understood, as the higher energetic cost of biomolecule synthesis aerobes (McCollom and Amend, 2005) would suggest that the minimum maintenance power of aerobes should be larger than that of anaerobes.

It is possible to estimate the power dissipation by the guild of fermenters in the deep sulfatic sediments older than 26,000 years that we studied, even though the proportion of fermenters vs. terminal oxidizers was not known. This is because the number of fermenters is essentially equal to the total cell numbers, only offset by 1% sulfate reducers or less. In contrast to the situation for sulfate reducers, the per cell power dissipation for the fermenters did not reach a plateau that could indicate a minimum power requirement of fermenting cells, although such a limit must exist. The lowest values reached in our dataset was 7 × 10⁻²² W cell⁻¹. This rate of power dissipation is so low that the cells would just barely cover the lowest estimate of the repair cost associated with spontaneous racemization of aspartic acid (Lever et al., 2015). But there are no indications in the data that 10⁻⁶ fmol C cell⁻¹ d⁻¹, corresponding to 10⁻²² W cell⁻¹ is the lower limit, it is simply where our dataset ends. In principle, the correlation could extend further back in time. But extrapolation of log–log plots back in time from 4 million years would rapidly reach the age of Planet Earth.

In conclusion, we found that the population size of sulfate-reducing microorganisms was in balance with the rate of sulfate reduction in sub-surface sediments. The minimum per-cell sulfate reduction rate, and thus the minimum per cell power dissipation, in 10,000 to 100,000 years old sediment was not radically different from the much shallower sub-surface. Thus, we do not expect sulfate reducers in the deep subsurface to have a fundamentally different maintenance metabolism compared to organisms thriving less than 1 m below the seafloor in coastal seas (Starnawski et al., 2017). We did not see a lower threshold for metabolic activity of cells not involved in terminal oxidation, although there was a clear log–log correlation between the total number of cells and the rate of carbon mineralization. It is unknown which physiological properties make the fermenters able to apparently subside with a minute fraction of the power needed for sulfate reducers. The large number of cells relative to the extremely low rates of mineralization in the deep biosphere therefore remain enigmatic.