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Overview of the GutCP algorithm
Our approach uses the idea that we can leverage cross-feeding interactions—which comprise knowing the metabolites that each microbial species is capable of consuming and producing—to mechanistically connect the levels of microbes and metabolites in the human gut. Several different mechanistic models in past studies have shown that this is indeed possible18,20,29,36,37. While GutCP is generalizable and can be used with any of these models, in this paper, we use a previously published consumer-resource model20. We use this model because of its context and performance: it is built specifically for the human gut and is best able to explain the experimentally measured species composition of the gut microbiome with its resulting metabolic environment, or fecal metabolome (compared with other state-of-the-art methods, such as ref. 29). To predict the metabolome from the microbiome, it relies on a manually curated set of known cross-feeding interactions9. It then uses these known interactions to follow the stepwise flow of metabolites through the gut. At each step (ecologically, at each trophic level), the metabolites available to the gut are utilized by microbial species that are capable of consuming them, and a fraction of these metabolites are secreted as metabolic byproducts. These byproducts are then available for consumption by another set of species in the next trophic level. After several such steps, the metabolites that are left unconsumed constitute the fecal metabolome.
We hypothesized that adding new, yet-undiscovered cross-feeding interactions would improve our ability to predict the levels of metabolites with our mechanistic and causal model. Specifically, we predict that the set of undiscovered interactions resulting in the most accurate and optimal improvement in predictions would be the most likely candidates for true cross-feeding interactions. Inferring such an optimal set of new cross-feeding interactions or reactions is the main logic driving GutCP. In what follows, we sometimes refer to cross-feeding reactions (i.e., metabolite consumption or production by microbes) as “links” in an overall cross-feeding network of the gut microbiome, whose nodes are microbes and metabolites (Fig. 1a; metabolites in blue, microbes in orange); the links themselves are directed edges connecting the nodes. Links can be of two types: consumption or nutrient uptake reactions (from nutrients to microbes) and production or nutrient secretion reactions (from microbes to their metabolic byproducts).
Fig. 1: Overview of the GutCP algorithm.

a Schematic of the original set of known cross-feeding interactions (top) and bar plot of the prediction error for each metabolite and microbe (bottom). The cross-feeding interactions are represented as a network, whose nodes are either metabolites (cyan circles) or microbial species (orange ellipses), and directed links represent the abilities of different species to consume (red arrows) and produce (blue arrows) individual metabolites. b GutCP adds a new consumption link (red) and production link (blue) as added links reduce the prediction errors for metabolites and microbes.

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The salient aspects of our method are outlined in Fig. 1. We start with the known set of consumption and production links that were originally used by the model; these links are known from direct experiments and represent a ground-truth dataset or original cross-feeding network9. These are shown in Fig. 1a through the pink and blue arrows connecting nutrients 1 through 6 with microbes (a) through (c). For each sample, using only the species abundance from the microbiome, we use the model to quantitatively estimate the microbiome’s species and metabolomic composition. Briefly, we assume that a defined set of polysaccharides, common to human diets, are available as the nutrient intake to the gut (nutrients 1 and 4 in Fig. 1a). We calculate the microbiome and metabolome profiles separately for each individual, which contain a different set of microbial species in their guts. At the first trophic level, all microbial species that are capable of using the polysaccharides (indicated by the pink arrows in Fig. 1a) consume each of them in proportion to their abundances (microbes a, b, and c in Fig. 1a). They subsequently secrete a fixed fraction of the consumed nutrients as metabolic byproducts; every species at this trophic level secretes all the metabolic byproducts it is known to secrete (blue arrows in Fig. 1a) in equal proportion (nutrients 2–6 in Fig. 1a). At the next trophic level, all species detected in the individual’s gut which can consume the newly secreted byproducts consume them as nutrients, secreting a new set of byproducts, and this continues for four trophic levels (not shown in Fig. 1a for simplicity). At the end of this process, all metabolites which remain unconsumed by the community comprise the metabolome of the individual and the microbial species which consume nutrients and grow comprise the microbiome of the individual (for a complete description, see “Methods” and previous work20).
For each metabolite and microbial species, there can be two kinds of prediction errors, or biases: individual (the sample-specific difference between predicted and measured levels) and systematic (average difference across all samples). We focused on the “systematic bias” for each metabolite and microbial species: the average deviation of the predicted levels from the measured levels across all samples in our dataset (Fig. 1a, bottom). The systematic bias for each metabolite and microbe tells us whether our model generally tends to predict their level to be greater than observed (overpredicted), less than observed (underpredicted), or neither (well-predicted). We assume that metabolites and microbes with a large systematic bias are most likely to harbor missing consumption or production links that are relevant across many samples. We prioritize adding links to them in proportion to their systematic biases.
After measuring the systematic bias for each metabolite and microbe, GutCP proceeds in discrete steps (Fig. 1a, b). At each step, we attempt to add a new link to the current cross-feeding network. This new link is chosen randomly from the entire set of combinatorially possible links (see “Methods”; for S species, M metabolites, and two kinds of links (consumption and production), there are a total of 2SM combinatorially possible links). We accept this link—keeping it in the current network—if it leads to an overall improvement in the agreement between the predicted and measured levels of microbes and metabolites. We repeat the process of adding new links—accepting or rejecting them—until the improvements in the levels of metabolites and microbes became insignificant. Overall, GutCP can add several links to improve the agreement between the predicted and measured levels of microbes and metabolites (in Fig. 1a, b, bottom, adding the extra red and blue link at the top results in improved predictions for metabolite (1), metabolite (3), and microbe (b). Figure 2a shows how the cross-feeding network improves over a typical GutCP run via the red trajectory, starting from the original network (Fig. 2a, top left) to the final network state (Fig. 2a, bottom right). Trajectories from 100 other runs are shown in gray. GutCP repeatably reduces both the error of the metabolome predictions (y axis; measured as ({text{log}}_{10}(frac{,text{pred}-text{meas}}{text{measurement},}))) and improves the correlation between the predicted and measured metabolomes (x axis).
Fig. 2: Improvement in predictions using GutCP.

a Improvement in log error (({text{log}}_{10}(frac{,text{pred}-text{meas}}{text{measurement},}))) and the correlation between the prediction and measured fecal metabolome during 100 typical runs of the GutCP algorithm. The gray point at the top left indicates the performance of the original cross-feeding network of Ref. 9, and the black points at the bottom right, that of improved networks predicted using GutCP. A trajectory example, highlighting how performance improves over a GutCP run, is shown in red, and others are shown in gray. b Rarefaction curve showing the number of unique cross-feeding interactions discovered by GutCP over 100 runs of the algorithm. c Prevalence of links, i.e., the number of GutCP runs in which they repeatedly appeared (red dots; total 100 runs) and for comparison, a corresponding binomial distribution with the same mean (black dotted line). P values for different prevalences are estimated using the one-sided binomial test.

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Cross-validating the newly predicted interactions
To test if the cross-feeding interactions predicted by GutCP are generalizable to unknown datasets, we performed fourfold cross-validation. We used a sample -omics dataset of the gut microbiome and metabolome sampled from 41 human individuals, comprising 221 metabolites and 72 microbial species (data from ref. 38). We split our -omics dataset into two subsets: training (three-fourths of the individuals) and test (one-fourth of the individuals) subsets. We then ran GutCP on the training subset to discover new interactions and added them to the ground-truth interactions taken from ref. 9. Doing so resulted in a network of cross-feeding interactions learned only from the training subset of the data. Finally, we evaluated the improvement in accuracy of metabolome predictions resulting from the trained network on the unseen, test subset of the data. We repeated this process three times, each time splitting the full dataset into a training subset (with a randomly chosen three-fourths of the individuals) and test subset (with the remaining one-fourth of the individuals); finally, we calculated the average improvement in prediction accuracy over all four splits.
We found that both the training and test set performances after using the links predicted by GutCP were significantly better than the baseline given by the original cross-feeding network (Table 1). Specifically, both measures of model performance, namely the logarithmic error and the average correlation, improved by 64% and 20%, respectively, after adding GutCP’s discovered interactions. In addition, the test set performance was comparable to the training set performance (6% difference; Table 1). This suggests that the cross-feeding interactions inferred by GutCP are not likely to be a result of over-fitting.
Table 1 Cross-validating the newly predicted interactions.
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Building a consensus-based atlas of predicted cross-feeding interactions
Having confirmed that GutCP is unlikely to over-fit data, we pooled the entire sample dataset of 41 individuals and ran 100 independent instances of our prediction algorithm on it; we verified that incorporating more instances did not qualitatively affect our results (Fig. 2b shows a rarefaction curve, which highlights the number of new links discovered by GutCP as we perform more runs the algorithm). Each run of the algorithm resulted in an average of 140 newly predicted cross-feeding interactions. Then, based on consensus from many runs, we assigned a confidence level to each predicted interaction, namely what fraction of GutCP runs it was discovered in. By calculating a null distribution (Fig. 2c, black), which predicts the fraction of GutCP runs where a random link would be discovered by chance, we assigned a P value to each link and set a threshold at P = 10−3 (Fig. 3c, red; see “Methods” for details). Doing so finally resulted in a complete consensus-based atlas of 293 predicted cross-feeding interactions, which we have provided as a resource for experimental verification in Supplementary Table 1. Figure 3a shows a condensed version of these interactions obtained from the simulation with the best performance (the trajectory example in Fig. 2a with the lowest log error and highest correlation coefficient) in the form of a matrix; specifically, newly added interactions are in dark colors, and old interactions in faded colors. Supplementary Fig. 3 shows a complete version of this matrix. Note that some of the predicted interactions in Fig. 3a are unrealistic, e.g., the production of certain sugars like D-Fructose and D-Sorbitol. Such interactions are unlikely to be predicted in repeated simulations, and thus will not be part of the final consensus set. This illustrates the power of pooling results from several simulations to arrive at a set of highly probable predictions.
Fig. 3: New cross-feeding interactions predicted by GutCP.

a Concise matrix representation of the improved cross-feeding network of the gut microbiome predicted by GutCP (the trajectory example in Fig. 2a with the best performance). The rows are metabolites, and columns, microbial species. Faded cells represent the original, known set of cross-feeding interactions, both production (light blue), consumption (light red), and bidirectional links (gray). The new cross-feeding interactions predicted by GutCP are shown in dark colors: production links in dark blue, consumption links in dark red, and bidirectional links in black. b Network of 293 new links predicted by GutCP (with a P value  More

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Radiation experiments
We experimentally quantified radiolytic hydrogen (H2) production in (i) pure water, (ii) seawater, and (iii) seawater-saturated sediment. We irradiated these materials with α- or γ-radiation for fixed time intervals and then determined the concentrations of H2 produced. Sediment samples were slurried with natural seawater to achieve a slurry porosity (φ) of ~0.83, which is the average porosity of abyssal clay in the South Pacific Gyre34. The seawater source is described below. To avoid microbiological uptake of radiolytic H2 during the course of the experiment, seawater and marine sediment slurries were pre-treated with HgCl2 (0.05% solution) or NaN3 (0.1% wt/vol). To ensure that addition of these chemicals did not impact radiolytic H2 yields, irradiation experiments with pure water plus HgCl2 or NaN3 were also conducted. HgCl2 or NaN3 addition had no statistically significant impact on H2 yields5,6,10.
Experimental samples were irradiated in 250 mL borosilicate vials. A solid-angle 137Cs source (beam energy of 0.67 MeV) was used for the γ-irradiation experiments at the Rhode Island Nuclear Science Center (RINSC). The calculated dose rate for sediment slurries was 2.19E−02 Gy h−1 accounting for the (i) source activity, (ii) distance between the source and the samples, (iii) sample vial geometry, and (iv) attenuation coefficient of γ-radiation through air, borosilicate, and sediment slurry. 210Po (5.3 MeV decay−1)-plated silver strips with total activities of 250 μCi were used for the α-irradiation experiments. For α-irradiation of each sediment slurry, a 210Po-plated strip was placed inside the borosilicate vial and immersed in the slurry. Calculated total absorbed doses were 4 Gy and 3 kGy for γ-irradiation and α-irradiation experiments, respectively.
The settling time of sediment grains in the slurries (1 week) was long compared to the time span of each experiment (tens of minutes to an hour for α-experiments, hours to days for γ-experiments). Therefore, we assumed that the suspension was homogenous during the course of each experiment.
H2 concentrations were measured by quantitative headspace analysis via gas chromatography. For headspace analysis, 30 mL of N2 was first injected into the sample vial. To avoid over-pressurization of the sample during injection, an equivalent amount of water was allowed to escape through a separate needle. The vials were then vigorously shaken for 5 min to concentrate the H2 into the headspace. Finally, a 500-μL-headspace subsample was injected into a reduced gas analyzer (Peak Performer 1, PP1). The reduced gas analyzer was calibrated using a 1077 ppmv H2 primary standard (Scott-Marrin, Inc.). A gas mixer was used to dilute the H2 standard with N2 gas to obtain various H2 concentrations and produce a five-point linear calibration curve (0.7, 2, 5, 20, and 45 ppm). H2 concentrations of procedural blanks consisting of sample vials filled with non-irradiated deionized 18-MΩ water were also determined. The concentration detection limit obtained using this protocol was 0.8–1 nM H2. Relative error was less than 5%. Radiation experiments were performed at a minimum in triplicate.
Sample selection and experimental radiolytic H2 yields, G(H2)
Millipore Milli-Q system water was used for our pure-water experiments. For seawater experiments, we used bottom water collected in the Hudson Canyon (water depth, 2136 m) by RV Endeavor expedition EN534. Salinity of North Atlantic bottom water in the vicinity of the Hudson Canyon (34.96 g kg−1) is similar to that of mean open-ocean bottom water (34.70 g kg−1)44,45.
The 20 sediment samples used for the experiments were collected by scientific coring expeditions in three ocean basins (expedition KN223 to the North Atlantic46, expedition KN195-3 to the Equatorial and North Pacific47, International Ocean Discovery Program (IODP) Expedition 329 to the South Pacific Gyre34, MONA expedition to the Guaymas Basin48, expedition EN32 to the Gulf of Mexico49, and expedition EN20 to the Venezuela Basin50). To capture the dominant sediment types present in the global ocean, we selected samples typical of five common sediment types [abyssal clay (11 samples), nannofossil-bearing clay or calcareous marl (2 samples), clay-bearing diatom ooze (3 samples), calcareous ooze (2 samples), and lithogenous sediment (2 samples)]. The locations, lithological descriptions, and mineral compositions of the samples are given in Supplementary Tables 1,  2,  3, and Supplementary Fig. 1. Additional chemical and physical descriptions of the sediment samples used in the radiation experiments can be found in the expedition reports for the expeditions on which the samples were collected34,46.
Energy-normalized radiolytic H2 yields are commonly expressed as G(H2)-values (molecules H2 per 100 eV absorbed)1. As shown in Supplementary Fig. 2, for all irradiated samples (pure water, seawater, and marine sediment slurries), H2 production increased linearly with absorbed α- and γ-ray-dose. We calculated G(H2)-values for each sample and radiation type (α or γ) as the slope of the least-square regression line of radiolytic H2 concentration versus absorbed dose (Supplementary Fig. 2). The error on the yields is less than 10% for each sample. G(H2)-values for each sample and radiation type (α or γ) are reported in Supplementary Table 3.
Although radiolytic OH• is known to react with dissolved organic matter51, total organic content does not appear to significantly impact radiolytic H2 production, since the most organic-rich sediment (e.g., Guaymas Basin and Gulf of Mexico sediment) did not yield particularly high H2 (Supplementary Table 3).
Calculated radiolytic production rates of H2 and oxidants in the cored sediment of individual sites
We calculated radiolytic H2 production rates (PH2, in molecules H2 cm−3 yr−1) for the cored sediment column at nine sites with oxic subseafloor sediment in the North Pacific, South Pacific, and North Atlantic; and seven sites with anoxic subseafloor sediment in the Bering Sea, South Pacific, Equatorial Pacific, and Peru Margin (see Supplementary Fig. 3 for site locations). For these calculations, we used the following equation from Blair et al.2:

$$P_{{mathrm{H}}_2} = {sum} A _{{mathrm{m}},i}rho left( {1 – {{upvarphi}} } right)E_i{mathrm{G}}({mathrm{H}}_2)_i$$
(1)

where i is alpha, beta, or gamma radiation; Am is radioactivity per mass solid; φ is porosity; ρ is density solid; (E_i) is decay energy; and ({mathrm{G}}({mathrm{H}}_2)_i) is radiolytic yield.
We calculated radiolytic oxidant production rates for these sediment columns from the H2 production rates. Because H2 production and oxidant production are stochiometrically balanced in water radiolysis [2H2O → H2 + H2O2], the calculated radiolytic H2 production rates (in electron equivalents) are equal to radiolytic oxidant production rates (in electron equivalents).
The in situ γ- and α-radiation dosages in marine sediment are, respectively, 13 and 15 orders of magnitude lower than the dosage used in our experiments. Because the measured G(H2) for pure water in our γ-irradiation experiment (dose rate = 2.19E-02 Gy h−1) is statistically indistinguishable from previously published G(H2) values at much higher dose rates (ca. 1.00E+3 Gy h−1)5, we infer that the γ-irradiation G(H2) value is constant with dose rate over five orders of magnitude. Similarly, our experimental pure water H2 yields following α-particle irradiation from a 210Po-source (dose rate of 2.55E+03 Gy h−1) are indistinguishable from the yield obtained by Crumière et al.6 [G(H2) = 1.30 ± 0.13] for air-saturated deionized water exposed to a cyclotron-generated He2+ particle beam at higher dose rate (dose rate 1.62E+05 Gy h−1). The close similarity in H2 yields obtained in both experiments implies that (i) radiolytic H2 yield from α-particle irradiation is identical to that from cyclotron-generated He2+ particle irradiation, and (ii) this yield is constant over a two-orders-of-magnitude range dose rate. Therefore, we use our experimentally determined α- and γ-irradiation G(H2) values for the low radiation dose rate found in the subseafloor. Because the G(H2) of β irradiation has not been experimentally determined for water-saturated materials, we assume that the G(H2) of β-radiation matches the G(H2) of γ-radiation for the same sediment types. In pure water, their G(H2) values differ by only 17%1. Because β radiation, on average, contributes only 11% of the total radiolytic H2 production from the U, Th series and K decay in marine sediment, these estimates of total H2 production differ by only 2–5% relative to estimates where the G(H2) of β radiation is assumed equal to that for pure water or for α radiation of the same sediment types.
To calculate H2 production rates for the entire sediment column at seven South Pacific sites and two North Atlantic sites, we measured downcore sediment profiles of U, Th, and K (i) 187 sediment samples from IODP Expedition 329 Sites U1365, U1366, U1367, U1368, U1369, U1370, and U137134,52, and (ii) 40 samples from KN223 expedition Sites 11 and 12 (ref. 46). Total U and Th (ppm) and K2O (wt%) for these sites are reported in the EarthChem SedDB data repository. We measured U, Th, and K abundances using standard atomic emission and mass spectrometry techniques (i.e. ICP-ES and ICP-MS) in the Analytical Geochemistry Facilities at Boston University. Sample preparation, analytical protocol, and data are reported in Dunlea et al.52. The precision for each element is ~2% of the measured value, based on three separate digestions of a homogenized in-house standard of deep-sea sediment.
To calculate H2 production rates for the sediment columns at North Pacific coring Sites EQP10 and EQP11 (ref. 47), we used radioactive element content data from Kyte et al.53, who measured chemical concentrations at high resolution in bulk sediment in core LL44-GPC3. Because Site EQP11 was cored at the same location as LL44-GPC3 (ref. 53) and the sediment retrieved at all three sites is homogeneous abyssal clay, we assume the radioactive element abundances measured in core LL44-GPC3 to be representative of Sites EQP10 and EQP11 (ref. 47). Calculated radiolytic H2 production rates for South Pacific sites are listed in Supplementary Table 4 and for North Atlantic and North Pacific sites in Supplementary Table 5.
For Bering Sea Sites U1343 and U1345 (ref. 54), sedimentary U, Th, and K content measurements are unavailable. Since sediment recovered at these two sites is primarily siliciclastic with a varying amount of diatom-rich clay, we use U, Th, and K concentration values reported for upper continental crust by Li and Schoonmaker for these Bering Sea sites55. Finally, we calculate downhole radiolytic H2 production rates for ODP Leg 201 Sites 1225, 1226, 1227, and 1230 (ref. 35). Sediment compositions for these sites include nannofossil-rich calcareous ooze (Site 1225), alternation of nannofossil (calcareous) ooze and diatom ooze (Site 1226), and siliciclastic with diatom-rich clay intervals (Sites 1227 and 1230). Because sedimentary U, Th, and K measurements are not available for Leg 201 sites, we used average U, Th, and K concentration values measured in North Atlantic46 and South Pacific Sites34,52 with corresponding lithologies.
We use isotopic abundance values reported in Erlank et al.56 to calculate the abundance of 238U, 235U, 232Th, and 40K from the measured ICP-MS values of total U, Th, and K concentration. We then converted radionuclide concentrations to activities using Avogadro’s number and each isotope’s decay constant2. We refer to Blair et al. for a detailed explanation of activities and radiolytic yield calculations2.
Calculation of global radiolytic H2 and oxidant production rates in marine sediment
We calculated global radiolytic H2 production in ocean sediment by applying Eq. (1) (ref. 2) globally. As with the rates at individual sites, we calculated global radiolytic oxidant production (in electron equivalents) from global H2 production and the stochiometry of water radiolysis [2H2O → H2 + H2O2].
Our global radiolytic H2 production calculation spatially integrates calculations of sedimentary porewater radiolysis rates that are based on (i) our experimentally constrained radiolytic H2 yields for the principal marine sediment types, (ii) measured radioactive element content of sediment cores in three ocean basins (North Atlantic46, North Pacific53, and South Pacific34,52), and (iii) global distributions of sediment lithology57, sediment porosity58, and sediment column length59,60.
To generate the global map of radiolytic H2 production, we created global maps of seafloor U, Th, and K concentrations, density, G(H2)-α values, and G(H2)-γ-and-β by assigning each grid cell in our compiled seafloor lithology map (Supplementary Fig. 4) its lithology-specific set of input variables (Supplementary Table 6). Because our model assumes that lithology is constant with depth, U, Th, and K content, grain density, and G(H2)-values are constant with depth.
The G(H2)-values (α, β, and γ radiation), radioactive element content (sedimentary U, Th, and K concentration), density, porosity, and sediment thickness are determined as follows.
Radiolytic yield [G(H2)] for α,β-&-γ radiation
Radiolytic yields for the main seafloor lithologies are obtained by averaging experimentally derived yields for the respective lithologies (Supplementary Table 6). We assume that G(H2)-β values equal G(H2)-γ values.
Sediment lithology
For these calculations of radiolytic chemical production, we generally used seafloor lithologies and assumed that sediment type is constant with sediment depth. For seafloor lithology, the geographic database of global bottom sediment types57 was compiled into five lithologic categories: abyssal clay, calcareous ooze, siliceous ooze, calcareous marl, and lithogenous (Supplementary Fig. 4). Some areas of the seafloor are not described in the database57. These include (i) high-latitude regions (as the seafloor lithology database extends from 70°N to 50°S)57 and (ii) some discrete areas located along continental margins (e.g., Mediterranean Sea, Timor Sea, South China Sea, Supplementary Fig. 4). We used other data sources to identify seafloor lithologies for these regions. We added an opal belt (siliceous ooze) in the Southern Ocean between 57°S and 66°S61,62. The geographic extent of this opal belt was based on DeMaster62 and Dutkiewicz et al.61. We defined the areas of the seafloor from 50°S to 57°S, from 66°S to 90°S, and in the Arctic Ocean as mostly composed of lithogenous material, based on (i) drillsite lithologies in the Southern Ocean [ODP: Site 695 (ref. 63), Site 694 (ref. 63), Site 1165 (ref. 64), Site 739 (ref. 65)], the Bering Sea and Arctic Ocean [International Ocean Discovery Program (IODP): Sites U1343 and U1345 (ref. 54), Site M0002 (ref. 66), ODP: Site 910 (ref. 67), Site 645 (ref. 68)] and between 50°S and 57°S [Deep Sea Drilling Project (DSDP): Site 326 (ref. 69), Ocean Drilling Program (ODP): Site 1138 (ref. 70), Site 1121 (ref. 71)], and Dutkiewicz et al.61.
In the North and South Atlantic, sediment type can be very different at depth than at the seafloor. For these regions, we departed from our assumption that sediment lithology is the same at depth as at the seafloor. Subseafloor lithologies at ODP Sites [1063 (ref. 72), 951 (ref. 73), 925 (ref. 74), and 662 (ref. 75)] and IODP Sites [U1403 (ref. 76) and U1312 (ref. 77)] indicate that sediment in the Atlantic Ocean basin is generally 30–90% biogenic carbonate content and detrital clay78, even where the seafloor lithology is abyssal clay57. Therefore, regions in the Atlantic Ocean described as abyssal clay in the seafloor lithology database57 were characterized as calcareous marl for our calculations (Supplementary Fig. 4). Because abyssal clay catalyzes radiolytic H2 production at a higher rate than calcareous marl, this characterization may underestimate production of radiolytic H2 and radiolytic oxidants in these Atlantic regions.
Radioactive element content
For four of the five lithologic types in our global maps (abyssal clay, siliceous ooze, calcareous ooze, and calcareous marl), we average U, Th, and K concentrations from sites in the North Atlantic46, North Pacific53, and South Pacific34,52. The average U, Th, and K concentration values are consistent with data reported in Li and Schoonmaker55 for the characteristic U, Th, and K content found in abyssal clay and calcareous ooze. For lithogenous sediment, we use U, Th, and K concentration values reported for upper continental crust by Li and Schoonmaker55. Lithology-specific radioactive element values are given in Supplementary Table 6 and used to calculate Am,i in Eq. (1).
Density
Characteristic density values for calcite, quartz, terrigenous clay, and opal-rich sediment were extracted from the Proceedings of the Integrated Ocean Drilling Program Volume 320/321 and are assigned to calcareous ooze, lithogenous sediment, abyssal clay, and siliceous ooze, respectively79.
Global porosity
For global porosity, we use a seafloor porosity data set by Martin et al.58 and accounted for sediment compaction with depth by using separate sediment compaction length scales for continental-shelf (0–200 m water depth; c0 = 0.5 × 10−3), continental-margin (200–2500 m; c0 = 1.7 × 10−3), and abyssal sediment ( >3500 m; c0 = 0.85 × 10−3)80,81. Once the porosity was 0.1%, the depth integration was halted.
Global sediment thickness
We calculated global depth-integrated radiolytic H2 production by summing the seafloor production rates over sediment depth in one-meter intervals (Fig. 3 in main text). Sediment thickness is from Whittaker et al., supplemented with Laske and Masters where needed82,83.
Ocean depth
For porosity calculations, water depths were determined using the General Bathymetric Chart of the Oceans84, resampled to a 5-arc minute grid, i.e. the resolution of the Naval Oceanographic Office’s Bottom Sediment Type (BTS) database “Enhanced dataset”57.
Dissolved H2 concentration profiles
H2 concentrations from South Pacific Sites U1365, U1369, U1370, and U1371, and the measurement protocol, are described in ref. 1. H2 concentrations from North Atlantic KN223 Sites 11, 12, and 15, and North Pacific Site EQP11 were determined using the same protocol and are posted on SedDB (see “Data availability”). The detection limit for H2 ranged between 1 and 5 nM H2, depending on site, and is displayed as gray vertical lines in Fig. 2 of the main text. H2 concentrations for Equatorial Pacific Site 1225 and Peru Trench Site 1230 were measured by the “headspace equilibration technique”, which measures steady-state H2 levels reached following laboratory incubation of the sediment samples85,86.
For comparison to these measured H2 concentrations, we use diffusion-reaction calculations to quantify what in situ H2 concentrations would be in the absence of H2-consuming reactions. The results of these calculations are represented as solid circles (•) in Fig. 2 of the main text. Temporal changes in H2 concentration due to diffusive processes and radiolytic H2 production in situ are expressed by Eq. (2):

$$frac{{partial {mathrm{H}}_2(x,t)}}{{partial t}} = frac{D}{{varphi F}}frac{{partial ^2{mathrm{H}}_2(x,t)}}{{partial x^2}} + P(x)$$
(2)

with
D: the diffusion coefficient of H2(aq) at in situ temperature
(varphi): porosity
F: formation factor
x: depth
Z: sediment column thickness
({mathrm{H}}_2): hydrogen concentration
P: radiolytic H2 production rate
t : time.
With constant radiolytic H2 production, P(x) = P with depth,
and at steady-state,

$$frac{{partial ^2{mathrm{H}}_2(x)}}{{partial x^2}} = – frac{{Pvarphi F}}{D}.$$
(3)

We integrate Eq. (3) over the length x twice,

$${mathrm{H}}_2(x) = – frac{1}{2}frac{{Pvarphi F}}{D}x^2 + Ax + B$$
(4)

where A and B in Eq. (4) are constants of integration. We use two boundary conditions to derive the value of these constants.
Boundary condition 1: concentration of H2 at the sediment-water interface, x = 0, is zero due to diffusive loss to the overlying water column.
Boundary condition 2: concentration of H2 at the basement–sediment-water interface, x = Z, is zero due to diffusive loss to the underlying basement.
With these boundary conditions, (A = frac{1}{2}frac{{Pvarphi F}}{D}Z) and B = 0
and

$${mathrm{H}}_2(x) = frac{1}{2}frac{{Pvarphi F}}{D}(xZ – x^2).$$
(5)

In cases where we expect radiolytic H2 production rates to significantly vary with depth due to changes in lithology, we adapted the boundary conditions and applied a two-layer diffusion model to account for this variation.
Calculation of Gibbs Energies for the Knallgas reaction
For H2 concentrations above the detection limits at South Pacific IODP Expedition 329 sites (Supplementary Fig. 5)34, we quantified in situ Gibbs energies (ΔGr) of the Knallgas reaction (H2 + ½O2 → H2O). In situ ΔGr values depend on pressure (P), temperature (T), ionic strength, and chemical concentrations, all of which are explicitly accounted for in our calculations:

$$Delta G_{mathrm{r}} = Delta G^circ _{mathrm{r}}left( {T,P} right) + 2.3,RT,{mathrm{log}}_{10}Q$$
(6)

where:
ΔGr: in situ Gibbs energy of reaction (kJ mol H2−1)
ΔG°r(T,P): Gibbs energy of reaction under in situ T and P conditions (kJ mol H2−1)
R: gas constant (8.314 kJ−1 mol K−1)
Q: activity quotient of compounds involved in the reaction.
We use the measured composition of the sedimentary pore fluid to determine values of Q.
For a more complete overview of in situ Gibbs energy-of-reaction calculations in subseafloor sediment, see Wang et al.87.
Calculation of organic oxidation rates (net rates of O2 reduction and DIC production)
We calculated the vertical distribution of net O2 reduction rates at nine sites where the sediment is oxic from seafloor to basement and the vertical distribution of DIC production rates at seven sites where the subseafloor sediment is anoxic (see Supplementary Fig. 3 for site locations). Dissolved O2 concentrations are from Røy et al.47 and D’Hondt et al.88. DIC concentrations are from ODP Leg 201 (ref. 35), and the Proceedings of the IODP Expedition 323 (Sites U12343, U1345)54 and IODP Expedition 329 (Site U1371 (ref. 34)).
The net rates are calculated using the MatLab program and numerical procedures of Wang et al.89, modified by using an Akima spline, rather than a 5-point running mean, to generate a best-fit line to the chemical concentration data. Details of the calculation protocol for O2 production rates and DIC production rates are respectively described in the supplementary information of D’Hondt et al.88 and in Walsh et al.90. The DIC reaction rates and their first standard deviations calculated for the seven sites are given in Supplementary Table 7.
To facilitate comparisons of radiolytic chemical rates to net DIC production rates, rates are converted to electron equivalents (2 electrons per H2, 4 electrons per O2, 4 electrons per organic C oxidized).
Estimation of sediment ages
We estimated sediment ages for Sites U1343 and U1343 using the sediment-age model of Takahashi et al.54, which is based on biostratigraphic and magnetostratigraphic data. Because detailed chronostratigraphic data are not available for the remaining sites (Equatorial Pacific sites (1225 and 1226), Peru Trench Site 1230 and Peru Basin Site 1231, South Pacific sites U1365, U1366, U1367, U1369, U1370, and U1371, North Pacific sites EQP9 and EQP10, and North Atlantic sites KN223-11 and KN223-12), we used the mean sediment accumulation rate for each of these sites (Supplementary Fig. 3) to convert its sediment depth (in meters below seafloor) to sediment age (in millions of years, Ma). Mean sediment accumulation rate was calculated by dividing sediment thickness by basement age91 (Supplementary Table 8). For Sites 1225, 1226, 1230, 1231, U1365, U1366, U1367, U1369, U1370, and U1371, sediment thickness was determined by drilling to basement34,35. For Sites EQP9, EQP10, KN223-11, and KN223-12, sediment thicknesses were determined from acoustic basement reflection data. More