dataesr/scientific-paragraphs-categorization huggingface dataset:
The BD was estimated using the pedotransfer function in Eq. (  2 ) proposed by  Hollis et al. (2012) : BD = 0. 80806 + 0. 823844*e -0. 27993×(SOCcontent /10)+0. 0014065*sand-0. 0010299*clay (2) where sand and clay are the mass percentage of sand and clay, respectively, and SOC content is expressed in gC kg -1. This function fitted the bulk density of 333 cultivated topsoils with a root mean square error of 0. 13 g cm -3 in the original study  (Hollis et al. , 2012). The volume fraction of coarse fragments was estimated from the mass fraction of coarse fragments available in the LUCAS dataset using Eq. (  3 )  (Pacini et al. , 2023) : Coarse volumefraction = Coarse massfraction ρ coarse BD + ( 1 -ρ coarse BD ) Coarse massfraction (3) where Coarse massfraction is the mass fraction of coarse fragments (unitless).
Natural references per pedoclimate The "natural reference per pedoclimate" is a novel approach based on pedoclimatic contextualisation of SOC content values. Pedoclimatic contextualization was performed by clustering the LUCAS 2015 dataset (dataset n. 2) according to its pedoclimatic features. As pedological features, we selected the clay and silt contents and the carbonate content. As climate features we selected the mean annual temperature, the standard deviation of monthly average temperature over the year, the total annual precipitation, and the aridity index (difference between the potential evapotranspiration and the total annual precipitation). These pedoclimatic features have been selected because they are known to influence the SOC content  (Roussel and Bourmeau, 2001; Arrouays et al.
, 2006; Fernández-Ugalde and Tóth, 2017; Chenu et al. , 2019; Büchi et al. , 2022)  and, as a first approximation, are independent of human activity. The goal is to isolate the factors that influence the SOC content regardless of the land management practices so that "intrinsic" SOC potentials independent of the human activity can be estimated. Because of this reason, the soil pH and C:N ratio were not retained as predictors, even though they influence the SOC content  (Rasmussen et al. , 2018). The clustering was performed in two parallel steps using the Python library Scikit-learn (version 1. 1. 1) (Pedregosa et al. , 2011). First, sites were clustered according to the four climatic features: mean annual temperature, standard deviation of monthly average temperature over the year, total annual precipitation, and aridity index.
As a first approximation, grasslands and woodlands can be considered as natural systems, where the SOC content has been much less affected by human activity compared to croplands  (Poeplau et al. , 2011; Sanderman et al. , 2017). Thus, they represent a reference of reachable SOC content values in a given pedoclimatic context under natural vegetation. Accordingly, a single SOC reference value expressed as SOC content (SOCref) was defined per pedoclimatic cluster based on the distribution of SOC content in grasslands and woodlands in that cluster. For each pedoclimatic cluster, we selected grasslands and woodlands in dataset n. 2 that belong to the cluster and we tested several percentiles of SOC content as a potential SOCref value. We tested the percentiles p = 0. 4, 0. 45, 0. 5, and 0. 55, i.
We used the implementation of the Python library Scikit-learn (version 1. 1. 1) (Pedregosa et al. , 2011). The model takes the pedoclimatic features of a site as input and outputs the K identifiers of the grassland or woodland sites that are the closest to the input site in the features space, as well as the corresponding K distances in the features space. Then, we set K = 1 and extracted the first neighbours of all the sites that are already in the cluster. These are candidate sites to populate the cluster. The candidate sites were sorted according to their distances from the sites already in the cluster. If the cluster initially contained N sites, then 30-N sites had to be added and Nc candidate sites (with Nc ≤ N) had been extracted. If Nc ≥ 30-N, then the first 30-N candidates were added to the cluster.
Otherwise, all Nc sites were added to the cluster and the procedure was repeated with K = 2 (second neighbours), K = 3 (third neighbours), etc. , until the populated cluster contained 30 sites. Seventeen pedoclimatic clusters over 44 were populated according to this procedure  (0-3, 1-0, 2-0, 2-3, 3-0, 3-3, 4-0, 4-3, 5-0, 5-3, 6-0, 6-3, 7-0, 7-3, 8-0, 8-3  and 9-0). We converted the SOCref values from content to stock using the formula described in Section 2. 2. Finally, for each site in the LUCAS 2015 croplands database (database n. 3), we extracted the pedoclimatic cluster to which it belongs and calculated the SOC storage potential as the difference between the SOCref of the pedoclimatic cluster and actual SOC content of the site.
Thus, the predicted "grassland-equivalent" SOC stocks can be interpreted as reference values SOCref for the LUCAS croplands that take into account the pedoclimatic features of the site. In their case study,  Schneider et al. (2021b)  used the following pedoclimatic features as predictors of SOC stocks: soil texture, pH, C:N ratio, carbonates content, soil group, elevation, slope, orientation of the slope (called "aspect" in the LUCAS dataset), and climate data. In this study, to allow for comparison with the "natural references per pedoclimate" method, we trained a modified version of the model. The first difference is that we removed the pH and C:N ratio from the list of predictors. The second difference is that we trained the model for the prediction of SOC contents instead of SOC stocks and only then we converted the observed SOC contents and the predicted SOCref values into stocks.
The most important difference with respect to the "natural references per pedoclimate" and the "data-driven reciprocal modelling" methods is that the SOCref values are estimated relative to other croplands and not to natural systems. Moreover, NPP is used as a feature, differently from the other methods. The method was originally developed for estimating SOC storage potential of croplands at the national scale in France  (Chen et al. , 2019a) , using the French soil monitoring network (RMQS) dataset  (Jolivet et al. , 2006). Here, we applied the same methodology to the LUCAS croplands dataset (database n. 3) with two differences. The first difference from the original methodology is that the clustering was performed using pedoclimatic features and NPP extracted at the LUCAS cropland sites only and not over the whole territory of the EU27 and the United Kingdom.
This choice was made for two reasons: first, to reduce the computational effort without reducing the accuracy of the climatic and NPP data, and second, to use only measured texture data and not spatial predictions. The second difference is that the SOCref values were extracted for each carbon landscape zone from the SOC content statistics and not from the SOC stock statistics. Only then, the conversion to SOC stocks was performed. The number of carbon landscape zones was set to twenty to minimise the Bayesian information criterion (BIC) while keeping a minimal number of ten LUCAS croplands in each carbon landscape zone. The BIC values as a function of the number of carbon landscape zones are shown in Supplementary Fig. 3A.
Estimation of the cumulative soil organic carbon storage potential of European croplands We determined the median SOCref and then estimated the total SOC storage potential in croplands topsoils of the European Union and the United Kingdom by first computing the median of the ΔSOC of all LUCAS sites per country, expressed in Mg ha -1 , and secondly by multiplying it by the country's croplands area and finally by summing the national estimates over the countries. The country croplands area data were obtained from Eurostat (Main farmland use by NUTS 2 regions, https://ec. europa. eu/eurostat/databrowser/view/EF_LUS_ MAIN__custom_3779332/default/table?lang=en, last visited 7th November 2022). We used data from 2016 and summed the arable land and permanent crop areas. It should be noted that the median ΔSOC per country is not an unbiased estimate, because LUCAS sampling sites were not chosen using probability sampling  (Teuling et al.
Pedoclimatic clusters The pedoclimatic clusters for the LUCAS dataset are shown in Fig. 1A  and the geographical regions to which the LUCAS sites of each pedoclimatic cluster belongs are reported in Table  1. Table  2  reports the carbonates content statistics and Fig. 2  shows the texture triangles of sites based on the soil cluster. From these distributions, at first order, the soil clusters correspond to calcareous soils (soil cluster n. 0), sandy soils (soil cluster n. 1), clay soils (soil cluster n. 3), and soils with average pedological features (soil cluster n. 2) (Table  1 ). Using only four classes of soils results in a very rough pedological classification; however, this allows for populating all pedoclimatic clusters after combining the soil and climate labels. We found that the SOC contents distributions in the 0-20 cm depth are different across different pedoclimatic clusters and for the same land cover (cropland, grassland, or woodland) (Supplementary Fig.
3 ). We choose to use p = 0. 5, i. e. the SOCref corresponding to median SOC content values for grasslands and woodlands in a pedoclimatic cluster. The choice of the percentile is necessarily arbitrary; however, using median values of grassland SOC contents as reference is consistent with the observation from long-term experiments at Rothamsted Research (UK) that 40 to 70 % of the SOC stock of topsoils (0-23 cm depth) under natural vegetation could be reached under arable land use undergoing well-chosen agricultural practices  (Powlson et al. , 2022). To allow for comparison with the "data-driven reciprocal modelling" and the "carbon landscape zones" approach, we have restricted the analysis to the dataset n. 3bis. Fig. 3A  shows the SOCref values of the LUCAS cropland sites. As expected, there is a high variability depending on the pedoclimatic cluster, with SOCref ranging from 10 gC kg -1 to 61 gC kg -1 (15 Mg ha -1   2A ).
Data-driven reciprocal modelling We have extracted the reference values SOCref and the resulting ΔSOC using the "data-driven reciprocal modelling" for the LUCAS croplands dataset (dataset n. 3bis). The results are shown in Fig. 3B  (SOCref values) and Fig. 4B  (ΔSOC values), expressed in terms of SOC content and SOC stocks. Compared to the "natural references per pedoclimate" method, a clearer influence of the latitude on the reference values is observed: higher SOCref in northern Europe and lower values in southern Europe (Fig. 3B ). This trend is found also for the ΔSOC values (Fig. 4B ). The existence of a trend of ΔSOC values with geographic coordinates may imply that the "Data-driven reciprocal modeling" method is slightly less appropriate in normalizing for the effect of pedoclimatic variables on SOC storage compared to the pedoclimatic clustering, Nevertheless, it has the advantage of providing continuous estimates of SOCref values as a function of pedoclimatic variables, contrarily to the clustering approaches that assign the same SOCref value to all croplands that belong to the same cluster, raising issues for the estimations at the frontier between clusters ("natural references per pedoclimate" and "carbon landscape zones" approaches).
Reachability of soil organic carbon reference values estimated with the novel "natural references per pedoclimate" method We investigated the possibility for a cropland to reach the SOCref value of its pedoclimatic cluster obtained using this method by assessing whether cropland sites with negative ΔSOC exist in each pedoclimatic cluster. We found that in dataset n. 3bis, 700 croplands over 6777 have negative ΔSOC evaluated with the "natural references per pedoclimate" method and that only four pedoclimatic clusters, 2-0, 5-0, 8-3, and 10-3, do not contain any cropland with negative ΔSOC (Supplementary Fig. 5A ). This suggests that the SOCref values estimated using the "natural references per predoclimate" are generally reachable in croplands. Nevertheless, even though we selected only sites that were The pedoclimatic cluster 5-0 contains only one cropland and none of the approaches predict a positive ΔSOC for it, while the pedoclimatic clusters 2-0 and 8-3 contain only seven and eleven croplands, respectively, among which only one and four croplands, respectively, have negative predicted ΔSOC using the "data-driven reciprocal modelling" and the "carbon landscape zones" approaches (Supplementary Fig.
5A ). Thus, the absence of negative ΔSOC using "natural references per pedoclimate" in the clusters 5-0, 2-0, and 8-3 is most probably due to the small number of occurrences of croplands in these pedoclimatic contexts. For comparison, the median number of croplands per pedoclimatic cluster is 79. Thus, the observed absence of negative ΔSOC values is likely due to undersampling. The pedoclimatic cluster 10-3 contains 44 croplands of the dataset n. 3bis. The "data-driven reciprocal modelling" and the "carbon landscape zones" approaches predict negative ΔSOC values in this pedoclimatic context for two and seven croplands, respectively (Supplementary Fig. 5A ). The pedoclimatic cluster 10-3 includes clay soils mostly located in France, England, Belgium, the Netherlands, and west Germany (Table  1 ).
, 2020; Schneider et al. , 2021a; Drexler et al. , 2022). In the dataset n. 3bis, we find 66 black sands soils according to this definition (sand content > 80 % and C:N ratio > 13), most of which are in Denmark and the north of Germany (Supplementary Fig. 7 ). A local model adapted to the specificity of black sands soils may be needed to correctly assess SOC reference values in this area, for example the "data-driven reciprocal modelling" method in its original implementation that includes the C:N ratio as a predictive feature  (Schneider et al. , 2021b) , or the benchmarking of German Agricultural Soils Inventory proposed by  Drexler et al. (2022)  where black sands soils are isolated in a specific stratum.
6E ). Nevertheless, attention should be paid to the estimates expressed as SOC stocks, that are of more practical significance than SOC contents, yet are highly uncertain when bulk density measurements are not available. Indeed, we needed to perform several approximations when converting SOC contents to stocks: the use of a pedotransfer function to estimate the bulk density, the use of a constant coarse fraction density for the conversion of coarse mass fractions to coarse volume fractions, and not accounting for the presence of stones, whose fraction is not available in the LUCAS Topsoil 2009 and 2015 datasets. Additionally, when SOC storage potentials ΔSOC are estimated relative to SOC measurements in best-performing sites, observing non-null ΔSOC stocks may be due to actual differences in SOC content but also to differences in bulk density and/or coarse fragments content.
Conclusion In summary, we found that different approaches based on different hypotheses, provided generally comparable estimates of SOCref values but with local discrepancies. The proposed ensemble modelling framework allows combining estimates from different approaches. It discards extreme estimations from single methods, which are likely erroneous. Using the ensemble modelling output and approximate bulk density values, we obtained a first rough estimate of 3. 5 Gt C of SOC storage potential in the European cropland topsoils. Nevertheless, this is probably an overestimation that should be interpreted as a long-term aspirational target. The use of additional methods and datasets in the ensemble modelling approach and more valid statistical spatial estimates may further refine our approach.
2009/12, because the texture was not remeasured in the second LUCAS campaign for resampled sites (European Commission, 2020). The texture was measured using laser diffraction in LUCAS 2015 instead of sieving and sedimentation used inLUCAS 2009/12 (European Commission, 2020). To ensure a homogeneous dataset, we decided to use only texture data from the LUCAS 2009/12, i. e. we discarded sites that were sampled in the LUCAS.
2009/12, because the texture was not remeasured in the second LUCAS campaign for resampled sites (European Commission, 2020). The texture was measured using laser diffraction in LUCAS 2015 instead of sieving and sedimentation used inLUCAS 2009/12 (European Commission, 2020). To ensure a homogeneous dataset, we decided to use only texture data from the LUCAS 2009/12, i. e. we discarded sites that were sampled in the LUCAS campaign only. LUCAS data are openly available in ESDAC and Eurostat at the following urls. LUCAS 2009/12 Topsoil (ESDAC, 2013): https://esdac. jr c. ec. europa. eu/content/lucas-2009-topsoil-data; LUCAS 2015 Topsoil (ESDAC, 2020): https://esdac. jrc. ec. europa. eu/content/lucas2015-to psoil-data; LUCAS 2009 land cover data (EUROSTAT, 2009): https:// ec. europa. eu/eurostat/web/lucas/data/primary-data/2009; LUCAS 2012 land cover data (EUROSTAT, 2012): https://ec.
europa. eu/eurosta t/web/lucas/data/primary-data/2012; LUCAS 2015 land cover data (EUROSTAT, 2015): https://ec. europa. eu/eurostat/web/lucas/dat a/primary-data/2015. • Dataset n. 2 -LUCAS 2015: topsoil data and land cover data of mineral soils (SOC < 120 gC kg -1 ) with cropland, grassland, or woodland land cover that were also sampled in LUCAS 2009/12 (15,251 sites). • Dataset n. 3 -LUCAS croplands: croplands of dataset n. 2 that were also croplands in dataset n. 1. (7324 sites). • Dataset n. 3bis: subset of dataset n. 3 including only cropland sites that fell in the predictor space of the "data-driven reciprocal modelling" model (see Section 2. 3) as described bySchneider et al. (2021b)and for which net primary production data could be extracted (see Section 2. 1. 3)(6777 sites). We used SOC content measurements from LUCAS 2015 and texture measurements from LUCAS.
In practice, structural flexibility is addressed by large dataset processing, and by using current algorithms of classification or variability estimation (like CryoSparc 3DVA or CryoDRGN  [61, 62] ). In contrast to cryo-EM, high-speed atomic force microscopy (HS-AFM) offers the possibility to directly capture the motions of a biomolecule with nanometer spatial resolution and millisecond temporal precision  [63]. LDL has been the target of classical AFM-studies, mostly by assessing its size  [64, 65]  or its biomechanical properties  [66, 67]. However, the intrinsic dynamics of LDL has never been recorded and visualized by HS-AFM before. In this study we combined both techniques, cryo-EM and HS-AFM. We addressed the fundamental question of the structure and inner organization of LDL particles, and simultaneously set a focus on its intrinsic flexibility.
From the top, this protrusion appears much thinner, extending only ~2 nm from the LDL surface. The "side" protrusion is about 13 nm apart from the "front" protrusion, as depicted in Fig. 5A  by the red arrow. The presence of protrusions is also clearly visible in high-speed atomic force microscopy (HS-AFM) recordings. Analysis of the HS-AFM dataset suggests that zero to three protrusions emerge from each LDL particle (Fig. 6 ). From N = 21 LDL particles observed, 33. 3 % showed no (visible) protrusion, 33. 3 % one protrusion, 14. 3 % two protrusions and 19 % three protrusions. The LDL particle seems to take a preferential orientation on the mica, with its flattened poles parallel to the mica surface. Topographical analysis suggests this orientation (Fig. S3 ), since we reproducibly measured heights of 14.
Despite the large dataset size and our efforts to isolate a homogeneous subset of LDL particles by classification methods, we could not resolve secondary structure elements of the protein. This is likely due to a large conformational heterogeneity of LDL, especially evident in the protrusion regions. HS-AFM allowed visualising the moving protein in millisecond time windows and underlined its extremely high flexibility. The metabolic conversion from VLDL to LDL requires large structural adaptations to the protein. Apo B-100 is an exception within the many apolipoproteins that are constantly exchanged within different lipoprotein speciesapo B-100 is non-exchangeable follows the transition from VLDL to LDL. Understanding the basic principles that connect structure, dynamics and function in health and disease are still a great source of motivation for further studies.
Particle picking In RELION, the particles on all micrographs were picked automatically using the templates generated from manually picked particles on a subset of micrographs. Additional sorting was performed with the calculation of a Z score  [93] , and discarding of all junk particles (Z score bigger than 1). In cryoSPARC, the template for automatic picking was a LDL 3D reconstruction computed prior from RELION. In both software packages, the picking parameters were optimized to reduce the number of false positives, while recovering enough particles. Subsequent sorting of the particles was conducted with several rounds of 2D classifications.
3D reconstruction Ab initio reconstruction, followed by iterative refinement were processed in cryoSPARC  [61]  with the selected 180 k particles from the 2D classification, and then with the whole dataset (700 k particles) with the 180 k 3D reconstruction as reference. The resolution was estimated for all following maps by a post-processing job in RELION, using the FSC 0. 143 criteria (see FSC curves in Fig. S10  of the Supporting Material). Sharpening was done with an ad-hoc B-factor of -500 Å 2 , which was chosen following first estimations given by the 3D refinement.
3D classification Different strategies for the 3D classification or local refinement were followed in cryoSPARC. Finally, the whole dataset (700 k particles) was randomly split in 100 k batches, from which a 3D map was refined from the consensus map for each batch. 3D classification with K = 3 3D classes was then performed on each subset, with K being the number of classes. This resulted in around 25 classes, with <50 k particles in each of them. Close inspection of all classes led to a rough separation in three categories (termed S, F, and SF). Similar classes were then gathered and refined to create the three maps presented in Fig. 4 , with their corresponding FSC shown in Fig. S10  (Supporting Material).
Variability analyses Similar to the bootstrap analysis and the calculation of a 3D map variance on the LDL reconstruction by  [38] , LDL flexibility was explored in detail. For that purpose, the two main current algorithms for the study of continuous heterogeneity were applied. First, the 3D Variability Analysis (3DVA) from cryoSPARC  [61]  was applied using the three main components of the partial component analysis. For each component, a series of volumes (also termed as frames) was reconstructed along the so-called latent coordinate, which indicates where the volume is along the variability component. Secondly, the LDL reference map was processed in the package cryoDRGN (Deep Reconstructing Generative Networks), whose algorithm is based on neural networks  [62, 95]. CryoDRGN which parametrizes the structures and the conformational space is not handled by a linear description, as in contrary to 3DVA, and potentially accesses more complex variations.