dataesr/scientific-paragraphs-categorization huggingface dataset:
Next, we applied ward hierarchical clustering to arrange the rows of the heatmap for each dataset. This clustering approach facilitated the identification of similar transcriptional patterns. Finally, to generate an overall profile for each dataset, we calculated the mean value of the pooled, maximum normalised transcriptional signal across all RNAPII consensus regions. Unsupervised feature selection, dimensionality reduction and predictive models Feature selection in scRNA-seq is a common step that allows to remove a large fraction of potentially uninformative bound regions/ genes (i. e. , those with very low expression or those with ubiquitous expression, which are not informative of the sample/cell biology). Typically, around 2000 to 3000 genes are kept in scRNA-seq experiments, but this number is generally tuned for each experiment.
To automatically select ''highly variable'' features for each dataset, we computed the sum of the squared pearson residuals, which are asymptotically following a c 2 distribution with n -p degrees of freedom, n being the number of samples, and p the number of parameters of the model (1 in our case). We performed an upper tail test for each gene/bound region and kept bound regions at an FDR of 5%. This selects only sufficiently expressed genes above the mean-variance trendline, and due to the clipping of the pearson residuals also removes outliers with an extreme variance (Figure  S22A ). We performed PCA on the Pearson Residuals of these highly variable features. To automatically identify the optimal number of Principal Components, we used Horn's Permutation Parallel Analysis, which has been found to be one of the most effective approaches to identify the number of components in factor analysis  72 (cit).
This approach generates row-wise permutations for each feature, computes PCA on these permuted datasets, then the selected number of components is the threshold at which the eigenvalues from the randomised dataset are larger than the real dataset. We performed 3 permutations due to the computational cost of this approach, which is acceptable as the randomised eigenvalues are very stable on large matrices (Figure  S22B ). We used the fast ''randomised'' solver from the python sklearn 59 library to compute PCAs. For UMAP visualisation, we used 30 neighbors, a min_dist parameter of 0. 5, Pearson correlation as the metric and use data in PCA space as input. For heatmaps, we used a similar approach as the RNAPII heatmap, except that the data was used in PCA space as input to the UMAP pass for the samples, and used Pearson correlation as the metric for both samples and RNAPII-bound regions.
Identification of per tissue markers and ''meta-clustering'' For each dataset (TCGA, ENCODE, GTEx, RNAPII), we identified markers for each annotation (i. e. , Pol2+Liver, GTEx+Blood). To identify markers in the three RNA-seq datasets, we performed a group-versus-rest, one sided t-test on the Pearson Residuals. We kept over-expressed bound regions with log2 Fold Change above 0. 25, and detectable in at least 10% or 2+ samples (whichever is the largest). For the RNAPII dataset, we performed an hypergeometric test for each RNAPII consensus, where: N, the population size, is the number of peaks across all experiments; K, the number of successes in the population, is the number of peaks across all experiments with the annotation of interest; n, the number of draws, is the number of experiments that has a peak at the studied consensus peak; k, the number of observed successes, is the number of experiments with the annotation of interest that has a peak at the studied consensus peak.
We used a BH FDR cutoff of 5% in both cases. This yields a binary vector which indicates whether a RNAPII-bound region is a marker or not for each dataset+annotation. We removed RNAPII-bound regions which are markers in more than 10% of the dataset+annotation combinations or in less than two dataset+annotation. An Average Linkage clustering using the Yule binary metric was performed, which we found to be less sensitive to the number of identified markers.
Tissue specific eQTL enrichments We downloaded per tissue eQTL data from GTEx ''GTEx_Analysis_v8_eQTL. tar'' and used the list of significant eQTL-gene pairs for each tissue. For each SNP listed as an eQTL we stored whether it is listed as an eQTL or not in each tissue. SNPs listed as eQTLs in more than 10% of the tissues (6 or more) were removed to keep variants that are likely located in tissue specific regulatory regions. Using the list of per dataset, per tissue marker RNAPII-bound regions, we kept RNAPII-bound regions that are markers in less than 10% of the tissues in a dataset (6 or less) and removed non-marker RNAPII-bound regions. We removed tissues having less than 50 markers left after this step. We computed pairwise intersection enrichment p values between the tissue-specific eQTLs and the marker RNAPII-bound regions (SNP intersection against whole bound region).
Differential expression To identify differentially expressed (DE) RNAPII-bound regions between tumor and normal tissues, we performed a t-test on the Pearson Residuals with an FDR cutoff of 5%. We constrained DE RNAPII-bound regions to have an absolute log2 Fold Change above 0. 25, and to be detectable in at least 10% or 2+ samples (whichever is the largest) of either class (normal/tumor). For the detection of Tumor Subtype specific markers, we compared the expression of samples of a subtype to reference normal samples. We used the same significance cutoffs. We considered a marker to be subtype-specific only if it appeared for this subtype. Linear modeling methods such as DESeq2 ran out of memory on large datasets and required an excessive computation time. A t-test was used to accommodate large datasets (100+ samples x 180 000 bound regions in most datasets) and to keep an uniform processing for each dataset for our cross-dataset analyses.
With sufficiently large sample sizes, the t-test yields robust markers, although with less statistical power (Figures  S22C  and S22D ). To evaluate our approach on a much smaller dataset with less statistical power, we selected samples from two similar types of heart tissues from GTEx and downsampled to obtain an n = 3 comparison. Here, we used DESeq2 73 to maximise statistical power. We performed 100 random sampling iterations to obtain 3 samples for each tissue, evaluated DE in each iteration, then kept bound regions supported as DE in at least half of the downsampling iterations. To evaluate the relationship between sample size and statistical power, we performed 10 downsampling iterations for each sample size. GREAT 65 v4. 0. 4 analyses were performed on BRCA TNBC specific RNAPII-bound regions, identifying enrichment of the ''MAP kinase tyrosine/serine/threonine phosphatase activity'' GO:0017017 term (Binom FDR Q-Val 1.
Survival analysis For survival analysis, we fit a linear Cox Proportional Hazards regression model on the Pearson residuals using the Python Lifelines library, and use a 5% FDR threshold. Kaplan-meier survival curves were created using the kaplanmeier python library. The maxstat R library was used to obtain the optimal expression cutpoint as well as the associated maximally selected log -rank statistic p value (using the most accurate ''condMC'' 0 method with 100 000 samples to compute the p value).
Enrichment of cancer hallmark-related genes To investigate the enrichment of cancer hallmark-related genes, we utilised a gene set enrichment analysis (GSEA) approach. The list of candidate genes associated with specific cancer hallmarks was obtained from the CHG database (http://www. bio-bigdata. com/ CHG/) which provides a comprehensive collection of genes with verified and putative links in various cancer-associated biological processes. We conducted GSEA analysis on RNAPII markers genomic regions. However, instead of utilising Gene Ontology (GO) terms, we employed the cancer hallmarks as defined in the CHG database. Cancer hallmarks encompass key biological processes and pathways that contribute to tumorigenesis and cancer progression. We assessed the enrichment of cancer hallmark-related genes nearby the pan-cancer RNAPII markers.
ACKNOWLEDGMENTS The authors would like to thank  Dr. Paul Flicek  for providing constructive criticism of the manuscript and  Dr. Sabrina Baaklini  for engaging discussions on meta-clustering. We thank  Dr. Jeremy J. Day  ( UAB Heersink School of Medicine ) for granting us permission to reproduce the DNA schematic in Figure 1A. This work was supported by a PhD fellowship to P. d. L. and J. -C. M. from the  French Ministry of Higher Education and Research (MESR) , a PhD fellowship to F. H. from the  Provence-Alpes-Côte d'Azur Regional Council (Region SUD) ,  Institut National de la Santeet de la Recherche Medicale (INSERM) , the  Core Cluster of the Institut Francais de Bioinformatique (IFB)  ( ANR-11-INBS-0013 ), and the  Centre de Calcul Intensif d'Aix-Marseille  by granting access to its high performance computing resources.
Stratified LD-Score Regression Finucane et al. 66 https://doi. org/10. 1038/ng. 3404 featureCounts Liao et al. 69 https://doi. org/10. 1093/bioinformatics/btt656 SCTransform Choudhary et al. 71 https://doi. org/10. 1186/s13059-021-02584-9 Other Code for main figures and analysis This paper; Github https://github. com/benoitballester/Pol2Atlas Intergenic RNAPII Atlas: input data This paper; Zenodo https://zenodo. org/record/7785393 Intergenic RNAPII Atlas: output data This paper; Zenodo https://zenodo. org/record/8091826.
METHOD DETAILS RNAPII ChIP-seq data processing We recovered from NCBI-GEO all existing RNA Polymerase II (RNAPII) ChIP-seq experiments targeting the POLR2A subunit (n = 1,135) in human, following the ReMap procedures and pipeline. 19  Briefly, we manually annotated and standardised the cell line and tissue of origin names (Table  S1 ). Every experiment was downloaded and processed uniformly starting from the fastq files, to quality checks, up to the peak calling stage using the ReMap pipeline. In more detail, ChIP-seq experiments were retrieved from the NCBI Gene Expression Omnibus (GEO) and ENCODE databases. For GEO, the query 'Genome binding/occupancy profiling by high-throughput sequencing' AND 'homo sapiens'[organism] AND NOT 'ENCODE'[project]' was used to return a list of all potential studies.
The selected experiments metadata are then manually curated and annotated with official nomenclatures for target names and biotypes. For incomplete metadata, the materials and methods of associated and published papers are often examined to complete the curation. We used the BRENDA Tissue Ontologies for cell lines at the EBI Ontology Lookup Service (www. ebi. ac. uk/ols/ ontologies/bto) as well as the Cellosaurus database to homogenize cell and tissue names (e. g. , MCF-7 not MCF7, Hep-G2, not HepG2, Hepg2 etc. ). We define a dataset as a DNA-binding experiment in a given GEO/ENCODE series (e. g. , GSE37345), for a given RNA Polymerase II subunit (e. g. , POLR2A), and in a particular biotype (e. g. , LNCaP, MCF-7) in a given biological condition. Datasets are labeled with the concatenation of these information (e.
g. , GSE37345. POLR2A. LNCAP_45min-DMSO). All data were re-analysed starting from raw FASTQ files. Both GEO and ENCODE datasets were manually curated, processed and analyzed in the same way. Bowtie 2 53 (version 2. 2. 9) with options -end-to-end -sensitive was used to align all reads on the human genome GRCh38/hg38 assembly. Trim Galore (https://github. com/FelixKrueger/TrimGalore) was used to remove adapters, trimming reads up to 30.
Protein structure analysis and classification, which is fundamental for predicting protein function, still poses formidable challenges in the fields of molecular biology, mathematics, physics and computer science. In the present work we exploit recent advances in computational topology to define a new intrinsic unsupervised topological fingerprint for proteins. These fingerprints, computed via Local Euler Curvature (LECs), identify secondary protein structures, such as Helices and Sheets, by capturing their distinctive topological signatures. Using an extensive protein residue database, the proposed computational framework not only distinguishes between structural classes via unsupervised clustering but also achieves remarkable accuracy in classifying proteins structures through supervised machine learning classifier.
1a , where for convenience we depict some distances related to each secondary structure. More recently, machine learning approaches have significantly advanced protein structural analysis research  [6] [7] [8] [9] [10] [11]. Among these, the most impressive is the Google Deep-Mind's AlphaFold AI program  12  , which has won the Casp and Lasker basic medical research awards for predicting (with circa 95% accuracy) protein's 3D structures from their amino-acid sequences. Despite these advances, machine learning models are essentially black-boxes, thus they fail to explain the biophysical mechanisms associated with protein's multi-scale structures, intricate folded patterns,  13  , interactions  14  or interfaces. [15] [16] [17] [18]. Consequently, a parallel line of research has been exploring more mathematical approaches based on geometry and topology.
89 To advance, we take the advantage of a key mathemat-90 ical property of the Euler characteristics (EC), which is 91 that it can be decomposed (or partitioned), leading to the 92 concept of Local Euler Curvature, or in this work some-93 times called also Local Euler Characteristics, (LEC)  [40] [41] [42]. 94 LEC lends itself to protein analysis since local properties 95 of proteins are crucial. Overall, this leads to a more 96 efficient compartmentalised analysis and interpretation, 97 while still connecting to the global topological properties 98 of proteins. Specifically, we will show that the basic 99 secondary structure of proteins are naturally described 100 by LEC. To validate this, we analysed a representative 101 database containing millions of protein residues, and sub-102 sequently modelled and scored using LEC representation.
2. Henceforth, we shall show that the observed LEC features are sufficient to classify protein  First, it is important to gauge the accuracy of DSSP and STRIDE themselves, considering that they assign different classifications. We find that they have an accuracy of 76% for the CATH dataset (including non-consensus residues) and 72% for the test set. In contrast, our rbLEC model was trained exclusively on the consensus classification, omitting residues when DSSP and STRIDE do not agree. Thus, a comparable (possibly similar) scores between our rbLEC classifier and the DSSP/STRIDE is to be expected. Indeed, Table  1  shows that our rbLEC achieves a test set accuracy of 79% and 74% concerning DSSP and STRIDE, respectively, while CATH dataset yields 81% and 71%. Moreover, our rbLEC model provides class probabilities for a given feature.
This allows us to compute the Top K = 2 accuracy, which is considered successful if the first or second most probable class matches the reference classification labels. We obtained scores of 90% and 87% for the test and CATH datasets, respectively. This remarkable result highlights the potential effectiveness of rbLEC and our training approach in providing a robust residue classifier for seven classes, based solely on the LEC of a given protein chain's three backbone atoms. Notably, our methodology requires no ad-hoc determinations of hydrogen bond networks or protein geometric backbone geometries. Additionally, Table  1  provides the f1-score for the four primary classes (encompassing over 95% of available residues): -Strand, ↵-Helix, Turns, and Coils. This score provides more information about the precision and recall balance of predicted classes.
451 Our dataset comprises 3D protein structures. The 452 training set includes structures sourced from the lat-453 est version of the CATH database,  43, 49  which catego-454 rizes protein structures from the Protein Data Bank 455 into non-redundant domains. This compilation of non-456 redundant protein domains contains 14,938 files, repre-457 senting 2,200,595 residues.
458 For the testing dataset, we acquired 22 proteins with 459 a total of 17,875 residues from RCSB PDB. 50  To ensure 460 fairness, we selected a diverse range of complete proteins, 461 encompassing both small (161 residues) and large (3797 462 residues) structures. This set encompasses prevalent 463 tertiary structure groups such as ↵ + , ↵/ , all-↵, and 464 all-, including notable representatives like beta barrels, 465 membrane proteins, and enzymes. Those are detailed in 466  There are numerous ways to achieve this but herein we 476 employ simplicial filtration method to construct the so 477 called Vietoris-Rips complex,  52, 53  (or equivalently clique 478 complex). For completeness, we provide the basic con-  = {v i } 2 K () B " (v i ) \ B " (v j ) 6 = ;, 8v i , v j 2. This is equivalently a clique complex of a graph with V as set of vertices and an edge (v i , v j ) if and only if kv j v i k < 2".
513 atoms or residues) and edges (1-simplex) are determined, where the edges have an assigned weight based on a distance measure between nodes. The minimal and maximum permissible distance between nodes are a priori defined. The input to the algorithm is the set of edges and iteratively, higher-order simplices (or cliques) are constructed by adding edges in increasing order of their distance (or weight) with the condition that the diameter of the generated simplex (clique) does not exceed a certain bound, where the diameter of a clique is the maximum (or minimum) weight of an edge in a clique. Specifically, we bound the computations to d = 13 and range the filtration cutoffs between 2. 5 to 7. 5 Å. Moreover, the edges representing a distance of less than 2 Å were excluded from our graph. To list all the cliques we use the NetworkX software package.
+  N R , (3) built Scikit-learn class  54   We chose to project the data to the first 5 PCs as the gains in explained variance ratio rapidly decreased after this point. For clustering, we fit a series of Gaussian Mixture Models (GMMs). GMMs represent a dataset as a mixture of multiple Gaussian distributions with (possibly) different parameters, allowing the model to capture more complex patterns than, for example, a kmeans based method. We fit GMMs with n clusters, n 2 {2, 3, 4, 5, 6, 7, 8, 9, 10} directly to the 5-dimensional projection effected by PCA. We tested the robustness of the clustering using a variety of measures. The Jensen-Shannon metric  55  quantifies the dissimilarity or divergence between two probability distributions. As GMMs are essentially probability distributions, the Jensen-Shannon metric can be used to measure the similarity of GMMs.
Acknowledgements This research is supported by the  Basque Government  through the  BERC 2022-2025 program  and by the  Ministry of Science and Innovation: BCAM Severo Ochoa  accreditation  CEX2021-001142-S/MICIN/AEI/10. 13039/501100011033. We also acknowledge financial support received from the  IKUR Strategy  under the collaboration agreement between  Ikerbasque Foundation  and  BCAM  on behalf of the  Department of Education of the Basque Government. Moreover, we thank the  Basque Modelling Task Force (BMTF)  grant from the  Basque Government. All authors thank  Prof. Oliver Knill  for useful discussions.
174 For example, two consecutive C ↵ of protein chains have more comprehensive analysis, which can only be cap-186 tured in the study of en ensemble of proteins. This is 187 critical if we are to establish a robust correlation between 188 topological invariants and protein secondary structures. 189 Ensemble Local Euler Curvature of Proteins 190 We considered a representative from the CATH 191 database 43 , which maintains a collection of non-192 redundant protein structures; see Methods. In all pro-193 teins we first selected the three backbone atoms CA, 194 C, and N as the nodes of our graph. Then following 195 our approach from the preceding section, we computed 196 the simplices and their corresponding local curvatures 197 (specifically Eq. (1)), which were then aggregated to yield 198 the LEC (Eq.
307 These combine together reliably to form 3 or 4 clusters 308 ( 308 see Fig. 3afor a schema of the relationships between 4 309 and 6 clusters detected by GMMs), which forms clearly 310 distinguishable looking LEC profiles in Fig. 3c. 311We tested the robustness of these clusterings via var-312 ious measures outlined in Methods and Fig. SI 9. The 313 broad characteristics of these clusters remain stable 314 whether fitted on the full CATH dataset or the consen-315 sus subset. Noteworthy, Fig. SI 5 compared to Fig. SI 6 316 and Fig. SI 7, and also produce stable predictions when 317 the GMM is fitted to a small portion of the dataset as 318 described in Methods and Fig. SI 9. 319 Numerous combinations of those "basic classes" can 320 arise as combinations if we select a different number of 321 clusters, which leads to several different GMM fits in 322 these cases.
1). Adding to the complexity are significant differences between the DSSP and STRIDE methodologies. From a geometric perspective, ⇡-Helix structures represent helices with an expanded radius, often nested within ↵-Helix, motifs. This arrangement introduces interruptions in the continuity of helices, potentially carrying significant functional implications for the protein. To gain deeper insights, future studies should explore these intertwined ↵-Helix structures using a more extensive dataset to establish a more robust consensus on ⇡-Helix classifications. Interestingly, our classifier demonstrates more consistent classification compared to DSSP than STRIDE, suggesting a potentially more uniform approach from DSSP authors theirs parameter choices.
C. Small-angle neutron scattering The SANS experiments were performed using a D22 installed at Institut Laue Langevin (ILL), Grenoble, France. Wavelength and sample-to-detector distances were 5. 6 Å and 4. 0 m, respectively, and the measurements were performed at 15 • C. The SANS intensity was corrected for background, empty cell, buffer scattering, and transmittance. Additionally, the SANS profiles were converted to the absolute intensities (cm -1 ) using incident beam flux. All the data reduction procedures were performed with the software program GRASP  [18].
F. MD simulation All-atom MD simulations of EcoO109I with explicit water molecules were conducted independently using the AM- BER16  [21]  software package with the AMBER ff15FB  [22]  force field and TIP3PFB  [23]  water model. An atomic model of the crystal structure (PDB accession code1WTD)  [15]  was used for the simulation, and the missing regions were modeled as described in a previous study  [16]. Moreover, the structure with identified crystal water molecules was solvated in a truncated octahedron box of a water model with a clearance of 20. 5 Å between EcoO109I and the face of the box. Next, Na + and Cl -ions were added to adjust the ionic strength of the system to that in the NSE measurement, 350 mM. Electrostatic interactions were treated using the particle-mesh Ewald method  [24]  with a real-space cutoff of 10 Å.
ACKNOWLEDGMENTS NSE and SANS experiments at ILL were performed under Proposals No. 8-04-715 and No. 8-03-875, respectively. This work was supported by  MEXT/JSPS KAKENHI  grants (Grants No. JP19KK0071  and No. JP20K06579  to R. I. , and Grants No. JP18H05229 , No. JP18H05534 , and No. JP18H03681  to M. S. ). Additionally, this work was partially supported by a project for the construction of a basis for advanced materials science and analytical studies through the innovative use of quantum beams and nuclear sciences at the  Institute for Integrated Radiation and Nuclear Science, Kyoto University. This study was also partially supported by the  Platform Project for Supporting Drug Discovery and Life Science Research [Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS) ] from  AMED  ( JP22ama121001j0001 ) to M.