dataesr/scientific-paragraphs-categorization huggingface dataset:
In UK1-II:1, UK2-III:1, UK2-III:2 and FR1-II:1 fresh blood was available for extraction of ultralong fragments. Therefore, these samples were subjected to Bionano optical genome mapping, confirming the presence of the ABCD3 repeat expansion (Figure  1C ). The existence of two obligate carriers (AUS2-III:4 and UK2-II:2), who both lived until their old age and did not develop the disease, suggests that the repeat may show reduced penetrance in rare cases. Unfortunately, DNA was not available for assessing the repeat size. ABCD3 repeat expansions were absent from optical genome mapping control datasets comprising 974 alleles and are very rare in large srWGS control datasets. There were no large expansions over 50 repeats, corresponding to the average read length of 150bp, in 32,884 alleles present on GnomAD.
Only one expanded allele out of 6,538 (0. 015%) was identified in the Broad Centre for Mendelian Genomics and Rare Genomes Project cohorts and ten expanded alleles out of 71,498 alleles (0. 013%) were identified in the 100,000 Genomes Project. In all control individuals the estimated repeat size was lower compared to OPDM cases. Further details of repeat size distribution in control datasets are available in Supplementary results and Supplementary Figure  S1.
10  Interestingly, all affected European individuals shared a 560 kb ancestral haplotype encompassing ABCD3, which has an allele frequency of 0. 2% in the Genomics England 100,000 Genomes Project. There are rare occurrences ABCD3 repeat expansions (>50 repeats, n=11 alleles) being detected in srWGS data from individuals without OPDM in both the Genomics England and gnomAD datasets (<~0. 01%). In two such individuals within Genomics England, for whom followup was possible, targeted ONT sequencing found the repeat expansions to be 88 and 120 repeats, below the pathogenic range observed in this OPDM cohort. Of note, Ishiura et al. also found CGG repeat expansions in LRP12 in a small number of control subjects (0. 2%). Also, hexanucleotide repeat expansions in C9orf72 that cause ALS are seen in 0.
Analysis of the ABCD3 locus in srWGS from population datasets To examine the population distribution of STR alleles at the ABCD3 locus, we ran ExpansionHunter on 16,442 srWGS samples from gnomAD by specifying the locus region as chr1:94418421-94418442 (GRCh38, 0-based coordinates) and repeat unit as GCC. We also used ExpansionHunter to genotype 3,270 srWGS rare disease samples from the Rare Genomes Project (RGP) and the Center for Mendelian Genomics (CMG). These included 1,608 cases from a wide range of disease and phenotype categories and 1,662 unaffected family members. Finally, we profiled the ABCD3 CCG expansion locus with EH in the entire 100,000 Genome Project cohort of 35,749 srWGS from non-neurological controls from the UK. We analysed its size in 724 controls, and 250 alleles from internal non-OPDM samples that underwent optical genome mapping at UCL Institute of Neurology (see methods below).
Adaptor sequences were removed and demultiplexed FASTQ files were provided by Genomics WA for download and further analysis. Processing of FASTQ files, including read quality control and alignment, was performed using the nf-core/rnaseq pipeline (https://nf-co. re/rnaseq/1. 3), version 3. 8. 1. Raw reads were aligned to the GRCh38 human reference genome using STAR (version 2. 7. 10a). Detection of aberrant expression was achieved using DROP (version 1. 3. 3),  13  as previously described. 14  DROP leverages OUTRIDER,  15  a method for detecting aberrant RNAseq read counts, which uses a denoising autoencoder to control for latent effects and returns multiple-testing corrected p-values (FDR) for each gene and sample. The cohort consisted of 130 skeletal muscle RNA-seq datasets from rare neuromuscular disease patients, including three OPDM patients and five unaffected controls.
ABCD3 repeat expansions are very rare in srWGS and optical genome mapping control datasets Analysis of 16,442 gnomAD samples using ExpansionHunter found that the repeat size distribution had a mean of 7. 1 x CCG repeats and a median of 7 x CCG repeats. The median is also 7 x CCG for each gnomAD subpopulation (ASJ, AMI, AMR, MID, SAS, EAS, NFE, FIN, AFR). The most expanded genotype among the gnomAD samples was 7/44 (CI: 7-7/43-58). The REViewer read visualisation for this sample contained several low-quality read alignments but supported a genotype of at least 38 repeats in the long allele, implying that ExpansionHunter works reasonably well for expansions at this locus (Figure  S1 ). Two samples in the CMG and RGP cohorts (n=3,270) had expansions longer than any of those found in gnomAD (ie.
ACKNOWLEDGEMENTS We thank  Profs Ichizo Nishino ,  Carolin Sewry , and  Werner Stenzel  for reading and review of the muscle biopsies and electron microscopy. This project was supported by an  NHMRC Ideas Grant  ( APP2002640 ) to G. R, N. G. L, M. R. D. , P. J. Lamont and M. C-S and  Medical Research Council  ( MR/T001712/1 ),  Fondazione Cariplo  (grant n. 2019-1836 ), the  Inherited Neuropathy Consortium ,  Fondazione Regionale per la Ricerca Biomedica (Regione Lombardia , project  ID 1751723 ) and  Italian Ministry of Health  ( Ricerca Corrente   2021-2022 ) to A. C. C. K. S. and L. D. are supported by an  Australian Government Research Training Program  (RTP) Scholarship, I. W. D. is supported by an  MRFF Investigator Grant  ( MRF1173594 ) and G. R. is supported by an  NHMRC   EL2 Investigator Grant  ( APP2007769 ).
MD simulations The behavior of GLC and βCD in water was traced by molecular dynamics (MD) simulations. All-atom CHARMM force fields were used  [22, 23]. TIP3P model  [24]  was adopted for water. Force field parameters for GLC were derived using the force field toolkit  [25]  of VMD program  [26]. Host βCD molecule was described using CHARMM force field for carbohydrates  [27]. For the GLC-βCD complex four coordination modes, corresponding to structures located in QM calculations were considered. Additional configurations were generated by rotating GLC molecule inside the βCD cavity. This resulted in 5 structures in total. For GLC-(βCD) 2 complexes three types of geometries were prepared. Namely one GLC molecule was encapsulated by two βCDs molecules facing each other from the (i) wide rim sides, (ii) narrow rim sides, (iii) wide to narrow rim side.
Here, the occurrence of the isosbestic point indicates the formation of both 1:1 and 1:2 complexes. To support these findings, a method of continuous variation, namely the Job method  [29] , was used. In this method, the total molar  concentrations of the two complexing compounds are kept constant while the relative ratio of their mole fractions is changed. Then, a Jobs' plot is constructed illustrating the dependence of UV absorption on the mole fraction of one of the components. The appearance of a maximum on this plot indicates complex formation and gives direct information about its stoichiometry. The Job plots obtained in this study are shown in Fig. 4. The UV absorption data recorded at 228 nm was used to draw the plots. Indeed, the maxima at GLC molar fractions of 0. 5 and 0. 34 confirm the formation of GLC-βCD and GLC-(βCD) 2 complexes respectively.
Next, we find that the fraction of NCFs that are chain-0 functions decays exponentially with the number of inputs, and exhibits a fractal-like behaviour as a function of the bias for a fixed number of inputs. Moreover, we explain several of these observations analytically. Then, by analyzing 5990 BFs extracted from a large dataset of reconstructed Boolean models, and 2 other datasets, we find that generalized chain functions are significantly enriched within the NCFs. Lastly, we illustrate the severe restriction imposed by generalized chain functions compared to NCFs for 3 biological models and perform model selection on them using known relative stability constraints.
Notably, some of us in our previous work have shown that two classes of BFs, namely NCFs and read-once-functions (RoFs) exhibit unexpected prevalence  [13]  within a compiled reference biological dataset of 2687 BFs derived from reconstructed Boolean models of biological systems despite their theoretical fraction within the space of all BFs being minuscule. We also showed that NCFs and RoFs have the 'simplest logic' with respect to the complexity measures 'average sensitivity'  [20]  and A Boolean model of a GRN consists of nodes and directed edges where nodes correspond to genes and directed edges correspond to the regulatory interactions between them  [2, 8, 9]. Genes in a BN are either in an upregulated ('on') or downregulated ('off') state. In a BN with N nodes, we denote the state of the i th gene at time t by x i (t), where i ∈ {1, 2,.
Description of the reference biological datasets In this section, we describe the 3 reference biological datasets containing the BFs used to quantify the abundance and enrichment of the ChF 0 , ChF 1 , ChF U and non-ChF U NCF types of BFs. • BBM benchmark dataset: This dataset was adapted from the BBM benchmark dataset provided in  [26] , which consisted of 219 models of Boolean GRNs. Of these, we selected only the manually reconstructed ones, amounting to total 134 models. From those 134 models, we extracted 5990 BFs (regulatory logic rules) when restricting to cases having at most 10 inputs. • MCBF dataset: This dataset was published in  [13]. It consists of 2687 BFs recovered from 88 manually reconstructed discrete models of Boolean GRNs. This was downloaded from the Github repository https: //github.
Relative enrichment and associated p-values Consider a type of BF T and one of its sub-types, say T s. In our study we are interested in relative enrichment of the sub-type T s within its englobing type T when considering a particular biological dataset. For instance we can examine the case where T = NCF and T s = ChF 1. We define the relative enrichment for a given number of inputs k by E R = (f s,1 /f 1 )/(f s,0 /f 0 ) where f s,1 and f 1 are the fraction of BFs belonging to ChF 1 and NCF respectively in the considered biological dataset, and f s,0 and f 0 are the fraction of BFs belonging to ChF 1 and NCF respectively when considering all possible such functions. In typical cases the biological dataset will have an over representation of BFs of type T and T s but by considering the relative enrichment we can test the hypothesis that this last enrichment is driven solely by the property of being in T ; if the relative enrichment of T s within T is statistically inconsistent with the value 1, then we can reject the hypothesis.
From Eq. (  14 ), it is easy to see that f CN (k + 1, P ̸ = 1) = 1  2 f CN (k, P ̸ = 1) since m last for P ̸ = 1 remains invariant for any k (see Appendix A, Property A. 2). However, when P = 1, m last = k and so f CN (k, P = 1) = (1 + k)/2 k. Replacing k by k + 1 in this equation, f CN (k + 1, P = 1) = 1 2 k+1 + 1 2 f CN (k, P = 1). 3. 5. Preponderance and enrichment of chain-0, chain-1 and generalized chain functions in various reference biological datasets.
BBM benchmark dataset We now shift our focus to quantifying the preponderance of ChF 0 , ChF 1 and ChF U in various biological datasets of regulatory logic rules. We first consider the case of the BBM benchmark dataset  [26]. When we quantify the fraction of odd and even bias BFs for a given number of inputs (k), we find that the fraction of BFs with odd bias are overwhelmingly larger compared to the fraction of BFs with even bias (see Fig. 4(a) ). Next, we compute the fraction of NCFs for each k and find that it is enriched for all k as shown in Fig. 4(b ). Both of these observations are in line with previous studies on the fraction of odd bias BFs and the fraction of NCFs in reference biological datasets  [13]. Lastly, for a k-input BF belonging to the sub-types of NCFs, namely, ChF 0 , ChF 1 , ChF U and non-ChF U NCF, we compute their fraction within the NCFs (shown by the bars in Fig.
MCBF and Harris datasets Repeating the previous set of analyses for the MCBF dataset, we find that for a given number of inputs, the fraction of the ChF 1 type within NCFs is typically larger than that of the ChF 0 and non-ChF U NCF types within the NCFs (see SI Fig. S3 (a) and SI Table  S9 ). In fact, ChF 1 is relatively enriched within NCFs for all values of k except k = 2, whereas ChF 0 is relatively enriched only when k = 6, 7, 8 (see SI Fig. S3 (a) and SI Table  S10 ). Furthermore, ChF U is relatively enriched within NCFs for all k ≥ 3, but only those enrichments where k > 3 are statistically significant. The complete set of values for the statistical significance associated with the relative enrichments is provided in SI Table  S11. These results obtained using the MCBF dataset are largely in agreement with those of the BBM benchmark dataset.
We now revisit an older dataset of BFs, namely the one published by Harris et al. [3, 24]. In this dataset, we find that for any given number of inputs, the fraction of ChF 0 within NCFs is larger than the corresponding fractions of ChF 1 and non-ChF U NCF types (see SI Fig. S3 (b) and SI Table  S12 ). Furthermore, the ChF 0 BFs are relatively enriched within NCFs and the enrichments are statistically significant (see SI Tables  S13  and S14  respectively). ChF 1 on the other hand is not relatively enriched within NCFs. The generalized chain functions, ChF U , are enriched for k = 3, 4, 5 but those enrichments are statistically significant only for k = 4, 5. These results are not so concordant with those arising from the BBM benchmark dataset in which the relative enrichment of ChF 0 is not statistically significant for k = 3, 4, 5, whereas it is so for ChF 1.
It is appropriate to note here that Kauffman et al. [3]  had observed that a significant fraction of the BFs in that dataset were NCFs and that most of those NCFs were ChF 0. In sum, the generalized chain functions (or ChF U ) comprise a special sub-type of NCFs that are quite consistently relatively enriched within NCFs across distinct reference biological datasets and are thereby able to reconcile the discrepancies observed in the relative enrichments of ChF 0 and ChF 1 within NCFs therein.
We then test for enrichment of the chain-0, chain-1 and generalized chain function within NCFs in a large dataset of reconstructed Boolean models (the BBM benchmark dataset): the result is that generalized chain functions are indeed highly enriched. In fact, using 2 other datasets of regulatory logics, namely, the MCBF and the Harris dataset, the same result holds. In addition, we demonstrate how generalized chain functions can severely constrain the space of biologically plausible models using 3 different biological models. Lastly, we perform model selection on those models using known relative stability constraints and are able to zero-in on a smaller subset of models that are more biologically plausible. Since their introduction by Gat-Viks and Shamir  [23] , the chain-0 functions have hardly received any attention.
Kauffman et al. identified that chain-0 functions were the sub-type of NCFs for which all the canalyzing input values are 0 and those authors showed its preponderance in the dataset of Harris et al. [24]. Akutsu et al. [25]  put forward the Boolean expression framework associated with chain-0 functions  [25] , making explicit the dependence of logical operators (∧, ∨) on the signs of the variables preceding it. Surprisingly, its dual class had never been proposed nor explored as a potentially biologically relevant type. Our work builds on all these works, piecing together several concepts pertaining to various representation of chain functions in a systematic manner, thereby providing insights into the nature of chain-0 (and chain-1) functions and the space they occupy within NCFs. Why are generalized chain functions preponderant in biological datasets? For one, the justifications for an enrichment of chain-0 functions given by Gat-Viks and Shamir  [23]  also apply to chain-1 functions.
Although these results provide novel insights, it is appropriate to make explicit some limitations in this work. Firstly, we have seen that chain-0 functions were enriched in the Harris dataset, however, when considering much larger datasets such as the BBM benchmark dataset and MCBF dataset, there are multiple values of the number of inputs where there is no such enrichment. Similarly, the chain-1 functions are enriched in the BBM benchmark dataset and MCBF dataset, whereas they are not enriched in the Harris dataset. With more data, we may expect that several other sub-types of NCFs may also contribute to the enrichment of NCFs. Furthermore, there is likely to be an (un)conscious subjective bias on BF logic when reconstructing Boolean models, and so we cannot exclude that such a bias is responsible for the enrichments found.
Secondly, the generalized chain functions can be so severely restrictive that it may be impossible to find corresponding BFs that satisfy both the fixed point and sign-conforming constraints as we found in the RSCN-2020 model. Our findings also invite several directions for future work. One is to quantify properties of the generalized chain functions that distinguish them from other NCFs and are likely responsible for their being so prevalent in these biological reference datasets. Another is to analytically tackle the question of whether the ratio of the number of the chain functions to that of the NCFs for a large number of inputs follows a rigorous exponential behaviour. still remain equal to m. In other words, any bias P ′ with the binary representation a n a n-1. a 1 b bb. b m-1 1, a i ∈ {0, 1} will have m last = m, ∀n ∈ N.
ACKNOWLEDGMENTS Areejit Samal  acknowledges support from the  Max Planck Society, Germany , through the award of a  Max Planck Partner Group in Mathematical Biology , and the  Department of Atomic Energy (DAE), Government of India , through the  Apex  project to The  Institute of Mathematical Sciences (IMSc), Chennai. IPS2 benefits from the support of  Saclay Plant Sciences-SPS  ( ANR-17-EUR-0007 ).
The mechanical stability of proteins is crucial for biological processes. To understand the mechanical functions of proteins, it is important to know the protein structure and mechanical properties. Protein mechanics is usually investigated through force spectroscopy experiments and simulations that probe the forces required to unfold the protein of interest. While there is a wealth of data in the literature on force spectroscopy experiments and steered molecular dynamics simulations of forced protein unfolding, this information is spread and difficult to access by non-experts. Here we introduce MechanoProDB, a novel web-based database resource for collecting and mining data obtained from experimental and computational works. MechanoProDB provides a curated repository for a wide range of proteins, including muscle proteins, adhesion molecules and membrane proteins.
The database incorporates relevant parameters that provide insights into the mechanical stability of proteins and their conformational stability such as the unfolding forces, energy landscape parameters and contour lengths of unfolding steps. Additionally, it provides intuitive annotations of the unfolding pathways of each protein, allowing users to explore the individual steps during mechanical unfolding. The user-friendly interface of MechanoProBD allows researchers to efficiently navigate, search and download data pertaining to specific protein folds or experimental conditions. Users can visualize protein structures using interactive tools integrated within the database, such as Mol*, and plot available data through integrated plotting tools. To ensure data quality and reliability, we have carefully manually verified and curated the data currently available on MechanoProDB.
In addition, computational 𝑥 β 𝑘 𝑜𝑓𝑓 techniques such as steered molecular dynamics simulations (SMD)  11  enable atomic level understanding of these molecular processes by mimicking SMFS experiments. Both experimental and computational approaches have been applied extensively to probe the mechanical stability of proteins in recent years, reporting unfolding forces at different pulling velocities or loading rates on hundreds of proteins  7. However, accessing and understanding the vast amount of available experimental and computational data of protein unfolding remains challenging for non-experts. While there are excellent reviews compiling a considerable amount of experimental forced unfolding data on different protein systems that inspired our work, compiled data is not available in the form of an accessible database  7, 12.
The only existing database in the field is the Biomolecule Stretch DataBase (BSDB)  13. BSDB mainly stores synthetic data obtained from a Go-like model  14. Experimental data extracted from a literature survey is also available in BSDB  13  , however the compiled parameters are limited to protein length, unfolding forces, velocities and CATH references  15  and to works published between 1997 and 2009. However, as unfolding forces depend on the experimental conditions, information about the energy landscape and kinetic parameters is missing. Moreover, an interactive and more user-friendly interface would allow the user to, for example, filter the data using keywords, broadening its usage. To fill this gap and to allow users to search, filter, interact and contribute with data, we introduce MechanoProDB, a web-based database that will serve as a comprehensive and curated resource for experimental and computational forced unfolding of proteins.
The user-friendly interface enables researchers to efficiently explore, search, and download data related to specific protein folds or experimental conditions. Moreover, interactive tools and plugins allow users to visualize protein structures, while integrated plotting tools allow them to easily represent data. To ensure the reliability and quality of the database, the available data has undergone meticulous manual verification and curation. Our manual annotation of the unfolding process, unfolding pathways, and structural features enhance the depth and accuracy of available high-quality experimental and computational information, which is not available in other resources.
DataBase structure, features and content The MechanoProDB database is composed of one main table: MPDB_Proteins which contains the collected and annotated data from literature. Contributions from users are manually annotated and inserted within MPDB_Proteins. MechanoProDB was developed in HTML5/PHP 8. 1 and MySQL 8. 0. The main JavaScript  18  DataTable of the database contains 34 columns storing both mechanical and structural information. Visualization of protein structure and sequence simultaneously is incorporated using the Mol*  19  plugin. Complementary information about protein structure and function is extracted from the protein data bank (PDB) using an automated python script. This information includes SCOP structural annotation, functional classification, organism, and protein length.
Contributions from users In MechanoProDB, users are given the possibility to contribute data and provide feedback. A dedicated page was built for this purpose. To facilitate this process, users who want to submit new results of proteins having a solved experimental structure, will need to provide only the Protein DataBank Identifier (PDB ID), as structural information, in addition to the unfolding forces with their respective velocities or loading rates. Other complementary information about structure and function such as SCOP annotation, functional classification, organism, and protein length, will then be extracted from the Protein DataBank (PDB) using our automated Python script. The contribution page takes as input measurements of the unfolding forces with their corresponding velocities and/or loading rates.