dataesr/scientific-paragraphs-categorization huggingface dataset:
The four sources IntAct, DIP, MINT, HPRD and SIFTS contained PPIs expressed as ordered pairs of UniProt sequence accession numbers (UniProtIds). In BioGRID and STRING, proteins are designated with an identifier system specific to each database. These identifiers were mapped to UniProtIds to produce the BioGRID and STRING datasets of PPIs. In the SIFTS database, associations between PDB chains were extracted and PPIs displaying a high possibility of interaction according to  [51]  were stored. Then, PDB chains possessing a representative UniProtId were replaced by this UniProtId. Algorithm 1 Calculating a Consensus Similarity Matrix from Multiple Sources of Common Neighbors The numbers of PPIs obtained from the input resources are shown in Table  1. A very large number of protein interactions is drawn from the STRING database, while the SIFTS database only provides a small collection of observed PPIs.
We then categorized the STRING PPIs according to experimental and non-experimental (Text mining, Neighborhood, Fusion-fission events, Occurrence, and Coexpression) labels and stored them as STRING-exp and STRINGrest datasets, respectively. Input: Mult ¼ fG d 1 ðX; Z d ; E d 1 Þ; G d 2 ðY; Z d ; E d 2 Þ; d ¼ 1;. For each data source, the PPIs ppi k were represented by ordered pairs of UniProtIds (L k , R k ), in which L k always precedes R k in the alphanumerical order to avoid redundancy. Associations between UniProtIds and Pfam domains were then extracted from UniProtKB/ SwissProt and UniProtKB/TrEMBL to give a dataset of UniProtIds-Pfam relationships for.
Methods for PPIDM result evaluation The set of inferred DDIs was compared with various other sets of DDIs using Python dataframes and a setwise representation for DDIs to avoid duplicate comparison of symmetrical pairs. The June2017, January2018, January2019 and April2020 releases of 3did were used after subtracting the Gold-Standard data set (7,254 DDIs), in order to check how many inferred DDIs correspond to DDIs in 3did that were not used as Gold-Standard during PPIDM generation, and how many inferred DDIs correspond to DDIs that were not known from 3did at the time PPDIM was generated. The DOMINE 2011  [39]  dataset was also downloaded from its web sites (https://manticore. niehs. nih. gov/cgi-bin/Domine and prepared for similar comparison purpose. Venn diagrams were generated using the matplotlib Python library.
The coverage of PPIs by DDIs was measured in a large set of non redundant PPIs, named here IMEx-PPIs, extracted from the curated database assembled by the International Molecular Exchange Consortium (IMEx;  [52, 53] ), downloaded from https://www. imexconsortium. org/ on 23 August, 2020. Another dataset was also built using the human STRING subset of PPIs  [54] , downloaded on 30 July, 2019, and filtered to retain only PPIs with a STRING score greater than 800. This dataset is named here hSTRING-PPIs. Only PPIs composed of proteins containing at least one Pfam domain were retained, leading to a total of 50,032 and 607,088 PPIs for IMEx-PPIs and hSTRING-PPIs respectively. A PPI is counted as covered by a DDI inferred from PPIDM when at least one DDI from this dataset is present among the pairs of domains derived from the domain composition of each protein in the PPI.
A corollary result is the estimation of the percentage of useful DDIs in the dataset. A useful DDI is a DDI used to cover at least one PPI. Counting was performed with PPIDM and DOMINE datasets. A negative control was added here thanks to a dataset of negatively labelled DDIs known as Nega-tome2. 0  [55]  that was downloaded from http://mips. helmholtz-muenchen. de/proj/ppi/ negatome/), and prepared similarly to the other datasets.
Data source weights and similarity score threshold Our merged dataset of scored DDIs contains 513,260 IntAct, 75,823 DIP, 97,487 MINT, 69,940 HPRD, 816,807 BioGRID, 4,131,112 STRING-EXP, 4,050,795 STRING-REST, and 60,114 SIFTS candidate DDIs between Pfam domains, giving a total of 4,592,763 distinct DDIs (Table  2 ). In our ROC-based training procedure, the best AUC value of 0. 9944 was obtained with weights w IntAct = 0. 05, w DIP = 0. 01, w MINT = 0. 01, w BioGRID = 0. 09, w STRING -Exp = 0. 12, w STRING -Rest = 0. 06, w HPRD = 0. 17, and w SIFTS = 1. 0. These weights give far greater importance to the candidate interactions in the SIFTS dataset, which is derived from the PDB, compared to those from other databases. This is consistent with the fact that our Gold-Standard positive instances are observed interactions extracted from PDB entries.
Analysis of the inferred DDIs The overall results of PPIDM execution are summarized in Table  2. This table shows the numbers of DDIs before and after filtering with the consensus score threshold. After applying the 0. 01586 score threshold, the number of pairwise DDIs falls to 84,552 i. e. 1. 84% of the merged dataset with an overlap of about 96. 3% (6,989�7,254) with the Gold-Standard (3did \ KBDOCK) reference DDIs. Table  3  shows the distribution of PPIDM inferred DDIs in our Gold, Silver, and Bronze categories, along with the degree of overlap with the Gold-Standard reference dataset. This table shows that PPIDM provides 9,175 Gold DDIs (with only statistically significant scores in more than 4 PPI sources) and 24,934 Silver DDIs (with only statistically significant scores in less than 4 PPI sources), and 50,443 Bronze DDIs (having at least one non statistically significant score).
Evaluation of PPIDM predictions It is very difficult to review individually the large amount of DDIs inferred by PPIDM. A first attempt of global evaluation has consisted in analyzing the capacity of PPIDM to infer experimental DDIs, for example observed in PDB complexes, outer from the Gold-Standard. For this purpose, we downloaded the DDI sets from the 2017(june), 2018, 2019 and 2020 releases of the 3did database, we subtracted the Gold-Standard set of DDIs (7,254 DDIs) leading to the so-called 3did δ dataset. We then checked the overlap between the remaining DDIs and the set of DDIs inferred by PPIDM (Fig 3  , panel A ) or DOMINE (panel B). It can be seen that the DDIs inferred by PPIDM cover an increasing number of DDIs from the various 3did releases. The percentage of coverage decreases with time (from 70% for the 2017 release to about 46% for the 2020 release).
A similar behaviour is observed with the DOMINE dataset but to a much lesser extend. The percentage of coverage varies from 28% for the 2017 release, to about 17% for the 2020 release of 3did, at the advantage of the PPIDM approach. More precisely, from the The disadvantage of DOMINE here is likely due to the fact that the datasets it contains have been produced several years ago (from 2004 to 2010). However for PPIDM, it shows that a non negligeable subset of inferred DDIs are validated by observations in 3did that did not exist at the time PPIDM was produced. The decrease in the percentage of coverage of 3did by PPIDM inferred DDIs can be explained by the rapid growth of 3did that directly follows the growth of the PDB. Recent PDB entries, posterior to 2017 could not be used by our version of PPIDM (2017).
Indeed, we determined that among the 3,859 DDIs not inferred by PPIDM in 3did 2020, 90. 3% had a very limited number (Nb � 5) of PDB entries before 2017, including 39. 1% of DDIs without any PDB entry in 2017 or before. By design, it was impossible for PPIDM to infer such DDIs. Another way to evaluate the PPIDM set of inferred DDIs was to study the coverage of existing PPIs by these DDIs. For this purpose, we used a recent dataset (august 2020) of 50,032 non redundant curated PPIs from the IMEX database  [53]. Only PPIs composed of proteins containing at least one Pfam domain were retained to allow coverage analysis by 3did 2020, PPIDM, DOMINE, and Negatome as a negative control. Results are presented in Fig  4A  and  reveal that PPIDM covers 13,316 PPIs from IMEx, i. e. about 4,000 PPIs more than DOMINE and almost 2.
2 times higher than the number covered by 3did 2020. To complement these results, we also computed the number of DDIs that cover at least one PPI of the IMEx dataset. The obtained results are shown in Fig 4B. The number of relevant DDIs for PPI coverage in PPIDM is more than 3 times the number of relevant DDIs in DOMINE and 4. 6 times higher than the number of relevant DDIs in 3did2020. Thus, the PPIDM dataset encompasses an interesting diversity of DDIs that deserves further studies. Similar results were obtained at a larger scale using a subset of STRING containing 607,088 human well-scored PPIs (Fig  5 ). These results yield an update of the capacity of existing available sets of DDIs to cover large-scale sets of PPIs on the basis of their Pfam composition: about 24%, 35% and 30% of the STRING subset of PPIs are covered by DDIs from 3did2020, PPIDM and DOMINE, respectively (Fig  5A ).
Moreover, a total of 23,297 DDIs (i. e. 27. 5% of the PPIDM dataset) are used to cover at least one PPI of the hSTRING-PPIs dataset (Fig  5B ). Finally we selected a few examples of newly inferred DDIs to study their possible biological interest. We selected the PPIDM (Gold) DDIs that cover at least one PPI from Imex and filtered out the DDIs present in 3did 2020 or DOMINE. There were 1,915 DDIs left. We extracted those DDIs covering more than 10 PPIs in IMEx (155 DDIs) and ranked them from higher to lower PPIDM consensus score. In Table  4 , we present five examples selected on the basis of interpretable Pfam description among the top-15 DDIs. Only the first DDI here is an homodimer. The concerned domain PF01352 is part of a zinc finger protein and is involved in protein-protein interactions.
The observation of this inferred DDI suggests that at least some zinc finger proteins could act as dimers. The second DDI   4. Description of selected Gold DDIs newly inferred by PPIDM and absent from 3did2020 or DOMINE. The PPIDM consensus score and the number of covered PPIs in the IMEx database are indicated. The domain short name is taken from the corresponding Pfam entry and followed by a short description adapted from the corresponding Pfam entry.
Discussion This paper has introduced and presented a new approach named PPIDM for mining proteinprotein interactions at the domain level. Threshold optimization was carried out with a Gold-Standard of positive and negative examples and yielded very high F-measure corresponding to high recall and precision values. The resulting dataset contains 84,552 inferred DDIs overlapping with 96. 3% of the Gold-Standard positive examples derived from 3did. The PPIDM dataset of inferred DDIs represents the largest available repository of inferred DDIs to date, that also includes the largest number of DDIs involved in explaining a large number of non redundant curated PPIs. The large size of the PPIDM dataset contrasts with the more limited sizes of DOMINE or DIMA 3. 0 datasets (around 26 and 50 thousands of DDIs respectively).
However, other authors already got even larger datasets in the past. In  [9] , a dataset of 288,098 DDIs was inferred using two neighborhood cohesiveness coefficients and a combined proportion method on the STRING interactome. In that work as in ours, the purpose is not the same as with the parsimonious methods that aim to explain a maximum number of PPIs in an interactome with the minimum number of DDIs. Indeed, large repositories of DDIs should rather be understood as reservoirs from which possible DDIs can be picked up to support working hypotheses or to select candidate interactants for a protein of interest. As the DDIs inferred by PPIDM are qualified with a score and a p-value, many explorations are possible from now on with this dataset. For example it will be interesting to analyse the 800 DDIs inferred in 2017 that were subsequently found new in 3did between 2017 and 2020, in order to learn which features or annotations associated with these DDIs have favored their experimental confirmation in 3did.
This difference in the distribution of connected components is consistent with the notion that PPIs can display much more interconnections than DDIs because proteins can interact with multiple partners via several domains. It should be noted that the number of connected components of size 1 correspond to isolated domains that only interact with themselves. However self-interacting domains (or homo-DDIs) are also present in the other components. In total PPIDM counts 7,203 homo-DDIs of which exactly 3000 and 4160 are present in the Gold and Silver subsets respectively, corresponding to 79. 6% and 45. 2% of the nodes respectively. These percentages can be compared to those observed in 3did 2020 (70. 6%), DOMINE (64. 2%), or the one reported for UniDomInt (32. 5%) in  [40]. This clearly indicates that not all domains are capable of self interactions and that, in terms of network properties, the PPIDM (Gold) dataset is closer to the reference 3did 2020 than are the PPIDM (Silver) or DOMINE datasets.
In DDI networks, these outliers indeed correspond to domains responsible for interactions in a large variety of proteins. Three of them (PF00018, PF00069 and PF00096) belong to the list of outliers observed in Uni-DomInt  [40]. A limit of this study is certainly that the PPIDM dataset has been produced on 2017 releases of available PPI resources. While it is always possible to update the dataset on more recent releases, it seemed relevant to us to explore the predictive value of these results derived from previous sources in the light of new data (PPIs or DDIs) obtained subsequently. Another limit lies in the fact that the PPI sources used in this study are overlapping. For example, STRING imports its experimental data from IMEx, BioGRID and PDB, among other sources and IMEx is made up of IntAct, MINT and DIP.
Thus, a non negligeable proportion of PPIs have been reused several times to infer DDIs. Nevertheless, it should be noted that the CODAC process computes similarity scores and p-values for each PPI source separately. These separated values are available in the datasets proposed for download at http://ppidm. loria. fr. Then, data reuse is only effective (and somewhat inevitable) when merging scores, as in the case of other combined DDI datasets such as DOMINE. Another study would be to estimate the impact of this reuse of PPIs on the number or quality of DDIs recovered. Reuse of PPIs also occurs at the evaluation step with IMEx and a subset of STRING. However, this evaluation step does not claim to be similar to the validation of a predictive model in machine learning. It is more akin to evaluating the quality of a corpus produced by an information retrieval procedure.
Indeed, the main outcome of our work is to produce a large reservoir of DDIs available for further studies. Just like all other studies dealing with DDIs, PPIDM encounters by design a limitation in explaining PPIs that do not interact through well-defined conserved domains but rather through intrinsically disordered regions  [56]. This is likely the reason why a certain percentage of the interactome cannot be explained by inferred DDIs even with a large dataset such as PPIDM. With the tripartite graph paradigm, our PPIDM inference method is related to link prediction methods in multipartite or knowledge graphs. Our generic graph formulation of link prediction has been found to be useful for modeling the multi-source approach. In addition, the PPIDM setting makes it possible to infer interactions with domains subsets in addition to single domain interactions.
Conclusion This paper has introduced and presented a new approach named PPIDM for inferring DDIs from multiple sources of PPIs. The obtained dataset displays interesting properties including a good scoring of experimental DDIs and a significant coverage of existing PPIs. Further studies will be devoted to better describe the inferred DDIs and possibly validate them through largescale experimental studies. It could be envisaged for instance to look for correspondences between PPIDM DDIs and cross-linked peptides obtained with cross-linked mass spectrometry, as already performed for PPIs in Drosophila embryos  [59]. We believe that the large set of inferred DDIs produced in this study can be used to interpret interactome data and provide added-value to protein network analyses.
In order to compare PPIDM with the DOMINE dataset, we extracted DDIs from the file available from the latest version of the DOMINE database (2011). The DOMINE file contains 26,219 inferred DDIs (Pfam-Pfam interactions) with 5,410 distinct Pfam domains. This set (shown as green in Fig 2) was compared with the set of all 84,552 DDIs inferred by PPIDM (blue in Fig 2). This comparison showed that 8,433 DDIs from DOMINE (about one third of this dataset) are present in the PPIDM dataset, including 4,824 DDIs from the Gold-Standard (Intersection between yellow, blue, and green in Fig 2).
remaining 17,676 DDIs in DOMINE were then compared with the DDIs from the Gold-Standard. This comparison (the intersection of purple and yellow minus blue) showed that only 110 DDIs are common to DOMINE and the Gold-Standard but not to PPIDM, indicating that PPIDM misses only 2% (110 � 4,934) of the DOMINE DDIs confirmed by the Gold-Standard. This comparison also shows that the PPIDM result set only infers 3, 609 DOMINE DDIs from its 21,285 (26,219 -4,934) DDIs not shared with the Gold-Standard. This percentage is rather low (around 17%) and likely reflects the heterogeneity of methods used for DDI inference in DOMINE and the lack of consensus between the datasets merged in DOMINE.
://doi. org/10. 1371/journal. pcbi. 1008844. t004 in the table (PF11620-PF16517) involves two domains sharing the same SARAH region which is reported to mediate the formation of homo and hetero complexes. The third DDI (PF03931-PF12937) is between a domain present in SKP1 proteins and a domain (F-Box-like) known to mediate interaction with SKP1 proteins. Our fourth example (PF00622-PF13765) appears to concern two frequently associated domains PRY and SPRY, that are very similar. The SPRY domain is reported as a protein-interaction module but it remains to be demonstrated whether the two domains actually interact together. Finally, the last DDI in the table (PF00104-PF11825) involves the hormone-binding and activator-site domains of nuclear receptors. It is well known that these two domains are close to each other on nuclear receptors and they are likely to interact because binding to hormones often induces allosteric conformational changes leading to binding of an activator.
� Degree Sup is the superior degree value for 99% of the nodes ranked according to increasing degree. �� PfamId or UniProtId corresponding to the nodes having the maximal degree. PF07686: Immunoglobulin V-set domain; PF00018: SH3 domain; PF00096: Zinc finger, C2H2 type, domain; PF00069: PKinase domain; A8MQ03: Cysteine-rich tail protein 1; Q09472: Histone acetyltransferase p300.
Funding: MDD was beneficiary of grants from  Agence Nationale de la Recherche ; grant numbers:  ANR-11-MONU-006-02  and  ANR-15-RHUS-0004 ; https://anr. fr/and from the  FEDER-Contrat de Plan Etat Region Sante   ´-IT2MP , Region Grand-Est; https://www. grandest. fr/la-fibre/contrats-de-plansetat-region-2015-2020/. MDD was recipient of a Contrat d' Interface  ( 2017-2020 ) at the  Faculty Hospital of Nancy ; http://www. chru-nancy. fr/index. php/formation-recherche-et-innovation SZA was recipient of an  Inria Cordi-S fellowship  ( 2014-2017 ); https://www. inria. fr/. AAN was recipient of a post-doctoral fellowship co-funded by the  Region Grand-Est ; https://www. grandest. fr/vos-aidesregionales/soutien-aux-jeunes-chercheurs/and the  Faculty Hospital of Nancy  cited above. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
More examples of relevant new DDIs can be found on the website displaying all Gold DDIs as a searchable table by Pfam identifier (http://ppidm. loria. fr). PPIDM Covered Domain 1 Domain 2 DDI score PPIs PF01352- 0. 456 31 KRAB box: the KRAB domain (or Kruppel-associated box) is KRAB box: see left. PF01352 present in about a third of zinc finger proteins containing C2H2 fingers. The KRAB domain is found to be involved in protein-protein interactions. PF11629- 0. 315 11 Mst1_SARAH: this family of proteins represents the C Nore1-SARAH: Nore1 forms homo-and hetero complexes PF16517 terminal SARAH domain of Mst1. through its C-terminal SARAH domain. PF03931- 0. 252 26 Skp1_POZ: Skp1 family, tetramerisation domain. This domain F-box-like: Through the F-box, proteins are linked to the PF12937 is found at the N-terminal of SKP1 proteins.
SKP1 protein. PF00622- 0. 202 15 SPRY: SPRY Domain is named from SPla and the RYanodine PRY: a 50-60 amino acids domain associated with SPRY PF13765 receptor. It is a protein-interaction module involved in many domains, adjacent to its N-terminal. PRY and SPRY domains important signalling pathways. are structurally very similar and consist of a beta sandwich fold. PF00104- 0. 184 12 Hormone_recep: this all helical domain is involved in binding Nuc_recep-AF1: Nuclear/hormone receptor activator site AF- PF11825 the hormone in these receptors. 1. https.
9% 48. 3% 74. 8% 71. 7% 97. 6% 99. 6% 1-node CCs 2,244 727 1,368 1,052 57 23 2-node CCs 404 239 271 143 69 12 Degree distribution (number of nodes) analysis Degree 1 1,110 445 1,248 722 2,496 1,189 Degree 2 2,807 894 2,154 1,401 1,466 917 Degree 3 1,683 720 1,419 708 1,047 702 % nodes with degree >3 30. 4% 45. 4% 47. 6% 47. 7% 50. 0% 81. 9% Degree Sup � 17 27 30 98 78 431 Degree Max 368 88 108 499 451 2,423 PfamId or UniProtId �� PF07686 PF00018 PF00096 PF00069 A8MQ03 Q09472 https://doi. org/10. 1371/journal. pcbi. 1008844. t005.
However, all of these approaches require ground truth signals x for learning the reconstruction function x = f (y), which hinders their applicability in many real-world scenarios where ground truth signals are either impossible or expensive to obtain. This limitation raises the natural question: can we learn the reconstruction function without imposing strong priors and without knowing the ground-truth signals? Here, we show that typical properties of physical models such as rotation or shift invariance, constitute mild prior information that can be exploited to learn beyond the range space of A. We present an end-to-end equivariant imaging framework which can learn the reconstruction function from compressed measurements y alone for a single forward operator. As shown in Figure  1 , the equivariant imaging approach performs almost as well as having a dataset of ground truth signals x and significantly outperforms simply enforcing the measurement consistency Af (y) = y in the training process.
Equivariant Imaging We propose to use a trainable deep neural network G θ : R n → R n and an approximate linear inverse (for example a pseudo-inverse) A † ∈ R n×m to define the inverse mapping as f θ = G θ • A †. We emphasize that while in principle the form of f θ is flexible, here we use the linear A † to first project y into R n to simplify the learning complexity. In practice A † can be chosen to be any approximate inverse that is cheap to compute. We propose a training strategy that enforces both the measurement consistency in (2) and the equivariance condition in (4) using only a dataset of compressed samples Algorithm 1 Pseudocode of EI in a PyTorch-like style. {y i } i=1,. ,N. In the forward pass, we first compute x (1) = f θ (y) as an estimate of the actual ground truth x which is not available for learning.