dataesr/scientific-paragraphs-categorization huggingface dataset:
PYTHIA We here describe how we modified the PYTHIA public code to include the effect of cascading in matter in an event-by-event basis. We improved with respect to our previous computation  [5]  where we had only included averaged energy losses in matter. Moreover, we here use PYTHIA version 8. 176 (version 6. 2 was used in  [5] ). The process of particles with mass m and initial energy E 0 m decaying with life-time τ , while at the same time losing energy due to interactions with the surrounding matter, is described by a differential equation for their energy E and their number n: dE dt = -α -βE, dn dt = - n τ m E ; (19) that is: the energy loss of particles in matter can by approximated as a constant term α plus a term β proportional to their energy, while their number n is just governed by τ (the factor m/E takes into account time dilatation).
Acknowledgments We thank  Nicolao Fornengo  for useful discussions and a patient cross-check of some of the results of Cirelli et al. in [5]. We thank  Paolo Panci ,  Teresa Montaruli  and  Sofia Vallecorsa  for useful discussions and  Eugenio Del Nobile  for pointing out a typo. We thank  Vladimir Kulikovskiy  for pointing out a typo in eq. ( 18) of the v2 of this work, now corrected. M. C. acknowledges the hospitality of the  Institut d'Astrophysique de Paris (IAP)  and of the Theory Unit of CERN where a part of this work was done.
Background: The genetic diversity observed among bacteriophages remains a major obstacle for the identification of homologs and the comparison of their functional modules. In the structural module, although several classes of homologous proteins contributing to the head and tail structure can be detected, proteins of the head-to-tail connection (or neck) are generally more divergent. Yet, molecular analyses of a few tailed phages belonging to different morphological classes suggested that only a limited number of structural solutions are used in order to produce a functional virion. To challenge this hypothesis and analyze proteins diversity at the virion neck, we developed a specific computational strategy to cope with sequence divergence in phage proteins. We searched for homologs of a set of proteins encoded in the structural module using a phage learning database.
Results: We show that using a combination of iterative profile-profile comparison and gene context analyses, we can identify a set of head, neck and tail proteins in most tailed bacteriophages of our database. Classification of phages based on neck protein sequences delineates 4 Types corresponding to known morphological subfamilies. Further analysis of the most abundant Type 1 yields 10 Clusters characterized by consistent sets of head, neck and tail proteins. We developed Virfam, a webserver that automatically identifies proteins of the phage head-neck-tail module and assign phages to the most closely related cluster of phages. This server was tested against 624 new phages from the NCBI database. 93% of the tailed and unclassified phages could be assigned to our head-neck-tail based categories, thus highlighting the large representativeness of the identified virion architectures.
As a result, the most abundant Type 1 could be divided into 10 Clusters, some exclusively containing Siphoviridae or Myoviridae, and others aggregating both Sipho-and Myoviridae. We developed a Webserver, called Virfam, to map any novel phage genome on our classification scheme. By testing this server on 624 phage genomes from the NCBI database not yet included in our dataset, we confirmed the large applicability of our classification approach, as 93% of them could be classified within one of the Type/Cluster classes. Beyond phage classification, this study also provides insights into the possible organization of ancestral neck modules in Caudovirales.
HMM Profiles generation for proteins of the learning database For all the 28300 phage sequences contained in the Aclame database (version 0. 4)  [30] , a profile was built following the protocol described in  [29]. In the latest release of Aclame (version 0. 4), 465 bacterial phage genomes are accessible but only 447 fulfilled the criteria of being bacteriophages (10 are phages infecting Archeae) with treatable sequences (8 were not properly implemented in Aclame). Briefly, for every sequence, a 3 iteration PSI-Blast  [31]  search was performed against the non-redundant (nr70 (dec. 2010)) database using a cutoff e-value of 10 -4. Whenever an iteration retrieved more than 1000 homologs, the previous iteration was kept so as to prevent divergence issues. The resulting multiple sequence alignment was filtered so as to keep the 100 most diverse sequences and was converted into a Hidden-Markov Model profile using the HHsuite programs  [32]  integrating the secondary structure prediction from Psi-pred  [33].
The detailed bioinformatics procedure described below was followed for each of the different component of the head-neck-tail module. To evaluate the sensitivity gains provided by profile-profile comparisons (HHsuite) with respect to profile-sequence ones (PSI-Blast), as presented in Table  2 , we followed the procedure described in Additional file 1: Method S1. Figure  1  Assembly pathway of tailed bacteriophages. In the tailed phages, capsid assembly starts with the construction of an icosahedral protein lattice called procapsid, essentially composed of a major capsid protein (noted MCP in brown in Figure  1 ). At a specialized vertex of the procapsid, the dodecameric portal protein (Portal in blue) forms a channel which is the docking point for an ATPase complex called terminase. This complex normally contains multiple copies of a large subunit with ATPase and endonuclease activities (TermL in orange), and a small DNA binding subunit that recognizes the cognate viral DNA Sun et al.
Detection of the head and tail proteins within the learning database We first searched for the major capsid proteins, portal proteins, terminases, major tail proteins and Sheath proteins within Aclame 0. 4. The various components of the head and the tail were identified starting from proteins whose 3D structures were solved and using our iterative profile-profile comparison procedure with a probability confidence threshold of 90% as described in  [29]. In the case of the major capsid proteins, the 3D structures are known from X-ray data for the Siphophage HK97 and the Myophage T4. The HK97 and T4 major capsid proteins exhibit a similar polypeptide fold  [34]. Consistently, they were detected as related by HHsearch with a confidence score of 93%. We used their profiles as starting points in order to detect other proteins belonging to the major capsid superfamily.
Search for the fold of these proteins using HHpred  [45]  against a profile database derived from the Protein Data Bank revealed that T4-like MTP likely share the fold of phage λ major tail protein gpV (probability score higher than 90%). This suggests that myophages of the T4 family also present a tail protein evolutionary linked to that of the siphophages. Finally, regarding Sheath proteins, the 3D structures are known for phages T4  [46]  and PhiKZ  [47]. These structures exhibit a common structural core  [47]  that was not detected by HHsearch. 70 Sheath proteins were identified starting from the T4 protein, out of the 74 Myophages in Aclame. Only 2 Sheath proteins were identified starting from the PhiKZ protein, corresponding to the giant phages PhiKZ and PhiEL. Within the 2 myophages left without any assigned Sheath protein, C-st was experimentally shown to be a myophage and should have a Sheath protein.
Detection of the head-and tail-completion proteins using remote homology search and genetic context A bioinformatics procedure was designed in order to systematically detect the phage head-completion and tail-completion proteins, also called head-to-tail connection proteins, within the Aclame database (Figure  2A ). To do so, the characterized head-to-tail connection proteins of phages SPP1, λ, HK97, T4, P22 and Φ29 were taken as starting point. Next, their profiles were compared to the database of 28300 HMMs profiles using the profile-profile comparison algorithm HHsearch  [32].
Type 1 First, all possible head-to-tail connection proteins Ad1, Hc1 and Tc1 were identified among the 447 genomes by searching for homologs of the SPP1 gp15, gp16 and gp17 proteins using the program HHsearch with a high confidence probability threshold of 90%. Next, the intergene distances between the detected Ad1, Hc1 and Tc1 proteins were calculated and averaged on all genomes. The resulting mean inter-gene distances were 1, 2 and 3 for the (Ad1, Hc1), (Hc1, Tc1) and (Ad1, Tc1) couples, respectively, corresponding to the gene ordering: Ad1-Hc1-x-Tc1. They could be organised into a mean distance matrix characteristic of Type 1 neck gene organisation. We also calculated for each couple the standard deviation on the inter-gene distances. From these calculations we deduced a tolerated distance matrix, formed by adding to each mean distance matrix term twice the inter-gene distance standard deviation.
Thus, our procedure did not detect any spurious remote homologs in the particular cases of necks comprising a gpW-like protein. We specifically analyzed the genomes lacking only one of the Ad1, Hc1 and Tc1 elements. Searching within the limits imposed by the tolerated distance matrix, 3 Ad1, 5 Hc1 and 13 Tc1 proteins were identified in Siphoviridae. These proteins were predicted as having the same secondary structure patterns as the missing ones and were located at distances from the other identified neck proteins compatible with the tolerated distance matrix. They were not automatically selected by our initial profileprofile procedure because their HMM profile was built from a too limited number of sequences (less than 5 homologous sequences in the nr database retrieved at the PSI-Blast stage).
Type 2 The head-to-tail connection proteins Ad2, Hc2 and Tc2 were identified by searching for homologs of the T4 gp13, gp14 and gp15 proteins using the program HHsearch with a 90% confidence threshold. Inter-gene distances were calculated between the identified proteins resulting in mean distances of 1, 1 and 2 for the (Ad2, Hc2), (Hc2, Tc2) and (Ad2, Tc2) couples, respectively. This corresponds to the ordering: Ad2-Hc2-Tc2. The tolerated distance was calculated as above by summing the mean and twice the standard deviation inter-gene distances. The tolerated Figure  2  Identification of head-to-tail connection proteins in tailed bacteriophages and representativeness of the different phage Types. (A) Schematic representation of the bioinformatics pipeline used to identify remote homologs of head-to-tail connection proteins.
Reference HMM profiles of known head-to-tail connection proteins (Table  1 ), as well as HMM profiles of each of the 28300 protein sequences contained in the Aclame database, were calculated using PSI-Blast (Step 1). These profiles were compared using HHsearch with a stringent probability threshold of 90%, and proteins detected as related to the reference head-to-tail connection proteins were iteratively used as probes in order to detect further homologs (Step 2). Inter-genes distances were then learned (Step 3) and applied as constraints to faithfully retrieve more remote homologs detected at a lower probability threshold (70%) (Step 4). (B) Components of the four neck Types are represented using the color code defined in Figure  1. Their mean inter-genes distances and standard errors were calculated as illustrated in Step 3 of panel A.
(C) Quantitative distribution of the tailed bacteriophages of known morphology and recognized neck Type. Sector color code is the following: white, Siphoviridae of Type 1; light gray, Myoviridae of Type 1; dark gray, Myoviridae of Type 2; hatched, Podoviridae of Type 3; black, Podoviridae of Type 4. Dotted surfaces in Type 1 sectors correspond to phages with incomplete necks, for which one to two canonical components of the neck were not identified. distances were 2, 2 and 3 for the (Ad2, Hc2), (Hc2, Tc2) and (Ad2, Tc2) couples, respectively. As for Type 1, we constrained the search using this inter-gene tolerated distance matrix and repeated the iterative profile-profile search with HHsearch, relaxing the probability threshold from 90% to 70%. As a result, we identified 49 Type 2 neck proteins (Table  2 ; Additional file 2: Table  S1 ).
Scoring of the evolutionary divergence between head-neck-tail modules for phage classification Our analysis identified a set of 9 classes of proteins of the head-neck-tail module comprising 2 classes from the head (major capsid, terminase), 5 from the neck (Portal, Ad, Hc, Tc, Ne) and 2 from the tail (major tail, Sheath). Every class encompasses a number of Aclame protein families that were previously thought unrelated and which are now connected through remote homology relationships by the procedure described above. Taking advantage of this global view of the head-neck-tail organisation, we searched for a metric which would account for the evolutionary divergence between the phage components of the head-neck-tail module. We used a score depending both on the HHsearch probability (ProbaHHsearch) but also on the sequence identity (PercentIdentity) for closely related sequences.
SimScore ¼ 1 Ã ProbaHHsearch þ 0:1 Ã PercentIdentity ð1Þ The weight of 0. 1 assigned to the PercentIdentity factor ensured that the latter term only contributes when ProbaHHsearch caps at 100% because values of Pro-baHHsearch below 100% generally correspond to remote homology relationships with PercentIdentity below 25%. For every pair of phages and for all the components of the capsid-neck-tail module (out of the nine possible components), a similarity score was calculated using equation 1. The mean value of all these scores was computed over all the components of the module common to both phages (Portal, Ad, Hc etc. …) in order to yield the similarity score between the pair of phages. It was calculated by adding scores corresponding to superfamilies detected in both phages and ignored superfamilies only detected in one of them.
The mean value was used as a metric of similarity of the capsid-neck-tail module between two phages and a NxN matrix of averaged scores was built from the systematic cross-comparison of all N phages of each type. To group together phages sharing similar average scores, the NxN matrices were then clustered using a hierarchical agglomerative clustering with WPGMA method (Weighted Pair Group Method with Averaging) together with Euclidian distance and a tree corresponding to each neck type was built from these calculations using the ete2 library  [50]. For the phage classification step, we took into account all phages with at least two detected head-to-tail connection proteins in the case of Type 1 and 2 phages (including T5 which has only Ad1 and Tc1 proteins), and one detected protein in the case of Type 3 and 4 phages (including N4 which has only one Ad3 protein).
Detection of head and tail proteins within the learning dataset Our structural classification of phages relies on the detection of 9 genes coding for head, neck and tail proteins. We first searched for homologs of 5 head and tail proteins using the homology detection tool HHsearch  [32] , which relies on the comparison between pairs of multiple sequence alignments (also called profiles). This tool can reveal more remote homologies between proteins than the profile-sequence comparison tool PSI-Blast  [31]. It was used with a high confidence probability threshold of 90% to search for the portal, large terminase subunit (noted here TermL but also often abbreviated as TerL) and major capsid protein (MCP) on the head side, the major tail (MTP) and sheath proteins on the tail side, among a set of 447 complete phage genomes, including 303 tailed phages (Caudovirales), 119 non tailed phages and 25 uncharacterised phages (taken from Aclame version 0.
Detection and classification of head-and tail-completion proteins within the learning dataset Once the head and tail proteins were identified, we focused on the head-to-tail connection proteins to capture the diversity of neck organisations in tailed phages. We concentrated on the identification of a maximum of highly divergent head-to-tail connection proteins. Therefore, we identified from the literature several proteins characterized as head-and tail-completion proteins in a number of model phages (Table  1 ), and we search for homologs of these proteins within the genomes of the same 447 completely sequenced phages. Our homology search was performed using the homology detection tool HHsearch, which was now used iteratively to detect highly remote homologs (Figure  2A ). A stringent confidence probability threshold of 90% was again chosen to identify homologs of our list of starting proteins (Table  1 ) among the 28300 proteins encoded by the 447 phages.
Using the gene context to detect additional head-and tail-completion proteins within the neck module At this stage, we observed that several phages could be assigned to one of the four types defined above but lacked one of the neck gene. In particular, about 13, 28 and 24% of Type 1 necks lacked an Ad1, Hc1 and Tc1, respectively, and about 85% of Type 3 necks lacked an Ad3 when using HHsearch with a confidence probability threshold of 90%. We wondered whether absence of these neck proteins was real or due to, once again, the huge sequence divergence. To further explore the existence of putative very remote homologs, we lowered the confidence probability threshold of HHsearch to 70%. However, such a threshold was found too permissive in some cases and led to the detection of spurious homologs.
To improve the detection specificity, we implemented an additional constraint related to the conserved head-to-tail connection module organisation observed among most of the phages (Figure  2A ). In practice, the distances between the previously detected head-to-tail connection genes were calculated from their positions in the genomes. Figure  2B  summarizes the mean distances (and corresponding standard deviations) observed between Type 1, 2, 3 and 4 detected genes. We observed strong constraints on the relative position of the head-to-tail connection protein genes, from which we defined distance interval thresholds, corresponding to the mean +/-two standard deviations. Using these distance thresholds, we could decrease the HHsearch confidence threshold from 90% down to 70% and detect additional head-to-tail connection proteins without inclusion of spurious homologs.
Two exceptions were identified corresponding to phages that are most probably mis-assigned in the NCBI database as deduced from recent experimental data: (i) 3 phages annotated as Siphoviridae for which we detected Podoviridae-like Ad3 and Hc3 proteins specific to Type 3 neck; these phages are Stx1 and Stx2 converting phages, which are closely related to 933 W unambiguously recognized as a Podoviridae  [53, 54] ; (ii) 1 phage annotated in NCBI as Siphoviridae for which we detected Type 1 neck proteins and a sheath; this phage was recently reported as a Myoviridae by  [55].
However, most Ne1 proteins were detected with a HHsearch confidence threshold higher than 95% (Additional file 1: Figure  S2 ). The remarkable systematic presence of their gene in Type 1 neck modules suggests a critical role in the head-to-tail connection assembly or function. Scattered experimental data exist on the function of Ne1 proteins. In the Siphophage λ, in the absence of the Ne1 protein GpZ, viral particles are produced, but they have low infectivity  [56]. GpZ was proposed to be part of the virion tail  [57]  and to represent a conserved family of tail proteins  [58] , although the systematic presence of a remote homolog in almost all Type 1 phages remained hidden due to sequence divergence. The phenotype is slightly different in mutants of the Ne1-encoding gene gpS of Myophage P2: phages form tails that are unable to attach to heads, and are non-infectious, suggesting a defect in the head-tail joining process  [59].
Phage classification from the "head-neck-tail" module analysis From our analysis of phage necks, we deduced that Type 1 necks are the most prevalent. Considering the large size of this group, we further subdivided it according to a metric which accounts for the "average" evolutionary divergence among the various proteins composing the defined head-neck-tail module. The probability that two protein profiles are similar as calculated by the HHsearch program is an interesting metric for quantifying the degree of remote homology between proteins. However, in case of close homology, typically above 35% of sequence identity, HHsearch probabilities peak at 100% and are not discriminative. To account for the whole spectrum of sequence divergence, we used a similarity score primarily driven by the HHsearch probability but with an additional contribution of sequence identity to properly recognize closely related phages (see Methods).
For every pair of phages, similarity scores were calculated between all components of the head-neck-tail module (comprising up to 9 proteins) and then averaged to yield a mean score reflecting the similarity between the head-neck-tail modules of the phage pair. From this metric, a hierarchical agglomerative clustering procedure was used to obtain a tree representation of phage similarities (Figure  3A ; this analysis is extended to Types 2-4 phages on the Virfam webserver). The clustering procedure discriminated ten major Clusters within the Type 1 phage family. Inside each Cluster, HHsearch probabilities between homologous proteins are often close to 100%, but even in these cases, identities between protein sequences can be very low (in the range 10-20%) (analysis of a representative subset of phages of Type 1 Cluster 1 in Additional file 1: Figure  3  Classification of the Type 1 bacteriophages.
(A) Tree representation of Type 1 phage similarities, built from a hierarchical agglomerative clustering procedure applied to a matrix of similarity scores between pairs of phages (combining HHsearch probabilities and percentage of identity) and represented using the ETE2 library  [50]. The different branches of the tree were sorted into 10 Clusters, highlighted by different background colors. Phage names labelled by black circles filled in grey indicate the Myoviridae phages. Bacterial hosts of the phages are indicated in the bottom for each Cluster with the same color code as in the classification tree, in order to highlight the consistency between the Cluster and host phyla. (B) Gene organisation of a representative phage of each Cluster. A more complete view of gene organisation sorted by Clusters is presented on the Virfam webserver, in order to highlight the consistency between the Cluster and neck gene order distributions.
Also, genome organization of the head-neck-tail module is partitioned in a homogeneous manner among the Clusters although no prior constraint related to gene order or to inter-gene distance was included in the clustering metrics (Figure  3B ; see also the Virfam webserver). An additional remarkable feature standing out from this classification is that phages from the Myoviridae family do not tend to cluster together. Phages with a sheath in their genome are spread over more than half of the Clusters, namely Clusters 1, 3, 6, 7, 8 and 9, together with closely related phages deprived from a contractile system. Such versatility in the presence/absence of a sheath protein had previously been noticed in the case of phages related to Mu (grouped in Cluster 8)  [15]  and appears as a general property of Type 1 phages.