dataesr/scientific-paragraphs-categorization huggingface dataset:
Discussion Altogether, the present results show that it is possible to computationally predict the affinity for FcRn of Fc variants mutated at the interface of the Fc/FcRn complex with reasonable precision (+/-1 log). To do so, we carefully collected as many as possible publicly available Fc variants/FcRn affinity data by scrutinizing the scientific literature and relevant patents. Since differences exist between protocols used to measure the affinities, we built two different datasets. The smallest one includes only values obtained using a single protocol; the largest includes all available values. To build the two models based on these data, a large number of features relevant to the affinity prediction of a protein complex as well as features relevant for this particular type of complex were included.
Model FLS Our entire dataset is composed of 1323 variants. However, we built our FLS model selecting only homogenous data, derived from an accurate technique (SPR), in order to limit noise that could be induced by outliers. The drawback is that the FLS model is biased towards a particular type of variants, namely variants engineered to have better affinity at pH 7. 0. Indeed, despite our efforts to get a maximum of unique variants from the patent database, our approach is still limited by the number and quality of data. For example, the exact K D value of a variant described as a non-binder cannot be known, yet the impact of its mutations would certainly increase performance. In addition, companies tend to only publish good results, i. e. , variants with better affinity, and not those with decreased affinity.
This results in a dataset with a majority of variants with high affinities for FcRn, which decreases the performance in estimating low affinities. The quality and consistency of data is also a prerequisite of any model. However, the accuracy of measures may be low, especially for variants that are discarded from the first round of selection. Moreover, there are also sometimes discrepancies between studies reporting affinities. For example, in a recent study  [17] , mutation N434S has been reported to reduce the binding affinity of Fc to FcRn, whereas in patent US20100204454 this sole mutation has been reported to enhance the binding by threefold. Another effect of the dataset bias is that not only K D but also the weight of the features could be over-or underestimated. The difference in importance of the features in this model can be explained by the composition of the FLS.
Structure-Based Feature Extraction To model the 3D structures of the Fc mutants, the 4N0U. pdb file was used as a template. Using the mutagenesis tool from PyMOL v2. 5. 4, the 3D structure of the complex between FcRn and each mutant from the dataset was generated and exported as a pdb file. CCP4 software v8. 0. 009 was used to compute the different features used in the algorithms. Features calculated for each residue by CCP4 were: BSA (buried surface area), ASA (accessible surface area), and solvation energy. General features calculated by CCP4 for the whole complex were: number of interface residues, ∆G (solvation energy gain score), p-value (hydrophobic score), BE (theoretical binding energy), and number of hydrogen and salt bridges between interfaces. Total number of hydrogen bonds (cutoff: 3.
Funding: This work was supported by the  French Higher Education and Research Ministry  under the program " Investissements d'Avenir ", grant agreement:  LabEx MAbImprove   ANR-10-LABX-53-01. Christophe Dumet was funded by a  Ph. D. grant by  LabEx MAbImprove. This work was also part of the  MAbMapping technological intelligence platform of the University of Tours ; MAbMapping was funded by the  European Regional Development Fund  and was funded by the regional program ARD 2020 Biopharmaceuticals. We thank  Yann Jullian  and  Thomas Bourquard  for their helpful comments. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable.
In addition, these approaches are agnostic and do not rely on biological knowledge. In contrast, mechanistic models of metastatic development have been developed during the last decades, integrating the pathophysiology of the metastatic process  [18]. They have been used to estimate the occult metastatic burden at diagnosis after the resection of the primary tumor  [19] [20] [21] , to predict the impact of individual treatments in pancreatic cancer  [22]  or to describe brain metastasis in lung cancer  [23]. Following pre-clinical validation  [24, 25] , we showed in a previous work  [26] , that a mechanistic approach based on simulation of the metastatic disease could be used to create a predictive tool of breast cancer relapse. Building upon this work, we here tested our mechanistic models on three datasets of eBC patients who did not receive any adjuvant systemic therapy.
Patient datasets The data consisted of distant metastasis-free survival (DMFS) information and main prognostic variables for patients with operated eBC from three databases. Inclusion criteria were: invasive breast carcinoma, early-stage, treated with primary surgery followed or not by adjuvant radiotherapy, without any adjuvant systemic therapy (hormone therapy, chemotherapy, trastuzumab), with clinicopathological data and follow-up available for DMFS. The patients who did not experience distant metastatic relapse were censored at the time of death or last follow-up. The first dataset contained data from 591 women who were treated at the Bergonié institute (Bordeaux, France) between 1989 and 1993. The clinicopathological parameters were: age at the time of diagnosis, pathological tumor size, axillary lymph node status, tumor grade, and expression of estrogen (ER) and progesterone (PR) receptors, HER2 and Ki67, based on immunohistochemistry (IHC) assays.
The tumors were considered ER-or PR-positive when more than 1% of the cells showed expression of the corresponding receptor in IHC, Ki67 high when 14% or more of the cells expressed the marker (and Ki67 low otherwise), and HER2-positive when the IHC score was 3+ or 2+ with 60% or more of the cells expressing HER2. The second dataset included data from 676 patients extracted from our clinically annotated database (8, 982 invasive breast cancer samples) made from aggregation of 36 public gene expression datasets  [27]. This set included the same clinicopathological annotations as the Bergonié set. The third dataset was composed of 167 patients treated between 1980 and 1990 at the public hospital of Marseille (AP-HM), France. Information on individual DMFS, age status, pathological tumor size, axillary lymph node status and grade were available with the same definition as for the other data sets.
Protein dosage information, based on biochemical assays, was available for ER, PR, Urokinase Plasminogen Activator (UPA) and Plasminogen Activator Inhibitor-1 (PAI-1) as well as the enzymatic activity for Thymidine Kinase 1 (TK). Tumors were considered ER-or PR-positive when the quantity of respective proteins was greater than 15 femtomoles per milligram of protein. Missing values could not be imputed uniformly across all three datasets and were thus removed from each dataset: 55 patients were removed from the Bergonié dataset (646 patients initially), 16 from the IPC dataset (692 patients initially), and 7 from the AP HM dataset (174 patients initially).
In the second step, the optimal covariate model for each dataset was selected using a backward elimination procedure based on the Bayesian information criteria (BIC) adapted for the selection of covariates in mixed-effects models  [35]. Specifically, we started from a model containing all statistically significant covariates for both  and. Then we iteratively generated all possible nested models with one covariate less and selected the model with the minimal BIC. To verify that  was correctly identifiable, the significance of each covariate coefficient in the selected multivariate model was then re-assessed in the multivariate model with a Wald test, based on 100-samples bootstrap estimation of the standard deviation.
Prediction performance metrics To assess the prediction performance of the models at a fixed time point, we used calibration plots. These were obtained by predicting the survival probabilities at landmark times   for all patients Ŝ  (  ), binning these into 8 quantiles groups and computing the median prediction in each bin. For each bin, this prediction was plotted against the actual data group DMFS at time   estimated by the Kaplan-Meier method  [36, 37]. Performance of the models for prediction was also assessed by the concordance index using the individual predicted DMFS probability at 5 years to order the comparable pairs  [38].
Biological parameters discrepancies between the datasets The distributions of the BPs were different in the three datasets (Table  1 ). There was significantly more Ki67 high patients in the IPC dataset (chi-squared test,  < 0. 001) and more node-positive patients in the Bergonié dataset when compared to the IPC dataset ( < 0. 001) and the AP-HM dataset ( < 0. 001). The distribution of the grade values was significatively different between the Bergonié and IPC datasets ( < 0. 001), with more low-grade tumors in the Bergonié data and more high-grade tumors in the IPC data. The proportion of ER-positive and PR-positive patients across the three datasets was also significatively different and no statistical difference was found for the distribution of HER2 in the Bergonié and IPC data. The distribution of primary tumor size appeared log-normal for the three datasets, with a smaller median in the Bergonié dataset than in the IPC set ( < 0.
001, Brown-Mood median test) whereas no statistical differences in median could be found between the IPC and AP-HM datasets (Supplementary Figure  ?? ). The three datasets also exhibited differences in DMFS (Supplementary Figure  ?? ), with lower DMFS in the IPC dataset than in the Bergonié dataset (Cox regression hazard ratio  = 2. 2,  < 0. 001) or in the AP-HM dataset ( = 1. 8,  < 0. 001). No significant difference in DMFS was found between the Bergonié and AP-HM datasets ( = 1. 3,  = 0. 157).
Inter-individual variability of the mathematical parameters accurately describes distant metastasis-free survival curves We first used our mechanistic model without covariates to see if individual variability in the pathological tumor size at diagnosis (included as a direct parameter of the model), associated to log-normal inter-individual variability of the MPs  and , was able to describe the observed TTR in the three datasets  (1). Figures  1B, 1C , 1D show the descriptive performances of the mechanistic models. For all three models, the model-based population survival curves correctly described the observed DMFS data and remained within the confidence intervals of the Kaplan-Meier estimators, except for a slight underestimation of the DMFS for small times. The population values    and    were estimated with good accuracy.
Mechanistic modelling yields biological insight on the impact of biological parameters on metastasis To study the association of the BPs with either growth or dissemination, we tested all univariate models with effect of a BP as a covariate on either  or  (Table  2 ). On the AP-HM dataset, the TK concentration had a significant effect on  and the concentrations of PAI 1 and UPA had a significant effect on. On the Bergonié and IPC datasets, the ER, PR, HER2, and Ki67 statuses had a significant effect on  and , and the lymph node status had a significant effect on. The grade of the tumor was also significantly associated with both  and  on the IPC dataset. For each dataset, an optimal BP set was selected using a backward elimination procedure starting from the model including all significant BPs (Supplementary Table  S1 ).
Model selection was performed based on the BIC to compromise between model performances and number of covariates. For each dataset, the covariate model with the lowest BIC amongst the nested models was kept as the best model (Figure  2 ). Ties on the minimum (differences on the BIC < 4) were resolved by choosing the larger model, as the BIC is known to be favor smaller models when compared to other criteria  [43]. The final models contained the ER and Ki67 statuses on  for the Bergonié dataset (Figure  2A ), a more complex model with effects of the grade and PR on  and the HER2 and nodes statuses on  for the IPC dataset (Figure  2B ), and only PAI 1 on  for the AP-HM dataset (Figure  2C ). Estimation of the population parameters for the selected models is presented in Table  3. The effects of PAI 1 on  for the AP-HM data and grade 3 for the IPC dataset were estimated with good precision ( < 30%), whereas the effects of the other variables were estimated with larger but still acceptable uncertainty ( < 50%).
Covariate models accurately describe DMFS curves To assess the ability of the models to describe different subpopulations of patients in each dataset, we analyzed the model predicted DMFS for different subgroups of patients (Figure  3 ). On the Bergonié dataset, the model captured well the DMFS difference between the ER-positive and ER-negative patients and between the Ki67 high and Ki67 low patients (Figure  3A-3B ). On the IPC dataset, the model was able to correctly describe the differences of DMFS when comparing patients with different grades, HER2, based on the presence of invaded lymph nodes, or between PR-positive and PR-negative patients (Figure  3C-F ). For the AP-HM dataset, the model captured very well the DMFS for patient in the upper PAI 1 tercile, was adequate for the second tercile but seemed to slightly overestimate DMFS for larger times, and the DMFS for the lower tercile of PAI 1 was underestimated by the model (Figure  3G ).
Predictive performances Next, we evaluated the prediction performances of the models. Calibration curves indicated excellent individual predictive power for all three models at the 5-, 10-and 15years landmark times (Figure  4 ). Calibrations at 5 years (Figure  4A-C  4D-F) were good for all three models and for all DMFS probabilities, with a slight trend to overestimate DMFS probability at 10 years for the higher probability group. In the Bergonié dataset, the model slightly underestimated DMFS at 15 years for smaller probabilities while the over-estimation of higher probabilities was more pronounced (Figure  4G ). Whereas for the IPC (4H) and AP-HM (Figure  4I ) datasets, the calibration at 15 years was still good. We then computed Harrell's concordance index (c-index) as another measure of the prediction performance  [38].
The standard deviation for the c-index was computed in 10folds (8-folds for the AP-HM dataset) cross-validation. The performances were modest with a c-index of 0. 63 (95% confidence interval (CI) [0. 44-0. 83]) in the Bergonié dataset, 0. 71 (95% CI [0. 42, 0. 99]) in the AP-HM dataset and 0. 60 (95% CI [0. 54, 0. 80]) in the IPC dataset.
Discussion Classical statistical models of metastatic risk, although able to detect correlation between biomarkers and outcome, fail to give causal insights about the mechanisms at stake. Several genomics-based prognostic tools are commercially available (Oncotype DX Recurrence Score, Prosigna Risk of Recurrence score, EndoPredict, Breast Cancer Index) for estimation of the recurrence risk in HR-positive and HER2-negative eBC. However, the cost of these tests limits their clinical use. Our approach helps to provide mechanistic information from routine clinical markers. We used a simple mechanistic model of metastatic development based on two processes -growth and dissemination -to analyze DMFS data from three different datasets of eBC patients, two of which contained only routinely available data, whereas the third contained also non-routine markers (UPA, PAI-1 and TK), known to have biological roles in the metastatic process  [44].
On the two other datasets (Bergonié and IPC), the model specifically associated the presence of invaded lymph nodes with. Overall, these findings support the ability of our mechanistic model to identify the biological role of specific markers. Based on the first step of our univariate analysis, we proposed a variable selection method to establish the best combination of biological parameters to include in a predictive model for each dataset. Using the BIC, we selected the best compromise between goodness-of-fit and the number of biological parameters. The selected models also improved the insights given by the univariate approach. In the Bergonié dataset, the model pinpointed the Ki67 marker as an important predictor of the growth parameter  and as the least important predictor of the dissemination parameter , in accordance with the established biological role of Ki67 as a marker of cell division and tumor proliferation  [48].
Similarly, in the IPC dataset, the lymph node status was selected in  (and was the vari-able to be eliminated in  in the Bergonié dataset). The hormone receptor statuses were relevant in  for both the IPC (where PR status was selected) and the Bergonié (where ER status was selected) datasets. Their effect on  was less clear, since no hormone receptor status was selected on  but PR status persisted in  up until late steps of the elimination process. The prediction performances of the best model for each dataset were mitigated, with very good performances in calibration at various time points, but surprisingly low c-index values. The c-index computation may not be very accurate considering that the crossvalidation sampling was not stratified on the event indicator variable, meaning that the number of events and thus the number of comparable pairs for the c-index computation was probably different between the cross-validation folds.
The differences in DMFS within each dataset (Supplementary Figure  2 ), the measurement methods (IHC staining for Bergonié, mRNA expression for IPC, and protein dosage for AP-HM) or variable availability prevented the possibility to properly compare the results across datasets. We chose to study routine clinical and biological data to gather as many patients as possible and to match as closely as possible the information available in the clinic. The prediction at the individual level still needs further investigation to be up-part with the existing agnostic models. In particular a larger and more homogenous dataset with more patients and raw values of the markers instead of dichotomized categories could give better results. The next step of the development of our model should be to integrate the impact of adjuvant treatment on the individual risk of metastatic recurrence.
With a better identification of the individual values of the MP in a mechanistic model of the metastatic process under the course of adjuvant therapies would give a relevant framework to tackle the problem of identifying patients who could avoid cytotoxic chemotherapy, or limit its extent to a minimal number of cycles. For each dataset, the base models correspond to the case with no BP effect (aside from the pathological tumor size). The full models correspond to the best models from the selection procedure, where conditionally to the vector of covariates (  ) included in the model, the mathematical parameters followed a log-normal distribution such that, log   and log   are gaussian with respective mean log   +   ⋅   and log   +   ⋅   (where   and   are vectors of the BP specific coefficients) and respective standard deviation   and.
, N = 591 IPC, N = 676 APHM, N = 167 p-value Patient and disease characteristics. For categorical variables (age, presence of invaded lymph nodes, ER, PR , HER2 and Ki67 statuses, grade), number of patients in each dataset (and proportion of the dataset's values (%)). For continuous variables (pathological tumor size and PAI-1), median value (first quartile -third quartile) in each dataset. P-values correspond to the adequate test of identical distributions in all datasets with available information (chi-squared test for categorical variables, Kruskal-Wallis rank sum test for continuous variables).
BIGARRÉFigure 1. Figure 2. 12 Figure 1. Mechanistic model of the time metastatic relapse. A. Overview of the mechanistic model. The model prediction of the time to metastatic relapse (TTR) is computed from the size of the primary tumor at diagnosis and two mathematical mechanistic parameters, α controlling the growth rate of the primary tumor and metastases, and μ controlling the seeding of new metastases. The scheme shows a unitless simulation of the model. B -D. Fits of the mechanistic model (without covariate effects) on the Bergonié (B), IPC (C) and AP-HM (D) datasets. Each panel presents for one dataset, the DMFS and the model's prediction of the survival function in the population. The model was trained and evaluated on the full dataset.
1a ). Analysis of individual responses clearly revealed two typical formalin-triggered nocifensive behaviors amongst females, with one group of females (hereafter called F1) exhibiting a short-lasting interphase and a second group (hereafter called F2), displaying a much longer-lasting interphase (Fig. 1b ). In contrast, no subgroups were observable in males (https:// figsh are. com/ artic les/ figure/ K-means_ clust ering_ for_ males/ 22036 304). We defined the interphase as the total duration of the quiescent period following the first phase and before the emergence of the second phase of the formalin-induced pain. Because large-enough datasets are required to increase the power of statistical analysis, especially when considering free-cycling females, we considerably increased the number of mice per sex (n = 24 males and 53 females).
3a ,b and Table  S1 ). As expected when comparing female versus male transcriptomes, the top-ranking DEG were X and Y-linked genes (Xist and Tsix, as well as Uty, Kdm5d, Eif2s3y and Ddx3y) (Table  S1 ). Functional analysis using Metascape software  26  revealed different pathways enriched in each sex (Fig. 3c ). For instance, female DEG were enriched for transcripts involved in glycosyl compound metabolic regulation, in the sensory regulation of pain and in the positive regulation of translation. Male DEG were enriched for transcripts involved in microglial activity and development, as well as in leukocyte chemotaxis (Fig. 3c ). We further used Ingenuity Patway Analysis (IPA) software to interpret the female-and male-enriched genes in the context of biological processes, pathways and networks (Table  S2 ).
In line with the Metascape analysis, IPA revealed a significant enrichment of male-DEG involved in the recruitment of leukocytes and recruitment of myeloid cells (Fig. 3d ). These genes included macrophages/microglial-associated transcripts such as colony stimulating factor receptor 1 and 2b (Csf1r, Csf2rb), Interleukin-16 (Il-16), as well as genes associated with neutrophil function such as myeloperoxidase (Mpo) and lipocalin2 (Lcn2). Thus, this analysis further highlights a potentially male-specific spinal neuro-immune regulation of formalin evoked pain, possibly involving microglia, as previously reported  20  , but also neutrophils. Taken together, our results underscore qualitative sex-related differences in the molecular mechanisms associated with neuronal and neuro-immune regulation in formalin-evoked pain.
RNA-Seq. RNA-Seq was performed on RNA from ipsilateral DHSC of males (n = 6), F1/proestrus (n = 6) and F2/metestrus (n = 6) females, at 2H following formalin injection. RNA-seq libraries were prepared using the TruSeq RNA Sample Preparation Kit (Illumina). All libraries were validated for concentration and fragment size using Agilent DNA1000 chips. Sequencing was performed on a HiSeq 2000 (Illumina), base calling performed using RTA (Illumina) and quality control performed using FastQC (FASTQC, 2010) and RSeQC  56. Sequences were uniquely mapped to the mm10 genome using Subread (C version 1. 4. 6-p2) using default values. Reads mapping to gene exons (GRCm38. p4 gene assembly) were counted using featureCounts  57  (C version 1. 4. 6-p2). Differential gene expression was performed using exon counts from biological replicates using the DESeq2 Bio-Conductor R package  58  , using a 5% false discovery rate (FDR) cutoff.