dataesr/scientific-paragraphs-categorization huggingface dataset:
Indeed, the parametrisation of RoBoost-PLSR can be a difficult task (three parameters have to be optimised for each LV). In this paper, the constants were fixed for all the latent variables. However, it would be relevant to define specific constants optimised for each latent variable. It is not conceivable to manually optimise constants for each latent variable. Secondly, in real applications, outliers can be present both in the calibration and validation sets. In this paper, the validation sets are not contaminated. To obtain a fully operational method, it should be completed with the development of a metric intended to determine the consistency of unknown samples with the model. This would enable to predict datasets containing potential outliers, and then only process data for which the model is calibrated for.
Acknowledgement This work was supported by the  French National Research Agency  under the Investments for the Future Program, referred as  ANR-16-CONV-0004. Authors care to thank  Vincent Baeten  and  Pierre Dardenne  from the  CRA-W (Agronomic Research Centre of Wallonia, Belgium)  for providing the real dataset used in this article. Authors wish to adress a special thanks to  Gilbert Saporta  from the  CNAM  for his thorough proofreading of the paper and his precious advice.
The spectrum of the free ion Er 3+ (Er IV) was the subject of a PhD dissertation by Carter  [14]  at Johns Hopkins University in 1966 but the conclusion of that work did not lead to a specific publication. Based on semi-empirical considerations on thermodynamical properties of lanthanides, Brewer  [15]  predicted an energy difference of 75000 ±3000 cm -1 between the lowest levels of the two configurations 4f 11 and 4f 10 5d, which was larger than the value of 52481 cm -1   given by Carter  [14]. The critical compilation by Martin, Zalubas and Hagan  [9]  retained none of the Er IV levels of Ref. [14]  because of inconsistencies with the energy separation derived later from the systematic behaviour of similar configurations in rare earths. Instead, calculated theoretical values from parametric studies of Er 3+ ions in crystals were listed for the lowest levels of 4f 11 in  [9]  (now transferred into the NIST Atomic Spectra Database  [16] ).
002 Å and 0. 005 Å , with the fewest possible free parameters. Only one section (1365 -1465 Å ) was better fitted with a polynomial of the third degree, resulting in a standard deviation of 0. 0025 Å. The previous analysis  [19]  reported that, for wavelength calibration, internal wavelength standards were chosen among lines of low-Z impurities, without giving explicitly the references  [27]  and  [28] , completed by lines measured by Carter in Er IV  [14]  and by Becher in Er III  [13]. In the present work, we aimed at improving the internal standards by identifying more emission lines from impurities and by avoiding as much as possible previous Er IV wavelengths  [14] , since their identifications were not confirmed. We updated the wavelengths of low-Z impurity lines (C, N, O, Si, Al), taking the values from the NIST Atomic Spectra Database  [16] , adopting Ritz wavelengths when available, or otherwise, from Kaufman and Edlen's compilation  [28].
The experimental level energies found in the course of the analysis were used as input data for the last Cowan's code RCE to iteratively improve the radial integral values. The latter were treated as adjustable energy parameters in a least squares fit (LSQ) minimising the mean error ∆E = i (E exp i -E calc i ) 2 /(N i -N p ), where N i and N p are respectively the number of experimental energies and the number of free parameters. In the previous work  [19] , to provide initial theoretical predictions of level energies and transition probabilities, the HFR radial integrals, or parameters P HF R , were multiplied by scaling factors SF(P ). These were estimated from appropriate previously studied lanthanide ion spectra mentioned above, in which SF(P )=P f it /P HF R , where P f it is the parameter value derived from the LSQ fit of energies using the RCE code.
Acknowledgements We are deeply indebted to the referee for his very thorough and instructive review, which helped us to greatly improve our data and their presentation. AC is thankful to the Algerian- French PROFAS B+ programme  for a sevenmonth grant. Supports from  Université Mouloud Mammeri, Tizi-Ouzou, Algeria  and from the project  A25N01UN150120150001 ,  CNEPRU , Algeria are acknowledged. Financial supports from the  French CNRS -PNPS national program  and from the  Paris Observatory Federal Action "Stars" (AFE)  are acknowledged.
φ [10 -14 mol s -1 m -1 Pa -1 ] D [10 -10 m 2 s   'Connell, 1969). The loops of silicone tubing were typically separated by 2 cm, and the associated diffusion time was estimated as t dif ≈ l 2 D ≈ (0. 02 m) 2 2 × 10 -9 m 2 s -1 = 56 h. (A6) (Robert F. Berg) to work at LNE. We thank Chris Meyer for numerous constructive comments, and we thank Fernando Sparasci for obtaining funding for the project. Financial support. This research has been supported by the EU-RAMET (grant no. ENV07 METEOMET, grant no. ENV58 ME-TEOMET2, and grant no. 20IND06 PROMETH2O). Review statement. This paper was edited by Fred Stroh and reviewed by two anonymous referees.
Sample freezing A 100 µL volume of the above sample was pipetted into a Kel-F sample cup and inserted into a 7. 05 T prototype Bruker Biospin polarizer equipped with a specialized dDNP probe, including a background-free radiofrequency (rf) coil insert  (Elliott et al. , 2021a) , running TopSpin 3. 5 software. The sample temperature was reduced to 1. 2 K by submerging the sample in liquid helium and reducing the pressure of the variable temperature insert (VTI) towards ∼ 0. 7 mbar.
Financial support. This research has been supported by ENS-Lyon, the French CNRS, Lyon 1 University and the European Research Council under the European Union's Horizon 2020 research and innovation programme (ERC grant agreements no. 714519/HP4all and Marie Skłodowska-Curie grant agreement no. 766402/ZULF). Review statement. This paper was edited by Daniel Abergel and reviewed by Andrea Capozzi and one anonymous referee.
Scheduling anticancer drug administration over 24 h may critically impact treatment success in a patient-specific manner. Here, we address personalization of treatment timing using a novel mathematical model of irinotecan cellular pharmacokinetics and -dynamics linked to a representation of the core clock and predict treatment toxicity in a colorectal cancer (CRC) cellular model. The mathematical model is fitted to three different scenarios: mouse liver, where the drug metabolism mainly occurs, and two human colorectal cancer cell lines representing an in vitro experimental system for human colorectal cancer progression. Our model successfully recapitulates quantitative circadian datasets of mRNA and protein expression together with timing-dependent irinotecan cytotoxicity data. The model also discriminates time-dependent toxicity between the different cells, suggesting that treatment can be optimized according to their cellular clock.
Several patientfriendly methods for measuring clock gene expression using saliva or blood sampling have been recently validated in the clinics  [18]. Such patient datasets, combined with mathematical modeling and machine learning, may allow to predict the times of least toxicity to healthy tissues, and optimal antitumor efficacy for an individual patient  [18]. In particular, computational models representing the chronopharmacology of a specific drug can help to predict therapy time windows of decreased toxicity and optimal efficacy  [8, 18]. Such models can also be optimized for a given patient and used to generate personalized treatment timing indications. In the past years, several ODE (ordinary differential equation) models have been developed, which either aim to model the circadian clock network  [19] [20] [21] [22] [23] [24] [25] [26]  or the biochemical and biophysical interplay between the circadian timing system and a given drug  [27, 28].
[23]  and a model of irinotecan chronoPK-PD from Ballesta et al. [27, 28] , which have been successfully used for simulating the mammalian core clock and the time-dependent cytotoxicity of irinotecan, respectively. The core-clock model was refined using newly available quantitative circadian datasets of gene and protein expression in the liver of C57Bl6 male mice. Representing the clock of the liver is important in view of predicting the drug metabolism that mainly occurs in this organ in the whole-body scenario  [29, 30]. To connect it with the PK-PD model, we extended the transcription-translation network of the core clock with a set of irinotecan-related genes. We fitted our new clock-irinotecan model with transcriptomic data from an in vitro colorectal cancer (CRC) experimental progression model and carried out timedependent irinotecan treatment in both cell lines across 24 h.
c-DNA and synthesis RT-qPCR For Real Time quantitative PCR (RT-qPCR) analysis, the extracted RNA was reverse transcribed into cDNA (4 ng/ml) using random hexamers (Eurofins MWG Operon, Huntsville, AL, USA) and Reverse Transcriptase (Life technologies). RT-qPCR was performed using SsoAdvanced Universal SYBR Green Supermix (Bio-Rad Laboratories, Hercules, CA, USA) in 96-well plates (see Table  1  for list of primers used). Human GAPDH (QuantiTect Primer, Qiagen) was used as reference housekeeping gene due to its high abundance and to the lack of circadian oscillations, as confirmed by a cosinor analysis carried out in microarray and RNA-seq data for SW480 cells (Supplementary Fig. 2d ). The qPCR reaction was performed using a CFX Connect Real-Time PCR Detection System (Biorad). Relative gene expression was calculated using the 2 -DDCt method  [33].
Omics data The models were fitted to microarray time series data of 24 h sampled with an interval of 3 h for the SW480 and SW620 cells and of 48 h sampled with an interval of 2 h for the liver, which was scaled to concentrations based on RNA-seq data. The microarray data and RNA-seq data for liver tissue was published by Zhang et al. 2014, accession numbers GSE54650 and GSE54652  [11]. For the SW480 and SW620 cells, the microarray time series data was published by El-Athman et al. 2018, accession number E-MTAB-5876  [34] , and the RNA-seq time series data was published by El-Athman et al. 2019, accession number E-MTAB-7779  [35]. To relate the microarray data with concentrations, the following steps were done for each gene separately. RNA-seq transcript data was used to calculate the temporal mean of the expression in TPM, which was then converted into mean concentrations in mol/L by a simple rescaling, see Supplementary Information for details.
Mathematical models Model equations and parameters of the core clock are listed in the Supplementary Information, Supplementary Equations (1. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]  and Supplementary Table  2 , model equations and parameters of the clock-irinotecan model are listed in Supplementary Equations  (3. 1-30)  and Supplementary Table  6. Parameter optimization was done using the evolutionary algorithm CMA-ES  [36]. Computations for the core clock were carried out on a laptop with i5 2. 9 gHz dual core processor using Python's pycma for the optimization and Python's scipy. integrate. odeint for the numerical integration (method: lsoda, relative tolerance = absolute tolerance = 10 -12 ). Computations for the clock-irinotecan network were carried out on a compute cluster with the same Python packages.
Results The effect of a drug results from an intricate interplay between its metabolites and the organism, which is under circadian control. Regarding the anticancer agent irinotecan, multiple genes and proteins involved in its PK-PD are directly or indirectly regulated by the cellular core clock. The aim of the study was to design a mathematical model combining the core clock and irinotecan PK-PDrelated elements to investigate possible cellular biomarkers predicting irinotecan chronotoxicity rhythms (Fig. 1a , top). This model was developed and calibrated for three biological systems: the healthy mouse liver, and two cell lines derived from human color-ectal cancer (CRC) (Fig. 1a bottom ). The combined model was trained for the CRC cell lines using circadian datasets of mRNA levels and with experimental results on time-related irinotecan cytotoxicity.
The equations now account for the ratio between the compartment volumes to ensure that the quantity of matter is conserved during transport (Supplementary Information, Section 1. 1. 5). The cytoplasm/nucleus volume ratio was set for mouse hepatocytes to 14  [44]. Our new core-clock model allows to quantitatively simulate gene and protein levels, expressed in mol/L, thus allowing for the fitting of quantitative datasets informing on absolute concentrations (Table  2 ). Parameter estimation was done using the time series data reported by Narumi et al. [32]  (Supplementary Information, Section 1. performed a linear change of variables, mapping the original model variables to their scaled versions with respect to the maximum of the observed data (Supplementary Information, Section 1. 3. 2). The obtained scaled parameter values were then used as an initial guess for the subsequent parameter estimation procedures.
The liver dataset also included protein expression for Bmal1 -/- mice  [32]. Assuming that Bmal1 knockout (KO) led to a loss of oscillations in the clock  [45] , this data could be seen as a glance at the system at steady state. This enabled us to derive functional relationships to compute three transcription rate parameters as a function of the KO mice data and other parameters (Supplementary Information, Section 1. 3. 3), thus decreasing the number of parameters to estimate. This led to a simplification in the parameter estimation. We further reduced the number of parameters by assuming that Hill power coefficients were equal for all activators (parameter b) and all inhibitors (parameter c) of the transcription across genes. This led to a decrease of 8 parameters to be estimated while producing next to no change in the goodness of fit as expected from the argument of unidentifiability.
Fig. 2  shows the model best-fit, which convincingly reproduced the data (R 2 = 0. 86). Bmal1 and Clock mRNA modelpredicted profiles presented a similar phase but different mean levels (5. 3 and 19. 5 pmol/L, respectively) and relative amplitude (84% and 62% of the mean, respectively). Differences were also observed at the protein level as free BMAL1 and CLOCK protein mean levels were equal to 13. 9 and 8. 85 nmol/L respectively, with relative amplitudes of 35% and 25%. These differences came as a justification to the addition of the Clock gene into the core-clock model. Validation of the model was done using an external time course dataset from mouse hepatocytes, which was not used for the model design and calibration  [43]. This study reports a phase between 8. 5 h and 10. 8 h for the circadian rhythm of REV-ERB nuclear expression and a relative amplitude of 98%, while the model simulation for phase and relative amplitude were 9.
The clock model reproduces the expression profiles of core-clock genes in CRC cell lines To test our mathematical model in a colon cancer context, we chose a well-known in vitro cellular model of CRC progression, which includes two cell lines from the same patient (SW480, SW620), derived from the primary tumour and from the metastasis, respectively. We carried out a time course of 45 h (9 h À 54 h, after synchronization) with a 3 h sampling interval, for the gene expression analysis of PER2, REV-ERBa and BMAL1 via RT-qPCR, in either control or shBMAL1 conditions. This dataset was combined with microarray data for the expression of Cry, Ror and Clock in order to calibrate the core-clock model for each of the CRC cell lines (see Section 2. 6). Quantitative mean concentration levels expressed in mol/L for the clock genes of CRC cell lines were derived from an already published RNA-seq transcriptomic dataset  [11].
Thus, in total, three datasets were combined for the calibration of the core-clock model for the CRC cell lines. The cytoplasm/nucleus volume ratio of the CRC cell lines was set to 5 (manual curation, using snapshots of SW480 and S620 cells from Abdulrehman et al. [48] , Fig. 2 , the cytoplasm/nucleus ratio was computed for each cell of the figure and an average value close to 5 was found for both cell lines). The transcription-translation network was assumed to be similar in either control or shBMAL1 conditions, yet with a single different parameter to account for shBMAL1 activity. Accordingly, the RT-qPCR datasets obtained from the control and shBMAL1 conditions were fitted simultaneously to their respective models using the same set of parameter values with the exception of BMAL1 basal transcription, which was allowed to differ between both conditions (Supplementary Fig.
3 ). The shBMAL1 condition provided a view of a dampened circadian clock, due to the knockdown of Bmal1, which induced a lo wer activation power of the transcription factor CLOCK/BMAL1. Upon model calibration, a 375fold reduction in the BMAL1 estimated basal transcription rate was necessary to allow for a good fit of both conditions. This demonstrates the ability of the model to reproduce two different physiological scenarios by tuning a single parameter. Concerning the SW480 cell line, the model achieved an excellent fit of the data (R 2 = 0. 75) (Fig. 3a , Supplementary Fig. 2a ). The fit for the SW620 was reasonable as well (R 2 = 0. 67), but lacked a proper fit of CRY, ROR and CLOCK expression reported in the microarray dataset (Fig. 3b , Supplementary Fig. 2b ). Oscillations of the core-clock genes, normalized to the mesor, showed larger relative amplitudes in the healthy mouse liver than in CRCderived cell lines, with the circadian rhythms in SW620 cells being largely dampened as compared to both other systems (Fig.
From the clock-irinotecan network fitted to experimental mRNA expression data, we use the mRNA dynamics of UGT1A1, CES2, ABCB1 and ABCC1 as an input to the protein dynamics and the PK-PD model to predict irinotecan toxicity, see below. The clock-irinotecan network was fitted to experimental timeseries datasets of mRNA concentrations  [35] , available for mouse liver  [11]  and extracted from microarray and RNA-seq data for CRC cell lines, see Section 2 for details. We fitted the clockirinotecan model to the temporal dynamics of mouse liver, as well as to untreated SW480 and SW620 cells, which resulted in R 2 scores of 0. 72, 0. 61 and 0. 40, respectively (Fig. 5a-c ), see Supplementary Fig. 4  for an example with all genes. For acrophases and relative amplitudes of the model fits see Supplementary Fig.
A comprehensive mathematical model for circadian regulation of irinotecan PK-PD Our clock-irinotecan model can be fitted to different scenarios providing different circadian toxicity profiles for CRC cells. The core-clock model was initially developed from multiple datasets of mammalian SCN cells  [23] , and was successfully refined here using quantitative measurements of the clock of the mouse liver, and of SW480 and SW620 cell lines. Regarding the model of irinotecan PK-PD, it was designed based on extensive datasets in Caco-2 cells  [28] , and was further validated in both SW480 and SW620 cell lines. Using SW480 and SW620 cell lines here provided a proof of principle that a personalization of the model to other cell lines was possible. Hence, models of both transcription-translation clock network and irinotecan PK-PD were validated in several in vitro and in vivo experimental settings, which argues in favour of their reliability.
Further, we included the gene Clock to the model, to incorporate available data on this gene and investigate its importance in the clock machinery. Finally, our model integrates both mRNA and protein circadian datasets in a quantitative manner, meaning that it does not only predict the phase and relative amplitude of the gene expression data as existing models do  [23, 26] , but also computes the protein expression levels, such information being critical for the connection to PK-PD models. A very interesting perspective for future studies would be to consider coupling the model by Woller et al. [26]  with ours to investigate the impact of feeding/fasting cycles on irinotecan chronopharmacology, as liver enzymes involved in the drug PK showed variations according to food intake  [63]. Our core-clock model represents intracellular regulatory feedback loops that implicitly include extrinsic circadian regulators such as temperature or light/dark cycles.
Personalized models to optimize timing in cancer treatment Chronotherapeutic studies aim at increasing treatment efficacy and minimizing toxicity for healthy cells leading to a reduction of the side effects for patients  [65]. Previous clinical results have shown that personalization is a key element of successful chronotherapy outcome, for example males and females have shown different toxicities depending on treatment timing  [6, 16, 66]. Sex should be considered as a relevant determinant of circadian rhythms and optimal drug timing in the light of recent preclinical and clinical findings  [6, 16, 66]. Here, the mouse liver data was obtained from male mice, and the cell lines were derived from a human male, so that the sex specificity seems out of the scope of this study. However, we have started to investigate the impact of sex on the circadian timing system as mentioned above and did find significant sex-related differences in the shape and intensity of systemic controls on the core clock in a mouse study.
Several sex-specific datasets related to irinotecan chronotoxicity are available in mice and in patients, and further modelling work would allow to investigate molecular determinants of male/female differences in irinotecan response with respect to timing  [8]. One aspect of personalized chronotherapy is an adaptation of medication timing to the patient's internal time, which can be best assessed by a combination of mathematical modelling and machine learning. Existing models of irinotecan PK-PD offer to predict best drug timing based on circadian rhythms of proteins involved in irinotecan pharmacology, in the organ of interest (e. g. liver, or intestine) or in the tumour. However, such datasets are unlikely to be obtained in the clinics on an individual patient basis as it would involve multiple around-the-clock biopsies, which obviously raises questions of feasibility and ethics regarding benefit/risk ratios.
Furthermore, circadian datasets on irinotecanrelated proteins would not be informative for personalizing the timing of other drugs, in particular the ones usually combined with irinotecan (e. g. 5-fluorouracil, oxaliplatin). Instead, our new combined model provides the option of computing irinotecan best timing from circadian rhythms of core-clock mRNA levels. The major advantage of measuring core-clock genes -and not directly drugrelated genes -is that it can be done in any organ, since the peripheral core clock is synchronized across healthy tissues as suggested by mouse and baboon studies  [11, 35, 67]. Several patient-friendly methods for measuring clock-gene expression in saliva or blood samples have been recently validated in the clinics (see  [12]  for a review). Furthermore, strong oscillations, clearly above noise level, are expected in core-clock gene expression, which facilitates the characterisation of their circadian profiles and reduces the number of needed time points to do so  [62].