dataesr/scientific-paragraphs-categorization huggingface dataset:
This bias was partially corrected in the modified versions of the models, which also improved the tightness of the relationship as indicated by higher r 2 than for the original algorithms, but at the expense of the number of individual retrievals with the lowest magnitude of error between different algorithms ("win ratio", Tables  3  and 4 ). Significantly different means in chla concentration between spring and fall in the NWA (see Section 3. 4. 1) suggest that the dataset could be further subdivided by season, but at the expense of a synoptical approach. It would also require a larger matchup dataset to achieve statistical significance. Our approach differed from NASA's in that the algorithms were fitted directly between satellite-derived and in situ chla, under the assumption that the satellite R rs were reliable, while the original algorithms were developed using both in situ radiometric and chla measurements.
Furthermore, the regional parameters were optimized, tested, and compared to the original algorithms using the entire dataset for a given region and sensor, rather than extracting a subset for training and using the remainder for testing. Confidence intervals for the polynomial algorithm coefficients were retrieved using a bootstrap method that subsamples the original dataset to compute 2000 different sets of coefficients (see Section 2. 4. 2), revealing interval widths ranging from 0. 08 to 1. 26 for the first three coefficients and 0. 38 to 2. 39 for the last two, which had the smallest impact on the shape of the polynomial in the region defined by the band ratio values. This suggests that the coefficients derived from the full dataset are representative of any subsets. For the GSM algorithms, the sensitivity study on combinations of spectral variations in P, S, and Y (see Section 2.
4. 4) was performed for each region, sensor, and set of g coefficients (spectral or constant), and the median of the subset of highest-scoring combinations was selected. For this reason, we can assume that using the entire dataset or a subset for each combination would have led to similar results after retrieving the median of the optimal combinations. Finally, the small size of some of the datasets, particularly the NEP SeaWiFS set, presented a challenge in developing a reliable set of parameters spanning a wide range of values for in situ chla and the environmental variables that were tested for correlations with algorithm error. For these reasons, the regional tuning of the algorithms was carried out on the full datasets rather than subsets. One of the main results of our studies was the identification of the 443 nm waveband as a strong contributor to the overall uncertainty in the OCx algorithms.
Note that uncertainties in HPLC-derived chla were partially accounted for in the linear model comparing the results by using Type 2 linear regression as described in Section 2. 5. 1, which minimizes the sum of areas of triangles between each point and the regression line, assuming that both variables contain errors. Here, we have addressed discrepancies between satellite-derived chla and in situ chla and included temporal and spatial effects. For the two areas of interest, namely the Northwest Atlantic and the Northeast Pacific, we did not find significant patterns of temporal drift, thanks to regular reprocessing of ocean colour products by NASA following a vicarious calibration exercise  [44]  that ensures stable measurements of the radiative field with time. We did not find spatial patterns, with the exception of minor positive correlations between latitude and magnitude of error in the NWA VIIRS dataset, and negative correlations between open ocean bathymetry and error magnitude in the NEP datasets, which are likely due to changes in chla concentration that affect the degree of error.
Seasonal biases were observed with an overall underestimation of chla in the spring and a small overestimation in the fall. This could be explained by the change in phytoplankton community composition (Table  5 ), such that when the ratio of fucoxanthin, a marker pigment for diatoms, to chla concentration increased, the magnitude of error in chla retrieval also increased. This pattern was observed across all algorithms, but weaker in the regionally-tuned algorithms. GSM-type algorithms offered the greatest improvements, in particular, GSM_GC in the VIIRS dataset where the correlation coefficient of |E chla | and the ratio of fucox to chla was reduced from 0. 54 to 0. 27. This demonstrates the effectiveness of regional algorithms at addressing changes in phytoplankton absorption properties, and notably the modified GSM algorithms, which include an exponent on the phytoplankton absorption term to account for changes in absorption properties with changes in phytoplankton community composition in the Northwest Atlantic  [45] [46] [47].
Resource Balance Analysis (RBA) is a computational method based on resource allocation, which performs accurate quantitative predictions of whole-cell states (i. e. growth rate, metabolic fluxes, abundances of molecular machines including enzymes) across growth conditions. We present an integrated workflow of RBA together with the Python package RBApy. RBApy builds bacterial RBA models from annotated genome-scale metabolic models by adding descriptions of cellular processes relevant for growth and maintenance. The package includes functions for model simulation and calibration and for interfacing to Escher maps and Proteomaps for visualization. We demonstrate that RBApy faithfully reproduces results obtained by a hand-curated and experimentally validated RBA model for Bacillus subtilis. We also present a calibrated RBA model of Escherichia coli generated from scratch, which obtained excellent fits to measured flux values and enzyme abundances.
To fulfil all of these requirements, we introduce a framework for automatically generating bacterial whole-cell resource allocation models and for their simulation in exponential growth by the RBA method  [12] , implemented in the open source Python package RBApy. The package requires as inputs an annotated genome-scale metabolic model (GSMM)  [35]. RBApy complements the provided metabolic network with a default set of molecular machines and parameters for quick and semi-automated model generation. Using helper files, users can refine and manually curate the resulting model. Finally, we provide algorithms for model calibration when datasets (e. g. quantitative proteomics) are provided by the user. We used RBApy to generate an RBA model of Bacillus subtilis and validated its predictions with the hand-curated model developed and experimentally validated in  [12].
RBApy package RBApy is a Python package providing four core functionalities (Supplementary Data S1): generating RBA models from biological network and sequence data, estimating various model parameters, converting RBA models to the generic XML-rba format and converting XML-rba files into an RBA optimization problem that can be solved as described in  [10, 11, 12]. The package runs on Linux, Mac and Windows systems and is distributed under the GNU GPL version 3 license. The complete documentation is available at https://sysbioinra. github. io/RBApy/ (Supplementary Notes S2).
RBApy. prerba: generating models from SBML and Uniprot The primary input of RBApy is an SBML file listing the metabolites and reactions of interest, as well as linking the reactions to catalyzing enzymes, in the syntax defined by COBRA or based on the SBML fbc package for constraint-based models. RBApy automatically retrieves the latest Uniprot protein sequences for the modelled organism and generates a fully functional RBA model, which is then stored in an XML-rba files. RBApy. prerba also generates a number of preconfigured helper files in TSV format, which serve as a template for the user to provide missing or additional information for a second run of RBA. prerba. Typical examples of missing information include enzymatic proteins that could not be retrieved in Uniprot, missing information about protein localization, or missing stoichiometrical information about the protein subunits of enzymes.
RBApy. xml: maintaining models in XML format RBApy. prerba is primarily designed to generate a minimal working RBA model, containing default processes such as translation and chaperoning. RBApy. xml stores these models in an XML-rba format that was designed to facilitate model extension, in particular by adding new macromolecular processes. The user may do this by changing the XML-rba files directly. Alternatively, RBApy. xml provides an Application Programming Interface (API) in which every XML-rba entity can be accessed through a Python class with identical name. This subpackage uses the lxml library.
XML-rba format A central question we had to tackle while developing RBApy was how to encode resource allocation models in a standard description format. In particular, we had to determine if the SBML format that is commonly used for encoding GSMM was suitable to describe all constraints and, especially, the reactions of synthesis and degradation of macromolecules that are performed by molecular machines  [15]. Macromolecules can be proteins, RNAs, DNA as well as heterologous complexes composed of proteins and/or RNAs, and/or metabolites. Let us take protein translation as an illustrative example. Translation is a cellular process that relies on ribosomes as a molecular machine and that produces proteins. During protein production, ribosomes consume and produce metabolites such as charged and uncharged-tRNAs and GTP/GDP, to cite a few.
Parameter estimation from existing datasets Global parameters. RBA models contain different types of parameters. A set of parameters that globally restrain the cell state are the cytosolic density and the growth-rate dependent total concentration of proteins, both expressed in millimoles of amino-acid residues per gram of cell dry weight [mmol. AA/gCDW]. To estimate these two parameters, we consolidated data available from three sources  [3, 23, 25] , choosing the most comprehensive dataset, which proved to be the one from  [3]  (Supplementary Notes S7). We estimated the maximal cytosolic density for a growth rate of ~1 [1/h], for which all three datasets provide information (albeit of a different kinds) and for which two data sources match almost perfectly, thereby obtaining the value of 4.
89 mmol. AA/gCDW (see Supplementary Notes S7 for detailed procedures). Additionally, we used proteomics data measured for different growth rates  [32]  to estimate the percentage of proteins allocated to individual compartments (extracellular, periplasm, cytoplasm, inner plasma membrane and outer plasma membrane). The estimated total protein concentration and the percentage of proteins allocated to individual compartments were used to compute the maximal protein density per compartment. Enzyme efficiencies. We calculated estimates of the individual apparent catalytic rates of enzymes for the growth on glucose minimal medium at 37°C, for which fluxomics and proteomics data of comparable growth rates (< 5% difference) and experimental setups were available  [32, 38]. We chose not to use the measurements done on galactose because the difference in growth rates between fluxomics and proteomics was quite big (~30%), which might imply a significant difference in cellular configurations.
To obtain complete and consistent flux distributions for the estimation, we ran an FBA simulation  [40]  of the original metabolic model, with flux constraints representing the experimentally measured fluxes. Apparent catalytic rates were computed as    =     ⁄ , when   and   do not vanish, and where   is taken from the resulting flux distribution and   is the enzyme concentration computed from proteomics data. Other molecular machine efficiencies. An RBA model requires parameters defining the efficiencies of molecular machines of the macromolecular processes. Using proteomics data from 12 different media  [32] , we estimated the molecular machine efficiencies for chaperoning and secretion as linear functions of the growth rate as in  [12]  (Supplementary Notes S7). For each of the twelve different media (and thus twelve different growth rates) we computed the efficiency of a molecular machine as the ratio between the production flow of molecules by the process at measured growth rate and the measured abundance of the molecular machine.
In the estimation procedure, the measured abundance of the molecular machine (e. g. chaperones and the secretion apparatus) is computed from proteomics data for each medium. The production flow of molecules by the process (e. g. the flow of folded and secreted proteins) at measured growth rate is estimated through the constraint C2. For chaperoning, the flow of folded proteins is computed as     (  ) where β is the fraction of total proteins that are folded by a chaperone and is equal to 10%  [5] , and the total concentration of proteins   is the one estimated previously. For secretion, we assumed that proteins that are located either in the inner membrane (  ), periplasm (  ), outer membrane (  )or in the medium (  )need to be translocated by the secretion apparatus. The flow of secreted proteins is thus computed as   (  (  ) +   (  ) +   (  ) +   (  )).
The choice of function and of the variables used is up to the modeller, and may depend on the biological phenomenon to be modelled and on the quantity of datasets available for model calibration. For instance, in  [12]  we used four datasets, each of them composed of fluxomics and quantitative proteomics, that were acquired in four growth conditions. The four growth conditions were chosen so as to obtain a wide range of growth rates to estimate linear functions of enzyme efficiencies. Estimating the maximal density and the fraction of housekeeping proteins per compartment requires quantitative proteomics data as well as information about protein localisation and about the belonging of each protein to the set of housekeeping proteins (Figure  2 ). Details on the procedure of parameter estimation from datasets are given below.
Pipeline description We designed RBApy, a free and open-source Python package, to assist RBA model generation and simulations (Supplementary Data S1, Supplementary Notes S2). RBApy is composed of three main modules (Figure  3 ): preRBA for generating of RBA models represented in an XML format, core for simulation and visualization of the results, and estim for parameter estimation. As inputs, the user needs to provide a GSMM in Systems Biology Markup Language (SBML) format  [15] , as well as the NCBI taxonomy identifier of the bacterium being modelled. The GSMM must contain gene annotations for each enzyme-catalyzed reaction. The first pipeline module, RBApy. preRBA, automatically downloads the latest Uniprot protein annotations of the modelled organism  [37]. Then it (1) extracts the metabolic network and the enzymatic proteins associated with each annotated metabolic reaction from the GSMM, and retrieves (2) the sequence, localization, subunit stoichiometry and cofactors of enzymatic proteins from their Uniprot annotations.
The lack of biological databases readily offering information of macromolecular processes such as translation or chaperoning (Figure  1 ) prevents the complete automatized generation of RBA models. The same holds true for certain model parameters, such as the maximal density of the cytosol. To complete the missing information, we offer a default set of parameters and macromolecular processes (translation and chaperoning) of E. coli. From all the collected information, RBApy. preRBA generates the resource allocation model encoded in a specific XML format, called XML-rba. The XML-rba format is based on SBML and was conceived to provide an efficient description of cellular processes. If the user provides data sets containing quantitative proteomics and fluxomics data in comparable growth conditions, the module RBApy.
estim can be used to estimate the main types of model parameters  [12] : maximal macromolecular compound densities within cellular compartments, abundance of housekeeping proteins for each compartment, and the efficiencies of molecular machines involved in metabolic and macromolecular processes (Figure  1 ). The RBApy. core module starts by converting the XML-rba files into an RBA convex optimization problem where growth rate is maximized by running a series of LP feasibility problems  [12]. Results can be exported in various formats suitable for visualizing the fluxome and proteome. If the reactions in the original SBML file carry BIGG identifiers  [18] , flux distributions can be visualized via Escher maps  [17] , a web-based tool for pathway visualization. Individual protein abundances and the cost of cellular processes can be visualized as Proteomaps  [21]  or pie charts using user-defined or COG functional annotations  [34].
A resource allocation model for an Escherichia coli wild-type strain RBApy can also be used to model bacteria with several compartments and to estimate their parameters. As an illustrative example, we have selected the Gram-negative model bacterium E. coli, which has two compartments: the cytoplasm and the periplasm (Supplementary Data S10). As a metabolic network reconstruction, we chose the iJO1366 model  [29] , which was the most up-to-date genome-scale metabolic reconstruction at the time of model generation. To supplement the metabolic reconstruction, we retrieved protein sequence information from the Uniprot database  [37]  (done automatically through RBApy), as well as the DNA, rRNA, tRNA and mRNA sequences from the NCBI database  [7]  (done manually).
Parameter estimation from existing datasets We estimated the model parameters from three sources  [3, 23, 25]  and datasets  [32, 38]  as described in Material and methods (see Supplementary Notes S7 for further details). Among the model parameters, the efficiency of enzymes, also called "apparent catalytic constant" (kapp) describes the reaction rate per amount of the catalyzing enzyme and can be directly compared to values reported in the literature. A default value of 12. 5 [1/s] is first set for all enzymes. This value was chosen since it maximized the coefficient of determination (R 2 ) of a linear fit between predicted and measured growth rates on 12 different media  [32]  (Supplementary Figure  S11 ), and is remarkably close to the median of reported maximal turnover rates of enzymes, 10 [1/s]  [2, 32].
We additionally estimated the individual apparent catalytic rates of 417 enzymes for growth on glucose minimal medium, for which fluxomics and proteomics data with comparable growth rates (< 5% difference) and experimental setups were available  [32] [33] [34] [35] [36] [37] [38]. We compared the statistical distribution of the computed apparent catalytic rates to the distribution of maximal turnover rates of E. coli enzymes reported in the BRENDA database  [30]. As shown in Figure  5A , the distributions span roughly the same range of values. A perfect match is not expected, considering the many possible sources for discrepancies. First, apparent catalytic rates are expected to be lower than the maximal turnover rates. Moreover, most of the values reported in BRENDA stem from in-vitro measurement, in many differing measurement conditions, which may differ strongly from in vivo conditions  [12].
Validation of the predictions of the RBA model We validated the predictions for two model versions. First, we used only the default apparent catalytic rate of 12. 5 [1/s] for all enzymes. Indeed, this case is representative of the use of RBA models when no datasets are available for model calibration. We ran simulations of the E. coli RBA model for 12 different media for which measured growth rates and proteomics were available for exponential growth in batch culture from  [32]. Except for the specified carbon sources and the added amino acids, the minimal medium assumed in the model was the one specified for the iJO1366 metabolic reconstruction  [29]. As can be seen in Figure  4 , the predicted growth rates show a good match to the measured ones (R 2 = 0. 54), even if the default apparent catalytic rate was used.
Using the kapp estimation values greatly improved the predictions, with the correlation for 233 cytosolic enzymes being R 2 = 0. 65 in log space (Figure  5D ). In an RBA model, the growth medium is defined by listing the concentrations of extracellular metabolites. The transporter efficiencies are computed from these concentrations by assuming a Michaelis-Menten transporter kinetics. The precise estimation of parameters of this Michaelis-Menten kinetics requires additional datasets describing the kinetics of consumption of the extracellular metabolites. Whenever such data were not available, we took as default values the ones estimated for B. subtilis transporters. Their abundances and corresponding fluxes are predicted from simulations. In the case of a glucose minimal medium with kapp estimates, the glucose uptake and acetate excretion fluxes were predicted almost exactly, with the overall flux distribution matching the measured one with R 2 = 0.
1 atm and O2 is present and normal atmospheric conditions and room temperature (Table  1 ). The parameter values used were taken from Brenda database for Rhodospirillum rubrum or as median, minimal and maximal values as reported in  [6]. The efficiency of the prk enzyme was set to 12. 5 [1/s], the default kapp value for E. coli. For the carbonic anhydrase efficiency, we used the median of the values reported in Brenda for that enzyme, which is ~10000  [.
While RBApy collects most information automatically, manual curation (through helper files) can be necessary to remove ambiguities in annotations or to extend the model by adding other macromolecular processes. To limit the need for manual curation, SBML files should be more systematically annotated using the protocol of  [35]. Cross-references to other databases, such as the ChEBI IDs  [13]  for metabolites or Uniprot IDs for proteins, should be present systematically. Furthermore, existing standard formats of Systems Biology are currently too limited to encode whole-cell models and especially to support DNA, RNA, and protein sequence-based reaction patterns  [41]. During RBApy development, we faced the same difficulties, which led us to develop the XML-rba format. We showed, through the models RBA-Bsub and RBA-Ecoli, that the XML-rba format is generic enough to describe (i) the major bacterial macromolecular processes in exponential growth easily, and (ii) resource allocation models.
, depending on the model type and on the kinetic parameter values chosen to describe Rubisco activity. The changes in resource allocation between different cellular functions can be seen on Supplementary FigureS17. Upon removal of CO2 from the medium, the simulated cell is no longer viable, confirming that CO2 is an indispensable carbon source for this engineered strain. RBApy offers unique ways of investigating the CO2-fixing E. coli model, especially through the possibility to screen parameters easily and to visualize the impacts of parameter changes on predictions on Escher maps and Proteomaps. Refined with dedicated datasets,.
Acknowledgments This work has received funding from the  French Lidex-IMSV of Université Paris-Saclay  and from the  People Programme  ( Marie Skłodowska-Curie Actions ) of the European Union's  Horizon 2020 Programme under REA  grant agreement no. 642836. This material reflects only the authors' views and the Union is not liable for any use that may be made of the information contained therein. We also thank  O. Inizan  for testing the pipeline.