dataesr/scientific-paragraphs-categorization huggingface dataset:
Acknowledgements The authors would like to thank the patients and their families for their participation and kind cooperation,  Pr. Jamel Chelly  and  Nicolas Lebrun  for fruitful discussions and advice during the first steps of the study,  Agnès Rastetter  for help in genetic analyses, the  Bioinformatics Platform of Imagine Institute  (linkage analyses), and the  IBPS Cell Imaging and Animal Facilities. The study received support and funding from the  University of Tours ,  INSERM ,  Fondation Maladies Rares  (to AT),  European Union   FP7  Project  GENCODYS  (to FL, grant number  241995 ),  Association pour le Développement de la Neurogénétique  (to FL), the  French Agency for Research  (to LT,  ANR-16-CE16-0014-01 ) and the  Jerôme Lejeune foundation  (to RH, grant numbers  1693  and  1959 ).
Boolean networks are largely employed to model the qualitative dynamics of cell fate processes by describing the change of binary activation states of genes and transcription factors with time. Being able to bridge such qualitative states with quantitative measurements of gene expressions in cells, as scRNA-Seq, is a cornerstone for data-driven model construction and validation. On one hand, scRNA-Seq binarisation is a key step for inferring and validating Boolean models. On the other hand, the generation of synthetic scRNA-Seq data from baseline Boolean models provides an important asset to benchmark inference methods. However, linking characteristics of scRNA-Seq datasets, including dropout events, with Boolean states is a challenging task. We present scBoolSeq, a method for the bidirectional linking of scRNA-Seq data and Boolean activation state of genes.
Given a reference scRNA-Seq dataset, scBoolSeq computes statistical criteria to classify the empirical gene pseudocount distributions as either unimodal, bimodal, or zero-inflated, and fit a probabilistic model of dropouts, with gene-dependent parameters. From these learnt distributions, scBoolSeq can perform both binarisation of scRNA-Seq datasets, and generate synthetic scRNA-Seq datasets from Boolean trajectories, as issued from Boolean networks, using biased sampling and dropout simulation. We present a case study demonstrating the application of scBoolSeq's binarisation scheme in data-driven model inference. Furthermore, we compare synthetic scRNA-Seq data generated by scBoolSeq with BoolODE from the same Boolean Network model. The comparison shows that our method better reproduces the statistics of real scRNA-Seq datasets, such as the mean-variance and mean-dropout relationships while exhibiting clearly defined trajectories in a two-dimensional projection of the data.
They revealed to be a powerful and relevant modelling approach to predict combinations of genetic perturbations to control cell fate decision  [25, 26]. Nevertheless, linking qualitative gene activation states with their quantitative measurements, such as count of RNA transcripts, is a delicate task with high stakes for Boolean modelling. We present scBoolSeq, which, given a reference dataset, provides a bidirectional link between scRNA-Seq and Boolean activation states. The binary coarse-graining of scRNA-Seq, we refer to as binarisation, consists in assigning a qualitative active or inactive state to a gene, from one single-cell or a pool of single-cell measurements. The pools of cells usually correspond to phenotypes and other important cellular states. As Boolean models aim at predicting stability and trajectories between such cellular states, binarised data are crucial to assess their fitness with trajectories and steady states.
Unfortunately this approach is only available for bulk RNA-Seq data. The inverse operation of binarisation consists in generating RNA pseudocounts from Boolean activation states. Coupled with simulations of Boolean models, this enables generating synthetic datasets from Boolean models subject to ranges of combinations of perturbations, simulating gene knock-out or constitutive activation, for instance. Resulting synthetic scRNA-Seq data can then serve as a basis to evaluate inference methods, such as gene regulatory networks inference, trajectory inference, and Boolean model inference. Generating single-cell and bulk RNA-Seq data has been addressed by count simulators  [29] [30] [31]. With different underlying assumptions, count simulators reproduce the statistical characteristics of real datasets via parametric and semi-parametric approaches.
BoolODE uses Hill functions to reflect the modulation of gene expression  [36] [37] [38]. However, this approach relies on a considerable amount of parameters such as mRNA transcription and degradation rates, Hill thresholds and coefficients, signalling timescales, and interaction strengths. Determining these parameters is an important bottleneck as they can hardly be estimated from experimental scRNA-Seq data and need therefore to be set arbitrarily or randomly sampled. Moreover, these ODE-based generators fail to produce data with statistical properties comparable to those of real scRNA-Seq datasets. We believe it is crucial that generated count data resemble as much as possible scRNA-Seq data to obtain fair inference benchmarks, which implies mimicking dropouts and other statistical features.
scBoolSeq relies on the learning of gene-wise RNA pseudocount statistics from a reference dataset. This learning is performed in three steps: (i) the classification of empirical gene pseudocount distributions; (ii) the use of Gaussian Mixtures with up to two components as a parametric model; and (iii) the simulation of dropout events with probabilities that are inversely proportional to the expression value. scBoolSeq requires the reference dataset to be constituted of only highly variable genes (HVGs). Functions to perform this filtering are available on major scRNA-Seq analysis distributions such as Stream  [15]  and scanpy  [17]. By selecting HVGs after quality control, normalisation, and batch correction, one ensures that scBoolSeq's reference reflects the underlying biological variation rather than technical noise.
In addition to HGVs which are automatically selected by the designated functions in scRNA-Seq analysis environments, differentially expressed genes (DEGs) and known markers can also be incorporated to scBoolSeq's reference in order to have a fuller image of the transcriptional landscape of the dynamic phenomenon of interest. Thus, from the preprocessed reference dataset, scBoolSeq is able to perform two distinct complementary operations: the binarisation of a scRNA-Seq dataset with respect to the reference dataset, and the generation of synthetic scRNA-Seq from Boolean activation states, as illustrated by Fig. (2) (3) (4)   4 ) A STREAM-plot reconstructing the branching trajectory from synthetic data generated from the Boolean traces  [15]. scBoolSeq can be used to go from gene expression matrices (such as 3) to Boolean matrices and vice-versa.
We first show that our 3-distribution model of scRNA-Seq counts and dropouts is able to accurately reproduce the statistical characteristics of a range of scRNA-Seq datasets. For the binarisation of scRNA-Seq data, we first apply our method to a publicly available scRNA-Seq dataset of early retinogenesis. We show that scBoolSeq correctly identifies the different cell types described in the original study, defined by a minimal set of marker genes. These identities can subsequently be used in order to label cell groups found by the louvain clustering algorithm  [39]. Going beyond cell type identification, we use the Boolean gene activity values determined by scBoolSeq in order to prune a mouse regulon database  [40]. The resulting GRN is validated via Gene Set Enrichment Analysis performed using METASCAPE  [41]  which yielded numerous relevant Gene Ontology terms related to the kept genes.
Finally, we show that scBoolSeq's synthetic scRNA-Seq data generated from Boolean traces produces both discernible trajectories when applying dimensionality reduction techniques and statistics that comparable to those of real datasets. Overall, scBoolSeq provides an efficient method to learn statistics of a scRNA-Seq dataset and derive binarisation and synthetic generation procedures with few parameters. scBoolSeq has been implemented as an open source Python package available at github. com/bnediction/scBoolSeq.
Results In the following, we assume that scRNA-Seq data is preprocessed as log pseudocounts x c,g = log(x norm c,g + 1), where c and g refer to cells and genes, respectively. Any size-factor based normalisation can be used, as long as it is of the form x norm c,g = x raw c,g α where α is a constant. For instance α c = g x c,g would represent the standard library size normalisation, yielding counts/reads per million (CPM/RPM). Our methodology is applicable to alternative normalisations such as TPM (transcripts per kilobase per million reads) or RPKM (reads per kilobase per million reads). The log transformation is necessary in order to ensure the validity of the underlying parametric distributions. with gene-dependent parameters, we were able to reproduce the per-gene dropout rates of different reference datasets.
Probabilistic Simulation of Dropout Events Dropouts arise from both biological (lack of transcription at measurement time)  [45]  and technical causes (sampling and amplification bias)  [46]. For this reason, we built a probabilistic model aiming to: (i) reproduce the distribution of dropout rates across genes in the studied reference datasets; (ii) have a minimal set of gene-dependent parameters; and (iii) have a physical interpretation that accounts for the biological and technical causes of dropouts. Dropout parameters are estimated on a gene-dependent basis because empirical sampling rates exhibit gene-specific bias rather than being uniform random samples of mRNA molecules present in the cell  [47]. By modelling this gene-dependent biases and simulating dropout events after sampling from parametric distributions, our dropout method mimics the physical phenomena that give rise to dropout events and generates data that reproduces the statistics of scRNA-Seq data, as illustrated by Fig.
2. October 22, 2023 5/24 Dropout model Under the hypothesis that the probability of not observing counts for a certain gene within any given cell is inversely proportional to its relative abundance, the relationship is defined as an exponential decay which has been shown to describe the mean-dropout relationship in several scRNA-Seq datasets  [48]. We denote by x c,g the prior pseudocount of gene g in cell c and by x obs c,g the measured pseudocount. The mathematical formulation of the proposed dropout model is of the following form: P (x obs c,g = 0 | x c,g ) = β g e -λgxc,g (1) When simulating dropout events based on these probabilities, the number of dropout events for a given gene across all cells follows a Poisson-binomial distribution  [49] , that is the discrete probability distribution of a series of independent Bernoulli trials whose success (dropout) probabilities are not necessarily identical.
Rate parameter The rate parameter λ g determines the shape of the exponential and thus how rapidly the dropout probabilities decay with the expression value. This parameter is learnt from the reference dataset, independently for each gene, in order to reflect the aforementioned gene-dependent sampling bias. It is calculated by setting the half-life of equation 1 to the gene's empirical non-zero mean as follows, for each gene g of the reference dataset: λ g = ln(2) μNZ (g) (2) where μNZ (g) is the mean of non-zero pseudocounts of gene g in the reference dataset.
Normalisation constant The normalisation constant β g is computed from sampled prior pseudocounts as the optimum value minimising the quadratic deviation between the expected dropout rate of the synthetic sample E [τ g ] and the reference dropout rate for that gene τ ref g (proportion of zero entries in the reference dataset): β g = nτ ref g n c=1 e -λgxc,g (3) where n is the number of sampled cells. This optimum is derived analytically from the expected value of a Poisson-binomial distribution. This ensures that for the same underlying non-zero distribution the dropout rate will, on average, be close to that of the reference.
S1 Fig shows an example of the distribution of rate parameters and the obtained dropout probabilities over the range of expression of a typical log-normalised scRNA-Seq dataset. Overall, we observe a trend depending on the gene pseudocount distribution category: for the same sampled value, zero-inflated genes have the highest probability of dropout, followed by bimodal genes. Genes presenting a unimodal distribution have the lowest dropout rates (and highest non-zero means) and therefore will be seldom dropped-out.
Validation We validated our model by sampling from the learnt parametric distributions and simulating dropouts with our exponential model of Eq. (  1 ). We found that our method reproduces extensive statistics of these datasets, specially the gene mean-variance and mean-dropout relationships which characterise scRNA-Seq data (Fig. 2 ). Furthermore, the correlation profile between all combinations of mean, variance, skewness, and excess kurtosis is globally recovered (S3 Fig). We find that these correlations are only recovered when applying our dropout simulation method.
Binarisation of scRNA-seq data The coarse-graining scheme of scBoolSeq is based on the classification of pseudocount distribution from a reference dataset, as illustrated by Fig. 3. For each gene, cells whose expression level is high (respectively low) enough to classify it as True/active (resp. False/inactive) will be binarised whilst cells whose expression level is ambiguous will be left as undefined. As shown in Fig. 3 , the category-dependent binarisation strategy causes each distribution type to have different proportions of False, True, and undetermined values. Bimodal genes are binarised using their corresponding univariate two-component Gaussian Mixture Model (GMM), whose parameters are estimated on the reference dataset. The GMM's density is given by Eq. 4. The model has two components denoted C i which are characterised by their parameters (φ i , µ i , σ 2 i ).
In the following, it always holds that µ 2 > µ 1 , for every bimodal gene. Therefore, we have two components which represent cells whose transcript level can be classified as active C 2 or inactive C 1. p(x) = φ 1 N (x|µ 1 , σ 2 1 ) + φ 2 N (x|µ 2 , σ 2 2 ) s. t. φ 1 + φ 2 = 1 (4) The probabilities of observation x belonging to each one of the two components are first calculated as detailed in Eq. (  5  Illustration of the category-dependent binarisation allows accounting for different shapes in empirical pseudocount distributions. For each category, plots show the empirical distribution for a selected gene in the GSE81682 dataset, and the part of the values which are binarised with parameters z = "?" for zero-inflated case, q = 0. 05 and α = 0 for unimodal and θ = 0. 95 for bimodal. p(C i |x) = p(C i )p(x|C i ) 2 j=1 p(C j )p(x|C j ) = φ i N (x|µ i , σ 2 i ) 2 j=1 φ j N (x|µ j , σ 2 j ) (5) Then, the binary classification is performed according to a given confidence threshold θ, with 0.
Left: Distribution of categories among the studied datasets. Right: Proportion of binarised values across datasets using the default parameters for each distribution type. These proportions are both determined by the categories and the specified thresholds. These were obtained using parameters z = ? for zero-inflated case, q = 0. 05 and α = 0 for unimodal, and θ = 0. 95 for bimodal. The dropout rate threshold for marking a gene as discarded was set to 0. 99. b zero-inflated (x) = 1 if x > 0 z otherwise (8) The proportion of observations classified as 0 or 1 can be approximated by Eq. (  9 ) ξ(1 -τ ) + β(p ) + η(2q) (9) with the average proportions of binarised observations for each category normalized by the proportion of genes classified as zero-inflated, bimodal, and unimodal, denoted by ξ, β, and η, respectively, and where τ represents the average empirical dropout rate.
Fig. 4  gives statistics on the fraction of observations that are binarised across the selected evaluation datasets. In general, zero-inflated genes with a high dropout rate will only have a few observations binarised to 1 and most cells will be classified as undefined. Bimodal genes are binarised across most cells because the underlying Gaussian Mixture correctly describes the bimodal genes' empirical distributions. Finally, unimodal genes will have twice the margin quantile q fraction of observations binarised in the case of α = 0 in Eq. (7).
Case study of binarisation: Early-born Retinal Neurons We applied scBoolSeq to a publicly available scRNA-Seq dataset in order to binarise expression data and obtain a qualitative description of phenotypes. We show that the obtained qualitative profiles can serve as a basis to perform inference of Boolean networks, which can mimic the differentiation process and identify key genes and interaction involved in the dynamics. The dataset originates from  [9]  (GEO accession GSE122466) which analysed how the diversity of cell types found in the early retina (from embryonic days 10 to 17) arises from a pool of progenitor cells. These neurons are retinal ganglion cells (RGCs), cone photoreceptors (cones), horizontal cells (HC) and amacrine cells (AC). The analyses extended previously known marker genes and showed how these appear to be organised in transcriptional waves of co-expression.
regulon database DoRothEA  [40]  in order to build logical models which reproduce the differentiation process. Our objective is to first evaluate how the binarisation preserves the cell type classification, and how the resulting qualitative description of phenotypes enables to identify core regulations that explain the Boolean differentiation process. Discriminating cellular types using prior-knowledge markers The reference study  [9]  considered prior knowledge markers for the cellular types at different stages of differentiation. We classified each cell according to its binarised expression profile and the markers it contains. Then, for each cellular type, we computed how many cells have the matching marker, and among them, how many match only with that cellular type. As shown in Table  1 , the majority of cells per group were unambiguously identified, except for Horizontal Cells.
Notice that Horizontal Cells share one marker Prox1 with Amacrine Cells. It should be noted, that in this case, a quarter of cells have been Data-driven inference of Boolean models The binarisation of scBoolSeq enables to specify Boolean dynamical properties that reflect the observed differentiation process: existence of trajectories linking (partially) binarised cellular states, including branches from pluripotent states to distinct differentiated states, as well as stability properties. Then, inference methods such as BoNesis  [51, 52]  can derive Boolean networks that reproduce the specified dynamics. The logical rules are derived from prior knowledge Gene Regulatory Networks (GRNs), typically extracted from TF-TF (transcription factor -transcription factor) interaction databases, possibly completed with statistical network inference from scRNA-Seq data.
Synthetic scRNA-seq generation biased by Boolean states As the inverse operation of binarisation, the parametric distributions and dropout model learned per genes from a reference dataset also enable generating synthetic pseudocounts corresponding to Boolean activation states. The main principle is to perform first biased sampling from distributions whose parameters are learnt on non-zero entries of the reference dataset. In a second step, dropout events are simulated according to the gene-dependant model of Eq. (1). Biased sampling ensures that cells in which a gene is active will exhibit higher expression (pseudocounts) than those in which it is inactive. In the case the gene follows a unimodal distribution of median µ and variance σ, the pseudocount are sampled from the half-normal distribution corresponding to the activation state (HN (µ, σ 2 ) for active, and µ -HN (0, σ 2 ) for inactive).
Application to artificial Boolean models The above steps enable generating synthetic scRNA-Seq datasets from collections of binary states of genes, as it would be typically generated from the simulation of Boolean networks  [53, 54]. This generation can then serve as a basis for benchmarking inference methods, by creating synthetic datasets from fixed dynamical models and evaluate the ability of inference methods to recover main features of the ground-truth model. This could notably be applied from artificial Boolean models of different scale and topology. In that cases, however, node are not directly referring to the genes of an experimental scRNA-Seq reference dataset, and one need criteria to associate a reference gene to them. A possible approach, proposed in scBoolSeq, is to analyse the shape of the node-wise distribution of Boolean values and assign genes having similar shape.
Intuitively, a gene is for instance active in most cells, it can be classified as Unimodal. Subsequently, genes which vary considerably can be considered to be Bimodal. Genes which are ubiquitously inactive with a couple exceptions (e. g. , it is active in only one state of the Boolean trace) would then be zero-inflated. scBoolSeq uses scaled versions of the first four moments to classify Boolean gene distributions as unimodal, bimodal, or zero-inflated. The scaled moments of Boolean distributions are fed to a k-nearest-neighbours classifier that was trained on the scaled moments of reference dataset, using their corresponding distribution types. Afterwards a by-category bijective matching is performed in order to ensure that the synthetic scRNA-Seq distributions correctly represent the underlying Boolean dynamics.
We applied this principle on three artificial Boolean models, exhibiting different type of emerging dynamics. For each one of the models, Boolean trajectories representing the dynamics of the network were obtained as described in the next paragraphs. Afterwards multiple observations (corresponding to single cells) were sampled using scBoolSeq with a selected reference dataset (GSE81682). Then, we applied classical scRNA-Seq dimensionality reduction methods to visualise the corresponding pseudocount trajectories. Further details regarding the sampling procedure and projections can be found in the supplementary materials. The first artificial model is a star-like network (Fig. 6a ) in which a single Transcription Factor (TF) up-regulates the expression of a set of genes. This model was simulated by performing one random walk with the fully asynchronous update mode starting from the state where the node tf is active and all genes are inactive.
The third model (Fig. 6e ) is a three-stable switch which has been designed automatically from random scale-free topology and such that it exhibits a two-level differentiation process: from an initial state three stable states are reachable, with an intermediate branching state giving access to two of them. In both cases, we generated Boolean trajectories covering the differentiation branches from the initial states. These trajectories remain apparent in the projections of generated scRNA-Seq data (Fig. 6d  and Fig. 6f  Comparison with BoolODE Given an artificial Boolean network, the tool boolODE  [34]  is capable of producing synthetic pseudocount datasets which exhibit clearly defined trajectories when applying dimensionality reduction techniques such as t-SNE. However, the generated dataset do not exhibit observed statistics of experimental scRNA-Seq dataset.