Maqdasy, S S Lecoutre

Keywords: Machine learning, Méthodes statistiques, Médecine de précision, Microbiote iii Machine learning, Statistical methodologies, Precision medicine, Microbiota iv

La prévalence de l'obésité et du diabète de type II a fortement augmenté ces dernières années, faisant de la recherche dans ces domaines une priorité de santé publique. Parallèlement à cela, le développement des technologies à haut débit ont permis d'obtenir un grand nombre de données hétérogènes provenant des patients et de leur microbiote intestinal. Ces données de grandes dimensions ont une structure qui est propre à chacun d'eux. Ainsi dans le but d'identifier différents schémas entre les patients et pouvoir les stratifier (c'est-à-dire les classifier en différents sous-groupes homogènes en fonction de leurs caractéristiques biologiques), il est nécessaire de développer de nouvelles méthodes computationnelles. Cette thèse présente le concept de « Double Clustering », qui implique la tâche de regrouper simultanément les types de cellules et les patients. Pour cela, nous proposons une nouvelle approche algorithmique appelée LDA-DC (Latent Dirichlet Allocation for Double Clustering) dont le but est d'identifier les groupes de cellules associés aux phénotypes des patients, facilitant ainsi une stratification efficace de ceux-ci. Nous démontrons l'efficacité de notre méthodologie en utilisant des données de patients disponibles publiquement. De plus, nous appliquons notre approche aux données métagénomiques des patients du laboratoire NutriOmics et stratifions les patients sous forme de réseau révélant des groupes de patients ayant des caractéristiques cliniques, biologiques et nutritionnelles communes. D'autre part, nous avons développé une méthodologie basée sur un réseau de neurones artificiel dans le but de prédire l'âge métabolique des patients atteints d'obésité et/ou de diabète de type II en comparaison des patients non-obèses, permettant une stratification des patients. Ainsi, cette thèse s'aligne avec les principes de la médecine de précision et de la médecine prédictive en proposant une approche computationnelle permettant la stratification des patients et l'identification de variables pouvant être modulées dans le cadre d'une stratégie de médecine préventive.

Dans un premier temps, je tiens à remercier Fariza Tahi, Sophie Donnet, Laura Cantini et Ingrid Lafontaine pour avoir accepté de faire partie de mon jury de thèse. En particulier, je souhaite adresser mes remerciements à Fariza Tahi et Sophie Donnet pour avoir consacré leur temps et leur expertise à l'évaluation de mon travail de thèse. Également, je tiens à remercier l'école doctorale Physiologie, Physiopathologie et Thérapeutiques (ED 394 : P2T) pour avoir soutenu financièrement mon projet de recherche ainsi que Karine Clément pour m'avoir accueilli, mon projet et moi, au sein du laboratoire NutriOmics.

Je tiens également à exprimer ma gratitude envers mes directeurs de thèse, Hédi Soula et Nataliya Sokolovska. Hédi, je te remercie du fond du coeur pour ta bienveillance, ton authenticité et ton amitié précieuse. Depuis mon entrée en Master, tu as été un mentor exceptionnel, en me transmettant ton savoir avec passion et en m'encourageant à chaque étape de mon parcours académique. Nataliya, merci pour ta gentillesse, ta simplicité, tes conseils inestimables, tes encouragements constants et ta disponibilité tout au long de ma thèse.

Je tiens à adresser mes plus sincères remerciements aux anciens membres de l'open-space qui m'ont accueilli avec une grande bienveillance à NutriOmics. Léa L. merci pour tes ravitaillements réguliers en nourriture, Jean D. pour tes assaisonnements à base d'insectes en plastique dans le café, Adèle W. pour ton soutien moral sans faille en bio-informatique, et enfin Lise V. pour ta patience légendaire durant les différentes lubies de l'open-space. Je remercie également les nouveaux résidents de l'open-space : Dounia M., référente healthy du laboratoire pour ses précieux conseils, Paul T. fillot de Master, pour les discussions sportives et les fou-rires inarrêtables qu'on a pu avoir, et enfin ma voisine de bureau, la lumineuse Clémentine R. a.k.a soleil du Sud, qui a illuminé ces trois années mémorables d'événements tout aussi incroyables les uns que les autres (« Switch », Bitcoin, Plantes, Piments, plan d'entreprise souvent très loin de la science), et qui a su résumer avec brio ma thèse aux « ordinateurs ». Merci du fond du coeur pour ces 3 années, Queen C. ! Je tiens aussi à remercier tous les protagonistes qui se sont succédés dans l'open-space au fil des années, en particulier Amanda C., Davide M., Mickael M., Hamda A., Alix A., Hugo L., Katy T. et Viva C.

Au-delà de l'open-space, je souhaite remercier Simon L. pour sa contribution à mon développement personnel et intellectuel, tes conseils et nos discussions passionnantes sur des sujets philosophiques et politiques, toujours en relation avec la science, m'ont permis de cultiver un sens critique plus aigu des relations humaines. Je tiens également à remercier Joelle O. pour ses encouragements à parler l'arabe, sa gentillesse, et sa touche moyen-orientale qui m'est très chère, Solia A. pour ses boutures et ses conseils pour l'entretien de la pépinière de l'open-space et Flavien J. pour ses astuces vélo. Je tiens également à féliciter Alois D., bientôt nouveau i Acknowledgment représentant de la bio-informatique : à toi de faire tous les staffs Axe 4 maintenant.

Aussi, je souhaite remercier tous les membres (et anciens membres) de l'équipe : Christine R., Fatiha M., Isabelle D., Florian M., Romane H., Eugeni B., Céline O., Patricia S., Emilie S., Agnès R., Geneviève M., Tiphaine LR., Emilie G., Marta V., Rafael P. N., Estelle A., Nathan F., Sébastien A. et. al. Chacun d'entre vous a apporté sa propre touche à cette expérience professionnelle et humaine, contribuant ainsi à la rendre inoubliable à sa manière. Merci infiniment pour ces moments de partage, de collaboration et de convivialité.

Il est temps maintenant de remercier mes amis les plus proches pour leur soutien sans faille durant cette expérience professionnelle. Je tiens à remercier les « Insécables » (Erik W., Antoine E., Arthur B., Axel C., Paul N., Kevin EK., Quentin M.) pour les soirées arrosées que nous avons partagées, pour avoir écouté patiemment mes doutes et mes frustrations, pour leurs hochements de tête complices à chaque fois que j'ai tenté de leur expliquer mes résultats de thèse (sans grand succès), et pour leur capacité à me remonter le moral lorsque la motivation faisait défaut. Je tiens aussi à remercier Paul B., Louis B., Elisa R., Olivier R., Asma H. pour leurs gloussements contagieux et notre amitié indéfectible, malgré la distance qui nous sépare. Je tiens également à remercier Alexandre G. pour ses conseils en boxe et sa personnalité haute en couleur, Winona T. pour sa joie de vivre contagieuse ainsi que Sirine S. pour sa gentillesse, son écoute et sa capacité à tempérer notre groupe d'amis. Aussi, Coline K. merci pour ta gentillesse, ta joie de vivre, ta capacité d'analyse et tes mots toujours justes et plein de sagesse. Enfin, je tiens à remercier mon ami d'enfance, Thibault H., ainsi que Melissa C. pour avoir été présents tout au long de ma vie et pour avoir suivi de près comme de loin mes aventures professionnelles et personnelles (tant les succès que les échecs), et pour avoir toujours su trouver les mots justes et la distance critique nécessaires pour m'aider à résoudre la plupart des défis que j'ai rencontrés.

Je tiens aussi à remercier l'ensemble des personnes que j'ai croisées au cours de mon parcours académique et professionnel contribuant de manière directe ou indirect à ma maturation intellectuelle, personnelle et scientifique.

List of figures

1.1 A schematic image of the conditions implicated in the pathophysiology of the metabolic syndrome and their potential interactions. IR: Insulin Resistance; HTN: Hypertension; HPA axis : Hypothalamic-Pituitary-Adrenal Axis; DMT2: Diabetes Mellitus type 2; CVD:Cardiovascular disease; CRH: Corticotropin Releasing Hormone; AVP: Arginine Vasopressin: from [Kassi, 2011] [Hwang, 2018]). a) The limiting dilution method isolates individual cells, leveraging the statistical distribution of diluted cells. b) Micromanipulation involves collecting single cells using microscope-guided capillary pipettes. c) FACS isolates highly purified single cells by tagging cells with fluorescent marker proteins. d) Laser capture microdissection (LCM) utilizes a laser system aided by a computer system to isolate cells from solid samples. e) Microfluidic technology for single-cell isolation requires nanoliter-sized volumes. An example of in-house microdroplet-based microfluidics (e.g., Drop-Seq). f) The CellSearch system enumerates CTCs from patient blood samples by using a magnet conjugated with CTC binding antibodies. g) A schematic example of droplet-based library generation. Libraries for scRNA-seq are typically generated via cell lysis, reverse transcription into first-strand cDNA using uniquely barcoded beads, second-strand synthesis, and cDNA amplification 1. 4 Sequencing Methodology for NGS methodology such as Illumina sequencing, and Nanopore methodology. Modified figure from [Shendure, 2017] . . 1.5 Analysis of scRNA-seq, after dimensionality reduction. Cell-to-cell distances can be computed to construct a distance-based graph. Unsupervised clustering algorithm are then performed to assign cells to clusters. Figure is partially extracted from [Kiselev, 2019] . . . . . . . . . . . . . . . . . . . 1.6 The Perceptron model from Rosemblatt from the publication of [Kuipers, 2022] obesity status. Adiponectine OGTT is the quantification of the adiponectin (mg/l), Leptine OGTT is the quantification of the leptin (ng/l), BMI is the body mass index (kg/m2) B. diabetes severity. GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTGLYC is the measurement of the fasting glycemia (plasmatic glucose) in mmol/l, FASTLIPTG is the measurement of triglycerides in mmol/l and Peptide C is the quantification of peptide c reactive in the blood while fasting (µg/l) C. immune status for each patient cluster, WBNEUTRO is the number of neutrophils, WBCLEUCO is the total number of leucocytes, WBMONOCY is the total number of monocytes, and WBLYMPHO is the total of lymphocytes. Variables are selected according to their relevance and significance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

x List of figures 3.4 Quantification for different A. nutritional variables. Nutr vitd is the total intake of vitamin d in log(µg), food breakfast is the daily consumption of breakfast cereals in log(g), food cereeals is the daily consumption of cereals, pasta and rice in log(g), food poultry is the daily consumption of poultry in log(g), food nuts is the daily consumption of nuts including peanuts in log(g), and food fat is the fat intake in log(g) and B. nutritional score with aHEI score (ranges from 0 to 70), aHEI Nuts related to intakes of nuts and seeds (ranges from 0 to 10), aHEI Fibreincereals related to intakes of fiber from cereals and cereal products (ranges from 0 to 10), aHEI PUFASFA related to the ratio of poly-unsaturated fatty acid (PUFA) to saturated fatty acid (SFA) intake (ranges from 0 to 10), aHEI vegetables related to intakes of vegetables (ranges from 0 to 10). . . . . . . . . . . . . . . . . . . 77 3.5 A.B. Network of patients using GENUS data from MetaCardis cohort using only 2a and 2b data. Patients are highlighted based on their label attributed by the agglomerative clustering. 3 distinct clusters were identified with different individuals inside each of them. Quantification for different. C. Cluster composition for different enterotypes and for 2a and 2b individuals. The count is normalized by the size of the cluster (i.e the number of individuals involved in the cluster). Cluster 0 is enriched with Bact1 individual enterotypes, while cluster 1 is enriched with Prevotella enterotype. Cluster 2 is enriched with Bact2 enterotypes. Each of this cluster is defined by a mixture of different enterotypes with an enrichment with some specific individuals.D. Biological and clinical data such as IMPROP (imidazole propionate in nM), GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTLIPTG is the measurement of triglycerides in mmol/l, Leptine OGTT is the quantification of the leptin (ng/l). E. nutritional variables, Nutr fiber is the global fiber intake in log(g), food bread is the daily bread consumption in log(g), food vegetables is the daily consumption of vegetables in log(g) and F. Nutritional score, with aHEI score (ranges from 0 to 70). aHEI vegetables related to intakes of vegetables (ranges from 0 to 10). . . . . . . . . . . . . . . . . . . . . . . 80 3.6 Bacterial network associated with GENUS stratification established for all patients. Three groups of bacteria can be identified, that may contribute to the stratification process. However, we are currently unable to link the functionality of certain bacteria to the underlying phenotypes due to incomplete information provided by various databases. . . . . . . . . . . . 81 3.7 Network of patients using KEGG data from MetaCardis cohort. Patients are highlighted based on their identified enterotype . . . . . . . . . . . . . 82 3.8 Network of patients using KEGG data from MetaCardis cohort. Patients are highlighted based on their label attributed by the agglomerative clustering 83 3.9 Composition of each cluster for each of the enterotypes for all the individuals using KO data. ers by CD4 cells in non-obese, obese, and obese-diabetic patients. The tree primarily centers around CD4 as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red. . . . . . . . . . . . . . . . . . . 4.4 Tree visualization depicting the average expression levels of various markers by CD8 cells in non-obese, obese, and obese-diabetic patients. The tree primarily centers around CD8 as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red. . . . . . . . . . . . . . . . . . . 4.5 Tree visualization depicting the average expression levels of various markers by CD4 cells in obese individuals before and 12 months after a bariatric surgery. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red (p-value < 0.05) . . . . . . . . . . . . . . . . . . . . 6.6 Sub-Network of patients using GENUS data from MetaCardis cohort. Each sub-network display patients based on there country of recruitment only. . 6.7 Sub-Network of patients using GENUS data from MetaCardis cohort. Each sub-network display patients based on there Enterotypes. . . . . . . . . . . 6.8 Sub-Network of patients using KEGG data from MetaCardis cohort. Each sub-network display patients based on there country of recruitment only. . 6.9 Sub-Network of patients using KEGG data from MetaCardis cohort

General Introduction

In this chapter, we address various aspects related to the development of methodologies for patient stratification. Firstly, I provide an overview of the general context of my thesis, which focuses on metabolic diseases like obesity and type 2 diabetes, and their association with gut microbiota. Secondly, we discuss high-throughput techniques for gathering extensive data from patients and microbiota, as well as data analysis approaches. Lastly, we explore the Bayesian methods and delve into the central research question involving the simultaneous clustering of cells and patients. We introduce the concept of "Double Clustering," defined as the simultaneous identification of cell clusters associated with patient phenotypes.

Objectives

Contents [Kassi, 2011] set that metabolic syndrome is a complex disorder defined by a cluster of interconnected factors that increase the risk of cardiovascular atherosclerosis diseases and type 2 diabetes mellitus. In fact, multiple conditions such as stress, visceral obesity, sleep apnea can increase the odds of developing one or multiple metabolic syndromes. Chapter 1. General Introduction Out of all the metabolic syndromes, type 2 diabetes mellitus (T2DM) stands out as one of the most prevalent. T2DM is a metabolic disorder in which an individual experiences persistent high blood sugar level. This can occur due to a combination of factors such as impaired insulin secretion or peripheral insulin resistance, or both. T2DM accounts for approximately 90% of all diabetes cases and is more commonly observed in individuals over the age of 45 [Goyal, 2022]. Its incidence and prevalence have increased over the past few decades, and it currently affects millions of people worldwide. According to estimations done by [Sun, 2022], the percentage of people worldwide between the age of 20 and 79 with diabetes was 10.5%, or 536.6 million individuals, in 2021. This number is projected to increase to 12.2%, or 783.2 million people, by the year 2045. Not only does diabetes have significant health implications, but it can also result in substantial economic consequences. According to the same study, the worldwide expenses associated with diabetes-related healthcare were estimated to be around 966 billion USD in 2021.

Moreover, these expenses are expected to increase to 1 054 billion USD by 2045 making research and prevention in this field a public health priority.

In parallel to the rise on type 2 diabetes, obesity has significantly grown during last years. Overweight and obesity are defined as abnormal or excessive fat accumulation that presents a risk to health. A body mass index (BMI) over 25 kg/m2 is considered as overweight, and over 30 kg/m2 is obese. One of the major concerns is the rapid increase in overweight and obesity among adults. In fact, in a study done by World Health

Organization in European region it was estimated that the prevalence for obesity rose by Overweight and obesity may increase significantly the range of diseases that could be developed, such as nonalcoholic fatty liver disease, chronic kidney disease, T2D, cardiovascular diseases [START_REF] Gbd ; Ashkan Afshin ; Reitsma | Health Effects of Overweight and Obesity in 195 Countries over 25 Years[END_REF]Obesity Collaborators, 2017;[START_REF] Malnick | [END_REF]. Thus, obesity and T2DM present significant challenges for public health agencies. Addressing these issues requires the development of innovative strategies to manage patient flow effectively. One promising approach involves identifying and preventing high-risk patients. This approach COSI, coordinated by the WHO Regional Office for Europe, is the largest surveillance initiative of its kind in the world, taking standardized weight and height measurements (Box 1.1). Data from the fourth round of COSI data collection, conducted between 2015 and 2017 in 36 countries of the WHO European Region, show that nearly one in three children (boys 29%, girls 27%) lived with overweight or obesity, and about one in 10 with obesity (boys 13%, girls 9%) (Fig. 1.8; Table A2.5) (38). offers two significant advantages. Firstly, it enables the identification of patient groups, facilitating tailored therapeutic management. Secondly, it allows for patient stratification, thereby enabling the development of novel preventive or therapeutic solutions that can be targeted to specific patient subgroups. This vision turns public health agencies to introduce the concept of "Predictive, Preventive and Personalized medicine" [Golubnitschaja, 2014]. In addition, multiple studies highlighted the potential of gut microbiota in personalized medicine for preventing and treating obesity and T2DM. Advances in microbiome research have enabled the identification of specific microbial signatures associated with different disease states.

Gut microbiota

The gut microbiome is composed of multiple bacteria that have developed beneficial relationships. Microbiota provides multiple functions and are involved in multiple processes Chapter 1. General Introduction such as nutrient absorption, drug metabolism, protection against pathogens, immunomodulation, and the maintenance of gut integrity. Indeed, gut microbiota plays a major role in the metabolism of certain nutrients, allowing the degradation of carbohydrates and fibers where the digestive system alone cannot do it. In addition, gut microbiota allows the production of metabolites and short-chain fatty acids (SCFA) that play an essential role in maintaining the metabolic health of individuals. In fact, the production of SCFAs has been reported to improve glucose metabolism by influencing gut hormone production [Rinninella, 2019;Tolhurst, 2012;Fan, 2021]. Additionally, a study from [START_REF] Jandhyala | [END_REF] shows that the microbiome has a crucial role in breaking down polyphenols found in food into multiple sub-components that can be absorbed by the host. Gut microbiota also plays an important role in drug metabolism, as studies from [START_REF] Jandhyala | [END_REF]Weersma, 2020] suggest that there are multiple complex interactions between commonly used drugs such as metformin, which influence the microbiome composition. In addition, gut microbiota plays an important role in regulating the host's immune response by modulating the production and release of various immune cells and cytokines. For example, by triggering immunoglobulin A [Fan, 2021], gut microbiota can help prevent inflammatory and autoimmune diseases.

Overall, the intestinal microbiota plays a major role in the maintenance of the homeostasis of the intestine via different roles previously stated. Thus, an alteration of the composition and/or functionality of it can lead to different biological or physiological states. Several studies have linked an alteration of gut microbiota composition to hypertension [Li, 2017], celiac disease [De Palma, 2010], kidney dysfunction [Cigarran Guldris, 2017], and even depression [Chen, 2021a] and Parkinson's disease [Shen, 2021].

Several studies have drawn attention to the relationship between microbiota and obesity as well as type 2 diabetes mellitus within the context of these conditions. More specifically, individuals suffering from obesity tend to have a lower diversity of gut bacteria compared to healthy individuals [Gao, 2018;Lv, 2019]. In the context of type 2 diabetes mellitus, a study done by [Qin, 2012] shows that individuals with type 2 diabetes present more opportunistic pathogens compared to healthy individuals. Moreover, in the same study, the authors show that the number of bacteria producing butyrate is decreased in 1. Biological Context individuals with type 2 diabetes. In fact, butyrate (a short-chain fatty acid) is known to enhance the production of gut hormone, thus regulating glucose metabolism as well as inflammation via multiple signaling pathways contributing to protect the gut from pathogens. Currently, the attention of the community has been drawn to enhancing the richness of the gut microbiota composition. This enrichment can be achieved through the supplementation of vitamins or the use of pre-or probiotics.

A study conducted by [Kemp, 2022] shows a significant decrease in vitamin K levels in patients with dysbiosis and chronic kidney disease. The study suggests that potential supplementation of vitamin K may help to enhance the dysbiotic state. Another study performed in our lab by [Belda, 2022] demonstrates that severe obesity is associated with a decreased abundance of biotin-producing bacteria, leading to inflammatory metabolic dysfunction and inflammation. Thus, supplementing obese individuals with biotin could prevent the deterioration of the metabolic state.

Probiotics are living microbial food supplements that, when consumed in adequate proportions, have a beneficial effect on the health of the host, while prebiotics are substrates that are selectively used by host microorganisms, conferring a health benefit [Hill, 2014].

While multiple studies show the benefits of probiotics in metabolic conditions in mouse models [Li, 2016;Everard, 2013], current state-of-the-art studies on humans report only moderate beneficial effects of probiotic supplementation on body weight, body mass index, waist circumference for overweight individuals, as well as glycated hemoglobin and fasting glycemia for patients with type 2 diabetes [Koutnikova, 2019]. However, the subject is largely debated in the community as some studies, such as one conducted by [Jones, 2018],

show an increase in adiposity in obese individuals supplementing with probiotics.

For prebiotics, studies on obese mouse models report an enhancement of metabolism (glucose metabolism, leptin sensitivity) [Everard, 2011]. However, studies on humans do not report significant impacts of prebiotics on the overall health of patients [Cerdó, 2019].

While probiotics and prebiotics have shown moderate effects on human metabolic health, another concept has gained attention in the field of gut microbiota research: enterotypes.

Chapter 1. General Introduction

Composition and concept of Enterotype

Enterotypes refer to the categorization of individuals' gut microbiota based on the dominant bacterial species present in their gut [Arumugam, 2011]. Gut microbiota is unique to each individual, mostly due to the diversity among the bacteria and their numbers (between 500 and 1000 species can constitute a healthy microbiota [Bäckhed, 2004]).

Despite this variability, the composition of the microbiota enables the identification of patterns or homogeneous groups of bacteria, even if two phyla of bacteria, Firmicutes and Bacteroidetes, constitute more than 90% of the total number of bacteria [Qin, 2010].

A study performed by [Arumugam, 2011] on the data from the "Human Microbiome

Project" [Human Microbiome Jumpstart Reference Strains Consortium, 2010] has demonstrated that the gut microbiome can be classified into three major groups based on the genus of each bacterium (which is a taxonomic rank below the phylum): Bacteroides (enterotype 1), Prevotella (enterotype 2), and Ruminococcus (enterotype 3). To obtain the different enterotypes, the authors performed a partitioning around medoids algorithm (PAM) and a principal component analysis for visualization. However, the clustering methodology used for metagenomic data has faced criticism due to the fact that these types of data are a discrete count matrix. Using PAM clustering, which relies on distance metrics such as Euclidean or Manhattan distance, can create inaccurate results and is not the best option for this type of task. Later, a study performed by [Holmes, 2012] solved this problem by introducing Dirichlet Multinomial mixture (DMM) for metagenomics. Dirichlet multinomial mixture (DMM) is a probabilistic methodology designed for community detection, where the Dirichlet distribution is used to model the probability distribution over the clusters, enabling to find an optimal number of clusters. The main advantage of this methodology lies in the fact that the number of clusters doesn't need to be set prior to clustering. Using this methodology, a study done by [Vandeputte, 2017] states that Bacteroides enterotype can be split into two different enterotypes, Bacteroides 1 and Bacteroides 2, and found the overall number of enterotypes to be four.

Each enterotype is tightly connected with some metabolic health condition and different types of diet, with Bacteroides 2 associated with a western diet, with a low microbial cell count and gene richness associated with intestinal inflammation, higher BMI, and 2. Development of high throughput technologies diabetic condition [Vandeputte, 2017;Vieira-Silva, 2019;Vieira-Silva, 2020]. Prevotella enterotype is characterized by an abundance of Prevotella genus and is known to be linked with carbohydrate consumption [Wu, 2011].

While the concept of enterotyping is mostly based on the genus abundance of some bacteria, multiple studies have emerged raising skepticism among the cohorts. In fact, a study done by [Huse, 2012] has shown that although some patients appear to be correctly assigned to an enterotype, many individuals appear to belong to an intermediate and transient group between enterotypes, and forcibly assigning an enterotype to these would create a significant bias.

In parallel, the emergence of high-throughput techniques, such as flow cytometry, Illumina sequencing, and single-cell RNA-sequencing, have revolutionized the field of life sciences by offering unprecedented resolution to study the heterogeneity in cell population. However, these cutting-edge technologies have generated a large quantity of heterogeneous data, presenting new challenges in terms of data interpretation and integration. This "big data" has paved the way for the development of new algorithmic procedures that could encompass and interpret these results, with the aim to gain more meaningful and interpretable outcomes and improve therapeutics care.

Development of high throughput technologies

Recently, new technologies have been introduced to better define and characterize patients' cells and microbiota. These technologies include flow cytometry, single cell RNA-seq and metagenomics.

Flow cytometry

Flow cytometry was designed to analyze cells coming from individuals using fluorescence and absorbance measurement at the single cell resolution. Flow cytometry has the power to identify and characterize cellular characteristics (such as pH, size of the cell), as well as cellular components such as protein, surface receptor or DNA [Rieseberg, 2001]. Nowadays, new flow-cytometry techniques have the capability of detecting more than 14 pa-Chapter 1. General Introduction rameters simultaneously [Wilkerson, 2012]. It relies on optical concept that when a laser beam strikes particles, fluorescence emission occurs. The extent of light scattering is directly linked to the structural and morphological attributes of the cell, whereas the fluorescence emission originating from a fluorescence probe is proportional to the amount of fluorescence probe bound to the cell or cellular component [Adan, 2017]. These light signals can be converted into electronic signals that can be analyzed using some computer software, and after a step of analysis some specific cell-types can be identified within a heterogeneous subgroup.

From RNA-seq to Single Cell RNA-sequencing (scRNA-seq)

Single-cell RNA-sequencing (scRNA-seq) is a cutting-edge technique that combines cell -isolation methodology with RNA sequencing (RNA-seq). The first scRNA-seq study was published in 2009 [Tang, 2009] with the premise that certain conditions may result in very few RNAs being present in a tissue or cluster of cells at the global scale, necessitating a higher resolution approach to reach the cellular level.

Initially, bulk-RNA-sequencing (bulk RNA-seq) has been used as an approach to detect and quantify the number of RNAs in a biological sample, giving a better understanding of underlying biological mechanisms. RNA-seq involves the isolation of RNA sequences, which are then transformed into complementary DNA (cDNA) via reverse-transcriptase.

However, given that nucleotide chains can be exceedingly long, it becomes necessary to break them down into smaller, identical-sized segments known as "reads". The size of these reads is an important factor in the sequencing process, as smaller reads have a higher likelihood of being unmatched with the reference genome. The subsequent step, referred to as mapping association, involves the matching of reads with the reference genome in order to identify their corresponding locations. At the end of the process, reads are aligned and can be analyzed using computational tools.

While RNA-seq provides many advantages in deciphering some biological mechanisms, it also has certain limitations that must be taken into account. First, it requires the isolation of a single cell-type beforehand, making it challenging to study mixed populations of cells. Furthermore, certain RNAs are present in small quantities, but are critical markers 2. Development of high throughput technologies of specific cell subtypes at the tissue level. As a result, these less abundant RNAs may be discarded in the global flow of RNAs that are more abundant in the tissue. Finally, RNA-seq does not allow precise quantification of gene expression within each cell, but only within a pool of cells, reducing the resolution of the analysis. These limitations have prompted the community to developed more precise approach, such as single-cell RNA-seq, providing a more detailed and comprehensive picture of gene expression within individual cells. A plethora of methodologies have been proposed for the development of RNA-sequencing techniques at the cellular level. In their publication [Hwang, 2018], the authors encompasses numerous techniques that have been used to overcome the challenge of isolating one cell (Figure 1.3). A major breakthrough in the field was the introduction of microfluidic (Figure 1.3 e) and microdroplet-based assays, which enable the manipulation and screening of a vast number of cells, ranging from thousands to millions, while minimizing the cost [Hwang, 2018]. The microdroplet-based method involves the isolation of individual cells within a lipid droplet that contains a hypotonic buffer, poly dT primers for mRNA capture, and reverse transcriptase for cDNA generation. During reverse transcription, unique molecular identifiers (UMIs) or barcodes are integrated, and this approach enables each read to be assigned to its corresponding original cell [Hwang, 2018].

Sequencing methodologies for Metagenomics

Since the composition of the gut microbiota depends on the sampling position in the gastrointestinal tract, different methodologies have been used to analyze the intestinal microbiota. After the DNA has been extracted, various approaches can be used to investigate the genetic material. The most common and extensive method involves sequencing the 16S ribosomal RNA coding region (16S rRNA) or utilizing a "shotgun" approach to sequence all genes present in the sample. Sequencing of 16S rRNA allows the study of the phylogeny of bacteria. Indeed, this gene is present in all living organisms and has conserved regions used as universal primers to amplify this region by PCR. Thus, the sequences obtained from a sample allow identification of the different taxa of bacteria present in the sample and characterization of different microbial communities.

Chapter 1. General Introduction On the other hand, shotgun methodology is based on random DNA fragmentation. Prior to sequencing, DNA is broken in a random manner, and each fragment is attached to a specific DNA sequence. Sequences are amplified by PCR, and sequence identification is performed via incorporation of a fluorescent tag (usually a nucleotide) in the complementary strand.

Both techniques generate multiple sequences, and using a bioinformatics framework, it is possible to identify the different genes in the sample. Thus, for each collected sample, multiple genes are identified, allowing identification of multiple groups or subgroups of genes related to one or multiple bacterial genera.

Recently, there have been advances in technology with the introduction of new generation sequencing (NGS) methodology. One of them is Nanopore technology [Lu, 2016].

A nanopore is a channel that is only a few nanometers in size. A fragment of DNA passes through the nanopore, and as each molecule passes through the pore, it creates an electrical change that can be detected and analyzed. Each nucleotide is known to create a specific modification in the electrical record. Thus, by finding different patterns of electrical changes, it is possible to link electrical changes to nucleic acid and sequence fragments of DNA. The main advantages of nanopore sequencing are its low cost, rapidity, and ability to sequence very long DNA (Figure 1.4).

Another NGS methodology is Illumina sequencing, which is widely used for DNA sequencing [Shendure, 2017]. The process involves breaking down DNA into smaller fragments and then coating each fragment with a short DNA sequence called an adapter that has a complementary sequence to Illumina primers. These fragments are then attached to a flow cell surface containing multiple reaction chambers, where a single DNA fragment is present in each chamber. PCR amplification is then performed to multiply the DNA fragments, resulting in the formation of bridges between the complementary oligonucleotides on the flow cell surface. This process, known as bridge amplification, creates clusters of identical DNA on the flow cell.

The next step involves adding fluorescently labeled nucleotides to the flow cell and recording the emission of light as each nucleotide is incorporated into the growing DNA strand using the Illumina sequencing instrument. After each cycle of nucleotide incorporation, 2. Development of high throughput technologies the fluorescent label is removed, and the process is repeated for the next nucleotide. The ultimate step is analysis using a bioinformatics workflow to generate reads. Reads are aligned with the reference genome, and genes can be identified for each sample (Figure 1.4).

Illumina sequencing is very powerful since the adapter allows for high read density, with multiple fragments being analyzed simultaneously. Also, the error rate of this sequencing technology is very low compared to other sequencing technologies and is suited for analyzing DNA that is present in low quantities. [Hwang, 2018]). a) The limiting dilution method isolates individual cells, leveraging the statistical distribution of diluted cells. b) Micromanipulation involves collecting single cells using microscope-guided capillary pipettes. c) FACS isolates highly purified single cells by tagging cells with fluorescent marker proteins. d) Laser capture microdissection (LCM) utilizes a laser system aided by a computer system to isolate cells from solid samples. e) Microfluidic technology for single-cell isolation requires nanoliter-sized volumes. An example of in-house microdroplet-based microfluidics (e.g., Drop-Seq). f) The CellSearch system enumerates CTCs from patient blood samples by using a magnet conjugated with CTC binding antibodies. g) A schematic example of droplet-based library generation. Libraries for scRNA-seq are typically generated via cell lysis, reverse transcription into first-strand cDNA using uniquely barcoded beads, second-strand synthesis, and cDNA amplification 16 2. Development of high throughput technologies [Shendure, 2017] 3 An analytic procedure to process big data-sets

The "omics" methods mentioned above have generated a large amount of heterogeneous data from both patient's cells and the microbiota. These data are complex to interpret for several reasons, but one being that they are of large dimensions. We refer to them as "high dimensional data set". High dimensional data are defined as data in which the numbers of features are bigger than the number of observations. For example, in scRNAseq, the number of features approximates 10K, where the number of observations can rise to 30K. To overcome this problem scientists came out with the idea to reduce the dimensionality.

Dimensionality reduction

Dimension reduction refers to the process of reducing the number of features by creating new variables while keeping as much as possible variation in the data. Generally speaking, reducing the dimensionality causes a non-negligible loss of variability in the dataset however it provides multiples advantages such as an increase of interpretability while minimizing information loss [Jolliffe, 2016]. Multiple methodologies have been designed to overcome this problem.

The best known of these is Principal Component Analysis (PCA). Principal component analysis, is a mathematical procedure which is widely used for dimensionality reduction.

PCA was introduced in [START_REF] Pearson | LIII. On lines and planes of closest fit to systems of points in space[END_REF] where it was initially defined as the linear projection that minimizes the average projection cost, which is represented by the mean squared distance between the data points and their corresponding projections. Then [Hotelling, 1933] proposed another definition for PCA explaining that the methodology can be characterized as a linear transformation that projects the data onto a lower-dimensional subspace, which is referred to as the principal subspace. The projection is performed in an orthogonal manner, with the objective of maximizing the variance of the projected data.

Currently, PCA is widely used to reduce the dimensionality and is used as a pre-processing step for speed up machine learning phase [Iliou, 2015], as feature engineering method to extract important features from the data [Ebied, 2012]. Some publications also consider

3. An analytic procedure to process big data-sets PCA as a great method for noise reduction [Salmon, 2014] as the step of projecting onto a lower dimensional subspace can improve the quality of the data. Also, PCA is widely used as visualization methodology, where result can be projected on two or three components.

However, PCA possesses multiple critical aspects that push scientists to develop novel solutions. First PCA assumes linearity between variables, and makes the assumption that the data can be represented as a combination of multiple linear features. Moreover, the lack of interpretability due to the previous assumption make it difficult to link the obtained new data representation with original features. To overcome these problems, scientists developed the Non-negative Matrix Factorization (NMF).

In my thesis, I did not use the NMF technique. However, it is worth mentioning that this methodology exists and can be used to address specific problems related to PCA. NMF was introduced by [Paatero, 1994] and popularized by [START_REF] Lee | [END_REF]. It is a method based on the assumption that data can be decomposed into two non-negative matrices such as the two decomposed matrices approximate the optimal solution. Mathematically, NMF is based on the fact that 2 non negatives matrices such as H and W can approximate a matrix V, where V ≈ W × H, with V is a matrix of data of size p ×r, W is a matrix of data p × f (where f is the number of features), and H is a matrix of size f * r. Also, the main difference between PCA and NMF is that NMF factors are collinear while PCA components are orthogonal meaning that in the case of NMF, factors are additive while in PCA the information depend on the preceding component. In bioinformatics, NMF has been widely used to recover biological information such as gene expression profiles in microarray data from cancer individuals [Brunet, 2004;Kim, 2007]. Moreover, it has been shown that NMF has a better performances in detecting mislabel sampled compared to PCA in microarray data [Liu, 2008]. Despite the advantages of NMF over PCA, there are multiple disadvantages: The first one is that NMF is designed for non-negative data, thus negative datasets or data centered around zero will not be able to be processed with NMF. Moreover, even if NMF can provide more interpretable results over the PCA, factors obtained by NMF may not result in meaningful or interpretable information.

The methods presented above are linear data reduction methods, and consider different assumptions, the first of which is that the relationships between all the variables are Chapter 1. General Introduction linear. Moreover, it considers each feature as being independent of the others which could be inaccurate if some correlations exist between them. One of the major examples is scRNA-seq data, where gene expression profiles for cells are known to be non-linear due to multiple interactions between genes. In fact, complex regulatory elements (such as transcription factors) can modify the expression level of a gene thus influencing the expression of multiple other genes from the same signaling pathway in a non-linear way. This major challenge, drive researchers to elaborate new methodologies that are robust from the computational viewpoint, with respect to the data structure. A large number of non-linear dimensionality reduction methods have been proposed. The state-of-the-art methodology is the t-SNE (t-distributed stochastic Neighbor Embedding) introduced by [Maaten, 2008]. As for the linear methodology, the main idea of the t-SNE is to map highdimensional data points to a low-dimensional space, by keeping the pairwise similarities between the data points. To achieve this goal, pairwise similarities are computed between the different points using Gaussian kernel, and probability distribution over the pairs of points in the sub-space are also computed in the same manner. The aim of the method is to find an optimized mapping between the high-dimensional space to the sub-space that minimises the difference between the two distributions.

Recently the community also developed the UMAP (Uniform Manifold Approximation and Projection) [McInnes, 2020] that challenged t-SNE in multiple ways: First the authors argue that UMAP preserves more of the global structure of the data, with superior run time performance. It also appears that their methodology has a superior capability for scaling data-set compared to t-SNE. UMAP gains a lot of popularity in the bioinformatics community especially for analyzing large scale data. In fact, several studies have demonstrated the capability of UMAP to process and visualize scRNA-seq data [Becht, 2018;Cao, 2019;Clark, 2019].

In Chapter 2 of my thesis, I used the UMAP methodology with the primary objective of visualizing specific cell types using the clustering technique developed in the same chapter. Although dimensionality reduction methods are very important for data exploration, visualisation and data interpretation, they do not identify patterns or data structure. In reality, these methods are often used as a preliminary step for the tasks of data clustering 20

3. An analytic procedure to process big data-sets or classification.

Machine learning approaches

Scaling high-dimensional data to a lower dimensional space can improve interpretability, but it does not always help to cluster data points that share similar features. To better understand and interpret the data, scientists have developed various clustering methods, including both supervised and unsupervised approaches. As a brief reminder, supervised machine learning are methodologies that involves training a model on a labeled dataset where inputs are associated with the corresponding output. The goal of supervised learning is to acquire a mathematical function that can map some input to the corresponding output. In contrast, unsupervised machine learning are methods where models are trained to identify patterns in the data on any sort of labeled data, with the ultimate goal to identify some hidden patterns.

Unsupervised methodology

In the bioinformatics community multiple frameworks have been developed to identify similarities in cells population using unsupervised methodology. The most popular one is the K-means clustering introduced by [Lloyd, 1982] where he describes the iterative process that minimizes the squared distance between each data point and it is assignation to the closest centroid defined as the center of a "Cluster". However, K-means clustering is known to have several disadvantages: the number of clusters should be defined in advance, thus creating some problems in identifying some underlying clusters. Furthermore, Kmeans clustering prioritizes the construction of clusters that are of comparable sizes, which can cause less common cell types to be hidden within a larger cluster.

Another practical clustering method is hierarchical clustering. The concept of hierarchical clustering has been defined by [Ward, 1963] where he defines a hierarchical procedure minimizing the sum of squared distances within each cluster. Currently, Hierarchical clustering is one of the most commonly used methodologies in bioinformatics. In fact a plethora of methodologies have been developed such as GeneRAGE [START_REF] Enright | [END_REF], SWORDS [Chaudhuri, 2002] that use at some point hierarchical clustering with the sake Chapter 1. General Introduction of identifying relationships between genes using large-scale genomic data. Nowadays, hierarchical clustering is still widely used in multiple frameworks to analyse scRNA-seq data such as CIDR [Lin, 2017], BackSPIN [Zeisel, 2015]. However, hierarchical clustering has multiple limitations. First, it is computationally intense especially for large dataset (as the complexity rises with the number of datapoints). Moreover, as for the K-means, the number of clusters needs to be set-up prior to the analysis, thus identifying optimal number of clusters that reflects the biological reality, and this step can be challenging.

In my thesis, I implemented a K-means clustering as an initial step to identify specific cellular phenotypes in Chapter 2. In Chapter 3, I applied agglomerative clustering to the patient graph matrix established using the methodology discussed in Chapter 2, to identify clusters of patients sharing similar microbial sub-structures. The primary objective was to link these cluster of patients with available clinical and nutritional data for further analysis and identify patterns of dietary habits or clinical features related to them (and by extension to there microbial structure) [Kiselev, 2019] Alongside K-means and hierarchical clustering, which are widely used in bioinformatics to analyze scRNA-seq data, another family of methods was shown to be efficient for high-dimensional data, namely supervised learning approaches.

Supervised methodology

In the case of high-dimensional data, supervised methodology is the task to automatically annotate single cells based on their mRNA expression profile. First it requires a 22

3. An analytic procedure to process big data-sets database encompassing information about gene expression profile of reference cells and there. Numerous supervised machine learning methods have been proposed. Among them we find the decision tree methodology introduced by [Morgan, 1963] whose primary goal is to create a model that can make predictions about the target variable learning straightforward decision rules that are derived from the characteristics of the data. From the computational viewpoint, decision tree is made of nodes, where a decision is made based on the value of the input features. Here, a decision is defined as a binary split, where each branch corresponds to passing or not a threshold. When the decision tree is constructed, it can be used to predict target variables for previously unobserved. One of the major advantages of decision trees is that they are very easy to interpret, due to the fact that the structure of the tree is known during the classifying process [Stiglic, 2012]. Moreover, a decision tree is less time consuming compared to other classification methodologies.

Currently the decision trees are widely used in bioinformatics, from protein interaction hotspot [Darnell, 2007], to gene expression classification [Williams-DeVane, 2013] as well as in medical field for computer aid diagnostics [Serrano-Aguilar, 2012]. However, decision trees face major issues namely, it is prone to overfitting, occurring when the model is too complex. In reality, instead of fitting the underlying patterns, the model fits the noise resulting in incorrect predictions when data are fitted. Another noteworthy aspect is that decision trees are sensitive to variations in the training data.

To tackle the problem of overfitting, scientists have developed a novel method that originated from the decision tree called Random Forest. The Random forest was introduced by [Breiman, 2001] who stated that the methodology combines multiple decision trees to create an ensemble of the model. First, the algorithm randomly samples some features and creates a decision tree using the sampled features. Then the process is repeated multiple times to build a forest and the prediction is made by aggregating the predictions of all trees (using the majority vote). The Random Forest has gained a lot of popularity in bioinformatics, especially for disease diagnostics [König, 2008] as well as for identification of multiple links between gene interactions.

In my thesis, I used the random forest algorithm during the exploratory phase, however, it did not yield conclusive results regarding the thesis global idea we aimed to address. The most basic artificial neural network, contains one neuron, called perceptron. The Perceptron concept was introduced by [Rosenblatt, 1958], where a single neuron was used for classification task. [Kuipers, 2022] 3. An analytic procedure to process big data-sets

The idea behind the perceptron of Rosemblatt is to update the weights of the neuron in response to the errors performed during the training processes. At each iteration, the error is computed which corresponds to the difference between the true label of the data and the predicted output. Weights are adjusted using delta rule until the error is minimized.

The delta rule is defined as ∆w = α(y -y)x where ∆w a modification of the weight, α is a learning rate, y is a real output, y is predicted output and x is the input vector.

Perceptrons are generally used for binary classification task and there is a plethora of literature on it. One example in biology, is a study from [Stormo, 1982] where they used the perceptron to classify and separate translational initiation site from all others sites in E.Coli strains using multiple mRNA sequences and it outperformed the state-of-the-art of the methodology based on rule decision. The perceptron's limitations are evident as it fails to capture intricate non-linear separable patterns, thereby hindering its ability to effectively model complex scenarios. To overcome these problems, it is possible to use a MLP (multi-layer perceptron). A multilayer perceptron is known to contain several layers of perceptrons connected to each other and forming different layers (i.e. several hidden layers). Thus the added layers allow to learn hidden and more complex patterns allowing to capture the different non-linear relations (Figure 1.7). This concept was introduced for the first time by [Rumelhart, 1986] where the authors discuss a gradient back-propagation concept allowing the training of multi-layer networks. Thus, in their paper, the authors demonstrate that the gradient back-propagation allows to adjust weights of network to learn and approximate complex functions. In Chapter 4, we will develop an artificial neural network based on a multi-layer perceptron whose objective will be to predict the metabolic age of patients according to the different immunological cell-types received.

Several methodologies have been developed briefly after the multilayer perceptrons: the first one being the convolutional neural networks (CNN) by [LeCun, 1998]. CNNs are based on convolution operations and are extensively employed in the field of image analysis, enabling the extraction of patterns from structured datasets. CNNs have found wide applications in computer vision and image segmentation. In the field of biology and medicine, several algorithms relying on CNNs have been developed for various pur- poses, including the identification of breast cancer metastases [Wang, 2016;Sun, 2017], melanoma (skin cancer) detection [Nasr-Esfahani, 2016], retinopathy detection [Maji, 2016], and the identification of cardiac ventricles in MRI scans [Emad, 2015].

Another approach that has been developed is autoencoders, introduced by [Hinton, 2006].

Autoencoders primarily serve the purpose of unsupervised data learning and data representation. The fundamental objective of autoencoders is to reconstruct the input data completely based on a compressed representation of the data, thereby contributing to the broader concept of dimensionality reduction [Hinton, 2006]. In a recent study done by [Shen, 2023], an autoencoder approach is employed to extract and learn the latent features of a genomic dataset, which contains significant amounts of missing information. This approach enhances the predictive performance of the model while mitigating overfitting. Furthermore, other sophisticated architectures have emerged, including generative adversarial neural networks (GANs) used for image and text content generation, as well as recurrent neural networks (RNNs) designed for sequential modeling tasks.

Soft, hard and bi-clustering methods

Here, we will explore three additional concepts: soft clustering, hard clustering and biclustering.

3. An analytic procedure to process big data-sets Soft clustering, also known as probabilistic clustering, encompasses unsupervised techniques that group data based on shared characteristics among data points. Unlike hard clustering, where each point is exclusively assigned to a single cluster, soft clustering allows for the possibility of a point belonging to multiple clusters with varying probabilities.

In soft clustering, each point can be represented by a vector that expresses the probabilities of its to belong to different clusters. This characteristic of soft clustering offers several advantages, including the ability to consider potential overlaps between points and gain a better understanding of inter-cluster structure. Moreover, soft clustering proves particularly valuable when cluster boundaries are indistinct or not clearly defined.

There are several methodologies available for soft clustering, with one of the most wellknown being the Expectation-Maximization (EM) algorithm [Dempster, 1977]. The EM algorithm is used to estimate the parameters of a probabilistic model, such as the Gaussian Mixture Model (GMM). It assumes that the weights of the data in each cluster are generated from a multivariate Gaussian distribution. The EM algorithm consists of two stages. In the expectation stage, the algorithm calculates the probability of each point belonging to a cluster using Bayes' theorem. Then, in the maximization stage, the algorithm updates the models parameters by maximizing the likelihood of the observed data, taking into account the information from the expectation stage [START_REF] Mclachlan | [END_REF].

Nevertheless, the EM algorithm faces significant challenges related to parameter initialization. Specifically, the algorithm's sensitivity to initial parameter values becomes apparent since the algorithm operates iteratively, the choice of initial parameters can greatly influence its convergence, potentially leading to convergence at a local minimum rather than the global optimum.

In my thesis, we will employ a soft clustering methodology to simultaneously group patients and cells. The rationale behind this choice stems from the fact that humans contribute significantly to the variability observed in the data presented in Chapters 2 and 3.

By adopting a soft clustering approach, we can effectively consider the potential overlaps between different patient groups. Furthermore, applying soft clustering rather than hard clustering appears to be the most appropriate strategy for stratifying patients.

Chapter 1. General Introduction Bi-clustering, also known as co-clustering, is a methodology for simultaneously clustering the rows and columns of a matrix. Unlike traditional clustering, where the main objective is to group points with similarities between them, the bi-clustering aims to identify subsets of rows and columns representing patterns with similar behaviors. In the biological context, bi-clustering methodologies only apply to a single data matrix, where the row represents the sample and the columns represent the quantified variable (e.g. genes).

There are several methodologies to performed bi-clustering especially for the case of microarray or scRNA-seq data. Some approaches are used to identify distribution parameters, and assume the existence of a statistical model linked to the bi-cluster structure and applying an iterative procedure to adapt its parameters. This is the case of Bayesian Bi-Clustering (BBC) introduced by [START_REF] Gu | [END_REF] where they build a Bayesian model combined with a Gibbs sampling for inferencing parameters.

While extensive literature exists on different bi-clustering methodologies listed by [Xie, 2018], currently no existing methodology addresses the simultaneous clustering of patients and cells using patient-derived data, such as scRNA, metagenomic, or flow cytometry data. In Chapter 2 we introduce a novel methodology that tackles this problems using a Bayesian framework, and introduce the concept of "Double clustering".

Preventing overfitting

In machine learning, overfitting occurs when a model is excessively fine-tuned using training data, causing it to lose its capacity to accurately generalize on unseen data. This appears when the model learns specific features of individual data points, such as noise or biases, rather than underlying patterns. Consequently, the model's performance significantly deteriorates when applied to new data.

When dealing with health data derived from diverse patient cohorts, the challenge stems from the limited availability of patients who possess similar biological characteristics, such as being in a healthy state. Consequently, while high-throughput methods can yield numerous high-dimensional datasets, learning different patterns remains constrained due to the scarcity of patients. Therefore, when learning on a specific type of patients, it becomes imperative to implement strategies that prevent overfitting in order to address

3. An analytic procedure to process big data-sets this limitation.

Multiple strategies are available to mitigate overfitting [Ying, 2019]. These include partitioning datasets into training subsets, applying weight constraints through regularizers like L1 or L2 penalty, implementing early stopping to stop model training when validation performance declines, and incorporating dropout in artificial neural networks, where a specific number of neurons are dropped during training. All of these techniques aim to alleviate the learning process and prevent overfitting. However, when the number of patients is small, it is difficult to divide the data into different subgroups.

In Chapter 4, we apply an artificial neural network to predict the metabolic age of obese and obese-diabetic patients, using data from lean individuals. Given the limited number of lean individuals in our dataset, the primary challenge involved learning distinct patterns without overfitting. To mitigate this issue, we employed multiple strategies, such as early stopping, dropout, and regularization penalties. Additionally, to verify the consistency of our results and prevent against overfitting, we repeated the learning and prediction process multiple times (10 000 times). Detailed methodological aspects are provided in Chapter 4.

Patient Stratification

Patient stratification is an approach that involves grouping patients into homogeneous subgroups based on relevant characteristics or criteria [Rucci, 2014]. Multiple approaches exist for achieving this, including stratification based on clinical features such as patient age, sex, and BMI. For instance, [Rucci, 2014] employed a decision tree to identify combinations of demographic and clinical characteristics for discriminating patients with differential annual glomerular filtration rate decline. Another recent study [Mueller, 2022] employed hierarchical clustering on immunological data from COVID-19 patients, identifying three patient groups with distinct disease responses based on some specific immunological biomarkers.

Furthermore, cellular-level approaches have also been applied. For example, [START_REF][END_REF] used pre-annotated flow cytometry data from patients with juvenile-onset systemic lupus erythematosus (SLE) and healthy idividuals to stratify them. The authors demon-strated that by using a random forest classifier, they achieved 90.9% accuracy in classifying the patients and subsequently employed K-means clustering on the data in order to stratify them in subgroups. It is interesting to note that the association between patient phenotypes and cellular types is not systematically known, meaning that patient stratification is always independent from the cellular information, meaning that recover cellular information from clustered patient is challenging.

In order to tackle this challenge, we chose a methodology that focuses on clustering patients while simultaneously preserving cellular information. This approach enables us to establish a potential link between patients and cell types. To solve this hypothesis, we turned to Bayesian methods.

Statistical inference

Statistical inference is defined as a process of finding model estimation from a sample collected from a population. Statistical inference uses mathematical and probability for the sake of analyse and interpret large scale data, making inference on a population from sample collected.

Definition of Bayesian Statistics

Bayesian statistics is a field of statistical analysis based on the principle of the Bayes' theorem. The Bayes theorem is defined as :

P (H|E) = P (E|H)P (H) P (E) (1.1)
Where P (H|E) is the posterior probability of H given E, P (E|H) is the likelihood of E given H, P (H) is the prior probability of H, and P (E) is the marginal porbability of E.

The likelihood function describes the probability to observe the data given the hypothesis, and is usually derived from a statistical model that specifies the relationship between the data and the parameters of interest. Its importance lies in the fact that it forms the foundation for calculating the posterior probability of the hypothesis. To achieve this, it is multiplied by the prior probability of the hypothesis and then normalized by Evidence.

Statistical inference

Evidence refers to the marginal probability of the data, and is important because it serves as a normalization term. It ensure that the posterior porbability is a valid probability by normalizing the product of the prior and the likelihood over all possible values of the hypothesis. The evidence can be expressed as:

P (E) = H P (E|H)P (H) dH (1.2)
Now let us extend this idea to data defined by y and model parameters defined by θ .

The Bayes rule can be written as

P (θ|y) = P (y|θ)P (θ) P (y) (1.3)
Here P (y) is a normalization factor (and does not depend on θ ) so we can simplify the equation to Prior knowledge or belief is the information known about the hypothesis prior to any data collection. The prior is defined in advance based on previous studies as it is the case for medical datasets. It is defined as a probability distribution, representing the level of belief in a range of potential outcomes.

P (θ|y) ∝ P (y|θ)P (θ) (1.
The likelihood is the conditional probability distribution of P (y|θ) of the data P (y)

given fixed parameters θ. Bayesian inference involves treating unknown parameters as random variables. It enables the generation of probability statements that inform about the probable values that the parameters can take. By varying the parameter values, the likelihood function can be established as a function of θ for the given fixed data y. Thus, the elements summarized by the likelihood is a model that stochastically generates all observed data, with a range of potential values for θ, and the observed data y.

Finding the posterior probability : Once the prior distribution has been specified, and the relationship between the prior and the likelihood function has been defined, the next step in Bayesian inference is to estimate the unknown parameters of the data.

This estimation involves calculating the posterior distribution of the parameters, which represents the updated probability distribution for the parameters given the observed data.

Obtaining the posterior distribution through direct inference may not be feasible due to mathematical and computational difficulties, particularly when dealing with complex models with high-dimensional parameter spaces. The posterior distribution is obtained by integrating the product of the likelihood function and the prior distribution across the parameter space. However, this integral may not have a closed-form solution, leading to challenging analytical computations or impossibility. Moreover, even if a closed-form solution is available, computing the posterior distribution can still be computationally demanding, particularly for high-dimensional models. Direct computation of the posterior distribution may involve computing the likelihood function and prior distribution numerous times, which can be computationally expensive and time-consuming.

To overcome these challenges, Bayesian inference often relies on approximates methods, such as Markov Chain Monte Carlo (MCMC), which provides a practical and efficient way to sample from the posterior distribution.

Markov Chain Monte Carlo: Markov Chain Monte Carlo (MCMC) is a methodology used to approximate the posterior distribution of parameters, given some observed data and a prior distribution. The basic idea of MCMC is to generate a sequence of random samples from the posterior distribution using a Markov chain.

Markov chain is an iterative process whereby the value of the Markov chain at time t + 1 are only dependent on the values of the chain at time t [Schoot, 2021]. In other words, the probability of transitioning to a particular state at time t depends only on the state at time t -1, and not on any earlier states. A Markov chain is a useful tool to obtain a set of parameter values from the posterior distribution. In MCMC, a Markov chain is constructed so that the sequence of samples generated by the chain converges to the

Statistical inference

posterior distribution of the model parameters.

Monte Carlo methodology is a stochastic algorithm that approximate integrals using the simulation of random numbers given a probability distribution [Schoot, 2021]. Monte

Carlo integration plays a crucial role in MCMC allowing to estimate integrals of sample values given the probability distribution of interest. Therefore, it is used to estimate the distribution of interest by computing empirical estimates based on the sample values [Robert, 1999].

The combination of Markov chain and Monte Carlo techniques in MCMC allows us to simulate random samples from complex probability distributions. MCMC methodology are widely used in bioinformatics ranging from genomic data analysis, protein folding, and network interaction modeling, mostly used in ecological studies. From the general concept of MCMC, multiple methodology have been describes such as Metropolis-Hastings method [START_REF] Metropolis | Equation of State Calculations by Fast Computing Machines[END_REF]Hastings, 1970], Hamiltonian Monte Carlo [Duane, 1987], Gibbs sampling [Geman, 1984].

Here we will mainly focus on the Metropolis-Hastings and Gibbs Sampling as they are one of the major algorithm that we will use in the Chapter 2.

Metropolis-Hastings:

Metropolis-Hastings is an MCMC methodology introduced by [START_REF] Metropolis | Equation of State Calculations by Fast Computing Machines[END_REF]Hastings, 1970], allowing to simulate complex distributions. It is based on the idea that a target distribution can be appproximate using proposal distribution enabeling to generate series of multiple samples reflecting the target distribution.

The Metropolis Hasting algorithm first step is to fix a state for the Markov chain. Then a new state is to generate based on a proposal distribution (ususally a normal distribution) (Algorithm 1). An evaluating ratio is set that encompass the target density at the proposed state, with the target density at the current state. The evaluation ratio is the acceptance ratio and is defined in the Algorithm 1. Based on the value of the acceptance ratio, if r ≥ u , the proposed state is accepted and is set as the new current state. However if the acceptance ratio is r < u the proposed state can be either accepted or rejected with a probability equal to α for acceptance and 1 -α for rejection.

The primary aims of Metropolis Hastings algorithm is to balance the exploration of the Chapter 1. General Introduction

Algorithm 1 Metropolis Hastings algorithm

Require: Target distribution P (θ). Initial state for the Markov Chain defined as θ 0 , and L for the number of iterations.

P (θ) ∝ π(θ) ▷ Target distribution approximated by π(θ) for i in L do θ * ∼ q(θ * |θ i-1 ) ▷ θ * for a new state, based on a proposal distribution α = π(θ * )q(θ i-1 |θ * ) π(θ i-1 )q(θ * |θ i-1 ) ▷ Calculate the acceptance ratio. r = min(1, α) u ∼ U (0, 1) ▷ Sample form uniform distribution if r ≥ u then θ i ← θ * else θ i ← θ i-1 end if end for
target distribution while proposing new states, with the acceptance ratio acting like a threshold to accept proposals resulting in assembling a set of samples from the target distribution.

The main advantage of the Metropolis Hastings algorithm that it is very easy to implement and it is able to simulated multiple types of distribution. Moreover, the algorithm is able to converges as the number of iterations approach to infinity (meanwhile the time for approaching the convergence can be exceeding long). However there is several inconvenient, such as the depence on the fixed distribution. In fact the performance of Metropolis algorithm relies on the choice of the proposed distribution (for example a narrow distribution result in a lower acceptance rate, thus leading to much more time to explore the target distribution and vice-versa). Moreover the Metropolis algorithm is not adaptive, thus it does not update the chosen distribution during the simulation.

In some senario, conditional distributions of the variables in the target distribution are known. Thus, scientists demonstrate that the use of the Gibbs Sampling is more efficient.

In fact, it can generate samples by iteratively sampling each variable from its conditional distribution, given the current values of the other variables.

Gibbs Sampling: Gibbs sampling was first introduced by [Geman, 1984]. Like Metropolis Hastings, it's an MCMC methodology and is widely used for iteratively sampling from conditional probability distributions. It is mainly derived from the Metropolis-Hastings algorithm however the main difference lies in the fact that a conditional probability distribution is always used as a chosen distribution, and at each iteration, a single variable is updated based on the fixed values of the other variables. Moreover at each iteration, the acceptance ratio is always 1 meaning that each variable is updated sequentially [Schoot, 2021;Liu, 2004]. The algorithm is described in Algorithm 2

Algorithm 2 Gibbs Sampling general algorithm

Suppose we want to sample a distribution from

P (θ) = P (ϑ 1 , ϑ 2 , • • • , ϑ d ). Require: Initialize θ 0 = ϑ 0 1 , ϑ 0 2 , • • • , ϑ 0 d , and L for the number of iterations. for i in L do ϑ i 1 ∼ P (ϑ 1 |ϑ i 2 , ϑ i 3 , • • • , ϑ L-i d ) ϑ i 2 ∼ P (ϑ 2 |ϑ i 1 , ϑ i 3 , • • • , ϑ L-i d ) . . . ϑ i d ∼ P (ϑ d |ϑ i 1 , ϑ i 2 , • • • , ϑ i d-1 ) end for
Gibbs sampling is widely used in multiple fields. In there publication, [START_REF] Adams | [END_REF] developed a novel approach based on Gibbs sampling to tackle the problem of blurry Xray radiography. Also, [Murata, 2023] developed an extension to the Denoising Diffusion Restoration model (DDRM) unsing the Gibbs sampling, that achieve higher performance in the task of deblurring image and dereverberation tasks. Moreover, Gibbs sampling has been widely used in bioinformatics. In fact, it allows the detection and allignement of conserved regions in aminoacids and nucleic acids, without any prior knowledge [START_REF] Neuwald | [END_REF]Lawrence, 1993;Thompson, 2003;Rouchka, 1997].

Also, [Andreatta, 2012] developped a novel framework where Gibbs sampling is used as an alignment and a clustering methodology for the task to simultaneously identify clusters and optimal sequence alignment for peptides. Recently, [Li, 2019] developed a framework based on the Gibbs sampling entitled ProSampler with to aim to find transcription factors motifs.

Not only Gibbs sampling was applied to bioinformatics, but it was widely used in the natural language processing (NLP) community. In fact [START_REF] Blunsom | [END_REF] introduced a novel Chapter 1. General Introduction framework for translation model that uses non-parametric Bayesian approach, where a modified Gibbs sampling is performed over synchronus derivation. Moreover [Mochihashi, 2009] proposed an novel approch for unsupervised word segmentation combining Pitman-Yor language and Gibbs sampling. Here, the authors modified the Gibbs simpling allowing the integration of some latent variables. Overall the modified Gibbs sampling was performed as a sampling methodology integrating remaning and latent variables.

The most widely methdology in NLP was developed by [Blei, 2003a], where the authors introduced the Latent Dirichlet Allocation (LDA), a generative probabilitic model. The principal idea in the LDA, is that a document can be represented as random mixtures over latent topics and each topic is defined by a distribution of words. Thus after multiple steps of calculations and by making the assumption that the convergence is reached, we are able to find a probability distribution of a set of words for every topic. The LDA algorithm is extensively studied in Chapter 2.

Latent Dirichlet allocation for omics data: Latent Dirichlet Allocation has gained a lot of popularity in the field of bioinformatics for analyzing large-scale data. More precisely, LDA has gained popularity in the field of genetics. For example, it allows the identification of the functionality of miRNA and mRNA. In fact, [Liu, 2010] developed a framework for identifying the miRNA and mRNA functionality by making the assumption that they are involved in the same latent function. Moreover, the LDA has been used to identify multiple genomic signatures in cancer studies. The methodology designed by [Shiraishi, 2015] used LDA as an alternative approach for the task of modeling different genomic signatures. Another study by [Matsutani, 2019] developed a methodology using Latent Dirichlet Allocation with variational Bayes inference with the aim to estimate the number of signatures related to mutations.

Beyond the use of LDA in genomics, it has also been used in microbiology. Some scientists developed the LEA (Latent Environment Allocation) to better understand the relationship between environmental labels given to retrieve microbial samples and the community structure [Higashi, 2018]. LEA uses a Correspondence-LDA (Coor-LDA) -a modified LDA introduced by [Blei, 2003b] -to identify the correspondence between the taxonomic composition and the samples of sequence between 16RNAseq. Another frame-5. Thesis Statement work, MetaTopics, designed by [Yan, 2017] integrates LDA, where the primary objective is to extract microbial communities that reflect the relationships between bacteria.

Recently, in a study done by [Hosoda, 2020], the LDA is used to perform a microbial analysis on a large gut microbial datasets with the aim to identify relationships between microbial assemblies and enterotype. Also, [Breuninger, 2021] applied Latent Dirichlet Allocation as a clustering methodology to identify subgroups of microbial communities that are associated with dietary habits linked to metabolic disorders.

In my thesis, I used LDA as the core of our methodology. The interest in LDA lies in the fact that it is a soft clustering method that enables us to obtain a probability vector for each patient to be assigned to one of the topics, as well as the probability of cell phenotypes being assigned to one of the topics. Therefore, by analyzing the topics, it is possible to identify the different patient phenotypes and their corresponding cell phenotypes.

Furthermore, in Chapters 2 and 3 of my thesis, I introduced an approach that involves increasing the number of topics. In this approach, each patient is assigned to the topic with the highest probability, and multiple runs of topic assignments are performed. The next step is to count the number of times each patient are grouped together in the same topic, resulting in a matrix that tracks the associations between them. This approach can also be extended to cells. To construct a patient graph that illustrates the various connections between them, we used a network approach and set a threshold for patient associations, excluding weaker relationships. By doing so, we can visualize the relationships between patients more effectively. Once the patient graph is generated, we can apply clustering techniques, utilizing the patient association matrix. This enables the identification of communities comprising similar patients. By examining different clinical or biological variables that were not used for clustering, we can associate specific groups of patients with distinct clinical phenotypes and effectively stratify them.

Thesis Statement

As mentioned previously, multiple methodologies have been developed to handle highdimensional data from high-throughput technologies. The traditional approach in biomedicine Chapter 1. General Introduction involves collecting data from multiple patients, where each patient is represented by a specific data matrix that includes various factors like genetics, dietary habits, physical activity, and environment. This matrix reflects the overall condition of the patient.

Despite the significant influence of genetic variability on the development of certain diseases, the fact that all humans share the same cellular architecture and functionality implies that there are commonalities between individuals, regardless of their genetic or environmental differences. Therefore, in a population of homogeneous individuals who share similar physiological states such as being healthy or sick, there exist both distinct and shared characteristics. By utilizing continuous data obtained from high-throughput technologies, reducing dimensionality, and applying clustering methodologies, it becomes possible to identify cell populations based on the various features they express, such as gene expression levels or protein expression.

Reduction of dimensionality and clustering

Cluster 1 to 8 can be related to immune cells, adipose cells, or blood cell-types identify clusters of cells that can be further investigated and labeled. The ultimate aim is to identify specific genes or signaling pathways within these labeled cells, which can then be tested in the laboratory or on smaller models such as cell cultures or organoids.

Although this approach effectively identifies cell types, it does not distinguish between patients. Consequently, in a heterogeneous patient population, different altered cells from ill and healthy patients may be grouped together in the same cluster. As a result, it becomes challenging to determine which cells are altered and associated with the patient condition.

Furthermore, the disease state varies among patients, leading to differences in cell phenotypes that are reflected in the data. Therefore, patient stratification becomes a significant challenge in terms of patient diagnosis and prevention. Thus, my thesis is part of this approach, aiming to develop a robust clustering methodology that can effectively group individuals with diverse characteristics while simultaneously identifying cell phenotypes associated with the patient phenotype. By accomplishing this, we aim to cluster cells and patients with high accuracy, facilitating the identification of meaningful cells phenotypes that are related to the phenotype of the patients.

As depicted on Figure 1.9, we consider the scenario involving individuals exhibiting diverse clinical phenotypes, such as lean, obese, and obese-diabetic individuals. Our primary objective is to develop a robust clustering methodology that can effectively group these individuals based on relevant cell phenotypes. To accomplish this, we aim to integrate various methodologies, including data grouping, dimensionality reduction, and clustering.

The ultimate goal is to obtain informative cell-level data closely associated with specific patient phenotypes, enabling us to gain deeper insights into the underlying patterns of cells that potentially drive the patient phenotypes. We refer to this task as a "Double clustering" approach. It is important to note that the double clustering task fundamentally differs from co-clustering methods. We introduce the concept of double clustering because our goal is to cluster matrices of data from different patients into two distinct and simultaneously optimized matrices: one for cell types and another for patients within each cluster. The main distinction lies in the fact that, unlike standard co-clustering (bi-clustering) approaches, where cell types are already known, in our case, the cell types are unknown, necessitating a preliminary clustering process to define them.

In Chapter 2, we discuss a method we developed called LDA-DC (Latent Dirichlet Allocation for Double Clustering) that enables simultaneous clustering of cells and patients using a Bayesian approach. This methodology is specifically designed to cluster patients while also identifying associated cell types, as demonstrated through simulations and benchmark datasets.

Then in Chapter 3, we apply our methodology to data obtained from the METACARDIS cohorts (composed of patients with diverse phenotypes) using metagenomic derived data.

We demonstrate that our method successfully generates a network of individuals that reflects the continuous and transient nature of microbiota data. Additionally, we identify various clusters of individuals, each comprising different patients with distinct enterotypes.

We further characterize these clusters by using clinical, biological, and nutritional data.

Moreover, we successfully establish a comprehensive network of bacteria and KOs (KEGG -Kyoto Encyclopedia of Genes and Genomes-Orthology) that are intricately associated with patient stratification. 40

Thesis Statement

In the last chapter, we introduce an additional methodology based on an artificial neural network applied to cytometry data obtained from the NutriOmics and derived from the CARMMA cohort. By applying ANN, we successfully demonstrate that individuals with obesity and type 2 diabetes can be predicted to be older than lean individuals of the same age based on their immunological profile. Furthermore, through the implementation of a tree-based approach, we were able to identify distinct sub-phenotypes of immune cells.

These findings offer potential avenues for future investigation to unravel the molecular mechanisms associated with immunosenescence.

Thus, the contribution of this thesis lies in the development and implementation of a method for simultaneously clustering both cells and patients. This method enables the identification of cells that may be associated with patient phenotypes (whether diseased or not), providing a strategy for patient stratification through a networking approach.

Additionally, the thesis presents a novel strategy for stratifying patients and identifying specific sub-phenotypes of cells affected by the patients' condition. In this sense, my thesis aligns with the concept of precision medicine by developing and employing innovative computational approaches. In this chapter, we present the double clustering approach, which enables the simultaneous clustering of cells and patients. To accomplish this, we introduce a novel methodology called LDA-DC (Latent Dirichlet Allocation for Double Clustering), based on Latent Dirichlet Allocation. The objective of LDA-DC is to assign patients and cell phenotypes to topics simultaneously. The initial stage involves identifying cell phenotypes, and through LDA, we can allocate cell phenotypes and patient phenotypes to topics and identify some links between them. We tested our approach on simulated data and on benchmark data obtained from patients with Acute Myeloid Leukemia (AML) and Crohn's disease, and found that our method accurately distinguishes diseased individuals from those in healthy conditions. Additionally, we could identify cells phenotypes as well as bacteria linked to the clusters. Furthermore, by conducting multiple LDA-DC runs, we constructed a network of patients that facilitated their stratification. Background: Current clinical routines rely more and more on "omics" data such as flow cytometry data from host and microbiota. Cohorts variability in addition to patients' heterogeneity and huge dimensions make it difficult to understand underlying structure of the data and decipher pathologies. Patients stratification and diagnostics from such complex data are extremely challenging. There is an acute need to develop novel statistical machine learning methods that are robust with respect to the data heterogeneity, efficient from the computational viewpoint, and can be understood by human experts.

Results:

We propose a novel approach to stratify cell-based observations within a single probabilistic framework, i.e., to extract meaningful phenotypes from both patients and cells data simultaneously. We define this problem as a double clustering problem that we tackle with the proposed approach. Our method is a practical extension of the Latent Dirichlet Allocation and is used for the Double Clustering task (LDA-DC). We first validate the method on artificial datasets, then we apply our method to two real problems of patients stratification based on cytometry and microbiota data. We observe that the LDA-DC returns clusters of patients and also clusters of cells related to patients' conditions.

We also construct a graphical representation of the results that can be easily understood by humans and are, therefore, of a big help for experts involved in pre-clinical research.

Background

Human disorders have a highly multifactorial nature and depend on genetic, behavioral, socio-economic, and environmental factors. There are many examples of such complex diseases: cardiovascular diseases, non-alcoholic liver cirrhosis, type II diabetes, or even other pathologies such as autoimmune diseases [ONeill, 2015] to name a few. The number of subjects with metabolic diseases, cancers, and autoimmune pathologies has increased significantly in recent years, making research in this field a public health priority [Zhao, 2021].

In parallel, bioclinical routine datasets have expanded in conjunction with all kind of 44 2. Background "omics" data, from both the host and microbiota, as well as metabolomic, proteomic, and cytometry data [Manzoni, 2016]. All these types of data have some underlying structure on their own, taking values on different scales, with different variability, and are differently distributed. In addition, human patients are an equally important source of variability even among carefully selected cohorts: phenotypic variability (age, gender, previous conditions), dietary habits, bad versus good responders to treatment, etc. As a result, the amount of available heterogeneous data has increased exponentially. In particular, cell based techniques such as single cell RNA sequencing (scRNA-seq) revolutionized the field of life sciences by bringing an unprecedented resolution to study heterogeneity in cell populations [Szabo, 2019]. So, single-cell transcriptome profiling of pathologic tissue isolates allows the characterization of heterogeneous pathologic cells along with neighboring immune cells. More precisely, flow cytometry and scRNAseq are cell-level data describing heterogeneous cells' behavior. The most recent results, either take into account the cell heterogeneity by itself (e.g., by deriving cell lineage) or compress the information into population proportion after a (usually arbitrary) clustering for patient-to-patient analyses that prevents us from simplistic data fusion in order to extract meaningful information.

Flow cytometry workflow, e.g., computes a so-called gating where bi-axial plots are used by human experts to distinct cells. This method is often performed by a researcher and is, therefore, accurate but expensive. A more computationally efficient way to identify cell populations are machine learning clustering methods. Among the state-of-the-art clustering methods for scRNA-seq data for cell-type identification are distance-based partitioning, density-based clustering, or graph-based clustering methods [Petegrosso, 2019;Qi, 2019;Ye, 2019;Liu, 2019]. One of the most widely used exploration method for cell data is the t-SNE [Maaten, 2008] which is a probabilistic dimensionality reduction and visualization method. It is not only widely used in the single cell analysis but also a number of methods were developed based on the t-SNE. So, in ACCENSE [Shekhar, 2013] and ClusterX [Chen, 2016], the t-SNE is used to estimate the density and also to project the data before the cell populations are identified. Another approach, viSNE [Amir, 2013],

where each cell is a point in high-dimensional space, proposes a distributed implementation of the t-SNE. Different combinations of t-SNE and graphical methods were explored, e.g., PhenoGraph [Levine, 2015], where a nearest-neighbor graph is applied to cell data Chapter 2. Latent Dirichlet Allocation for Double Clustering (LDA-DC): Discovering patients phenotypes and cell populations within a single Bayesian framework to reveal the partitioning, determines phenotypes in single cell data. A similar idea is also considered in Xshift [N, 2016]: the k-nearest-neighbor algorithm is used to identify connectivity and density peaks in cell data.

Dimensionality reduction is a natural way to process the single cell data. So, FlowSOM [Gassen, 2015] is a cell clustering technique based on Self-Organising Maps (SOM), where the result of stratification is a grid of cell clusters, and it can be visualized by showing the average marker values of each identified cluster. Some practical packages, e.g., CITRUS [Bruggner, 2014] which relies on hierarchical clustering, were proposed. Their goal is to apply some standard robust clustering methods to the single cell data.

Currently, research is focused on the development of graph-based clustering methods.

Indeed, in [Choobdar, 2019], the authors compare different graph clustering methods for community identification. These methods can take into account a single network (i.e., co-expression, protein-protein interaction) or aggregate information of several networks. Among the most efficient methods are kernel clustering, modularity optimization, random-walk-based methods and local methods allowing to identify communities related to particular pathologies. In parallel, [Ma, 2022] have developed a layer specific module in multi-layer network based on non-negative matrix factorization (LSNMF). In this approach, LSNMF learns latent features of vertices and decomposes them into two types of features: common and specific ones, where the specificity of features for vertices is explicitly measured, thereby improving the accuracy of algorithms. As a result of different experiments, the features identified in these modules appeared to accurately characterize different modules. Moreover, the attention of the community has been extended to the clustering of scRNA-seq data, through the use of network-based methods. Indeed, [Wu, 2022] has developed a network-based structural learning non-negative matrix factorization algorithm (SLNMF) for cell type identification. The authors show that their approach based on the topology of the reconstructed from data network, is much more efficient and accurate for cell types identification than standard approaches based on expression data.

Recently, the attention of the systems biology community was drawn by Bayesian probabilistic methods. The intuition behind these approaches in relation to the biological tasks is to model individuals who belong to multiple populations. For example, [Sun, 2018] 2. Background proposes a method based on a Dirichlet mixture model to cluster single cell transcriptomic data, pointing out that model-based (probabilistic) methods are underexplored for single cell data analysis. The estimation of the model is done using the Expectation-Maximisation (EM) algorithm.

Some attempts to adopt the Latent Dirichlet Allocation (LDA) to the single cell data were recently made. So, [Dey, 2017] applied the LDA to a database with approximately 50 human tissues to discover similarities between them; the LDA was also tested on single cell mouse data to discover variations in early embryonic development stages. An important characteristic of the single-cell data is that the data is structured; [Wu, 2020] states that any clustering method for the single-cell data should account for the hierarchical structure of cell types, and proposes new metrics to evaluate clustering performance. To construct tree structures which reflect the hierarchical nature of single cell data, [duVerle, 2016] explore a hierarchical extension of the LDA to identify clusters of cells. Cellular LDA (Celda) was introduced by [Wang, 2021b] to perform bi-clustering of co-expressed genes and also of cells into subpopulations. The Celda takes into account the hierarchical relationships in data.

Recently, the Latent Dirichlet Allocation (LDA) was considered to partition the singlecell data [González-Blas, 2019; H-JKim, 2020]: the LDA was applied to binary data,

where each cell was treated as a document, and each chromatin site (chromatic contact)

was considered as a word. So, [González-Blas, 2019] proposed a Bayesian topic modeling framework called cisTopic for robust identification of cell types. In [H-JKim, 2020], the LDA is tested on the extremely sparse data to capture cell type differences.

From the analytical viewpoint, the single cell data are huge-dimensional matrices produced for each subject. The data dimension, i.e., the number of cells, vary from one individual to another, and note that cell types, as well as the correspondence between the cell populations of the subjects, has to be identified before applying any statistical machine learning method. We refer to the challenge we introduce and consider here as to a double clustering problem, where the aim is to simultaneously, purely from observations without any prior knowledge determine cell types, as well as stratify patients in order to study mechanisms of pathologies explained by particular cell subpopulations. (LDA-DC) which is a novel method to identify cell types from flow cytometry data, and cluster patients in the same flow. We discuss the advantages coming from the Bayesian probabilistic nature of our approach, and we illustrate its strengths on real benchmarks. Latent Dirichlet Allocation (LDA) [Blei, 2003a] was originally proposed as a probabilistic topic modeling method. It is a Bayesian approach which was developed to identify topics given a corpus of documents, where the topics are not known in advance. Note that the standard LDA considers discrete (counts) data. The LDA is based on several assumptions.

Methods

Latent Dirichlet Allocation for Double Clustering

First, each document can be represented by a mixture of topics (Figure 2.1). Second, as a result of the learning procedure, one learns not only the topic distribution representing

P(z i = k|z -i , w i , d i ) ∝ C W K wk + β W w=1 C W K wk + W β ϕ × C DK dk + α K k=1 C DK dk + Kα θ // z -i topic
θ ∼ Dirichlet(α), (2.1)
where α is a hyper-parameter. The distribution of words is also modeled by the Dirichlet:

ϕ ∼ Dirichlet(β), (2.2)
where β is another hyper-parameter of the LDA model to control the topic-words distribution.

To estimate the parameters of the model and to perform clustering, we are particularly interested in the following conditional probability computed from two Dirichlet distributions. The conditional probability of assigning ith token to cluster j is given:

P(z i = j|z -i , w i , d i ) ∝ C W K wj + β W w=1 C W K wj + W β ϕ × C DK dk + α K k=1 C DK dk + Kα θ , (2.3)
where D is the number of documents, W is the number of words, K is the number of clusters (topics), C W K is the word-topic matrix, W w=1 C W K wj is the total number of words in each topic, C DK is the document-topic matrix, C DK dk is the total number of words in a document; z -i is the topic assignments for all other topics.

The intuition behind the hyper-parameters is as follows. The higher α, the more likely a document is described by more topics. The higher β, the more likely each topic is described by more words. As in the majority of clustering methods, the number of topics (clusters) has to be fixed.

Although a number of optimization approaches were proposed to estimate the parameters of the LDA framework, we use the standard Gibbs sampling [Bishop, 2006] Taking into consideration that our algorithm was developed with the single cell data in mind, where the form of the distribution is supposed to be known, i.e., Gaussian, the words (cell types) identification is done using the K-means clustering which is known to be more robust compared to the Expectation-Maximisation algorithm that is sensitive to its initialization.

Once the cell types are fixed, the LDA can be efficiently used to estimate both the probabilities of a phenotype given a patient, and the probability of a cell type given a phenotype.

Thus in addition to provide a topic for each patient, our method provides a topic for each cell phenotype.

Simulated data

Cell generation: We constructed an artificial dataset to validate the proposed method.

In order to mimic real flow cytometry datasets, our main hypothesis for the data generation is that the underlying distribution of fluorescent data can be efficiently approximated by (multivariate) Gaussian distributions. So, each marker can be seen as a mixture of two Gaussians with different means: one is associated with positive subsets (high mean), and the second one is associated with negative subsets (low mean). In order to test for robustness we can vary the standard deviation (std) of the distribution with high standard deviation making more difficult to separate low from high. Therefore, the phenotype of patients phenotypes and cell populations within a single Bayesian framework a cell is a real vector of dimension N (think of N as the number of fluorescent marker under consideration). To these continuous vectors we have associated the binary vector of dimension N with highs and lows describing the cell's phenotype. There are therefore 2 N possible cell phenotypes.

Simulated patients:

In order to create patients, we construct probability distribution vectors of cell type density that differ according to patients' phenotype, i.e., different classes of patients will have different cells' type distribution. Here, we tested two cases: two classes of patients and four classes of patients with prescribed cell's type distribution for these 2 or 4 classes. We can simulate the patients by choosing their cell's type distribution and compute the cell's fluorescent values according to the current cell type.

Note that at this point we also fix the standard deviation. Thus, an artificial patient is represented by a random subset of cells whose number is p cell from which we derive the cell type according to the phenotype distribution. We can compute real values for the cell according to its type. The distributions are chosen using a simple parameter that can vary the distance between classes.

Real Benchmarks

To illustrate the efficiency of the proposed method, we selected two real annotated benchmarks.

AML (Acute Myeloid Leukemia) dataset:

This dataset [Aghaeepour, 2013] has 2872 samples of flow cytometry standards collected from 359 AML (n=43) and non-AML (n=316) individuals. It contains results from 8 experiments corresponding to different tubes with different markers (note that tube 1 is an isotope control, and tube 8 is unstained).

Cytometry and genus data:

The dataset we use contains FACS cytometry and 16rRNA sequencing data coming from two studies: [Rubbens, 2021] and [Vandeputte, 2017] respectively. Note that the original cytometry data comes from [Vandeputte, 2017] and are paired with the 16rRNA data. However, we use the data from [Rubbens, 2021],

3. Methods since this data set is pre-processed (noise reduction using various transformations and algorithmic methods, see Analysis part in [Rubbens, 2021] for more details). So, we have a cohort composed of patients diagnosed with Crohn's disease (CD, n = 29) and healthy subjects (HC, n = 66). The cohort of patients having the Crohn's disease is described in details in [Sabino, 2016], and the samples of HC patients come from the Flemish Gut Flora Project [Falony, 2016].

The Double Clustering Workflow

Here we provide the details of the proposed approach. We discuss its application to our artificial dataset, where we generate both, cells populations and patients in a controlled manner and compare it with the ground truth for both the cell's type and patient's phenotype. For the subsequent real datasets the method is strictly identical.

Cells clustering:

We generate according to the method described above about 50 subjects per phenotype (note that cell type density distribution is a vector of size 2 N ). As already mentioned, we focus on a setting with 2 and with 4 phenotypes; 50 patients per phenotype. Per one patient, we generate a matrix of 10 4 cells measurements. These measurements can be encoded as continuous and binary (low/high) values. We perform the following pre-processing: we concatenate all patients and apply the Z-score on all patients. Then, we apply a K-means on the concatenated observations. Note that the number of clusters (cells types) is fixed to 2 N . As a result of the cells clustering, each cell (of each patient) is assigned to a cluster, and we can consider the counts of cells in each cluster.

Patients clustering:

In the previous step (cells clustering), we obtained the matrix of cells types counts per patient, where a cell type corresponds to the class assigned to the cell by the clustering method. The Latent Dirichlet Allocation (LDA) can be directly applied to the count matrix. Using the topic modeling terminology, we can imagine that the patients are considered as documents, and words are considered as cell types. The LDA model gives us the probability for each patient to be assigned to each cluster. Note that the number of phenotypes is also fixed in advance. The resulting conditional probability can be used in various ways. Traditionally, it is used to cluster observations based on the maximal probability value. Alternatively, we can apply a hierarchical clustering, e.g., with a tree cut to visualize and to explore the results.

Results

Validation of the proposed method on simulated data

Results

We tested the double clustering approach on different scenarios. We tested 2 and 4 phenotypes, and we varied the distance between the probability vectors to vary the difficulty of the clustering problem. If the Euclidean distance between the phenotype probability vectors is small, the clusters are not well-separable, there is a significant overlap between the groups. If the Euclidean distance between the probability vectors associated with the phenotypes is big, the clusters are easily separable, and we can expect a reasonable performance. The overlap between the clusters can be controlled by the variance.

Real High-Dimensional Datasets

Acute Myeloid Leukemia: AML Dataset

The AML benchmark dataset is an unbalanced dataset of individuals with AML syndrome and healthy subjects. This dataset includes flow cytometry measurements for several batches (tubes) of different biomarkers sets. In order to balance the learning procedure, for each tube, we selected the same number of AML and non-AML patients excluding several non-AML patients. First, we applied the K-means with 2 D clusters, where D is the number of markers in a tube. Then, we annotate each cell according to its origin (patient) and its cluster. For each patient, we obtain a list of cell types. We also define the vocabulary equivalent to the number of clusters of the K-means as well as the number Chapter 2. Latent Dirichlet Allocation for Double Clustering (LDA-DC): Discovering patients phenotypes and cell populations within a single Bayesian framework of topics (here 2, since there are 2 conditions: AML and non-AML). At this point, each patient (observation) is a list of cell types, and we apply the LDA on the count data. In each experiment corresponding to each tube, we assign each patient to a cluster. We have the ground truth for all observations, however, since we consider a clustering task, we face the label switching problem. So, to cope with the label switching problem, we applied the majority vote to the obtained clusters. We compared the final clustering to the real classes (AML and non-AML). The accuracy is shown on Figure 2.3. Note that some tubes are more predictive than others, due to different biomarkers used in the experiments.

We run a cross validation (number of folds is equal to 20 in our experiments). It is important to perform the cross-validation here, since the number of ill and healthy individuals is unbalanced, at each run we sample (uniformly) the same number of observations from both classes.

Results

To compare with a baseline approach, we tested the standard K-means instead of the LDA approach to identify the clusters of subjects, and we found out that there is not any advantage in terms of predictive performance of the K-means over the LDA. We observed that our method is less efficient on the data of tube 6 (adjusted p-value = 0.002 for tube 4 and adjusted p-value = 0.001 for tube 6; the results of the t-test and false discovery rate adjustment are provided in Supplementary Table S1). However, the LDA-DC provides us with some additional information. Indeed, we are able to extract the probability distribution of cell types related to each phenotype. So, we can detect which cell phenotypes drive the clustering and explain the disease. In the last panel, we quantified the number of cells assigned to Topics 0 and 1 from AML and non-AML patients (see Supplementary Figure S1 and Supplementary Table S2), and tested the differences using Chi-squared test. We found out that the p-value < 2.2e-16, indicating that there is a significant difference in the distribution of the cells between AML and non-AML individuals within the two topics. Thus, the last panel is an indication that the cell populations we found are clearly associated with the disease. Our numerical results confirm that the double clustering predicts the clinical conditions with the unsupervised method and provides new information which allow us to relate the disease (or its absence) with cell subpopulations.

Cytometry and genus Data: Crohn Disease Prediction

Nowadays, the number of studies dedicated to the human microbiota, increases steadily.

We focused on the problem described in [Vandeputte, 2017], where there two phenotypes:

Crohn disease (CD) and healthy subjects. Our goal is to apply the LDA-DC to stratify the patients efficiently based on their cytometry as well as sequencing data. First, we selected all the data coming from [Rubbens, 2021] and selected 4 markers identified in the paper as markers of membrane bacteria. We tested a setting with two topics to separate the patients into two groups. However, the markers used were not adapted and we could not stratify the patients into two groups correctly. We arbitrarily fixed the number of topics to 8 (we also tested several values using the grid search), and applied our double clustering workflow.

To stratify the patients and see whether the result is consistent, we repeated the training procedure 40 times, and we count the number of times each patient is associated with a particular cluster. We considered a diagonal matrix, where patients are in columns and 4. Results rows, showing how many times the patients are clustered together, and we normalized these values by the number of experiments. Also, we applied an arbitrary threshold of 30%, and removed the links between patients that occur less than 30% of experiments. This matrix can be considered as one describing connectivity in the data, and we visualise a network where nodes are patients, edges are the connections between the patients, and edge weights are the connection frequencies. The obtained networks are shown on Figure 2.5. Adding more information to such a graph, we modify the size of the nodes so that it reflects the connectivity (the bigger node degree, the bigger the node). The patients are colored according to their clinical condition (CD or Healthy), or to their enterotypes which are also provided with the dataset. So, a network generated from the cytometry data, can separate patients into 3 groups: one group with data of sick patients only, and two other groups containing both sick and healthy subjects (Figure 2.5 B). However, one of these mixed groups contains significantly more ill patients.

Applying the same approach to the genus data, we observe that patients are well clustered by the double clustering method. On the left (orange nodes) we have a cluster of mainly sick patients, and on the right healthy ones (Figure 2.5 A). Then we consider the patients enterotypes (provided with the data and identified by [Vandeputte, 2017]), and we notice that the patients from left to right form a continuum of enterotypes; and are all well separated too. Subsequently, we decided to set the number of clusters -as done previously -(topics in the LDA terminology) to 2, and to stratify patients into two groups according to their conditions. Our aim here is to identify bacteria related to the disease. Indeed, we identified some bacteria that are linked to specific cell phenotypes and to conditions. Thus, we are able to find bacteria related to Crohn disease, and by extension, cells that drive the phenotypes. They are shown on Figure 2.5, subplot D.

Discussion

In this article, we proposed a simple method to obtain clusters of cells and patients simultaneously in the context of bioclinical datasets such as flow cytometry. We first validated our approach on simulated data: we noticed that it separates patients with a reasonable accuracy which depends on the difficulty of the clustering problem. We also showed how robust this method is according to noise (embodied as the standard deviation of the Gaussian). This result is a simple proof of concept of the method for cytometry-like data.

We then applied our approach on two publicly available datasets: For the AML study, our method correctly predicted patients status but also provided cell phenotypes associated 60 5. Discussion to this status. Indeed, we isolated some cellular phenotypes associated with AML. This phenotypes are identified by specifics fluorescence values and biological markers that can be investigated further. Therefore, one of our main results is shown on Finally, we applied our approach to microbiota data where we have access to two data types: cytometry data and bacterial abundance. The cytometry dataset is mainly targeting bacterial membrane proteins. Wehereas, the second one is a count matrix for each patient, where each bacteria is identified (genus data). Our main result on the cytometry dataset is the patients' stratification according to their clinical status using two topics, the separation is reasonable but not perfect. The error rate in this experiment can be explained either by the heterogeneity of bacteria in their membrane protein composition, or by the fact that the type of targeted membrane proteins are not specific to one type or sub-types of bacteria and are, therefore, not very good predictors of the Crohn disease.

Even if these markers are not strong predictors, the clustering results are still reasonable (accuracy ≈ 70%). On the other hand, using the genus data, we are able to separate correctly the patients into two distinct groups. As for the AML experiement, we were able to pinpoint actual bacteria species/genus directly associated with Crohn disease and these can be further investigated. Indeed, on Figure 2.5 it is easy to see the patients partitioning based on their enterotypes (subplot C). On subplot D, we show the bacteria which are related to the disease. For cluster 0, which corresponds to the Crohn's disease, we identified the following bacteria:

Fusobacteriacceae whose abundance increases in Crohn's disease [Gevers, 2014;Allen-Vercoe, 2011;Hall, 2014], Enterobacteriacean and Veillonella reported by [Gevers, 2014] to be increased with the Crohn's disease. [Hall, 2014] also state that the abundance of Haemophilus increases with the Crohn's condition. Topic 1 (Figure 2.5, subplot D) is associated with the healthy individuals, and we identified different bacteria known to reflect the healthy condition. So, [Wang, 2021a] states that Faecalibacterium, Clostridium IV, Roseburia, Ruminococcus are decreased in patients with the Crohn's disease compared to healthy subjects. In addition, [Hall, 2014] states that Blautia,Coprococcus (identified patients phenotypes and cell populations within a single Bayesian framework in topic 1) are less abundant in Crohn's patients compared to healthy subjects. In this regard, we confirm that bacteria identified in topic 0 are markers of the Crohn's disease, while those identified in topic 1 are markers of the healthy condition.

Conclusions

In this paper, we introduce a new method called Latent Dirichlet Allocation for Double Clustering (LDA-DC) to cluster features (e.g., cells) and patients from high dimensional data. Globally speaking, this method unifies clustering methods within one Bayesian framework to group cells into different cellular phenotypes from quantitative data, and stratify patients based on the clustered cells. We validated the method, and illustrated that it performs both, cells and patients partitioning reasonably well (we considered accuracy, since the ground truth was provided for the cohorts). This method allows us to stratify patients and cells simultaneously. In addition, it allows us to identify relationships between cells phenotypes and patients clusters. Thus, we obtain more information compared to the majority of the state-of-the-art clustering methods.

Currently we are working on a hierarchical version of the proposed LDA-DC which is in some sense similar to the hLDA actively used by the topic modeling community. A particular interest to develop this direction is a hierarchical nature of the cells data.

Another avenue of research is to propose novel methods based on soft clustering of the cells: note that the Expectation-Maximization method can be considered as a baseline method only, due to its known drawbacks such as initialization and scalability issues. An important question to consider is also cost-sensitive clustering, since real data are often extremely unbalanced. We would also like to go further into the graphical representations of the results, since such a visual clustering showing more refined phenotypes could be an avenue for the development of methods of personalized medicine.

Chapter 3

Application of the LDA-DC Method to stratify patients using GENUS and KEGG data In this chapter, we applied the method introduced in the previous chapter (LDA-DC) to stratify patients from the METACARDIS cohort. Our approach involved analyzing gut microbiota data, specifically the patient GENUS and gene KOs (KEGG Orthology). We successfully stratified the patients into a network and proposed new clusters that deviate from the traditional enterotypes, although each cluster appeared to be enriched with a specific enterotype. By comparing these clusters with the patients' clinical, biological, and nutritional data, we discovered distinct variables that linked with the severity of their disease and were specific to these new clusters. Importantly, this novel stratification seems to offer a more accurate representation of the patients continuum. Additionally, we identified both the bacterial network and the gene network that drive this patient network. This work, carried out in collaboration with the METACARDIS consortium, has been drafted and will be submitted to Scientific Reports.

Objectives 1 Introduction

According to the World Health organization (WHO), overweight and obesity are defined as abnormal or excessive fat accumulation that presents a risk to health (overweight is defined as a body mass index (BMI) ≥ 25 and < 30kg/m 2 and obesity as a BMI ≥ 30kg/m 2 ). Understanding cardiometabolic diseases, obesity, and type two diabetes has proven challenging due to the multitude of confounding factors involved. Factors such as dietary habits [Lissner, 2000], genetics [Herrera, 2010], social environment, and biological factors have been found to be associated with various types of obesity [Papas, 2007].

The gut microbiota has recently gained significant attention due to its potential involvement in obesity and cardiometabolic disorders. It is now widely recognized that alterations in the composition and diversity of the gut microbiota are significant factors in the development of obesity and type 2 diabete. Multiple studies shows that it alterations of its composition and richness were associated with obesity [Crovesy, 2020;Debédat, 2022], as well as tunk-fat mass and comorbidities such as type 2 diabetes and hypertension [Aron-Wisnewsky, 2019]. In parallel, a study done by [Chen, 2021b] demonstrate that a higher alpha-diversity is associated a lower risk of type 2 diabetes and insulin resistance.

Furthermore, the impact of the gut microbiota extends beyond metabolic function. Research has shown that the gut microbiota can modify gene expression regulation in white adipose tissue, further highlighting its potential influence on obesity and related disorders [START_REF] Kong | Gut microbiota after gastric bypass in human obesity: increased richness and associations of bacterial genera with adipose tissue genes[END_REF]. Moreover, the previous findings, it was reported that the gut microbiota is involved in metabolites production, and, therefore, plays an important role in metabolic health [Agus, 2021].

Additionally, different types of diets and drugs (including antibiotics and commonly used medications) are known to affect the microbial population in the gut [Karim, 2023]. Specifically, some dietary habits are associated with a lower occurrence of diseases such as cancer, metabolic disorders, and cardiovascular diseases, through their impact on the gut microbiome [START_REF] Del Chierico | Mediterranean Diet and Health: Food Effects on Gut Microbiota and Disease Control[END_REF]. On the other side, it was shown that high-fat diet alters microbiota gut composition and physiology paving the way to obesity and type 2 diabetes [START_REF] Murphy | [END_REF].

Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data With the aim to gain more insights in the link between microbiota and health, studies suggested that the gut microbiome can be classified in multiple enterotypes. The concept of enterotypes was introduced by [Arumugam, 2011] where they identified clusters of individuals with difference abundances of specific bacterial. From the analytic point of view, each enterotype was associated with the host-metabolic health and dietary habits.

The concept of enterotypes has motivated several studies on various populations, and have revealed that the number of enterotype differs according to the geographical location of the patients involved [Liang, 2017;Lim, 2014;Nakayama, 2017;Zhang, 2014] as well as different computational methodology performed [Wu, 2011]. Therefore, it is essential to compare the various enterotypes with clinical and biological variable to identify with more predictive power factors of metabolic status.

In parallel to these biological and medical findings, numerous bioinformatics tools have been developed with the aim to gain insight into metagenomic information. One of them is mOTUs [Sunagawa, 2013] (metagenomic operational taxonomic units) where the technique employs universal, single-copy marker genes to attain a more refined delineation of prokaryotic species compared to 16SrDNA11. Also MetaPhlAn2 [Truong, 2015] is a method to characterize the taxonomic profiles of whole-metagenome shotgun (WMS) samples that has been used successfully in large-scale microbial community studies. While these techniques enable to investigate sequencing data leading to assign patient to one of the enterotypes, they do not facilitate the connection between metagenomic and biological data at a population scale level. Therefore, there is an acute need to use computational approaches capable of identifying biological factors associated with distinct enterotypes and can be applied to a large scale of populations. Recently, a novel framework LDA-DC (Latent Dirichlet allocation for Double Clustering) has been introduced by (El [START_REF] Hachem | Latent dirichlet allocation for double clustering (LDA-DC): discovering patients phenotypes and cell populations within a single Bayesian framework[END_REF] to cluster both cellular (bacterial) and patient information simultaneously, with the goal to stratify patients from their metagenomic data.

In the context of obesity and cardiometabolic disorders, we have undertaken an exploration of metagenomic data in order to stratify patients without any prior knowledge of their clinical status. Our goal is to use metagenomic data to identify clusters of individuals and investigate their clinical, biological, and nutritional traits. Furthermore, we aim 66 2. Material and method to construct a network based on bacterial (Genus) information to elucidate the patients stratification.

Material and method

Cohort description

The MetaCardis study provides valuable insights into the relationship between microbiota and metabolic syndromes and cardio-metabolic diseases. This groundbreaking research draws on data collected from a diverse range of patient phenotypes, enabling a comprehensive analysis of the role of microbiota in health and disease. With a collaborative network of 15 partners, patient recruitment has taken place across Europe, including France, Germany, and Denmark. The extensive data extraction process involved in this study has allowed for a thorough investigation of the complex interplay between the microbiome and metabolic disorders, paving the way for new strategies for disease prevention and treatment. The study population of the research project is composed of eight distinct patient groups, each with unique characteristics and medical backgrounds. These groups range from individuals without diabetes, coronary heart disease, or a BMI < 25, to patients with metabolic syndromes, severe obesity, and those undergoing evaluation for bariatric surgery. Additionally, the study includes patients suffering from a variety of heart conditions, including chronic coronary artery disease and heart failure. The detailed cohort description are set in Table 3.1 and 3.2. ical data related to patients recruited. In order to optimize our analysis, we conducted a rigorous matching process, identifying 1 977 individuals with GENUS data as well as clinical data available for analysis. This allowed us to draw conclusions from a robust dataset consisting of GENUS data from 710 bacterial taxa and 1 977 individuals, and 392 clinical variables. Overall, our study includes 862 patients recruited in France, 574 in Germany, and 541 in Denmark. The Methodology section found in [Belda, 2022] provides a comprehensive explanation of how the various patients were selected and included, as well as how their lifestyle and dietary data were collected, and how the metagenomics data was processed and sequenced, including the process of Enterotyping.

Group of

Stratification, patient clustering and investigation

Patient and cell clustering. To ensure unbiased stratification of patients and avoid any prior assumptions about their medical status, we used only the GENUS information in our analysis. Using the methodology designed by [START_REF] Hachem | [END_REF], we allocated patients to different topics and simultaneously assigned bacteria to specific topics. To ensure that our results were reliable and accurate, we conducted 20 runs of calculations, and each time the results of the clustering of patients and bacteria were stored in a database (Figure

3.1).

Network stratification. To reconstruct a network, we determined the frequency with which each patient or bacteria was associated with another one within the same topic, resulting in a count matrix. This count matrix was subsequently normalized based on the total number of computations conducted. Using this normalized matrix, we constructed a network of the data using a spring layout, based on the Fruchterman-Reingold forcedirected algorithm. This method allowed us to create a visually elegant representation of the complex relationships within the dataset, where the edges of the network contain information about the strength of the connections between each patient or bacteria.

Specifically, the thickness of the links between nodes within the network indicates the strength of the association, with thicker edges denoting stronger connections and thinner edges representing weaker associations between the patients or bacteria. Sub-network patient clustering. Our analysis involves the normalized matrix of counts computed for the network stratification. To gain further insights into the structure of the data, we decided to apply a clustering technique to the matrix. Taking into consideration that the literature defines the number of enterotypes as 4, we decided to use an Agglomerative clustering method with the number of clusters fixed to 4.

Patient clustering investigation.

Using patient's anonymized ID provided by the database, we can match each patient node with their corresponding clinical data, thereby gaining a more comprehensive understanding of the network stratification. In order to enhance our analysis, we highlighted different attributes associated with each patient, such as the country of recruitment, their enterotype, or other relevant characteristics (e.g., diabetic status). By leveraging this information, we can effectively identify patterns and Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data relationships within the network. Additionally, we used the cluster assignments generated by the Agglomerative clustering technique to provide a more precise view of the underlying data, allowing us to identify sub-network of patient that could be investigated to gain a more nuanced understanding of the complex interplay of clinical/nutritional variables linked to this stratification (i.e., Genus stratification). Here, we have decided to focus our analysis on patients belonging to the same cluster assigned by the agglomerative clustering (graph clustering). By doing so, we compared and contrast the similarities and differences between the different clusters, and gain valuable insights into the factors that could explain the relationships between microbiota and the clinical outcome.

Statistical analysis.

We investigated the differences between the different clusters of patients by extracting their clinical/biological, nutritional data, as well as their nutritionscores. For biological/clinical and nutrition-scores, we did not performed any normalization techniques on the data. However, we did apply a log-transformation on the nutritional data in order to achieve a more appropriate distribution. In order to identify significant variables and differences between the clusters of patients, we conducted a one-way ANOVA on the data. We adjusted the p-values using FDR correction. Subsequently, we employed a Tuckey HSD test to investigate the specific contrasts between the different groups. Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data Using the proposed methodology, we were able to stratify patients. On the displayed graph (Figure 3.2 A,B,C), each dot represents one patient, and the thickness of the edges represent the connection between the patients. Hence, the display algorithm tends to group patients that have strong association with each other. We were able to stratify according to their country of recruitment (France, Germany, Danemark). In fact, the analysis of the network shown on Figure 3.2 A. reveals that individuals from Denmark tended to be clustered at the top of the network. Meanwhile, German individuals were primarily grouped towards the bottom right and bottom left of the network. As for French individuals, they were found to be evenly dispersed throughout the network. The display indicate that individuals can be stratified according to the country of recruitment due to the fact that the patient recruitment process is not homogeneous across all countries, as mentioned in the Methodology section.

Results

Results

GENUS Results

Patients stratification and straightforward observations

Another noteworthy aspect is the analysis of patients enterotypes. By highlighting patients based on their enterotypes, we were able to stratify individuals into distinct clusters.

Notably, patients identified as having the Bacteroides 2 enterotype were predominantly clustered on the bottom right of the network (Figure 3.2 B). On the other hand, patients identified as having the Prevotella enterotype tended to cluster on the bottom left of the network. Patients with the Ruminococcus enterotype, meanwhile, were primarily grouped at the top of the network (Figure 3.2 B). Patients with the Bacteroides 1 enterotype were found to be distributed more broadly throughout the network, from the top to the bottom right. An intriguing finding of our analysis is the observation that patients with different enterotypes appeared to form a continuum from the top to the bottom of the network, with Prevotella Individual forming an assembly outside the network (Figure 3.2 B). Enterotypes seems to be well captured by the methodology, and can be considered as a sanity check, since enterotyping methods and stratification method are both based on the Genus data. More specifically, Ruminococcus/Bacteroides 1 and Bacteroides 2 and Prevotella seems to be more homogeneous. These results motivated us to carry out graph clustering and examine the distinctions among these clusters. Specifically, we investigated the differences between clinical/biological factors, nutritional aspects, and nutritional-scores Using the graph clustering method outlined in the methodology section, we identified 4 Although, even if some clusters may have a higher enrichment in some enterotype, it is a more accurate representation of reality as individuals can have similarities in their gut microbiome composition without necessarily sharing the same enterotype. Biological data. A plethora of biological data have exhibited significant differences among clusters, and we decided to investigate relevant markers in the context of metabolic disorders only. We considered the body mass index (BMI) of the obtained clusters, and determined that individuals belonging to cluster 2 exhibited a significantly higher BMI compared to patients in clusters 0 and 1 (Figure 3.3 A). We also observed that patients in cluster 0 have a significantly lower BMI compared to clusters 2 and 3, but a higher BMI compared to cluster 1 (Figure 3.3 A). Additionally, we observed that patients in cluster 0 had a significantly lower BMI compared to clusters 2 and 3, but a higher BMI compared to cluster 1 (Figure 3.3 A). Furthermore, cluster 3 demonstrated a significantly higher BMI in comparison to patients in cluster 1. Subsequently, we examined the levels of leptin and adiponectin among individuals and observed that patients in cluster 1 shown significantly lower levels of leptin compared to patients in clusters 0, 2, and 3 (Figure 3.3 A). Similarly, patients in cluster 0 had significantly lower levels of leptin in comparison to patients in cluster 2. Patients in cluster 2 exhibited higher levels of leptin compared to all other clusters, whereas patients in cluster 3 had lower levels of leptin compared to patients in cluster 2 but higher levels compared to patients in other clusters (Figure 3.3 A). On the other hand, comparing the adiponectin levels, we discovered that patients in cluster 1 exhibited significantly higher levels of adiponectin compared to patients in other clusters. Moreover, patients in cluster 0 demonstrated significantly higher levels of adiponectin than patients in cluster 2 (Figure Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data

A).

We also considered some markers associated with type 2 diabetes and found out that patients in cluster 0 exhibited lower levels of fasting glycemia compared to patients in cluster 2 (Figure 3.3 B). Similarly, patients in cluster 1 displayed significantly lower levels of fasting glycemia in comparison to patients in cluster 2. Additionally, patients in cluster 3 have lower levels of fasting glycemia compared to patients in cluster 2 (Figure 3.3 B).

We obtained similar results when investigating glycated hemoglobin. Our analysis of triglycerides revealed that patients belonging to cluster 1 exhibit significantly lower levels of triglycerides in comparison to those from cluster 2 and 3. We also observed that patients in cluster 3 have significantly lower triglyceride levels than those in cluster 2 but higher levels than those in cluster 0 (Figure 3.3 B). Patients in cluster 0 had significantly lower triglyceride levels than those in cluster 3 and 2. Similarly, we considered the quantity of fasting peptide C, and our findings revealed that patients belonging to cluster 1 exhibited significantly lower levels of peptide C in comparison to the other clusters (Figure 3.3 B).

We also conducted an investigation into certain immunological markers, and our findings indicate that patients in cluster 1 have significantly lower levels of lymphocytes when compared to the other clusters (Figure 3.3 C). Furthermore, we found that patients in cluster 0 have significantly lower levels of monocytes compared to clusters 2 and 1, while patients in cluster 3 also have significantly lower levels of monocytes when compared to patients in cluster 2. Additionally, individuals in cluster 2 exhibited higher levels of neutrophils when compared to patients in clusters 0 and 1. Moreover, patients in cluster 1 had significantly lower levels of leukocytes when compared to patients in the other clusters

(Figure 3.3 C).
Based on the clinical data, individuals in cluster 2 exhibit a degraded metabolic health compared to individuals in other clusters, and they are more likely to have the Bacteroidetes 2 enterotype. In contrast, individuals in cluster 1 are in a better metabolic health than those in other clusters, and is enriched with Ruminococcus individuals. Cluster 3 individuals are in a milder state with better condition than cluster 2 individuals, but still have lower metabolic health compared to those in cluster 1. These patients are associated with a prevalence of Prevotella enterotype. Adiponectine OGTT is the quantification of the adiponectin (mg/l), Leptine OGTT is the quantification of the leptin (ng/l), BMI is the body mass index (kg/m2) B. diabetes severity. GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTGLYC is the measurement of the fasting glycemia (plasmatic glucose) in mmol/l, FASTLIPTG is the measurement of triglycerides in mmol/l and Peptide C is the quantification of peptide c reactive in the blood while fasting (µg/l) C. immune status for each patient cluster, WBNEUTRO is the number of neutrophils, WBCLEUCO is the total number of leucocytes, WBMONOCY is the total number of monocytes, and WBLYMPHO is the total of lymphocytes. Variables are selected according to their relevance and significance.

Nutritional and scores data. We considered nutritional variables that could be linked to the gut microbiota that can potentially alter the bacterial composition and, consequently, the genus data. The stratification can also be impacted. Our results show that individuals in cluster 2 exhibited lower levels of vitamin D in their diet when compared to those in clusters 1, 0, and 3. Furthermore, we observed that individuals in cluster 1 have significantly higher levels of vitamin D compared to those in cluster 0 (Figure 3.4 A).

The consumption of cereals for breakfast appeared to be important (as depicted in Figure 3.4 A), and we found that individuals in cluster 2 have significantly lower cereal intake Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data compared to individuals in the other clusters. Moreover, our analysis of the total amount of cereals ingested throughout the day (as indicated in Figure 3.4 A by food cereals) revealed that subjects in cluster 3 consume more cereals compared to individuals in the other clusters. We also found that cluster 1 individuals have a significantly lower consumption of poultry in comparison to those in the other clusters. Clusters 2 and 3 have the highest poultry consumption. In addition, we paid attention to the nut consumption, and we observed that cluster 2 individuals consume notably fewer nuts compared to those in clusters 0 and 1. Our analysis also highlights significant variations between cluster 2 and 1 subjects, with cluster 2 individuals having significantly more unsaturated and saturated fats in their food (food fat in Figure 3.4 A) than cluster 1 individuals. Furthermore, cluster 0 individuals consume significantly more fat than cluster 1 individuals (Figure 3.4 A).

The row nutritional data can introduce bias in the analysis, so, we made the decision to consider various scores that were calculated from the nutritional data. One of such scores is the Alternative Healthy Eating Index (aHEI), which was proposed by [McCullough, 2002]. This index is based on foods and nutrients that have been shown to be predictive for chronic disease risk. Higher scores of the aHEI have been strongly linked to a reduced risk of chronic diseases such as cardiovascular disease, diabetes, heart failure, and colorectal cancer [Belin, 2011;Chiuve, 2012;Fung, 2007;Reedy, 2008].

In general, patients in cluster 1 have a significantly higher aHEI score compared to those in the other clusters, while patients in cluster 2 have the lowest aHEI score among all the clusters (Figure 3.4 B). We also examined each of the individual components that contribute to the aHEI score separately. Through our analysis, we discovered that cluster 1 patients had significantly higher AHEI scores for nuts in comparison to individuals in the other clusters. Additionally, they had significantly higher AHEI scores for fibers in cereals compared to individuals in clusters 2 and 0, as well as a significantly higher AHEI score for the ratio of polyunsaturated fat to saturated fat. Meanwhile, individuals in cluster 3 have the highest AHEI scores for vegetables compared to individuals in the other clusters (Figure 3.4 B).

Results

A B

Figure 3.4: Quantification for different A. nutritional variables. Nutr vitd is the total intake of vitamin d in log(µg), food breakfast is the daily consumption of breakfast cereals in log(g), food cereeals is the daily consumption of cereals, pasta and rice in log(g), food poultry is the daily consumption of poultry in log(g), food nuts is the daily consumption of nuts including peanuts in log(g), and food fat is the fat intake in log(g) and B. nutritional score with aHEI score (ranges from 0 to 70), aHEI Nuts related to intakes of nuts and seeds (ranges from 0 to 10), aHEI Fibreincereals related to intakes of fiber from cereals and cereal products (ranges from 0 to 10), aHEI PUFASFA related to the ratio of poly-unsaturated fatty acid (PUFA) to saturated fatty acid (SFA) intake (ranges from 0 to 10), aHEI vegetables related to intakes of vegetables (ranges from 0 to 10).

Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data

Specific subgroup analysis, case of 2a and 2b individuals

Using the workflow previously detailed, we decided to highlight only individuals from that are associated to 2a and 2b groups. Among all the patients, it appear that individual seems to be stratified in 3 groups as shows in Figure 3.5 A.

With the aim to decipher more precisely the differences between these 3 groups, we decided to perform the global workflow on patients identified as 2a and 2b individuals only. Our analysis showed that patients from clusters 2a and 2b appeared to form three distinct clusters, which prompted us to conduct further investigation. To go deeper, we chose to exclusively sample individuals from these clusters and employ graph clustering techniques while simultaneously analysing their clinical and nutritional data (Figure 3.5 B).

Initially, our findings indicated that cluster 2 exhibited a significant presence of Bacteroidetes 2 enterotypes, whereas cluster 1 displayed an enrichment of Prevotella enterotype (Figure 3.5 C). Notably, cluster 0 displayed a higher level of diversity in terms of composition, with an abundance of individual with Bacteroidetes 1 enterotypes, as well as individuals with Ruminococcus, Prevotella, and Bacteroidetes 2 enterotypes (Figure 3.5 C).

We decided to consider the differences between the two groups (2a and 2b). These two groups were stratified into three clusters (Figure 3.5 B), and we analysed their clinical and nutritional data (Figure 3.5 D,E,F). We observe clear discrepancies between these clusters. Specifically, IMPROP (imidazole propionate) levels were significantly different between individuals in clusters 2 versus those in clusters 1 and 0 (Figure 3.5 D). There are significant differences in fasting lipid levels between cluster 2 and both clusters 0 and 1. Further, glycated hemoglobin levels were found to be significantly distinct between individuals in clusters 0 and 2, while leptin levels exhibited significant variations between individuals in clusters 2 and 1 (Figure 3.5 D). Subsequently, we observed that individuals in cluster 2 consumed significantly less fiber and bread compared to those in cluster 0. Additionally, individuals in cluster 2 had lower vegetable consumption than individuals in cluster 0 (Figure 3.5 E). Further analysis concerning vegetables consumption, with the nutrition scores aHEI and aHEI also showed 3. Results significant differences between individuals in cluster 2 versus those in clusters 0 and 1, with lower scores for both aHEI and aHEI vegetables (Figure 3.5 F). The count is normalized by the size of the cluster (i.e the number of individuals involved in the cluster). Cluster 0 is enriched with Bact1 individual enterotypes, while cluster 1 is enriched with Prevotella enterotype. Cluster 2 is enriched with Bact2 enterotypes. Each of this cluster is defined by a mixture of different enterotypes with an enrichment with some specific individuals.D. Biological and clinical data such as IMPROP (imidazole propionate in nM), GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTLIPTG is the measurement of triglycerides in mmol/l, Leptine OGTT is the quantification of the leptin (ng/l). E. nutritional variables, Nutr fiber is the global fiber intake in log(g), food bread is the daily bread consumption in log(g), food vegetables is the daily consumption of vegetables in log(g) and F. Nutritional score, with aHEI score (ranges from 0 to 70). aHEI vegetables related to intakes of vegetables (ranges from 0 to 10).

Results

Bacteria Clustering

Using our methodology for patients stratification, we also obtained a network of bacteria. By investigating the network, we were able to distinguish two subgroups of bacteria based on their connections in the network: one group of highly connected bacteria, a less connected network in the middle, and on the top a subnetwork (Figure 3.6) Three groups of bacteria can be identified, that may contribute to the stratification process. However, we are currently unable to link the functionality of certain bacteria to the underlying phenotypes due to incomplete information provided by various databases.

Similarly, it is possible to differentiate bacteria based on their phylum, taxa, and clade. However, no structural information was found in the data. Nevertheless, certain bacteria with particular functions appear to be highly interconnected, allowing them to form clusters.

KEGG Results

Patients stratification, clustering and investigation

Similar to the GENUS data, we employed the workflow described in the methodology section to classify patients according to the KEGG.. Notably, upon analyzing patient data according to their recruitment country, we observed unique grouping patterns. Specifi-Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data cally, Danish subjects were located in the lower section of the network, while French participants were scattered across the network. German participants, however, were grouped in the lower left and upper left regions of the network. This discrepancy was particularly apparent in the subnetworks of patients recruited from the same country (as illustrated in the Supplementary Figure 6.8).

In our analysis, we examined patient enterotypes, enabling us to classify individuals into separate clusters based on their microbiome composition. The outcomes were interesting, as patients with a Prevotella enterotype were primarily grouped at the top of the network, while those with a Bacteroide 2 enterotype were mostly located at the top right of the network. Ruminococcus patients were mainly grouped at the bottom left of the network, whereas patients with a Bacteroide 1 enterotype were more evenly distributed throughout the network (depicted in Figure 3.7 and Supplementary Figure 6.9). These results were unsurprising, considering that both the GENUS data and KEGG data were obtained from the same metagenomic analysis. Like the GENUS data, we chose to perform graph clustering to assess the differences among clusters. Our focus was on exploring variations between clinical/biological factors, nutritional aspects, and nutritional scores. We applied the graph clustering approach 3. Results described in the section and identified the existence of four clusters, as shown in the network cluster diagram (Figure 3.8). Further analysis of enterotype enrichment within each cluster revealed that cluster 0 had a higher occurrence of patients with Bacteroide 1 enterotype. In contrast, cluster 1 had a marked enrichment of patients with Bacteroides 2 enterotype, while cluster 2 had a prevalence of individuals with Ruminococcus enterotype, and cluster 3 had a predominance of patients with Prevotella enterotype, as demonstrated in the cluster composition (Figure 3.9). Biological data. Although a large amount of biological data has shown significant differences among clusters, we chose to focus only on investigating pertinent markers in relation to metabolic disorders. Initially, we examined the BMI and found that individuals in clusters 1 and 3 demonstrated a significantly greater BMI in comparison to patients in clusters 0 and 2. Similarly, individuals in cluster 3 displayed a significantly higher BMI than those in cluster 1 (Figure 3.10 A). Furthermore, we evaluated the levels of leptin and adiponectin and observed that individuals in cluster 3 had significantly higher levels of adiponectin compared to individuals in clusters 2 and 0. In contrast, individuals in cluster 1 had lower levels of adiponectin compared to those in cluster 0. Meanwhile, individuals in cluster 1 displayed significantly higher levels of leptin in comparison to those in clusters 0 and 2 (Figure 3.10 B). Subsequently, we opted to examine markers related to diabetes and discovered that individuals in cluster 1 had elevated levels of glycated hemoglobin in comparison to those in clusters 2 and 0. Additionally, individuals in cluster 1 demonstrated significantly higher levels of fasting glycemia than those in clusters 2 and 0 (Figure 3.10 B). Furthermore, individuals in clusters 1 and 3 displayed elevated levels of triglycerides in contrast to those in clusters 0 and 2. Additionally, individuals in clusters 1 and 3 had significantly 3. Results higher levels of peptide C compared to those in clusters 0 and 2 (Figure 3.10 B). Last but not least, investigated specific immunological indicators, and our findings indicate that patients in clusters 0 and 2 exhibited significantly reduced levels of leukocytes and monocytes compared to those in cluster 1. Additionally, individuals in clusters 3 and 1 had higher levels of lymphocytes than those in cluster 2 (Figure 3.10 C).

Nutritional condition and scores

We also analyzed certain nutritional information that could be linked to the gut microbiota, which can alter the bacterial makeup and consequently influence the metagenomic data presented in our table, potentially influencing the clustering results.

Our results indicated that individuals in cluster 1 had lower levels of vitamin D in their diet than those in clusters 0 and 2 (as shown in Figure 3.11 A). Moreover, the intake of cereal during breakfast was notably lower for individuals in cluster 3 in comparison Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data to clusters 0 and 2. Conversely, the consumption of poultry and processed meat was significantly higher for individuals in cluster 3 than for those in cluster 0. Additionally, individuals in cluster 2 had significantly higher consumption of nuts than those in cluster 1 (Figure 3.11 A)

We then examined the AHEI score and discovered that individuals in clusters 0 and 2 had a significantly higher overall score compared to those in cluster 1. Specifically, their AHEI score for nuts was significantly higher. Furthermore, the AHEI score for the ratio of polyunsaturated fat to saturated fat was notably higher for individuals in cluster 0 than for those in clusters 1 and 3 (Figure 3 Figure 3.13: Subcluster of KO matched to genes and the result of Gene Ontology (GO) applied on the genes identified. The GO was performed using Escherichia coli K-12 substrain as reference.

Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data

Discussion

Metabolic condition

GENUS case on all MetaCardis Patients. With the developed methodology (see Methods section), we stratification MetaCardis patients from their GENUS data. Our methodology does not only allow us to stratify subjects but also to reorganize the enterotypes. Using a graph clustering approach, we identified four distinct clusters, which we thoroughly analyzed. Each cluster was found to be enriched with a specific enterotype, indicating significant differences in the composition of the gut microbiome among the patient groups.

Remarkably, our analysis of clinical data revealed a strong association between patients exhibiting the Bacteroides 2 enterotype and significantly higher BMI and Leptin levels, as well as lower levels of adiponectin (Figure 3.3 A). This finding is in line with recent research from [Alili, 2022] which suggests that Bacteroides 2 enterotype is more prevalent in subjects with severe obesity and metabolic dysfunction. Furthermore, we discovered that patients with the Bacteroides 2 enterotype have the highest incidence of diabetes among all participants. Specifically, our analysis of patients stratified into four clusters revealed that cluster 2, which was highly enriched with Bacteroides 2 individuals, exhibited significantly higher fasting glycemia and glycated hemoglobin levels compared to other clusters.

These results are consistent with a study [START_REF] Wang | [END_REF] which found that the Bacteroides enterotype was associated with an increased risk of type 2 diabetes, potentially leading to the development of this disease.

An additional noteworthy finding is related to cluster 3, in which individuals are grouped together outside the network, forming an assembly that is highly enriched with patients with Prevotella enterotypes. Upon analysis of their clinical data, it became apparent that patients in this cluster do not exhibit significant differences in terms of BMI, leptin or adiponectin when compared to patients in cluster 2. However, there are significant differences in data related to the severity of diabetes, with significantly lower fasting glycemia and glycated hemoglobin observed in patients from cluster 3. This finding is particularly interesting as previous studies have suggested a potential link between the 90

Discussion

Prevotella enterotype and improved glucose metabolism and insulin sensitivity in T2D

individuals [Karlsson, 2013;Kovatcheva-Datchary, 2015]. Patients with a Bacteroides 2 enrichment appear to have a more dysbiotic state compared to individuals with a Prevotella enterotype. This finding is consistent with a study by [Al Bataineh, 2021] which demonstrated that individuals with type 2 diabetes mellitus (T2DM) had a higher proportion of dysbiotic Bacteroides 2 enterotypes, while non-T2DM healthy controls had different microbiome compositions, with an enrichment in Prevotella.

To further elaborate on the results, we observed that cluster 1, which is primarily composed of individuals with a Ruminococcus enterotype, exhibits the most favorable metabolic profile among all clusters. These individuals have a lower BMI, higher levels of adiponectin, and lower levels of leptin compared to individuals in the other clusters. Additionally, when investigating parameters related to diabetes severity, such as fasting glycemia and glycated hemoglobin, cluster 1 has the lowest levels compared to the other clusters. These findings align with previous research, as studies have shown that individuals with a higher abundance of Akkermansia bacteria (involved in the Ruminococcus enterotype) in their gut microbiome have a decreased risk of developing metabolic disorders and type 2 diabetes [Dao, 2016;Shin, 2014], and [Palmas, 2021] states that normal weight individuals are highly associated with Ruminococcus enterotypes.

Individuals belonging to cluster 0, which is enriched with the Bacteroides 1 enterotype, appear to be in a better metabolic condition compared to individuals from clusters 2 and 3. They have lower BMI, higher levels of adiponectin, and lower levels of leptin.

Furthermore, they appear to be in a better diabetic condition than other individuals.

GENUS case on 2a and 2b individuals. Subjects from 2a and 2b are individuals with severe obesity and without diabetes or coronary artery disease, and candidates for bariatric surgery. We aimed to categorize two groups of obese individuals and identify any significant associations with a specific phenotype. Our investigation led us to discover that these individuals can be classified into three distinct clusters, each with a unique biological and nutritional profile. Specifically, we found that individuals in cluster 2, who have an abundance of Bacteroides 2 enterotype, produce significantly higher levels of imidazole propionate than those in clusters 0 and 1. This finding is consistent with previ-Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data ous research indicating that obese individuals with the Bacteroides 2 enterotype produce more imidazole propionate [Molinaro, 2020] compared to other enterotypes. Moreover, individuals in cluster 2 exhibit significantly higher levels of leptin, glycated hemoglobin, and fasting glycemia than those in other clusters. These results suggest that the gut microbiome composition may explain the metabolic condition of individuals in cluster 2, independent of their biological or clinical status.

KEGG Orthology case on all individuals

We also analyzed the results obtained from clustering methodology for different clusters. For instance, in the case of the genus data, we observed that individuals from cluster 1, who had an abundance of Bacteroide 2 enterotype, had a less favorable metabolic health profile compared to those in other clusters. These individuals exhibited lower levels of adiponectin and higher levels of leptin. Additionally, individuals from cluster 3, which had an abundance of Prevotella, had a significantly higher BMI compared to those in other clusters. Our investigation also revealed that variables associated with diabetes, such as Glycated hemoglobin, fasting glycemia, peptide C, and fasting lipid (triglycerides), were significantly higher in individuals from cluster 2, which was enriched with Bacteroides 2 enterotype. These results were consistent with the findings from the GENUS data and the literature. In summary, the observations made using both levels of information were in agreement.

Nutritional and Score conditions

GENUS case and all MetaCardis Patients. By employing the previously established approach, we examined the nutritional information and discovered that individuals belonging to clusters 1 and 3 exhibit significantly elevated levels of vitamin D in comparison to those in cluster 2. [Singh, 2020] claims that vitamin D supplementation can restore the microbiota by reducing Bacteroides acidifaciens and increasing the Bacteroidetes to Firmicutes ratio, which led to significant changes in the two dominant genera, Bacteroides and Prevotella, indicating a variation in enterotypes after supplementation. Additionally, the supplementation also increased the abundance of health-promoting probiotic taxa such as Akkermansia and Bifidobacterium.

Moreover, individuals in clusters 1 and 3 tend to consume a larger quantity of cereals for 92 4. Discussion breakfast, while those in cluster 2 consume more fats compared to cluster 1. Additionally, a study by [Matsuoka, 2022] found that consuming barley in the Japanese population is associated with a modification of the gut microbiota, leading to an increase in some bacteria that belong to the Ruminococcus enterotype.

Furthermore, [Wu, 2021] compared different diets within the South-Korean population, including the Korean-diet (KBD) rich in energy and fiber, the Rice based diet (RBD) rich in carbohydrates, and the Western diet (WSD) rich in fats, to investigate their links with metabolic syndromes. Their findings showed that participants who had a KBD had lower serum C-reactive protein and triglyceride concentrations than those who had an RBD or WSD. Additionally, the KBD was highly associated with the Ruminococcus type and linked to lower metabolic syndromes in the Korean population. In a related study, [Quatela, 2017] explored the relationship between breakfast cereal consumption among women and obesity. Their findings revealed that consuming oat-based cereals, muesli, and All-bran was associated with a notable decrease in the risk of obesity.

In a same way for all the groups, the aHEI score is significantly higher for individuals from cluster 1 compared to other groups. More precisely, individuals from cluster 2 have an aHEI index lower than other groups for fiber in cereals, and nuts. According to [Akbaraly, 2011] individuals who scored higher on aHEI tend to have lower incidence of cardiovascular disease (CVD) mortality, and one of the contributing factors to this result is their consumption of nuts and soy. In addition [Mirashrafi, 2021] demonstrated (on Iranian cohort) a significant difference in aHEI scores between obese and non-obese individuals.

Specifically, their study found an inverse relationship between the consumption of nuts and soybeans and the Waist-to-Hip Ratio (WHR), while the cereal fiber score was negatively correlated with BMI.

Furthermore, individuals in cluster 0 and 1 had a significantly higher intake of nuts compared to those in cluster 2. The consumption of nuts has been associated with numerous health benefits. For example, studies have shown that consuming nuts can lower the risk of developing type 2 diabetes [Viguiliouk, 2014] and coronary heart disease [Kris-Etherton, 2008] as well as reducing various cardiovascular risk factors [START_REF] Mohammadifard | [END_REF]. Additionally, a recent review [Fitzgerald, 2021] found that the overall consumption of nuts Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data is positively associated with bacterial diversity, with the consumption of different types of nuts promoting different sub-strains of bacteria. Therefore, based on this finding, we propose that individuals in cluster 2, who have been shown to have the poorest metabolic health, may also be characterized by a low intake of nuts. This association between low nut consumption and unfavorable metabolic outcomes highlights the potential importance of nut consumption in promoting metabolic health.

Also, our analysis reveals that individuals in cluster 2 have a significantly higher intake of fats compared to those in cluster 1. The consumption of dietary fat has been shown

to impact obesity, as discussed in a review by [START_REF] Bray | [END_REF] that analyzed multiple clinical studies. More recent research by [Field, 2007;Guasch-Ferré, 2017;Schwab, 2014] suggests that the type of dietary fat consumed may have different effects on the risk of obesity and type 2 diabetes. Therefore, variations in the pattern of fat consumption could potentially explain the differences in enterotype observed in our study.

GENUS case on 2a and 2b individuals.

We explored the nutritional factors that contribute to the variations between three groups obtained by clustering. Our findings indicate that individuals in cluster 2 consume lower amounts of fiber, bread, and vegetables in comparison to those in the other clusters. This pattern of low fiber and vegetable intake, along with high consumption of sugar (e.g., bread), is known to be associated with obesity and type 2 diabetes [Ojo, 2020]. Additionally, individuals in cluster 2 have lower global aHEI index and aHEI vegetable score, indicating that their nutritional status is inferior to that of individuals in the other clusters. These results provide some insights into the reasons why individuals in cluster 2 are classified differently within the obese population.

KEGG Orthology case on all individuals

As for the GENUS data, we found that individuals from cluster enriched in Bacteroides 2 (Cluster 2) have significantly lower levels of vitamin d compared to other individuals. This finding is aligned with previous results showed using the GENUS data. Moreover we found that individual from cluster, enriched with Prevotella enterotypes individuals, consume significantly more poultry, more processed meat compared to individuals from cluster 0 and 2. Moreover Cluster 3 tend to consume lower levels of fiber during the breakfast (food breakfast) compared to 4. Discussion individuals from cluster 2 and 0. This findings are aligned with the findings previously highlight using GENUS data, and literature that shows that the consumption of fibers, nuts, and vitamin d, is associated with a healthier gut microbiome. These findings are in line with the results obtained from the GENUS data when we analyzed the different aHEI scores. As both the GENUS and KEGG data are derived from metagenomic data, the consistency in results is not surprising. However, it is important to note that the KEGG data allows for a deeper level of investigation into the clustering, specifically at the level of individual bacteria and KO.

Bacterial networks and KO investigation. We obtained a network that simultaneously represents the relationships between patients, bacteria or KO. Upon examining this network, we were able to identify three distinct subgroups of bacteria and four distinct subgroups of KO. We thoroughly investigated the information contained within the network of bacteria to identify any underlying patterns that could explain our prediction, but unfortunately, we were unable to find any reliable information that was suited to explaining it. Although the network of bacteria was stratified into three distinct groups, we were unable to access deeper levels of information such as functionality that could provide further insights into this grouping. Additionally, we explored the different levels of taxonomy of the bacteria, but we did not find any relevant patterns that could explain this stratification. Despite our best efforts, we did not find any relevant methods that could leverage the hidden patterns within the data.

Moreover, we were able to identify clusters of genes within the KO data that are related to different metabolic pathways. However, the pathways that were highlighted were based on the assumption that Escherichia coli K-12 substrain possesses all bacterial genes and that their functionality is the same for every bacteria. This approach overlooks potential pathways that may be specific to certain bacteria. Additionally, some KO to gene have yet to be identified and linked to specific pathways, which greatly reduces the possible interpretations of our findings. While we did identify some pathways that were related to ATP and other metabolic functions, these were not sufficient to reveal the underlying pathways or understand the hidden structure of the KO clustering. Nevertheless, we provide the network in the hope that future bioinformatic frameworks will be designed to Chapter 3. Application of the LDA-DC Method to stratify patients using GENUS and KEGG data help us identify specific pathways.

Conclusion

In this study, we applied a novel framework to perform graph clustering on GENUS data, enabling us to stratify individuals without prior knowledge of their enterotype or clinical condition. Through this approach, we were able to identify distinct clusters of individuals with different microbial composition. While patients within the same cluster may share similarities in terms of enterotype, the composition of each cluster is unique. Therefore, the novelty of our study lies in the fact that each cluster is a combination of various enterotypes, with a fraction of patients sharing the same enterotype. This approach provides more flexibility than the traditional analysis of distinct enterotype separately, allowing us to capture patients who share similarities in their gut microbiota but do not necessarily have the same assigned enterotype. This methodology enables us to maximize the detection of enterotype-related patterns among patients.

Subsequently we conducted a comprehensive analyses of their clinical, biological, and nutritional profiles. Our findings revealed that individuals within each cluster shared similar biological and clinical phenotypes and nutritional behaviors. Additionally, we identified a significant association between specific enterotypes and certain clusters, with some clusters being highly enriched with particular enterotypes. Ultimately, our method reveals that the gut microbiota data among different patients form a continuum, with each patient occupying a unique position in space is associated with biological, clinical or nutritional characteristics, that build upon classical enterotype approach but give more insight for precise patient diagnostic. Furthermore, our approach allows us to project individuals onto this spectrum using only their clinical data, without the need for metagenomic data (since the biological, or clinical features can be sufficient to project patient onto space).

Furthermore, while we were able to identify networks of bacteria that could potentially, explain the observed stratification (since they're organized in community with some bacteria grouped together in the network), we were limited by our current knowledge and could not uncover any significant hidden information that would further elucidate the 96 5. Conclusion prediction. Nonetheless, we present these findings, which may serve as a stepping stone for future investigations.

Our networking approach proved to be a valuable tool in identifying metabolic conditions using data derived from sequencing technologies. Furthermore, this approach allows us to gain insights into the concept of metabolic health in a highly diverse cohort, and pave the way for future decision-making algorithm and personalized medicine.

Chapter 4

Metabolic age prediction using Artificial

Neural Networks

In this chapter, the main objective was to estimate the immunosenescence of obese and obese-diabetic patients compared to non-obese patients using immune data from flow cytometry of the CARMMA cohort. To achieve this, we developed a multi-layer perceptron (MLP) to learn the age of non-obese patients based on immune data (specifically from CD4 and CD8 subsets) and predict the age of obese and obese-diabetic patients. By comparing the predicted age with the actual age, it is possible to estimate the immunosenescence of obese and obese-diabetic patients compared to non-obese patients of similar age. Additionally, using a tree-based methodology, we identified different immune cell sub-phenotypes that are impacted by obesity and type II diabetes. These sub-phenotypes could be further investigated to enhance our understanding of patient immunosenescence. We also conducted an analysis on patients 12 months after bariatric surgery and found that certain cell sub-phenotypes related to immunosenescence were reduced. This suggests that bariatric surgery may decrease inflammation and consequently reduce immunosenescence. This chapter is a part of a larger project that includes laboratory experiments (not discussed or shown) aimed at understanding immunosenescence and the impact of bariatric surgery on it.

Objectives 1 Abstract

Metabolic disorders are rapidly increasing in prevalence as a consequence of the continued obesity epidemic: 6% of the French population have diabetes. Diabetes has the highest prevalence among all chronic diseases. To better understand how obesity and diabetes affect immunosenescence, we use patient's data coming from the CARMMA (CARdiac and skeletal Muscle alteration in relation to Metabolic diseases and Ageing: role of Adipose tissue) cohort, set of non-obese, obese and obese-diabetic patients. For each patient, the immune profile of CD4 and CD8 lymphocytes are extensively phenotyped using Flowcytometry technique. Subtypes of CD4 and CD8 are determined using cell-gating method according to their fluorescence profile. Based on this stratification, we build a binarization method allowing us to provide a binary label to each cell according to the expression of its markers. In order to stratify patients, we designed a deep learning algorithm suite to predict patient-age using immune-binary annotation for CD4 and CD8 subsets. The algorithm is trained on non-obese data, and the test is performed on obese and obesediabetic data. We demonstrate that obese and obese-diabetic patients are predicted to be significantly elder than their real age while non-obese patients are not, meaning that obese or obese-diabetic condition seems to highly impact CD4 and CD8 sub-population and thus confirm some immunosenescence. We also designed tree-based method allowing us to identify key immune cell sub-phenotypes in CD4 and CD8 subsets that are highly modified between non-obese, obese and obese-diabetic patients. This study gives interesting insights to better understand immunosenescence linked to obese and obese-diabetic status in the era of big data.

Introduction

Chronic low-grade inflammation in obesity contributes to the development of metabolic disorders. Proinflammatory cytokines, including tumor necrosis factor-α (TNF-α), interleukin (IL)-1β, and IL-6, play crucial roles in the pathogenesis of insulin resistance (IR), ultimately leading to the onset of type-2 Diabetes and non-alcoholic fatty liver disease (NAFLD) [Ganeshan, 2014;Johnson, 2013;Vajro, 2013]. Moreover, individuals with obesity ex-2. Introduction hibit a heightened susceptibility to viral, bacterial, and fungal infections [Falagas, 2006;Karlsson, 2010;OShea, 2013], along with a diminished response to vaccination [Painter, 2015]. Consequences of obesity and type-2 diabetes seem to be close to metabolic alterations induced by aging. Immunosenescence, which refers to the progressive decline in immune system function associated with aging, is believed to contribute to age-related comorbidities [Fukushima, 2018] and changes in T-cell immunity are prominent features of immunosenescence. Increasing evidence suggests that senescent T cells [Strioga, 2011;Dong, 2019] play a role in the pathogenesis of cardiovascular diseases (CVDs), such as atherosclerosis, acute coronary syndrome, and hypertension. The impact of immunosenescence extends to various cell types, including those found in the bone marrow, thymus, peripheral blood, secondary lymphatic organs, and elements of the innate immune system. However, it appears that innate immunity is relatively better preserved, while more pronounced age-related changes occur in the adaptive immune system [Franceschi, 2000;Frasca, 2016;Larbi, 2014]. In human aging, immune exhaustion and senescence result from repeated antigenic stimulation of T cells. T cell exhaustion is characterized by a progressive loss of proliferation, cytokine production, and cytotoxic T lymphocyte (CTL) activity during chronic infections such as HIV, HCV, HBV, or in cancer cases [Crespo, 2013;Gianesin, 2016]. Various inhibitory markers have been described in the literature to define senescence or exhaustion, such as telomere length, PD1, KLRG1, CD57, Tim3, Lag2, Tigit, and others [Lee, 2016]. PD1 plays a crucial role in maintaining a balance between protective immunity, immunopathology, homeostasis, and tolerance. However, in response to chronic pathogens and tumors, PD1 expression can limit protective immunity [Sharpe, 2018]. The percentage of T cells co-expressing NK cell markers, such as CD57 and KLRG1, also increases with aging [START_REF] Ibegbu | Expression of killer cell lectin-like receptor G1 on antigen-specific human CD8+ T lymphocytes during active, latent, and resolved infection and its relation with CD57[END_REF]Brenchley, 2003]. Currently, no longitudinal studies have evaluated whether increased T-cell senescence is induced by obesity and type-2 diabetes in humans. The main objective of our study was to investigate the induction of senescent T cells in the context of obesity and type II diabetes, and to determine whether bariatric surgery can reverse this alteration. We proposed the hypothesis that the obesogenic environment triggers chronic activation of T cells, leading to their exhaustion and subsequently contributing to the development of type II diabetes. Our findings reveal that obese patients exhibited an elevated frequency of CD4+ PD1+ and CD8+ CD45RA+ T cells in the peripheral blood. Furthermore, we observed a significant reduction in naïve CD4 T cells specifically among patients with type II diabetes. In summary, our study suggests that both obesity and type II diabetes induce a senescent-associated phenotype in CD4 T cells, which can be reversed by significant weight loss achieved through bariatric surgery. These data provide insights into the existence of an immunometabolic link between T-cell-associated senescence and the underlying pathophysiology of obesity and type II diabetes.

3 Data of CARMMA project and artificial neural network Data preparation: First, we extracted FlowJo data from 33 non-obese, 43 obese, and 44 obese-diabetic patients, all included in the CARMMA cohort. For each patient, we identified and pulled fluorescent data from 18 sub-phenotypes of lymphocyte cells (Lymphocytes, CD3, CD4, CD4-CCR7, CD4-CD27, CD4-CD28, CD4-CD45RA, CD4-CD57, CD4-PD1, CD4-KLRG1, CD8, CD8-CCR7, CD8-CD27, CD8-CD28, CD8-CD45RA, CD8-CD57, CD8-PD1, CD8-KLRG1). We removed all patients for whom we had fewer than 5,000 cells quantified. We then had 113 patients, including 33 non-obese, 40 obese, and 40 obese-diabetic patients. We then transformed the raw cytometry signal (fluorescence) into binary.

Binary Annotation: Based on the stratification established by the cell-gating method and using the data previously extracted from FlowJo, we were able to provide binary labels for all cells where a marker is expressed or not. For each patient and for each cell in the lymphocyte file, we investigated if its fluorescence characteristics are present in one of the sub-phenotype files. If we found a match, then the cell is considered positive for the specific marker of the sub-phenotype (and we assigned a value of 1 for the corresponding marker). Thus, in an iterative manner, we were able to determine the complete stratification for each cell, using its binary annotation. tients were predicted to be significantly older than their real age. We also examined cases where non-obese patients were not predicted to be significantly older than their actual age. This allowed us to define a metric called SSN (Significant for obese, Significant for obese-diabetic, and Not-significant for non-obese), which quantified the number of experiments where each combination appeared. This helped us evaluate the robustness and consistency of our predictions A Tree based method: In order to identify the most significant/modifiable factors among obese, obese-diabetic, and non-obese patients, we developed a tree-based methodology. Our approach uses the information from our Bit-Binary matrix, which contained the average quantity of each cellular phenotype for the different patient groups. Initially, we opted to focus on the 15 most prevalent cellular characteristics and indentify the most frequent biomarkers associated with them. Subsequently, we computed the proportion of cells considered as positive and negative for this specific marker. Then, we proceeded to identify the second most prevalent marker and calculate the ratio of positive and negative cells concerning the previous marker's positivity or negativity. We followed a recursive and iterative process to establish the tree-like distribution of cells based on the markers. Here we decided to center the tree on all CD45RA and CCR7 characteristics for CD4 and CD8 subsets. Starting point are respectively Naive cells corresponding to CD45RA+ccr7+ expression, Center Memory (CM) corresponding to a non expression of CD45RA and an expression of CCR7 (CD45RA-CCR7+), Effector Memory identified as

Results

CD45RA-CCR7-and Terminally Differentiated Effector Memory (TEMRA) identified as CD45RA+ CCR7-expression. To improve visualization, we chose to exclude all nodes that accounted for less than 2% of the cells.

Statistical analysis:

The comparison between predicted age and real age between patient was performed using t-test on two related samples.

Software, Packages: All code was written in Python 3.6. Machine learning algorithm was performed using Pytorch 1.8.1+cu102 and scikit-learn 0.23.2 and Statistical analysis using SciPy library. Graphical figures were generated using Plotline Matplotlib and Pydot library.

Results

Metabolic Age prediction on CD4 and CD8 subsets using ANN

After using our Artificial Neural Network (ANN) on the CD4 subset data of obese and obese-diabetic patients, we observed that our model significantly and consistently overestimated the age of these individuals compared to their actual age. (p-value<0.05 on 10,000 runs of prediction) while non-obese patients are predicted not significantly older than their actual age (p-val>0.05 on 9,946 out of 10,000 runs of prediction).

Our custom SSN metrics calculated a value of 9,946, indicating a systematic overestimation of the age of obese and obese-diabetic patients by our predictive model. One of the primary explanations for this phenomenon is the profound impact of obesity and type II diabetes on specific immune cell phenotypes, which can lead to immunosenescence.

(Figure 4.1).

Similarly, we utilized our ANN to analyze the CD8 subsets of obese and obese-diabetic patients, and the results showed that these patient groups are predicted significantly older by our predictive model compared to their actual age (p-value<0.05 on 10,000 runs of prediction) while non-obese patients are not significantly predicted older than their real age (p-val>0.05 on 10,000). Our custom SSN metrics is 10,000 meaning that obese and . months for obese patients, but this increase was not statistically significant. In contrast, the predicted age did not change in obese-diabetic patients when comparing T0 and T12.

Results

While these findings do not provide evidence regarding the reduction in metabolic age following bariatric surgery, it would be valuable to explore the long-term trajectory of metabolic age prediction. This investigation could involve analysis of various key time points (such as 1 year, 5 years, and 10 years) after bariatric surgery to identify potential modifications and compare different patient subgroups. It is important to note that not all patients returned for the 12-month follow-up, and only a small subset of the total cohort was available for the analysis. Consequently, it is not possible to draw strong conclusions from these data We decided in this section to use our recursive tree method to identify cellular populations or sub-populations that are modified in obese and obese-diabetic patients compared to non-obese patients. In order to accomplish this, we use data at time point 0 months for all our patients. as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red.

We identified different CD4 sub-population whose proportions are significantly different in non-obese, obese and obese-diabetic patients. Indeed, we observed that the proportion of Naive cells is altered in obese and diabetic patients compared to non-obese patients.

Furthermore, we observed that all the sub-phenotypes of these cells are also proportionally altered in obese and diabetic patients Figure 4.3 (p-value < 0. 05 -ANOVA) raising the hypothesis that some CD4 sub-populations seem to be highly impacted by the patients' status.

Similarly, we identified different CD8 sub-population whose proportions are significantly

Results

different in non-obese, obese and obese-diabetic patients.

While the proportion of Naive cells remained consistent among the groups, the percentage of subpopulations expressing PD1 was higher in obese and obese-diabetic patients compared to non-obese patients. Additionally, the proportion of subpopulations within the Naive cell group, characterized by the absence of KLRG1 expression and the presence of CD27, CD28, and CD57-, appeared to be altered in obese and obese-diabetic patients (NAIVE+PD+KLRG1-CD27+CD58+CD57-) when compared to non-obese patients. Moreover, we observed modifications in the proportion of cells expressing both KLRG1 and CD27+ in obese and obese-diabetic patients (NAIVE+PD+KLRG1+CD27+) (Figure 4.4).

Comparison with the patients profile 12 months after the bariatric surgery

Subsequently, we decided to reanalyze the data and compare the outcomes between obese or obese-diabetic patients who underwent bariatric surgery and returned for follow-up after 1 year. The same methodology was applied to both the T12 (12 months after surgery) and T0 (baseline) datasets, and the results from the tree analysis were compared between the two time points. Only patients who had data available at both T0 and T12 months were included in this analysis.

We observed a significant evolution of specific cell populations, particularly CD4 cells, in patients after bariatric surgery. Notably, the Naive subpopulations (NAIVE+ PD1+ KLRG+ / NAIVE+ PD1+ KLRG+ CD27+ / NAIVE+ PD1+ KLRG+ CD27+ CD28+ / NAIVE+ PD1+ KLRG+ CD27+ CD28+ CD57-) were significantly reduced one year after bariatric surgery. Similarly, there was a significant decrease in the CM cell subpopulations (CM+ PD1+ / CM+ PD1+ KLRG1-/ CM+ PD1+ KLRG1-CD27+ / CM+ PD1+ KLRG1-CD27+ CD28+ / CM+ PD1+ KLRG1-CD27+ CD28+ CD57-) following the surgery. Additionally, a notable reduction in the subpopulation expressing the PD1+ marker in the EM cells was observed (Figure 4.5). We investigated CD8-subset, but we did not find any significant results. as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red. .

Discussion

In our study, we demonstrated that obesity and type II diabetes have a significant impact on the phenotype of circulating T cells. Previous studies conducted by [Shimada, 2009;Shirakawa, 2016] have shown in mouse models that senescence is associated with the expression of PD1 in CD4 T cells, and a high-fat diet accelerates the local accumulation of senescence-associated T cells. In humans, obesity and diabetes appear to have an impact on the CD4 T cell population, potentially through metabolic changes. These conditions are associated with an increased frequency of PD1 expression in the immune cell population, which can lead to alterations in their activation capacity against pathogens. A study conducted by [Papathanassoglou, 2006] indicates that leptin production is known to enhance cytokine production by CD4 T cells, thereby triggering inflammation. Furthermore, two studies by [Genser, 2018;Chakaroun, 2020] demonstrate that individuals who are obese or obese-diabetic tend to exhibit a condition known as leaky gut, which leads to an increase in the presence of opportunistic bacteria that can travel into the bloodstream. In response to this, adipose tissue produces higher levels of leptin, which in turn leads to an increase in IL-6 production. The elevated IL-6 levels contribute to the chronicization of leaky gut and inflammation. This creates a vicious cycle, where increased leptin production further exacerbates the condition. Thus, the expression of the inhibitory marker PD1 on CD4 T cells may be a protective mechanism to limit intrinsic activation induced by chronic low-grade inflammation in obesity and type2 diabetes. We were also interested in the predicted age of patients, and although the majority of obese or obese diabetic patients are predicted to be older than their actual age, we are talking here about immunological age specific to the selected markers and their alterations in the non-obese non-type2 diabetes reference population.

Conclusion

Our study makes use of artificial neural networks (ANN) to demonstrate that obese and obese-diabetic patients are consistently predicted to have an older age in the beginning of the study based on immunological data compared to their real age. This finding can be explained through various factors, the first being that obese and obese-diabetic patients 6. Conclusion exhibit a significantly higher number of senescent cells compared to non-obese individuals.

Additionally, we highlight the fact that obese and diabetic patients have a greater proportion of cells expressing markers associated with senescence when compared to healthy patients. Moreover, we examined the predictive age of obese and obese-diabetic patients 12 months after undergoing bariatric surgery. We observed that the surgery appears to influence CD4 cell subpopulations by reducing the number of cells expressing specific markers of senescence. However, we did not find any statistically significant that highlight the impact of the surgery on CD8 cells. In summary, our research successfully demonstrates that obesity and diabetic status affect specific immune subpopulations however, the underlying molecular and cellular mechanisms responsible for this phenomenon require further exploration. Thus, this study validates the hypothesis of immunosenescence occurring in obese and obese-diabetic patients and highlights some unexplored phenotypes of immune cells.

General Conclusion

Obesity and type II diabetes are intricate and multifactorial conditions. Consequently, each individual experiences a distinct form of obesity. Nonetheless, obesity has similar physiological effects on all patients, varying in intensity depending on the severity of the disease. Currently, high-throughput techniques enable the identification of these similarities by gathering data from patients and their microbiota. Simultaneously, the integration of bioclinical data and nutritional surveys can establish potential links between lifestyle choices and diseases severity. The development of data analysis pipelines to study the diversity of patients' phenotypes is urgently needed.

This sets the foundation for my thesis, which seeks to introduce an algorithmic approach for the stratification of patients. The primary objective is to classify them into distinct and cohesive subgroups, based on their biological characteristics in relation to the severity of the disease. Consequently, even within a clinically homogeneous population (i.e., individuals sharing the same disease diagnosis), it becomes feasible to discern diverse groups or subgroups that accurately reflect the varying degrees of disease severity. The novelty of my thesis lies in its innovative fusion and application of different algorithmic methods utilized in computer data-sciences, to real-world biological data, all achieved without relying on benchmarking.

First, I developed an approach to classify cells and patients, with the objective of identifying distinct cells associated with different patients phenotypes. My second contribution relies on artificial neural networks to quantify immunosenescence, with the goal of detecting a change in age prediction among obese and obese-diabetic patients compared to non-obese patients of similar age.

Chapter 2 describes our approach titled LDA-DC to perform the double clustering task to flow cytometry data and setting the number of dimensions to identify different potential cell clusters. Although the number of established clusters is greater than the real number of cell types, this still allows for the identification of a large number of genuine cell phenotypes, as the first clusters group together a maximum number of cells. We then apply a Bayesian approach, specifically Latent Dirichlet Allocation, to these cluster-labeled cells.

Using this method offers several advantages.

Our novel approach enables the identification of topics related to both patient phenotype and cell type, facilitating the connection between patient phenotypes (the disease) and the cell types that contribute to these outcomes. Secondly, the LDA is a soft clustering method, meaning that each cell phenotype has a probability of being associated with each cluster (and the same applies to patients). Therefore, a cell type (or a patient) can belong to different topics with some estimated probability. Moreover, the probabilistic assignment of belonging to one of the topics reveals the substructures among the various clusters and any potential overlap between them.

An important aspect to highlight is that the initial clustering step is based on K-means.

We experimented with various probabilistic approaches, such as the Expectation-Maximisation (EM) algorithm, but the results were not convincing. In practice, the task of clustering cells using FACS data is typically performed manually by an experimentalist through a gating strategy. These gates can vary and depend on both the specific markers used and the user. Furthermore, there is no algorithmic procedure that can fully replace the gating strategy. As a preliminary study, we attempted to develop an artificial neural network to learn the different gates for cell classification using FACS data for which we had access to the associated gating information in our laboratory. However, our neural network turned out to be specific to the marker combinations and learned the human expert's biases, thus limiting its generalizability to other types of data (markers). Unfortunately, in public databases, FACS data is often provided without the accompanying gating strategy, which hinders the identification and development of effective methods for cell clustering.

To unveil the connections between topics, we opted to perform multiple runs of LDA and General Conclusion count the frequency of each patient being assigned to the same cluster. This approach allows us to circumvent LDA topics and identify patients with similar structures. Consequently, we generate an adjacency matrix that highlights the presence of similar patients, and through a networking approach, we can construct a network of patients. This patient network captures the underlying data structure and organizes patients spatially based on their similarities. By exploring this patient network and investing it with various clinical or biological variables, we can discern patterns and characteristics shared by similar patients and stratify them.

Indeed, in Chapter 3, we approach the MetaCardis cohort data from this perspective, using data obtained from metagenomics. Since the GENUS and genes-count datas are derived from metagenomic sources, the initial LDA-DC clustering step is not necessary.

Consequently, after applying the framework globally, we can generate both a patient network and a network highlighting bacteria or genes associated with stratification. It is worth noting that, without any prior assumptions about the data, it becomes possible to identify distinct clusters of patients by clustering the matrix that incorporates information on patient connections. These clusters appear to be enriched with patients who share a common enterotype, although not exclusively. In other words, even if patients do not exhibit the same enterotypes, they can still be grouped together in the same cluster if they share similarities in their microbiota data. Therefore, when we intersect these newly identified clusters with clinical and biological data, including nutrition data and patient nutrition scores, we can determine the key variables that contribute to these clusters. In fact, we identified multiple variables specific to these clusters, which exhibit significant differences compared to other groups. Consequently, we can stratify patients in subgroups of patients that share similarity in microbiome community and in life-style (such as nutritional and biological data) and propose a more detailed distinction that goes beyond the enterotype strategy. Furthermore, we successfully constructed a network of bacteria and metagenomic data associated with this stratification. Further analysis needs to be performed by biologists and physicians to assess the relevance of this new associations.

In Chapter 4, we employed a different approach for patient stratification. Using FACS General Conclusion data, we employed an artificial neural network to learn the distinct immune cell types identified through the gating strategy, with the objective of predicting patient age. The primary hypothesis was that obese and obese-diabetic patients exhibit greater immunosenescence compared to non-obese patients of the same age, and therefore, their predicted age would not surpass their actual age. To achieve this, we trained the neural network on various immune-cell markers combinations of non-obese patients and makes use of it to predict the age of obese and diabetic patients. We observed that, on average, these patients were consistently predicted to be older than their actual age. However, it is intriguing to note that some patients were predicted to be younger than their actual age, which might be attributed to significant differences in their immune phenotype compared to other patients. In parallel, we have developed a tree-based approach to visualize the effects of obesity or diabetic status on immune cell phenotypes. By setting the primary node as either CD4 or CD8, we can observe substantial variations in the number of cells expressing different markers. Through this analysis, we have demonstrated that specific CD4 and CD8 lymphocyte phenotypes are influenced by obesity and diabetes, though the underlying mechanisms remain to be fully understood. The computational approach we propose has allowed us to identify the groups of affected cells, thereby generating hypotheses that can be further investigated in the NutriOmics team.

Thus, this thesis explored various approaches for patient stratification using heterogeneous types of data. However, there are several future perspectives that could be pursued:

First, there is wide range for improvement in the LDA-DC method to find alternative ways to cluster cells without relying on the gating strategy. Eliminating the need for gating would enhance the ability to cluster cells more effectively. Additionally, the initial step of double clustering can become computationally expensive when dealing with larger datasets such as scRNA-seq data. It would be beneficial to develop a computationally efficient and stable approach that can handle larger datasets within a reasonable timeframe.

Secondly, developing a prediction solution is another potential venue. Currently, when new individuals are added to the dataset, the entire analysis needs to be rerun. Predicting patient outcomes and assigning them to specific topics or clusters (as in the case of

General Conclusion

MetaCardis) could offer a practical solution for precision medicine. This approach would allow for individual patient predictions without requiring a complete model retraining every time new data is added.

Last but not least, we are also exploring an inverted model in which we aim to predict the microbial cluster of a new patient based on their clinical, biological, or nutritional data. In other words, even in the absence of patient-specific metagenomic data, we can identify the cluster to which the patient belongs and potentially simulate their microbiota data. Furthermore, we can test various nutritional interventions that have the potential to modulate the composition of the microbiota using an "in-silico approach." This approach provides a means to manipulate the gut microbiota and, consequently, impact the clinical outcomes. Through these simulations, we can further refine our understanding of how different interventions may influence patient outcomes and contribute to the development of more effective and precise medical approaches.

In conclusion, this thesis explores diverse approaches for the analysis of extensive biological data. We showcase the adaptability of methodologies from different computer science disciplines such as natural language processing that are adapted to biological data, where patients are considered as documents and cells-types as words, and are efficient for this real world data. By applying these methods, we reveal that they yield more insightful information than a simplistic binary classification of patients as either sick or not sick, especially when dealing with complex diseases. Specifically, we present a patient network that clinicians can use to stratify and identify patients effectively. Additionally, we have developed a neural network that allows for drawing biological conclusions regarding the metabolic age of patients, an outcome unattainable through conventional data analysis techniques.

Furthermore, this project encompasses multiple disciplines such as computer science, mathematics, biology, and medicine with the primary objective was to develop a computationally robust solution for patient stratification while at the same time making biological and medical sense.

Therefore, this thesis aligns with the concept of "precision medicine" and makes a contribution to the advancement of this research field by implementing a variety of computational techniques for patient stratification, ultimately empowering healthcare professionals to provide improved patient care.

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.7 Multilayer Perceptron with one input layer, multiple hidden layers and one output layer with a single neuron. . . . . . . . . . . . . . . . . . . . . . . 1.8 Traditional approch to cluster cells coming from different individuals that share the same physiological status. . . . . . . . . . . . . . . . . . . . . . . viii List of figures 1.9 Illustration of the Double Clustering Approach. Diverse data matrices are obtained from individuals including lean, obese, and obese-diabetic individuals. The primary goal of this approach is to simultaneously cluster cells and patients, aiming to identify clusters or sub-clusters of cells that are closely associated with the patients' conditions. . . . . . . . . . . . . . 40 2.1 The proposed pipeline to perform the double clustering: from the observations (where one patient is represented by a matrix) to the conditional probability distributions of clusters given patients and cellular types given clusters. N is the number of fluorescent markers, K is the number of clusters, W is the number of words. . . . . . . . . . . . . . . . . . . . . . . 48 2.2 Mean accuracy for the simulated scenarios with 2 and 4 phenotypes. We vary the distance between the phenotype vectors, standard deviation (std), and the number of clusters (k), n cell = 10000. (A) Mean accuracy for 2 phenotypes, N = 2, W = 4. (B) Mean accuracy for 2 phenotypes, N = 4, W = 16. (C) Mean accuracy for 4 phenotypes, N = 2, W = 4. (D) Mean accuracy for 4 phenotypes, N = 4, W = 16. . . . . . . . . . . . . . . . . . 54 2.3 The accuracy of the double clustering method on the 8 tubes of the AML dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.4 A. Conditional probabilities of cell types given the topics. B. Cells projection (UMAP), the cells plotted are ones whose probability of assignment to the clusters is bigger than 90%; C. the cells are colored according to the topic (ill/healthy) ; D. the cells are colored according to the true label (phenotype). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.5 A. Networks of patients constructed from 40 LDA-DC runs from the genus data; B. Networks from the cytometry data; C. Network of patients based on the genus data, where the colour of the node represents patients enterotypes; D. Conditional probability distributions of bacteria given a cluster (here 2 clusters considered: CD and Healthy). . . . . . . . . . . . . . . 60 3.1 Workflow for Generating Patient and Bacterial Networks. The network generation process involves 20 runs of LDA-DC calculations using patient information such as GENUS or KEGG data. The results of patient and bacterial topic attribution are stored after each run, and subsequently used to count the number of time each patients and bacteria are assign to the same cluster topic. The resulting count matrix is then used for networking analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . of patients using GENUS data from the MetaCardis cohort. Patients are highlighted based on their country of recruitment. Danish patients are highlighted in blue, German yellow and French in red. The thickness is linked to the number of times each individual is associated with another one is the same topic B.Network of patients using GENUS data from MetaCardis cohort. Patients are highlighted based on their enterotypes. Bact2 enterotypes are highlighted in blue and are on the bottom right on the network, Prevotella enterotypes are highlighted in red and are mostly on the bottom left of the network. Ruminococcus individuals are on the top of the network and Bact1 individuals are in the middle. The thickness is linked to the number of times each individual is associated with another one is the same topic.C.Network of patients using GENUS data from MetaCardis cohort. Patients are highlighted based on their label attributed by the agglomerative clustering. The agglomerative clustering was performed on the count matrix. Individual allocated to the same topic multiple times are clustered together. Thus, we distinct 4 clusters of individuals. D. Cluster composition for different enterotypes and for all individuals. The count is normalized by the size of the cluster (i.e the number of individuals involved in the cluster). Cluster 0 is enriched with Bact1 individual enterotypes, while cluster 1 is enriched with Ruminococcus enterotype. Cluster 2 is enriched with Bact2 enterotypes and Cluster 3 is enriched with Prevotella enterotypes. Each of this cluster is defined by a mixture of different enterotypes with an enrichment with some specific individuals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3 Quantification for different clinical and biological data in relation to A.

Figure 1

 1 Figure 1.1: A schematic image of the conditions implicated in the pathophysiology of the metabolic syndrome and their potential interactions. IR: Insulin Resistance; HTN: Hypertension; HPA axis : Hypothalamic-Pituitary-Adrenal Axis; DMT2: Diabetes Mellitus type 2; CVD:Cardiovascular disease; CRH: Corticotropin Releasing Hormone; AVP: Arginine Vasopressin: from[Kassi, 2011]

  21% in the 10 years before 2016 and by 138% since 1975 and for overweight (including obesity), by 8% in the 10 years before 2016 and by 51% since 1975 [Europe, 2022] (Figure 1.2)

FigFigure 1 . 2 :

 12 Fig. 1.7

Figure 1 . 3 :

 13 Figure 1.3: Single-cell isolation and library preparation from[Hwang, 2018]). a) The limiting dilution method isolates individual cells, leveraging the statistical distribution of diluted cells. b) Micromanipulation involves collecting single cells using microscope-guided capillary pipettes. c) FACS isolates highly purified single cells by tagging cells with fluorescent marker proteins. d) Laser capture microdissection (LCM) utilizes a laser system aided by a computer system to isolate cells from solid samples. e) Microfluidic technology for single-cell isolation requires nanoliter-sized volumes. An example of in-house microdroplet-based microfluidics (e.g., Drop-Seq). f) The CellSearch system enumerates CTCs from patient blood samples by using a magnet conjugated with CTC binding antibodies. g) A schematic example of droplet-based library generation. Libraries for scRNA-seq are typically generated via cell lysis, reverse transcription into first-strand cDNA using uniquely barcoded beads, second-strand synthesis, and cDNA amplification

Figure 1 . 4 :

 14 Figure 1.4: Sequencing Methodology for NGS methodology such as Illumina sequencing, and Nanopore methodology. Modified figure from[Shendure, 2017]

Figure 1

 1 Figure 1.5: Analysis of scRNA-seq, after dimensionality reduction. Cell-to-cell distances can be computed to construct a distance-based graph. Unsupervised clustering algorithm are then performed to assign cells to clusters. Figure is partially extracted from[Kiselev, 2019]

  Chapter 1. General Introduction Moreover, while Random Forest has proven to be effective in handling certain types of data and tasks, neural networks, particularly deep learning models, have emerged as powerful alternatives with the ability to learn complex patterns and representations from large-scale datasets.Deep learning is a subpart of supervised machine learning methodology, based on the idea of training an artificial neural network for the task of learning different data representations. An artificial neural network (ANN) is mostly inspired by the biology of the brain, where multiple neurons are interconnected forming different layers enabling the transmission of information. Each connection between the artificial neurons mimics the brain-biology, where connections between neurons are able to transmit the information (called a synapse). In an ANN, neurons are called nodes and the overall structure of the network can have different architectures depending on the number of layers and neurons inside a network.

  Figure 1.6 illustrates the perceptron principle, where it receives a vector of input values, multiplied by a set of weights. All the weights are then summed and the value passes through an activation function before giving the output value.

Figure 1

 1 Figure1.6: The Perceptron model from Rosemblatt from the publication of[Kuipers, 2022]

Figure 1

 1 Figure 1.7: Multilayer Perceptron with one input layer, multiple hidden layers and one output layer with a single neuron.

4 )P

 4 (θ|y) is the posterior distribution. It represents the conditional probability where the probability of the model θ is conditional on the data y. P (y|θ) is the likelihood function, and P (θ) is the prior distribution, representing the probability of a certain model parameter.

Figure 1

 1 Figure 1.8: Traditional approch to cluster cells coming from different individuals that share the same physiological status.

Figure 1 .

 1 Figure 1.8 illustrates the traditional approach, where individuals with different genetic backgrounds are labeled as "healthy individuals" and can be analyzed. It is clear that certain cellular patterns are shared across individuals. Therefore, by aggregating the data from individuals, reducing dimensionality, and applying clustering methodologies, we can

Cluster 1

 1 Figure 1.9: Illustration of the Double Clustering Approach. Diverse data matrices are obtained from individuals including lean, obese, and obese-diabetic individuals. The primary goal of this approach is to simultaneously cluster cells and patients, aiming to identify clusters or subclusters of cells that are closely associated with the patients' conditions.

Chapter 2 Latent

 2 Dirichlet Allocation for Double Clustering (LDA-DC): Discovering patients phenotypes and cell populations within a single Bayesian framework

Chapter 2 .

 2 Latent Dirichlet Allocation for Double Clustering (LDA-DC): Discovering patients phenotypes and cell populations within a single Bayesian framework In this contribution, we propose the Latent Dirichlet Allocation for Double Clustering

Figure 2 . 1 :

 21 Figure 2.1: The proposed pipeline to perform the double clustering: from the observations (where one patient is represented by a matrix) to the conditional probability distributions of clusters given patients and cellular types given clusters. N is the number of fluorescent markers, K is the number of clusters, W is the number of words.

Algorithm 3 2 /

 32 Latent Dirichlet Allocation for Double Clustering Input: Data matrices (one per patient) N × p (N is the number of fluorescent markers and p is the number of cells), number of clusters K, number of words W , α, β Output: Clusters of cells w ∈ W, probabilities of words given topics, documents assignments to topics // Construction of words = Identification of cell types // Find the repartition of X into W clusters with centers µ: arg min W W i=1 w∈W i ∥w -µ i ∥ 2 / Latent Dirichlet Allocation on the newly constructed words ϕ k=1...K,w=1...W ∼ Dir W (β) // Probability of word w occurring in topic k θ d=1...D,k=1...K ∼ Dir K (α) // Probability of topic k occurring in document d Assume that w d=1...D,n=1...W ∼ Cat W (ϕ z dn ) // Identity of word n in document d Assign d ∈ D to clusters randomly // Initialisation for for t = 1, . . . , T do for all w ∈ W and all d ∈ D do

  assignments for all clusters except for the ith Draw z i according toP(z i = k|z -i , w i , d i ) Update C W K wj + = 1, C DK dk + =1 end for end for // Assign documents to topics = Cluster patients For all d ∈ D: z d = arg max θ d = arg max(P(z = k|d) : k = {1, . . . , K}) patients phenotypes and cell populations within a single Bayesian framework each document, but also the distribution of words associated with each topic. The word distribution is helpful to interpret the topics. The main goal of the LDA learning procedure is to estimate the model parameters θ (words distribution describing topics) and ϕ (topics distribution describing documents). The Latent Dirichlet Allocation framework is formalised as follows. The topics are distributed according to a Dirichlet distribution:

  our approach is the extension of the LDA to the double clustering framework. The complete learning procedure, called Latent Dirichlet Allocation for Double Clustering (LDA-DC) is drafted as Algorithm 3. The algorithm takes the patients data matrices, where the number of lines p is the number of cells, and N is the number of columns (fluorescence markers) (Figure2.1). Note that cells are different across patients, and a straightforward application of any state-of-the-art machine learning method such as Support Vector Machines or Random Forests, is not possible. The first step of the double clustering is the identification of the cell types. Using the (topic modeling) LDA terminology, the cell identification is the identification of words (note that in the standard LDA the words are well-defined and provided).

Figure 2 . 2 :

 22 Figure 2.2: Mean accuracy for the simulated scenarios with 2 and 4 phenotypes. We vary the distance between the phenotype vectors, standard deviation (std), and the number of clusters (k), n cell = 10000. (A) Mean accuracy for 2 phenotypes, N = 2, W = 4. (B) Mean accuracy for 2 phenotypes, N = 4, W = 16. (C) Mean accuracy for 4 phenotypes, N = 2, W = 4. (D) Mean accuracy for 4 phenotypes, N = 4, W = 16.

Figure 2 .

 2 Figure 2.2 illustrates the results on the synthetic dataset. The subplots A and B show our results for the case with 2 phenotypes, andC and D illustrate the setting with 4 phenotypes. The subplots A and C report the results for the problem with a lower dimension (4), and the subplots B and D show the accuracy for the case with more features (16). Thus, when two groups of patients (Figure 2.2 A and B) have the phenotype probability vectors that are difficult to distinguish (Euclidean distance is lower than 0.25 in the experiments), the accuracy is close to 50%, which is what is expected. If the number of dimensions increases (the size of vocabulary in the LDA increases), the accuracy does not seem to degrade (Figure 2.2 A and B). We obtain similar results for the setting with 4 phenotypes (Figure 2.2 C and D). If the clusters are hardly separable (generated with a Euclidean distance lower than 0.25), the accuracy is close to 30%. Increasing the dimensionality of the problem does not alter the performance significantly.

Figure 2 . 3 :

 23 Figure 2.3: The accuracy of the double clustering method on the 8 tubes of the AML dataset.

Figure 2 . 4 :

 24 Figure 2.4: A. Conditional probabilities of cell types given the topics. B. Cells projection (UMAP), the cells plotted are ones whose probability of assignment to the clusters is bigger than 90%; C. the cells are colored according to the topic (ill/healthy) ; D. the cells are colored according to the true label (phenotype).

Chapter 2 .

 2 Figure 2.4 illustrates our findings obtained with the LDA-DC. Panel A shows the topic density for each cell type. Although some cells are present in both, it is clear that some cell populations are associated with high probability, with the patient's phenotypes. Visualizing the cells with the Uniform Manifold Approximation and Projection for Dimension Reduction (UMAP) [McInnes, 2020] methods (panels B, C, D), we color-coded the cells according to: 1) appearance in a cell population (subplot B), 2) cells associated with disease/healthy estimated clusters (subplot C), and 3) cells colored according to the true clinical condition (panel D). In the last panel, we quantified the number of cells assigned

Figure 2 .

 2 Figure 2.5: A. Networks of patients constructed from 40 LDA-DC runs from the genus data; B. Networks from the cytometry data; C. Network of patients based on the genus data, where the colour of the node represents patients enterotypes; D. Conditional probability distributions of bacteria given a cluster (here 2 clusters considered: CD and Healthy).

Figure 2 .

 2 4, panel D: the identified cell populations are well distinguished according to the clinical condition (AML versus non-AML).

Figure 3 . 1 :

 31 Figure 3.1: Workflow for Generating Patient and Bacterial Networks.The network generation process involves 20 runs of LDA-DC calculations using patient information such as GENUS or KEGG data. The results of patient and bacterial topic attribution are stored after each run, and subsequently used to count the number of time each patients and bacteria are assign to the same cluster topic. The resulting count matrix is then used for networking analysis.

Figure 3 . 2 :

 32 Figure 3.2: A.Network of patients using GENUS data from the MetaCardis cohort. Patients are highlighted based on their country of recruitment. Danish patients are highlighted in blue, German yellow and French in red. The thickness is linked to the number of times each individual is associated with another one is the same topic B.Network of patients using GENUS data from MetaCardis cohort. Patients are highlighted based on their enterotypes. Bact2 enterotypes are highlighted in blue and are on the bottom right on the network, Prevotella enterotypes are highlighted in red and are mostly on the bottom left of the network. Ruminococcus individuals are on the top of the network and Bact1 individuals are in the middle. The thickness is linked to the number of times each individual is associated with another one is the same topic.C.Network of patients using GENUS data from MetaCardis cohort. Patients are highlighted based on their label attributed by the agglomerative clustering. The agglomerative clustering was performed on the count matrix. Individual allocated to the same topic multiple times are clustered together. Thus, we distinct 4 clusters of individuals. D. Cluster composition for different enterotypes and for all individuals. The count is normalized by the size of the cluster (i.e the number of individuals involved in the cluster). Cluster 0 is enriched with Bact1 individual enterotypes, while cluster 1 is enriched with Ruminococcus enterotype. Cluster 2 is enriched with Bact2 enterotypes and Cluster 3 is enriched with Prevotella enterotypes. Each of this cluster is defined by a mixture of different enterotypes with an enrichment with some specific individuals.

  depicted on Figure3.2 C. Upon scrutinizing the enterotype enrichment of patients within each cluster, we discovered that patients with Bacteroide 1 enterotype were more prevalent in cluster 0. Conversely, cluster 1 displayed a significant enrichment of patients with Ruminococcus enterotype, while cluster 2 was enriched with individuals having Bacteroides 2 enterotype and cluster 3 with Prevotella enterotype, as illustrated in the cluster composition (Figure3.2 D). Each cluster can be defined as a unique new categorization, comprising of several individuals with varying enterotypes in proportion.

Figure 3 . 3 :

 33 Figure 3.3: Quantification for different clinical and biological data in relation to A. obesity status.Adiponectine OGTT is the quantification of the adiponectin (mg/l), Leptine OGTT is the quantification of the leptin (ng/l), BMI is the body mass index (kg/m2) B. diabetes severity. GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTGLYC is the measurement of the fasting glycemia (plasmatic glucose) in mmol/l, FASTLIPTG is the measurement of triglycerides in mmol/l and Peptide C is the quantification of peptide c reactive in the blood while fasting (µg/l) C. immune status for each patient cluster, WBNEUTRO is the number of neutrophils, WBCLEUCO is the total number of leucocytes, WBMONOCY is the total number of monocytes, and WBLYMPHO is the total of lymphocytes. Variables are selected according to their relevance and significance.

Figure 3

 3 Figure 3.5: A.B. Network of patients using GENUS data from MetaCardis cohort using only 2a and 2b data. Patients are highlighted based on their label attributed by the agglomerative clustering. 3 distinct clusters were identified with different individuals inside each of them. Quantification for different. C. Cluster composition for different enterotypes and for 2a and 2b individuals.The count is normalized by the size of the cluster (i.e the number of individuals involved in the cluster). Cluster 0 is enriched with Bact1 individual enterotypes, while cluster 1 is enriched with Prevotella enterotype. Cluster 2 is enriched with Bact2 enterotypes. Each of this cluster is defined by a mixture of different enterotypes with an enrichment with some specific individuals.D. Biological and clinical data such as IMPROP (imidazole propionate in nM), GLYCATHB is the glycated hemoglobin quantified in % (also named HbA1C), FASTLIPTG is the measurement of triglycerides in mmol/l, Leptine OGTT is the quantification of the leptin (ng/l). E. nutritional variables, Nutr fiber is the global fiber intake in log(g), food bread is the daily bread consumption in log(g), food vegetables is the daily consumption of vegetables in log(g) and F. Nutritional score, with aHEI score (ranges from 0 to 70). aHEI vegetables related to intakes of vegetables (ranges from 0 to 10).

Figure 3 .

 3 Figure 3.6: Bacterial network associated with GENUS stratification established for all patients.Three groups of bacteria can be identified, that may contribute to the stratification process. However, we are currently unable to link the functionality of certain bacteria to the underlying phenotypes due to incomplete information provided by various databases.

Figure 3 . 7 :

 37 Figure 3.7: Network of patients using KEGG data from MetaCardis cohort. Patients are highlighted based on their identified enterotype

Figure 3 .

 3 Figure 3.8: Network of patients using KEGG data from MetaCardis cohort. Patients are highlighted based on their label attributed by the agglomerative clustering

Figure 3 .

 3 Figure 3.10: Quantification for different clinical and biological data in relation to A. obesity status B. diabetes severity C. immune status for each patient cluster, using KO data.

Figure 3 .

 3 Figure 3.11: Quantification for different A. nutritional variables and B. nutritional score.

Figure 4 . 2 :

 42 Figure 4.2: Tree visualization depicting the average expression levels of various markers by CD4 cells in obese individuals before and 12 months after a bariatric surgery. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red (p-value < 0.05)

Figure 4 . 3 :

 43 Figure 4.3: Tree visualization depicting the average expression levels of various markers by CD4 cells in non-obese, obese, and obese-diabetic patients. The tree primarily centers around CD4 as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red.

Figure 4 . 4 :

 44 Figure 4.4: Tree visualization depicting the average expression levels of various markers by CD8 cells in non-obese, obese, and obese-diabetic patients. The tree primarily centers around CD8 as the main node and incorporates markers specific to Naive, CM, EM, and TEMRA cells. Each leaf in the tree represents a sub-marker that indicates whether it is expressed or not by the corresponding cell type. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red.

Figure 4 . 5 :

 45 Figure 4.5: Tree visualization depicting the average expression levels of various markers by CD4 cells in obese individuals before and 12 months after a bariatric surgery. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red (p-value < 0.05)

  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Overweight and obesity trajectory according to WHO from 1975 to 2016

from [Europe, 2022] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Single-cell isolation and library preparation from

  The count is normalized by the total number of individuals for each cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . 84 3.10 Quantification for different clinical and biological data in relation to A. nutritional score. 3.12 Network of KO, clustered using Agglomerative clustering. KO are highlighted according to there cluster attribution . . . . . . . . . . . . . . . . 3.13 Subcluster of KO matched to genes and the result of Gene Ontology (GO) applied on the genes identified. The GO was performed using Escherichia coli K-12 substrain as reference. . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Results of the ANN for age prediction using cytometry data A. Age prediction using CD4 subsets B. Ratio of age-predicted under real age using CD4 subsets. Individuals predicted older have a ratio greater than 1 C. Age prediction using CD8 subsets D. ratio of age-predicted under real age using CD8 subsets cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Tree visualization depicting the average expression levels of various markers by CD4 cells in obese individuals before and 12 months after a bariatric surgery. Submarkers present in less than 2% of cases are excluded from the visualization. Significant differences between patient groups for a marker are highlighted in red (p-value < 0.05) . . . . . . . . . . . . . . . . . . . . 4.3 Tree visualization depicting the average expression levels of various mark-

obesity status B. diabetes severity C. immune status for each patient cluster, using KO data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 xi List of figures 3.11 Quantification for different A. nutritional variables and B.

  Workflow to match and convert KEGG orthology ID to GENE ID in order to perform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Metacardis table of Clinical data available. . . . . . . . . . . . . . . . . . . 67 3.2 Metacardis table explaining the different groups and their different charac-

	List of figures
	xii 6.10 xiii List of Tables 3.1

. Each sub-network display patients based on there Enterotypes. . . . . . . . . . . teristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 xiv Chapter 1

1

  Biological Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Metabolic Disorders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Gut microbiota . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Development of high throughput technologies . . . . . . . . . . . . . . . . . . . . . . 2.1 Flow cytometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 From RNA-seq to Single Cell RNA-sequencing (scRNA-seq) . . . . . . . . . . 2.3 Sequencing methodologies for Metagenomics . . . . . . . . . . . . . . . . . . . 3 An analytic procedure to process big data-sets . . . . . . . . . . . . . . . . . . . . . 3.1 Dimensionality reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Machine learning approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Unsupervised methodology . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Supervised methodology . . . . . . . . . . . . . . . . . . . . . . . .

	1 Biological Context
	1.1 Metabolic Disorders
	Metabolic disorders are composed of different medical conditions occurring when metabolic
	processes are disrupted in the body, that could lead to a wide range of symptoms and
	complications. Metabolic disorders affect different metabolic pathways such as energy
	metabolism, carbohydrate, lipid metabolism, and raise the risk of coronary heart disease,
	diabetes or strokes. According to the National Institutes of Health (NIH), metabolic syn-
	drome is common in the United States with about one third of the adults and it is largely
	preventable. Moreover,

3.3 Soft, hard and bi-clustering methods . . . . . . . . . . . . . . . . . . . . . . . 3.4 Preventing overfitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Patient Stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Statistical inference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Thesis Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

  Our work is published in BMC Bioinformatics. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Latent Dirichlet Allocation for Double Clustering . . . . . . . . . . . . . . . . 3.2 Simulated data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Real Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 The Double Clustering Workflow . . . . . . . . . . . . . . . . . . . . . . . . . 4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Validation of the proposed method on simulated data . . . . . . . . . . . . . . 4.2 Real High-Dimensional Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Acute Myeloid Leukemia: AML Dataset . . . . . . . . . . . . . . . . 4.2.2 Cytometry and genus Data: Crohn Disease Prediction . . . . . . . .

Objectives Contents 1 5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 2. Latent Dirichlet Allocation for Double Clustering (LDA-DC): Discovering patients phenotypes and cell populations within a single Bayesian framework 1 Abstract

Table 3 .

 3 2: Metacardis table explaining the different groups and their different characteristics

Training/validation and testing procedure: First

  Using the binary annotation, we computed a Bit-Binary Annotation. We defined a list of markers whose order is fixed and maintained throughout the study. The first marker is considered a high-weighted bit, and the last marker is considered a low-weighted bit. Since we had binary values and a set of 7 markers, the total number of combinations is 128. Based on this, we identified 128 pseudo-phenotypes of CD4 and CD8 cells. We then phenotyped each cell for each patient and calculated the total number of positive cells for each phenotype, which we divided by the total number of cells. This allowed us to quantify the average number of cells per patient for each of the 128 phenotypes for CD4 and CD8 subsets. The output of this transformation was two matrices (one for CD4 and another for CD8) with 114 rows (representing the total number of patients) and 128 columns representing the average number of cells for each of the 128 phenotypes (114 patients x 128 sub-phenotypes). , we divided non-obese patients into k well-balanced age classes, and created a weighting criterion assigning a weight to each patient according to the number of patients in a the same class of age. Thus, higher is the number of patients in a class of age, stronger is the impact of the weighting and vice versa. The loss fuction is described as: Loss = W (y pred )(|y real -y pred |) 2 + λ Metabolic age prediction using Artificial Neural Networks is the predicted values, λ is the regularisation parameter, p is a parameter and P is the ensemble of parameters. Then, we launched our learning runs on transformed and normalized data of non-obese patients with the aim of predicting patient age. Due to the low number of non-obese patients, we decided to use the same set for both training and validation. Once the training was completed, we applied our previously trained ANN to data from obese and obese-diabetic patients, considered as the testing set, in order to obtain predicted age values. These predicted values were then statistically compared (see Statistics section) with the actual age values of the patients, and we calculated the ratio of predicted age to real age. We repeated this procedure of training/validation and testing 10,000 times and investigated the number of times obese and obese-diabetic pa-

	3. Data of CARMMA project and artificial neural network
	Bit-Binary matrix: Artificial p∈P	|w p |	(4.1)
	102

neural network (ANN) architecture: Our ANN model is designed to take as input the bit-binary matrix from the CD4 or CD8 subset. The first layer of our model is a linear transformation with 128 phenotypes as input and a projection onto 824 neurons for CD4 and 512 for CD8. A linear regression is then applied to these neurons, and the result of this transformation is projected onto a single output. To prevent overfitting during the training process, we applied dropout between the first and second layers. We used the sigmoid activation function on the output neuron.

where W (y pred ) is the weighted vector according to age, y real is the observed values, y pred 103 Chapter 4.

Je ne peux finir ces remerciements de thèse sans remercier ma famille. A ma mère Samia EH. et mon père Joseph EH., merci pour vos encouragements et pour m'avoir toujours poussé à donner le meilleur de moi-même. Ce travail de thèse je vous le dédie, à vous qui avez tant sacrifié pour nous voir arrivés là où nous en sommes Sami et moi. Au meilleur frère et modèle Sami EH., merci pour ton écoute, tes conseils, ta patience et présence durant cette longue quête que fut la thèse. Enfin, je tiens à remercier toute ma famille du Liban à la Tunisie, en passant par la France, la Belgique, l'Australie, le Koweït, Dubaï, l'Arabie-Saoudite et le Canada, pour leur encouragement malgré la distance qui nous sépare.En fin de compte, durant ces 3 dernières années, c'est grâce à vous, mentors, collègues, amis, et famille que j'ai pu grandir en tant que chercheur, mais également en tant qu'être humain.

Figure 3.12: Network of KO, clustered using Agglomerative clustering. KO are highlighted according to there cluster attribution

Acknowledgment

Data availability. To ensure the utmost precision and accuracy of our findings, we carefully selected data derived from Metagenomic analysis, utilizing GENUS data. Specifically, our GENUS data include information from 1982 unique individuals, with 2214 clin-

Results

KEGG to Gene and pathways investigation

To discover a KO that could account for the prediction, we opted to cluster the data. By following the pre-established methodology, we constructed a KO network and observed that the KO were distributed among 3 to 4 clusters. We then proceeded to investigate each cluster individually and employed Agglomerative clustering on the data (Figure 3.12) resulting in the identification of 4 distinct clusters.

We start with a pre-processing step where we eliminate all KO that do not have any connection with microbial function. Then, for each KO in every cluster, we search for gene-related information in the KEGG database. This allows us to identify genes that are linked with the KO. Once we have a list of genes for each cluster, we conduct Gene Ontology enrichment (GO) analysis using Escherichia coli K-12 substrain as a reference.

By doing so, we are able to decipher pathways associated with the genes present in each cluster (refer to Supplementary Figure 6.10).

We observed that genes in cluster 0 are significantly enriched with xenobiotic transmembrane transporter activity and antiporter activity (total of 4 genes). In cluster 1, we found genes that are involved in the purine ribonucleoside triphosphate binding pathway, ATP binding, and adenyl ribonucleotide binding. Overall, the pathways that are representative of these clusters are those associated with ATP activity. cluster 2 also has genes that are associated with ATP pathways, but some of the genes are involved in hydrolyzing glycosyl compounds and/or nucleic activities. On the other hand, cluster 3 has a slight enrichment of genes that are involved in calcium activity, hydrolyzing glycosyl compounds, helicase activity, and ATP-dependent activities (Figure 3.13). obese diabetic patients are also systematically predicted older than their real age. One of the major hypothesis is that obesity and type II diabetes impact some immune cell phenotypes and thus lead to immunosenescence (Figure 4.1).

We then decided to apply our neural network to analyze the data of patients who underwent bariatric surgery and returned for follow-up at 12 months. Similar to the procedure at T0, we used the same network to predict their metabolic age. Interestingly, we observed that some patients had a lower predicted age compared to their predicted age at T0 when the analysis was performed on CD4 in obese patients (but nothing statistically consistent). However, for obese-diabetic patients, the predicted age at 12 months showed a slight increase, although this trend was not statistically significant (Figure 4.2)

Furthermore, when examining CD8, we noticed a slight increase in the predicted age at 12 Appendices Supplementary Figure 6.6: Sub-Network of patients using GENUS data from MetaCardis cohort. Each sub-network display patients based on there country of recruitment only.

Appendices

Supplementary Figure 6.7: Sub-Network of patients using GENUS data from MetaCardis cohort. Each sub-network display patients based on there Enterotypes.

Appendices

Supplementary Figure 6.8: Sub-Network of patients using KEGG data from MetaCardis cohort. Each sub-network display patients based on there country of recruitment only.

Supplementary Figure 6.9: Sub-Network of patients using KEGG data from MetaCardis cohort. Each sub-network display patients based on there Enterotypes.

MOTS CLÉS

Machine learning, Méthodes statistiques, Médecine de précision, Microbiote RÉSUMÉ La prévalence de l'obésité et du diabète de type II a fortement augmenté ces dernières années, faisant de la recherche dans ces domaines une priorité de santé publique. Parallèlement à cela, le développement des technologies à haut débit ont permis d'obtenir un grand nombre de données hétérogènes provenant des patients et de leur microbiote intestinal.

Ces données de grandes dimensions ont une structure qui est propre à chacun d'eux. Ainsi dans le but d'identifier différents schémas entre les patients et pouvoir les stratifier (c'est-à-dire les classifier en différents sous-groupes homogènes en fonction de leurs caractéristiques biologiques), il est nécessaire de développer de nouvelles méthodes computationnelles. Cette thèse présente le concept de « Double Clustering », qui implique la tâche de regrouper simultanément les types de cellules et les patients. Pour cela, nous proposons une nouvelle approche algorithmique appelée LDA-DC (Latent Dirichlet Allocation for Double Clustering) dont le but est d'identifier les groupes de cellules associés aux phénotypes des patients, facilitant ainsi une stratification efficace de ceux-ci. Nous démontrons l'efficacité de notre méthodologie en utilisant des données de patients disponibles publiquement. De plus, nous appliquons notre approche aux données métagénomiques des patients du laboratoire NutriOmics et stratifions les patients sous forme de réseau révélant des groupes de patients ayant des caractéristiques cliniques, biologiques et nutritionnelles communes. D'autre part, nous avons développé une méthodologie basée sur un réseau de neurones artificiel dans le but de prédire l'âge métabolique des patients atteints d'obésité et/ou de diabète de type II en comparaison des patients non-obèses, permettant une stratification des patients. Ainsi, cette thèse s'aligne avec les principes de la médecine de précision et de la médecine prédictive en proposant une approche computationnelle permettant la stratification des patients et l'identification de variables pouvant être modulées dans le cadre d'une stratégie de médecine préventive.

ABSTRACT

The prevalence of obesity and type II diabetes has experienced a significant surge in recent times, underscoring the urgent need for public health research in this domain. Concurrently, the advent of high-throughput technologies has enabled the collection of extensive and diverse data from patients as well as the intestinal microbiota. This high-dimensional data has a structure that is unique to each patient. So, in order to identify different patterns between patients and to be able to stratify (i.e. classify them into different homogeneous subgroups based on their biological characteristics) them, it is necessary to develop new computational methods. This thesis presents the concept of Double Clustering, which involves the task of simultaneously grouping cell types and patients. To address this challenge, we propose a novel algorithmic approach called LDA-DC (Latent Dirichlet Allocation for Double Clustering). This method aims to identify clusters of cells associated with patient phenotypes, facilitating effective patient stratification. Through the utilization of publicly available patient data, we demonstrate the efficacy of our methodology. Furthermore, we apply our approach on metagenomic data from patients of the NutriOmics laboratory and clustered them into a network structure that reveals groups of patients with shared clinical, biological, and nutritional characteristics. Additionally, we have developed an artificial neural network-based methodology to predict the metabolic age of patients suffering from obesity and/or diabetes, allowing for a comparison with non-obese patients and enabling further patient stratification. This thesis is therefore in line with the concept of precision and predictive medicine, proposing a computational framework for stratifying patients and identifying different variables that can be modulated as part of preventive health strategies.

KEYWORDS

Machine learning, Statistical methodologies, Precision medicine, Microbiota