Suite `a ces travaux, plusieurs perspectives peuvent ˆetre envisag´ees. Tout d’abord, nous avons pr´esent´e dans le Chapitre 9 une perspective de travail sur laquelle des travaux sont d´ej`a en cours. En effet, nous y avons propos´e une m´ethode permettant de s´electionner les cibles optimales sur lesquelles notre mod´elisation math´ematique pr´edit un impact maximal “dans le sens de la gu´erison”. Cette derni`ere notion est bas´ee sur l’expression des g`enes qui s’expriment aux temps tardifs ; notre but est alors de cibler des g`enes aux temps pr´ecoces dont l’inhibition entraˆınera l’inhibition de g`enes aux temps tardifs diff´erentiellement exprim´es chez les patients canc´ereux et non diff´erentiellement exprim´es chez les sujets sains. Pour trouver ces cibles optimales nous avons essay´e de proposer la m´ethode la plus robuste possible. En particulier, nous avons tenu compte des points suivants :
— utilisation de trois m´ethodes de normalisation des micropuces, — utilisation de deux m´ethodes de s´election de variables robustes (dont
celle pr´esent´ee au Chapitre 8),
— ´evolutions m´ethodologiques du mod`ele d’inf´erence de r´eseau (voir Chapitre 9).
Mais d’autres perspectives sont envisageables suite `a ce travail. En particulier, l’id´ee de planification d’exp´erience semble ˆetre une perspective naturelle, et notre m´ethode permet de choisir un compromis entre mod`ele vide et pr´ecision. Il devient alors possible de se fixer un niveau de pr´ecision,
10.3. CONCLUSION 157
et de faire des exp´eriences d’interventions successives pour r´eduire le nombre de mod`eles vides (dans ce cas il s’agirait de g`enes sans r´egulateurs) tout en gardant le mˆeme niveau de pr´ecision. De ce point de vue, il serait int´eressant de comparer notre approche avec celle d´evelopp´ee dans Rau et al. (2010) o`u la m´ethode ABC permet ´egalement de connaˆıtre les sous-r´eseaux du r´eseau total inf´er´e avec peu de certitude.
Une autre perspective int´eressante serait de d´evelopper le travail qui a ´et´e soumis lors des journ´ees SFdS (voir Annexe F). Si nous posons l’hypo-th`ese que les diff´erents r´eseaux (sains et tumoraux) partagent une partie de leur topologie, il devient possible d’utiliser cette information commune pour am´eliorer l’inf´erence. En particulier, cela nous permettrait ´egalement de d´eterminer de fa¸con fiable le “cœur” du r´eseau commun `a tous les ´etats des patients et des sujets sains.
10.3 Conclusion
Il est temps de mettre un point final au manuscrit de cette th`ese. Il y a eu dans cette th`ese plusieurs d´efis que j’ai du relever.
De formation purement math´ematicienne, j’ai du me plonger dans l’univers de la biologie. Tout le but de ma d´emarche a ´et´e d’apporter aux biologistes les meilleures mod´elisations utilisant les meilleurs outils statis-tiques possibles. Pour r´eussir `a faire cela, j’ai ´et´e contraint de saisir toutes les subtilit´es du syst`eme complexe que nous avons ´etudi´e. Il serait faux de dire que cet apprentissage a ´et´e facile, d’autant plus que le dialogue avec les biologistes est un exercice d´elicat. De la biologie aux math´ematiques, les raisonnements ne sont pas toujours les mˆemes, et les mots peuvent revˆetir des significations ´equivoques.
Mais au final, ces difficult´es furent surmont´ees, laissant ainsi la place `
a une collaboration heureuse. En effet, outre les articles d´ej`a publi´es et pr´esent´es dans cette th`ese, l’article en cours de publication qui fait l’objet du Chapitre 8, se dresse la perspective que nous avons ´evoqu´e dans le Chapitre 9. De plus, du fait d’appartenir `a une ´equipe de biologie, j’ai pu participer `a plusieurs projets d’importance qui n’ont ´et´e ´evoqu´es que rapidement dans la pr´eface de ce manuscrit, mais qui devraient conduire tr`es prochainement `a des publications.
Quatri`eme partie
Annexes
A
Supporting information for
Chapter 3
Method Possible Designed
for
Short description
prediction large
net-works TD-ARACNE
Zoppoli et al.
(2010)
No No Time delay regression
com-bined to ARACNE Margolin et al. (2006a) method.
ARACNE is an information theory model, based on mu-tual information.
GeneNet
Scha-fer et Strimmer (2005)
No Yes Graphical Gaussian Model
(GGM) using partial correla-tion.
GeneReg Huang
et al. (2010)
Yes No Regression with spline
inter-polation to increase the num-ber of time points.
Morrissey et al. Morrissey et al. (2011)
Yes No Dynamic Bayesian Network
(DBN).
Table A.1 – Short description of selected methods used for inference methods com-parisons.
Method User fixed parameter Note TD-ARACNE Zoppoli
et al. (2010)
The number N of bin in the discretization pro-cess
The best performing va-lue of N was retained af-ter sequential tests (N value varying from 6 to 20, by 0.5).
GeneNet Schafer et
Strimmer (2005)
None None
GeneReg Huang et al. (2010)
Number of interpolated time points
The ratio (number of in-terpolated time points) /
(number of initial time points) used by the au-thors has been conser-ved.
Morrissey et al. Morris-sey et al. (2011)
None None
Table A.2 – Settings of selected methods used for inference methods comparisons.
Supplemental Figure A.1 – Venn Diagram : distribution of the 960 probe sets bet-ween the 3 cell groups. A total of 960 probe sets was retained for all the subjects across the three different cell groups. A core of 183 probe sets is shared by the 3 groups.
163
T1 T2 T3 T4
Supplemental Figure A.2 – Each graphic represents genes in a specific categorical time label (1 to 4, from left to right) and their connections, showing how the signal is spreading through the aggressive network.
Supplemental Figure A.3 – DUSP1 is the targeted gene for the knock-down expe-riment. We show its expression before and after the inhibition expeexpe-riment.
Gene e xpression Observed measure t1 t2 t3 t4 = − +b Gene e xpression Comparison t1 t2 t3 t4 False Ok Ok d Gene e xpression
Wild type downstream gene
t1 t2 t3 t4 a Gene e xpression Predicted measure t1 t2 t3 t4 − − +c
Supplemental Figure A.4 – Principle of the validation experiment. Graphic (a) represents a gene expression before inhibition of a targeted gene. Graphic (b) shows how this gene expression evolves after silencing this targeted gene whereas graphic (c) shows the predicted gene expression. For these two last graphics, for time t2
to t4 we assigned a +,- or = label if gene expression after silencing is respectively greater, smaller, or equal to gene expression before silencing. For this gene, graphic (d) shows that we made two good predictions out of three in this example.
Our me-thod TD-ARACNE Zoppoli et al. (2010) GeneNet Schafer et Strimmer (2005) GeneReg Huang et al. (2010) Our method 1528 28 39 7 TD-ARACNE Zoppoli et al. (2010) 28 5236 87 66 GeneNet Scha-fer et Strimmer (2005) 39 87 2241 86 GeneReg Huang et al. (2010) 7 66 86 1567
Table A.3 – Supplemental Table 3. A comparison of our method with three other benchmark methods applied to the more aggressive CLL data set. Total number of inferred links for each selected method and intersection between the methods, in total common inferred links. The biological data set of patients with more aggressive CLL type is used.
Supplemental Figure A.5 – Schematic representation of specific constraints related to prediction abilities in model inference. This ability to predict the transcriptional effect of a modulation in the network is crucial in order to predict a gene expression level modification after a knock-down experiment. For instance, given a situation where a gene A regulates the expression of a gene B (with a time lag between activation of gene A and gene B as schematically shown in (a)), which in turn regulates gene C, we want to predict the absence of link between B and C if gene A is knocked-down. Importantly, this predictive capacity requires much more com-plexity than inference alone. More than inferring a network topology, a predictive method should be able to learn how the biological signal spreads in this network. To go further, the best algorithms for reverse-engineering are not necessarily the best methods for predicting purposes, as explained in (b) with two simple examples. In the first example, a real network is composed of a gene A that activates a gene B, which in turn activates gene C (upper-left quadrant). An inference method could infer a statistical link between A and C, leading to two false negative links (two existing links are not presents) and one false positive link (upper-right quadrant). However, to predict gene C’s expression, given the expression of gene A, this in-ference method will probably give adequate results. In the 2nd example (lower-right quadrant), a better inference method could give six true positive inferred links and only one false negative, omitting the link between A and B. However, in this case, we have a dramatic situation for prediction purpose as gene A cannot activate gene B anymore.
165
Supplemental Figure A.6 – Significance of selected patterns in the clustering step. To evaluate the relevance of our selected patterns used for enrichment, we compared these patterns with various temporal gene clusters obtained with a gold standard unsupervised clustering method. One of the most widely used clustering methods is fuzzy c-means . The preponderant aspect of this algorithm relies on the fuzzy parameter that allows taking into account the inherent noise of transcriptional data (when this parameter increases, more genes are randomly assigned into clusters). For comparison purposes, we focused on the biological data set of patients with more aggressive CLL type and we first select relevant genes with Limma , using a p-value of 0.01. An unsupervised temporal clustering of the 8,113 genes retained with Limma is then performed showing 16 distinct clusters. Importantly, these clusters emphasize the existence of genes with transient expressions (peaks) at t1 (cluster#1, 7, 9), at t2 (within cluster#2, 4), at t3 (cluster#2, 3, 4, 11, 13, 15) and t4 (cluster#5, 6, 8, 10, 12, 14, 16) ; as shown by our method. The fact that through this unsupervised clustering method we reach similar patterns that those produced by our method, confirms the pertinence of our own gene selection process.
B
Application 1 :
B.1 Introduction
In a cell, after a specific activation, a gene contained in the DNA can be expressed as RNA molecules that are later traduced in proteins that will sustain the cell response (Crick et al. (1970)). Cells are in continuous contact with their environment within the organism and display an adapted response to its modifications (Barab´asi et Oltvai (2004)). For this, each transient environmental modification activates cell’ surface receptors (and co-receptors) that induce multiple integrated signaling cascades whose ultimate events are expression of specific transcriptional factors (TF). These first TF induce the expression of other genes within the cell. Some of these genes code themselves for TF or transcriptional regulators (TR) that induce sequential activation of other genes. At the end, concerted expression of these multiple genes induces protein expressions that are the substratum of the adapted cellular reaction to the initial stimulus.
One Common tool to analyze such complex systems is regulatory networks (RN). When studying transcriptional data, this RN is called a gene regulatory network (GRN) in which the vertex represent genes and edges represent potential (orientated) interactions between these genes.
Since the emergence of high-throughput technologies that allow simul-taneously measuring mRNA expression of thousands of genes, many tools have been developed to analyze and reverse engineer their underlying GRN (Hecker et al. (2009), Bar-Joseph et al. (2012)). These methods should be splitted between static and time dependent methods. While the former relies on the assumption than co-expressed genes share some biological characte-ristics, the latter infers a directed network. In this last case, another impor-tant distinction should be made between temporal phenomenom induced by exogenous stimulus (e.g, stress response) or endogenous stimulus (e.g., cell cycle) (Zhu et al. (2007), Luscombe et al. (2004), Yosef et Regev (2011)). These two stimulii result in different network topologies. Indeed, after an exogenous stimulus, networks topologies seem to have larger hubs and shor-ter paths leading to a quick response to exshor-ternal conditions (Luscombe et al. (2004)) and resulting in a cascade topology (Figure 1).
The Cascade package is a tool dedicated to the analysis of microarray data and to the inference cascade networks. The statistical tools provided in this library are based on the methodology described by Vallat et al. (Vallat et al. (2013)) and contained several major improvements described here.