Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des réseaux biologiques, comme par exemple des réseaux d'interaction de protéines ou des réseaux métaboliques. Graph Motif a fait depuis l'objet d'une attention particulière qui se traduit par un nombre relativement élevé de publications, essentiellement orientées autour de sa complexité algorithmique.
Je présenterai un certain nombre de résultats algorithmiques concernant le problème Graph Motif, en particulier des résultats de FPT (Fixed-Parameter Tractability), ainsi que des bornes inférieures de complexité algorithmique.
Ceci m'amènera à détailler diverses techniques de preuves dont certaines sont plutôt originales, et qui seront je l'espère d'intérêt pour le public.[-]

Le problème Graph Motif est défini comme suit : étant donné un graphe sommet colorié G=(V,E) et un multi-ensemble M de couleurs, déterminer s'il existe une occurrence de M dans G, c'est-à-dire un sous ensemble V' de V tel que
(1) le multi-ensemble des couleurs de V' correspond à M,
(2) le sous-graphe G' induit par V' est connexe.
Ce problème a été introduit, il y a un peu plus de 10 ans, dans le but de rechercher des motifs fonctionnels dans des réseaux biologiques, comme par exemple des réseaux d'interaction de protéines ou des réseaux métaboliques. Graph Motif a fait depuis l'objet d'une attention particulière qui se traduit par un nombre relativement élevé de publications, essentiellement orientées autour de sa complexité algorithmique.
Je présenterai un certain nombre de résultats algorithmiques concernant le problème Graph Motif, en particulier des résultats de FPT (Fixed-Parameter Tractability), ainsi que des bornes inférieures de complexité algorithmique.
Ceci m'amènera à détailler diverses techniques de preuves dont certaines sont plutôt originales, et qui seront je l'espère d'intérêt pour le public.[-]

Dans une première partie, je présenterai différentes problématiques liées à des statistiques d'occurrences de mots dans des génomes et décortiquerai plus en détail la question de savoir comment détecter si un mot a une fréquence d'apparition significativement anormale dans une séquence. Dans une deuxième partie, je présenterai différentes extensions pour tenir compte du fait qu'un motif d'ADN fonctionnel n'est pas toujours un « mot », mais qu'il peut avoir une structure plus complexe qui nécessite le développement de nouvelles méthodes statistiques.[-]

Cell-extracellular matrix interaction and the mechanical properties of cell nucleus have been demonstrated to play a fundamental role in cell movement across fibre networks and micro-channels and then in the spread of cancer metastases. The lectures will be aimed at presenting several mathematical models dealing with such a problem, starting from modelling cell adhesion mechanics to the inclusion of influence of nucleus stiffness in the motion of cells, through continuum mechanics, kinetic models and individual cell-based models.[-]

Computational modeling can be used to reveal insights into the mechanisms and potential side effects of a new drug. Here we will focus on two major diseases: diabetes, which affects 1 in 10 people in North America, and hypertension, which affects 1 in 3 adults. For diabetes, we are interested in a class of relatively novel drug treatment, the SGLT2 inhibitors (sodium-glucose co-transporter 2 inhibitors). E.g., Dapagliflozin, Canagliflozin, and Empagliflozin. We conduct simulations to better understand any side effect these drugs may have on our kidneys (which are the targets of SGLT2 inhibitors). Interestingly, these drugs may have both positive and negative side effects. For hypertension, we want to better understand the sex differences in the efficacy of some of the drug treatments. Women generally respond better to ARBs (angiotensin receptor blockers) than ACE inhibitors (angiontensin converting enzyme inhibitors), whereas the opposite is true for men. We have developed the first sex-specific computational model of blood pressure regulation, and applied that model to assess whether the ”one-size-fits-all” approach to blood pressure control is appropriate with regards to sex.[-]

Macrophages are a type of immune cells that can be present in high numbers in some solid tumours. The heterogeneity of macrophage populations (with the anti-tumour M1 cells and thepro-tumour M2 cells being the two extreme phenotypes) has led to difficulties in understanding the innate immune responses to tumours. Here we introduce a class of mathematical models for the interactions between a population of tumour-associated macrophages (structured by their phenotype) and a population of cancer cells (that could be structured by their mutation status). We then use this class of models to confirm that the M1 cells kill tumours, while the M2 cells can lead to tumour growth. In addition, we show that macrophages with mixed phenotypes can contribute to either tumour growth or tumour decay. We also show that tumour dormancy is associated not only with an increased heterogeneity of cancer population, but also with an increased heterogeneity of macrophage population.[-]

Modern technologies allow us to profile in high detail biomedical samples at fast decreasing costs. New technologies are opening new data modalities, in particular to measure at the single cell level. Prior knowledge, and biological networks in particular, are useful to integrate this data and distill mechanistic insight. This can help to interpret the result of machine learning or statistical analysis, as well as generate input features for these methods. In addition, they can be converted in dynamic mechanistic models to gain more specific insight. I will give an overview of these approaches showcasing some examples and approaches used in the field. [-]

Baker's yeast (Saccharomyces cerevisiae) has a diploid life-style, but under stress conditions, it forms spores, which then release haploid cells of mating types MATa and MATα. MATa cells are a frequently used model organism for many cell biological studies of cell cycle, metabolism or signaling. MATa and MATα cells can also mate to form diploid cells again. To this end, they secrete the pheromones α-factor and a-factor, sense the opposite pheromone and form protrusions in the direction of a potential mating partner. Importantly, they cannot move towards their mating partner, thus, the formation of the mating shape called shmoo is a significant growth investment.
Combining experimental studies of the cellular responses to mating factor and the resulting shape changes with spatial mathematical modeling, we investigated three major steps in the mating process. Specifically, we asked the following questions: (i) How do yeast cells communicate to form sharp gradients of pheromones allowing for precise decisions about whether to engage in mating or to continue dividing instead ? (ii) How do the individual cells sense the resulting gradients and how do they implement this information in order to decide about the spatial location of the polarization spot and later mating project? (iii) How do they translate the sensed information into shape changes, i.e. directed growth?
While we here use data and further information on yeast cells, the investigated processes occur in many cells under different circumstances. The developed theoretical concepts are therefore of general importance.[-]

Differences in disease predisposition or response to treatment can be explained in great part by genomic differences between individuals. This has given birth to precision medicine, where treatment is tailored to the genome of patients. This field depends on collecting considerable amounts of molecular data for large numbers of individuals, which is being enabled by thriving developments in genome sequencing and other high-throughput experimental technologies.
Unfortunately, we still lack effective methods to reliably detect, from this data, which of the genomic features determine a phenotype such as disease predisposition or response to treatment. One of the major issues is that the number of features that can be measured is large (easily reaching tens of millions) with respect to the number of samples for which they can be collected (more usually of the order of hundreds or thousands), posing both computational and statistical difficulties.
In my talk I will discuss how to use biological networks, which allow us to understand mutations in their genomic context, to address these issues. All the methods I will present share the common hypotheses that genomic regions that are involved in a given phenotype are more likely to be connected on a given biological network than not.[-]