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Résumé : Purpose. Using artificial intelligence techniques, we compute optimal personalized protocols for temozolomide administration in a population of patients with variability.
Methods. Our optimizations are based on a Pharmacokinetics / Pharmacodynamics (PK/PD) model with population variability for temozolomide. The patient pharmacokinetic parameters can only be partially observed at admission and are progressively learned by Bayesian inference during treatment. For every patient, we seek to minimize tumor size while avoiding severe toxicity, i.e. maintaining an acceptable toxicity level. The optimization algorithm we rely on borrows from the field of artificial intelligence.
Results. Optimal personalized protocols (OPP) achieve a sizable decrease in tumor size at the population level but also patient-wise. The tumor size is on average 67.2 grams lighter than with the standard maximum-tolerated dose protocol (MTD) after 336 days (12 MTD cycles). The corresponding 90% confidence interval for tumor size reduction amounts to [58.6−82.7] (grams). When treated with OPP, less patients experience severe toxicity in comparison to MTD.
Major findings. We quantify in-silico the benefits offered by personalized oncology in the case of temozolomide administration. To do so, we compute optimal personalized protocols for a population of heterogeneous patients using artificial intelligence techniques. At each treatment day, the protocol is updated by taking into account the feedback obtained from patient’s reaction to the drug administration. Personalized protocols greatly differ from each other, and from the standard MTD protocol. Benefits of personalization are very sizable: tumor sizes are much smaller on average and also patient-wise, while severe toxicity is made less frequent. |
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Résumé : In a packed tissue neighboring cells exert high pressure on each other at all times. Such mechanical interactions are believed to play an important role on the dynamics of the tissue. However, their contribution to the tissue shape is not yet fully understood. In this talk I will first present a framework to model this type of systems based on a geometric representation of individual cells. The cells interact with each other aiming at minimizing a local potential energy, subjected to non-overlapping constraints. Mathematically, the problem is formulated as a non-convex minimization problem, which will be tackled with the recently proposed damped Arrow-Hurwicz algorithm. I then apply this framework to the study of a pseudo-stratified epithelial tissue. Some preliminary numerical results will be presented to show how the tissue may be deformed when simple defects on individual cells are introduced. |
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Résumé : Regular, partly periodic oscillations in the size of animal and plant populations are believed to be widespread in ecosystems ranging from the tundra to the oceans, affecting about a third of monitored populations. These fluctuations can have large amplitude, so that population size varies across several orders of magnitude. Numerous mechanisms, most notoriously interactions between predator and prey or diseased and healthy individuals are known to promote oscillatory phenomena but the causes of cycles in most wild populations remain unknown. In this talk, I will outline how this problem has developed over the years in ecology, as well as recent modelling trends in research into the causes (and consequences) of such widespread variation in population size, using varied examples from mammals to plants. We will see in particular how current research tends to move away from the now classic bivariate oscillators to embrace high-dimensionality, seasonal and stochastic forcing, as well as demographic intricacies. |
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Résumé : Cette présentation sera centrée sur les modèles de croissance-fragmentation, pouvant servir à modéliser la croissance d’une population de cellules. D’un point de vue stochastique, nous nous intéressons à un système de particules évoluant à travers deux phénomènes. D’une part, les particules évoluent de façon déterministe (elles vieillissent, elles croissent). D’autre part, les particules se divisent au bout d'un temps aléatoire : une particule d'âge a ou de taille x se divise en deux nouvelles particules (d'âge 0, de taille initiale x/2) selon un taux de division B(.) dépendant de l'âge a ou de la taille x de la particule. Un objectif majeur est alors de reconstruire le taux de division, et nous le ferons de façon non-paramétrique.
Différents schémas d'observation seront envisagés : 1) l’observation des traits de toutes des cellules jusqu’à une génération fixée dans l’arbre généalogique de la population ; 2) l’observation de la prolifération des cellules en temps continu entre les instants 0 et T (induisant un phénomène de biais de sélection). |
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Résumé : A major problem in developmental biology is to understand how different cell types emerge from the one genome of multipotent precursor cells. In 1957, C.H. Waddington introduced the so-called epigenetic landscape to represent the complex regulatory dynamics driving the differentiation process. The differentiating cell explores the landscape, and by encountering successive decision points, proceeds towards its eventual fate. Changes in the morphology of the landscape that favour one cell type over others are a reflection of dynamical changes occurring in the underlying cellular gene regulatory network. Despite much progress in the field, what drives these changes still remains a largely unanswered question.
In this talk I will review some of the possible mathematical scenarios that have been proposed to describe decision points in Waddington’s landscape. Within the context of Dynamical Systems Theory these decision points are seen as mathematical bifurcations, which can be further modified and enriched when stochastic fluctuations (so-called noise) are considered. Noise is ubiquitous in molecular biology, and occurs in many aspects of gene regulation and other cellular activities, accounting for much if not all of the variability that we see in biological systems. I will present some recent results obtained in my group in the case of simple stochastic gene systems exhibiting time scale separation between fast and slow variables. I will discuss conditions involving the time-scale of the system and the correlation time of the noise, which lead to the emergence of non-trivial reduced dynamics and new types of noise-induced bifurcations.
Not only our theoretical findings suggest a fundamental role played by biological noise in development, but they are also relevant in the broader context of understanding the stochastic dynamics of gene regulatory circuits. Our predictions, if experimentally confirmed, will have implications far beyond the fundamental biology of the cell differentiation process, with medical implications in congenital diseases and cancer. |
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Résumé : to be announced |
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Résumé : Biological and medical sciences are today facing an irreversible shift: one from reasoning and statistics used to detect differences between a few data points, to computer-aided reasoning and mechanistic modelling, based on large-scale datasets. This shift requires a rapid development of both new concepts and new technologies, both within the biological and the mathematical/computer sciences. In this presentation, I will outline some of my contributions to these developments, which involves: i) How to borrow data and knowledge from neighboring cells using nonlinear mixed-effects modelling, ii) How to uniquely identify parameters and predictions despite parameter unidentifiability, iii) How to scale mechanistic models to the omics level, also encompassing multiple cell-types and levels (cell, organ, whole-body). The result of this is a multi-resolution model, which combines all prior knowledge and data into a single descriptive, and which has different known degrees of "resolution" - i.e. detail and predication accuracy - in its different parts. I will illustrate how we have used this to draw useful conclusions that could not have been drawn without the modelling, both regarding basic research, and regarding clinical and pharmaceutical end-usage. |
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Résumé : In this talk, I would like to contrast some of my findings on gene network evolution and then place them in a single framework. First, evolution may mean rapid adaptation, or being evolvable. It has been observed both in nature and in the lab, and it has puzzled biologists. Can evolvability be selected for? Inspired by experimental evolution on yeast, I studied network evolution in changing environments. Using computer simulations, I found that network structure evolves to allow for rapid adaptation. A clear example of the evolution of evolvability, that neatly demonstrates how function and evolution are intertwined. Second, evolution may mean robustness, or an apparent lack of change. Together with experimental biologists, I studied the evolution of the gap gene network, which is involved in body plan patterning of the fruit fly Drosophila and the scuttle fly Megaselia. Both flies have differences in upstream factors and gap gene expression dynamics, while the final gap gene patterns are virtually identical. With a detailed analysis of gap gene regulation, I show how the flies compensate for species-specific differences. We named the phenomenon "quantitative system drift" and suggested it is a common mode of evolution in development. Finally, I discuss how both studies may be understood in the framework of "evolving on a genotype network". |
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Résumé : The RAS-RAF-MEK-ERK pathway is an important signal transduction cascade that is found activated in many types of human tumours. The hepatocellular carcinoma (HCC), the most frequent form of primary liver tumour, is a cancer with one of the worst prognoses, partially due to the small number of efficient therapeutic strategies. In order to design a more efficient strategy against cancer cells, further knowledge about the aspect of dynamic regulation of the RAS-RAF-MEK-ERK cascade is required. We decided to investigate the dynamic regulation of the RAS-RAF-MEK-ERK cascade in HCC cells exposed to sorafenib by using a systems biology approach.
First, a mathematical model based on the Michaelis-Menten equation will be introduced to analyse the dynamic regulation of BRAF, CRAF, MEK and ERK. The results of the sensitivity analyse and the model prediction provided new insights on the therapeutic target. In a second time, the model will be extended to the all components set of the RAS-RAF-MEK-ERK pathway. The first results of the model prediction will be presented. |
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Résumé : Adaptive evolution is at the core of multiple major issues, such as the emergence of drug resistance in human pathogens and pests. It is thus of great importance to deeply understand the mechanisms and dynamics of adaptive evolution in order to improve our ability to predict and manage such complex processes. In this context, I will present my work on modeling the dynamics of adaptation in diploids. Contrary to what has been previously assumed, I have found that adaptation in diploids is qualitatively different from haploids. I will present a diploid version of Fisher's geometric model implemented in an evolutionary simulation. I will show that adaptive evolution in diploids proceeds by transient states of balancing selection due to heterozygote advantage, the state under which a heterozygote individual is more fit than both homozygotes. This finding has important implications for our understanding of the origin and maintenance of variation in nature. I will conclude with some recent developments and extensions of the simulations exploring the predictability of evolution. |
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Résumé : "You don't need to be good in mathematics to be successful in science. You just need to know a good mathematician." This statement is typically made as a joke, but it is obviously also meant to stress the importance of mathematics in science. As I would argue, it also provides a good description of how biology has in many cases been dealing with the new challenges resulting from the rapidly improving capacities in data collection in the last decades: through collaborations between biologists and theorists with a clear separation of experimental and data analysis tasks. In this talk, I will argue that as we are moving mathematics closer and closer to the experiments, a separation of tasks becomes less and less possible, i.e. that all of us need to understand more and more of both sides to make interdisciplinary projects succeed. More specifically, I will outline how my own research has evolved from developing methods for the analysis of given data to methods that guide the data acquisition, and finally on to algorithms that analyze the data in real time and take autonomous decisions on how to continue the experiment. On the mathematical side, the talk will be focused on parameter inference, experimental design and model-predictive control for stochastic reaction networks described by continuous-time Markov chains. On the biological side, I will talk about light-inducible gene expression circuits in yeast and E. Coli and flow cytometry as well as single-cell microscopy data. |
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Résumé : Intermediate filaments are one of the components of cytoskeletal networks; they organize via a series of assembly/disassembly and transport events in cells. Understanding the dynamics of intermediate filaments, their organization and resulting mechanical properties is essential to elucidate their functions in cells. Combining mathematical modelling and experimental data we investigate the assembly of intermediate filaments and their organization in cells. A collection of models will be presented to address several questions: What contributes to the organization? What process or combination of processes does the organization emerge from? What process dominates? |
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Résumé : A growing body of evidence supports the idea that solid tumours are complex ecosystems populated by heterogeneous cells, whose dynamics can be described in terms of evolutionary and ecological principles. In this light, it has become increasingly recognised that models that are akin to those arising from mathematical ecology can complement experimental cancer research by capturing the crucial assumptions that underlie given hypotheses, and by offering an alternative means of understanding experimental results that are currently available. This talk deals with partial differential equations modelling the dynamics of structured cancer cell populations. Analyses and numerical simulations of these equations help to uncover fresh insights into the critical mechanisms underpinning tumour progression and the emergence of resistance to anti-cancer therapies. |
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Résumé : Intracellular processes rarely work in isolation but continually interact with the rest of the cell. The mechanisms driving such global regulation, however, are not well understood. Here I will consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and construct a mechanistic model that comprises these trade-offs. I will show that the model recovers Monod's law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, I will discuss growth-related effects in dosage compensation by paralogs, host-circuit interactions in synthetic biology, and simple models of evolution. |
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Résumé : Numerical simulations and bifurcation analyses are widely used in computational biology to unravel dynamical properties of biological systems. This will be illustrated here through two examples.
Circadian clocks are usually modeled by limit cycle oscillators. These models account for the emergence of oscillations at the level of single cells and allow theoretical analyses of the dynamical properties of circadian oscillations, including their entrainment by light-dark cycles and resetting by light pulses. Recent single cell experiments however revealed a great cell-to-cell heterogeneity in the oscillatory behaviour, with many cells displaying damped oscillations. Numerical and analytical investigation of the circadian Goodwin model shows that damped oscillators can be entrained over larger ranges of period of the light-dark cycle.
During embryonic development, the specification of different cell fates results from interactions between transcription factors. These regulatory networks often exhibit multiple stable steady states (multistability), providing a common dynamical basis for differentiation. I will present here a model for early murine embryogenesis which describes the specification of cells from the inner cell mass (ICM) into epiblast (Epi) or primitive endoderm (PrE). The model incorporates the intracellular gene regulatory network as well as the intercellular interactions involving Erk/Fgf4 signaling pathway. The results are analyzed by means of bifurcation diagrams. The model displays tristability in a range of Fgf4 concentrations, accounts for the self-organized specification process observed in vivo, and predicts that heterogeneities in extracellular Fgf4 concentration play a primary role in the spatial arrangement of the Epi/PrE cells in a salt-and-pepper pattern. |
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Source : Indico - Math évènementiel - GDS Mathrice |