Modélisation de l'infection par le VIH, identification et aide au diagnostic

Ce travail de thèse a été réalisée en collaboration avec le Service d'Infectiologie du CHU de Nantes (France) qui a financé et supervisé la mise en place de l'étude clinique BRD 04/12-G (intiulé EDV05 dans la thèse)Recherche supportée par les programmes PROTEA (fiancement No. 05 STIC F4/SA) et CNRS/NSF (fiancement No. 18385) dans le cadre des accords de recherche Franco/Sud-Africains.HIV patients have to get a life-time therapy. The latter has to be adaptedto the evolution of the infection taking into account virus mutations, resistance,immunological and virological failures.The goal of this research work was to study the mathematical modelling theHIV/AIDS infection for an early aid to the clinical diagnosis of HIV/AIDS patients.Our methods consist in modelling the kinetics of the dynamics of the infection– mainly the dynamic of the viral load, the counts of CD4 and CD8 T-cells –to predict their evolutions. These models take into account several parameters(related to the virus effectiveness and to the immune system status) and enableus to characterize some phenomena of the infection that are now misunderstood.This report presents the identification (the estimation) of the parameters of theHIV infection from standard clinical data (that means the viral load, the CD4 andthe CD8 counts). We introduced new estimation methods that allow computingthe parameters of the infection with a very limited number of data. We show howthese estimated parameters can be used to help clinicians in the therapeuticalcare of the patients. Our results show that therapeutical failures can be predictedmathematically thanks to a clinical trial initiated by the CHU (UniversityHospital Centre) of Nantes.To begin, this report presents the HIV infection modelling, with an overviewof standard models that exist and two new models that we introduced for thisstudy. Then, the identifiability of continuous-time and discrete-time systems arepresented. We show that the presented models are all identifiable from the clinicaldata. Finally, we present the parameters identification and their uses for an aidto the clinical diagnosis.Les patients infectés par le VIH se voient proposer des traitements anti-virauxlourds (avec des effets secondaires handicapants) qui sont destinés à être mis enplace à vie. Les différentes souches de virus, les mutations, les résistances ou toutsimplement les spécificités de chaque patient conduisent parfois à interrompre ouà modifier le traitement après quelques semaines d'observation.Ce travail de thèse s'inscrit dans une thématique pluridisciplinaire et son objectifa été d'étudier la modélisation mathématique de l'évolution de l'infectionVIH/SIDA pour une aide précoce au diagnostic clinique. Notre approche consisteà modéliser l'évolution des dynamiques de l'infection – essentiellement la dynamiquede la charge virale, du taux de CD4 et de CD8 – dans le but de prédireson évolution. Cette modélisation met en jeu plusieurs paramètres (liés à la virulencedu virus et à l'état du système immunitaire du malade) qui nous permettentd'interpréter et de caractériser certains phénomènes encore mal connus de l'infection.Ce rapport présente donc l'identification (l'estimation) des paramètresde l'infection à partir des mesures cliniques standard (à savoir la charge virale,le taux de CD4 et de CD8), ainsi que la manière dont ces paramètres peuventêtre utilisés pour l'aide à la prise en charge thérapeutique du malade. D'un pointde vue technique, il a fallu développer des méthodes d'identification ad hoc quipermettent de calculer les paramètres de l'infection à partir d'un faible nombrede mesures.Les résultats obtenus – grâce à un essai clinique mis en place par le CHU deNantes – montrent que les patients en échec thérapeutique, peuvent être précocementdétectés par l'analyse mathématique de leurs paramètres respectifs.Ce rapport présente dans un premier temps la modélisation de l'infection VIH,avec un aperçu des modèles standard qui existent ainsi que deux nouveaux modèlesque nous avons introduits pour le besoin de cette étude. Ensuite, l'identifiabilitédes systèmes dynamiques en temps continu et discret y est présentée. Nousmontrons que les modèles étudiés sont identifiables à partir des données cliniquesusuelles. Enfin, nous présentons l'identification des paramètres des modèles à partirdes données cliniques et son application à l'aide au diagnostic clinique

Modélisation de l'infection par le VIH, identification et aide au diagnostic

Les patients infectés par le VIH se voient proposer des traitements anti-viraux lourds (avec des effets secondaires handicapants) qui sont destinés à être mis en place à vie. Les différentes souches de virus, les mutations, les résistances ou tout simplement les spécificités de chaque patient conduisent parfois à interrompre ou à modifier le traitement après quelques semaines d'observation. Ce travail de thèse s'inscrit dans une thématique pluridisciplinaire et son objectif a été d'étudier la modélisation mathématique de l'évolution de l'infection VIH/SIDA pour une aide précoce au diagnostic clinique. Notre approche consiste à modéliser l'évolution des dynamiques de l'infection essentiellement la dynamique de la charge virale, du taux de CD4 et de CD8 dans le but de prédire son évolution. Cette odélisation met en jeu plusieurs paramètres (liés à la virulence du virus et à l'état du système immunitaire du malade) qui nous permettent d'interpréter et de caractériser certains phénomènes encore mal connus de l'infection. Ce rapport présente donc l'identification (l'estimation) de ces paramètres à partir des mesures cliniques standard (à savoir la charge virale, le taux de CD4 et de CD8), ainsi que la manière dont ces paramètres peuvent être utilisés pour l'aide à la prise en charge thérapeutique du malade. D'un point de vue technique, il a fallu développer des méthodes d'identification ad hoc qui permettent de calculer les paramètres de l'infection à partir d'un faible nombre de mesures. Les résultats obtenus grâce à un essai clinique mis en place par le CHU de Nantes montrent que les patients en échec thérapeutique, peuvent être précocement détectés par l'analyse mathématique de leurs paramètres respectifs. Ce rapport présente dans un premier temps la modélisation de l'infection VIH, avec un aperçu des modèles standard qui existent ainsi que deux nouveaux modèles que nous avons introduits pour le besoin de cette étude. Ensuite, l'identifiabilité des systèmes dynamiques en temps continu et discret y est présentée. Nous montrons que les modèles étudiés sont identifiables à partir des données cliniques usuelles Enfin, nous présentons l'identification des paramètres des modèles à partir des données cliniques et son application à l'aide au diagnostic clinique.NANTES-BU Sciences (441092104) / SudocNANTES-Ecole Centrale (441092306) / SudocSudocFranceF

From structure to dynamics: frequency tuning in the p53-Mdm2 network. II Differential and stochastic approaches.

In Part I of this work, we carried out a logical analysis of a simple model describing the interplay between protein p53, its main negative regulator Mdm2 and DNA damage, and briefly discussed the corresponding differential model (Abou-Jaoudé et al. 2009). This analysis allowed us to reproduce several qualitative features of the kinetics of the p53 response to damage and provided an interpretation of the short and long characteristic periods of oscillation reported by Geva-Zatorsky et al. (2006) depending on the irradiation dose. Starting from this analysis, we focus here on more quantitative aspects of the dynamics of our network and combine the differential description of our system with stochastic simulations which take molecular fluctuations into account. We find that the amplitude of the p53 and Mdm2 oscillations is highly variable (to a degree that depends, however, on the bifurcation properties of the system). In contrast, peak width and timing remain more regular, consistent with the experimental data. Our simulations also show that noise can induce repeated pulses of p53 and Mdm2 that, at low damage, resemble the slow irregular fluctuations observed experimentally. Adding the stochastic dimension in our modeling further allowed us to account for an increase of the fraction of cells oscillating with a high frequency when the irradiation dose increases, as observed by Geva-Zatorsky et al. (2006).Journal ArticleResearch Support, Non-U.S. Gov'tSCOPUS: ar.jinfo:eu-repo/semantics/publishe

From structure to dynamics: frequency tuning in the p53-Mdm2 network I. Logical approach.

We investigate the dynamical properties of a simple four-variable model describing the interactions between the tumour suppressor protein p53, its main negative regulator Mdm2 and DNA damage, a model inspired by the work of Ciliberto et al. [2005. Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4(3), 488-493]. Its core consists of an antagonist circuit between p53 and nuclear Mdm2 embedded in a three-element negative circuit involving p53, cytoplasmic and nuclear Mdm2. A major concern has been to develop an integrated approach in which various types of descriptions complement each other. Here we present the logical analysis of our network and briefly discuss the corresponding differential model. Introducing the new notion of "logical bifurcation diagrams", we show that the essential qualitative dynamical properties of our network can be summarized by a small number of bifurcation scenarios, which can be understood in terms of the balance between the positive and negative circuits of the core network. The model displays a wide variety of behaviours depending on the level of damage, the efficiency of damage repair and, importantly, the DNA-binding affinity and transcriptional activity of p53, which are both stress- and cell-type specific. Our results qualitatively account for several experimental observations such as p53 pulses after irradiation, failure to respond to irradiation, shifts in the frequency of the oscillations, or rapid dampening of the oscillations in a cell population. They also suggest a great variability of behaviour from cell to cell and between different cell-types on the basis of different post-translational modifications and transactivation properties of p53. Finally, our differential analysis provides an interpretation of the high and low frequency oscillations observed by Geva-Zatorsky et al. [2006. Oscillations and variability in the p53 system. Mol. Syst. Biol. 2, 2006.0033] depending on the irradiation dose. A more detailed analysis of our differential model as well as its stochastic analysis will be developed in a next paper.Journal ArticleSCOPUS: ar.jinfo:eu-repo/semantics/publishe

Clinical tests of therapeutical failures based on mathematical modeling of the HIV infection

Clinical tests which are displayed are based on a system-theoretic approach for an early diagnosis of the immunological and virological failure of HIV patients. Mathematical characterizations of therapeutical failures are presented in this paper. Mathematical modeling is used for individual patients to help for an early diagnosis of the evolution of the infection. The feasibility of the method is depicted on some patients who start highly active antiretroviral therapy (HAART). The identifiability of the continuous-time models which are used is proved, and it is shown to be invariant under discretization. © 2008 IEEE.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Excitability in the host-pathogen interactions of HIV infection and emergence of viral load blips

International audienceHIV viral blips are characterized by intermittent episodes of detectable low-level viraemia which return spontaneously to an undetectable level in patients with full suppression of viraemia . The precise mechanisms responsible for viraemia blips and their clinical significance are not known. In this work, we analyze HIV blips using a mathematical model describing basic host-pathogen interactions, in particular regulatory processes involving CD4+, CD8+ T-cells and the virus. We show that under adequate conditions, this interaction system can be excitable and small perturbations of the system by external stimuli can generate robust viral load (VL) blips of regular or irregular frequency and peak amplitudes. Importantly, our analysis showed that direct perturbations of the viral load (by latent reservoirs or opportunistic diseases for example) more efficiently trigger VL blips on contrary to direct perturbations of the immune system, in particular the levels of uninfected CD4+ and cytotoxic CD8+ T-cells. This feature is shown to rely on specific stability properties in this interaction system. Our analysis moreover suggests that blips should be of low clinical significance since any other VL or immune system perturbations could trigger transient viraemia under adequate excitability conditions

How molecular should your molecular model be? On the level of molecular detail required to simulate biological networks in systems and synthetic biology.

The recent advance of genetic studies and the rapid accumulation of molecular data, together with the increasing performance of computers, led researchers to design more and more detailed mathematical models of biological systems. Many modeling approaches rely on ordinary differential equations (ODE) which are based on standard enzyme kinetics. Michaelis-Menten and Hill functions are indeed commonly used in dynamical models in systems and synthetic biology because they provide the necessary nonlinearity to make the dynamics nontrivial (i.e. limit-cycle oscillations or multistability). For most of the systems modeled, the actual molecular mechanism is unknown, and the enzyme equations should be regarded as phenomenological. In this chapter, we discuss the validity and accuracy of these approximations. In particular, we focus on the validity of the Michaelis-Menten function for open systems and on the use of Hill kinetics to describe transcription rates of regulated genes. Our discussion is illustrated by numerical simulations of prototype systems, including the Repressilator (a genetic oscillator) and the Toggle Switch model (a bistable system). We systematically compare the results obtained with the compact version (based on Michaelis-Menten and Hill functions) with its corresponding developed versions (based on "elementary" reaction steps and mass action laws). We also discuss the use of compact approaches to perform stochastic simulations (Gillespie algorithm). On the basis of these results, we argue that using compact models is suitable to model qualitatively biological systems.Journal ArticleSCOPUS: ar.kinfo:eu-repo/semantics/publishe

Kinetic modelling of in vitro cell-based assays to characterize non-specific bindings and ADME processes in a static and a perfused fluidic system

International audienceRecently, physiologically based perfusion in vitro systems have been developed to provide cell culture environment close to in vivo cell environment (e.g., fluidic conditions, organ interactions). In this work, we model and compare the fate of a chemical, benzo[a]pyrene (B[a]P), in a perfusion and a standard (static well-plate) system. These in vitro systems are composed of Caco-2 and HepG2 cells so as to mimic absorption across the small intestine and intestinal and hepatic metabolism. Compartmental models were developed and calibrated with B[a]P kinetics data in the culture medium to estimate the apparent permeability of Caco-2 cells, the in vitro biotransformation of B[a]P, as well as the different routes of loss by non-specific adsorption. Our results show that non-specific binding is the main process responsible for the depletion of B[a]P in the culture media : at steady state, only 40% and 24% of the total concentration of B[a]P are bioavailable in the static and perfused systems, respectively. We also showed that Caco-2 permeability in the perfused culture system is closer to in vivo conditions than the one obtained in the static system and that higher cellular metabolic activities are observed in static conditions. Perfused in vitro systems combined with kinetic modelling are promising tools for studying in vitro the different processes involved in the toxicokinetics of xenobiotics

Metabolomics-on-a-chip and metabolic flux analysis for label-free modeling of the internal metabolism of HepG2/C3A cells

International audienceIn vitro microfluidic systems are increasingly used as an alternative to standard Petri dishes in bioengineering and metabolomic investigations, as they are expected to provide cellular environments close to the in vivo conditions. In this work, we combined the recently developed "metabolomics-on-a-chip" approach with metabolic flux analysis to model the metabolic network of the hepatoma HepG2/C3A cell line and to infer the distribution of intracellular metabolic fluxes in standard Petri dishes and microfluidic biochips. A high pyruvate reduction to lactate was observed in both systems, suggesting that the cells operate in oxygen-limited environments. Our results also indicate that HepG2/C3A cells in the biochip are characterized by a higher consumption rate of oxygen, presumably due to a higher oxygenation rate in the microfluidic environment. This leads to a higher entry of the ultimate glycolytic product, acetyl-CoA, into the Krebs cycle. These findings are supported by the transcriptional activity of HepG2/C3A cells in both systems since we observed that genes regulated by a HIF-1 (hypoxia-regulated factor-1) transcriptional factor were over expressed under the Petri conditions, but to a lesser extent in the biochip