Search

Your search keyword '"Pujo-Menjouet, Laurent"' showing total 166 results
Start Over Author "Pujo-Menjouet, Laurent"
166 results on '"Pujo-Menjouet, Laurent"'

1. A refractory density approach to a multi-scale SEIRS epidemic model

Author

Chizhov, Anton, Pujo-Menjouet, Laurent, Schwalger, Tilo, and Sensi, Mattia

Subjects
Quantitative Biology - Populations and Evolution, Mathematics - Dynamical Systems, Physics - Physics and Society
Abstract

We propose a novel multi-scale modeling framework for infectious disease spreading, borrowing ideas and modeling tools from the so-called Refractory Density (RD) approach. We introduce a microscopic model that describes the probability of infection for a single individual and the evolution of the disease within their body. From the individual-level description, we then present the corresponding population-level model of epidemic spreading on the mesoscopic and macroscopic scale. We conclude with numerical illustrations taking into account either a white Gaussian noise or an escape noise to showcase the potential of our approach in producing both transient and asymptotic complex dynamics as well as finite-size fluctuations consistently across multiple scales. A comparison with the epidemiology of coronaviruses is also given to corroborate the qualitative relevance of our new approach., Comment: 17 pages, 7 figures

Published
2024

2. Oscillations in neuronal activity: a neuron-centered spatiotemporal model of the Unfolded Protein Response in prion diseases

Author

Miller, Elliot M., Chan, Tat Chung D., Montes-Matamoros, Carlos, Sharif, Omar, Pujo-Menjouet, Laurent, and Lindstrom, Michael R.

Subjects
Quantitative Biology - Neurons and Cognition, Mathematics - Dynamical Systems
Abstract

Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P (healthy) and S (toxic) interacting with heterodimer dynamics (S interacts with P to form two S's). The model takes the form of a coupled system of nonlinear reaction-diffusion equations with a delayed, nonlinear flux for P (delay from the UPR). Through the delay, we find parameter regimes that exhibit oscillations in the P- and S-protein levels. We find that oscillations are more pronounced when the S-clearance rate and S-diffusivity are small in comparison to the P-clearance rate and P-diffusivity, respectively. The oscillations become more pronounced as delays in initiating the UPR increase. We also consider quasi-realistic clinical parameters to understand how possible drug therapies can alter the course of a prion disease. We find that decreasing the production of P, decreasing the recruitment rate, increasing the diffusivity of S, increasing the UPR S-threshold, and increasing the S clearance rate appear to be the most powerful modifications to reduce the mean UPR intensity and potentially moderate the disease progression., Comment: 35 pages, 11 tables, 13 figures

Published
2024

3. A multigroup approach to delayed prion production

Author

Adimy, Mostafa, Chekroun, Abdennasser, Pujo-Menjouet, Laurent, and Sensi, Mattia

Subjects
Mathematics - Dynamical Systems, Quantitative Biology - Populations and Evolution, 34K20, 37G99, 37N25, 92B05, 92C20
Abstract

We generalize the model proposed in [Adimy, Babin, Pujo-Menjouet, \emph{SIAM Journal on Applied Dynamical Systems} (2022)] for prion infection to a network of neurons. We do so by applying a so-called \emph{multigroup approach} to the system of Delay Differential Equations (DDEs) proposed in the aforementioned paper. We derive the classical threshold quantity $\mathcal{R}_0$, \textit{i.e.} the basic reproduction number, exploiting the fact that the DDEs of our model qualitatively behave like Ordinary Differential Equations (ODEs) when evaluated at the Disease Free Equilibrium. We prove analytically that the disease naturally goes extinct when $\mathcal{R}_0<1$, whereas it persists when $\mathcal{R}_0>1$. We conclude with some selected numerical simulations of the system, to illustrate our analytical results., Comment: 21 pages, 11 figures

Published
2023
Full Text
View/download PDF

5. A qualitative analysis of a A$\beta$-monomer model with inflammation processes for Alzheimer's disease

Author

Ciuperca, Ionel, Pujo-Menjouet, Laurent, Matar-Tine, Leon, Torres, Nicolas, and Volpert, Vitaly

Subjects
Physics - Biological Physics, Quantitative Biology - Cell Behavior
Abstract

We introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of A$\beta$-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progression of Alzheimer's disease. We also present numerical simulations that allow to observe the effect of initial inflammation and concentration of monomers in our model.

Published
2022

10. Generalizing a mathematical model of prion aggregation allows strain coexistence and co-stability by including a novel misfolded species

Author

Lemarre, Paul, Pujo-Menjouet, Laurent, and Sindi, Suzanne S

Subjects
Biochemistry and Cell Biology, Biological Sciences, Rare Diseases, Emerging Infectious Diseases, Infectious Diseases, Neurodegenerative, Transmissible Spongiform Encephalopathy (TSE), Brain Disorders, Neurosciences, Aetiology, 2.1 Biological and endogenous factors, Neurological, Animals, Computational Biology, Computer Simulation, Humans, Kinetics, Mathematical Concepts, Models, Biological, Models, Molecular, Phenotype, Prion Diseases, Prions, Protein Aggregation, Pathological, Protein Conformation, Protein Folding, Protein Stability, Proteostasis Deficiencies, Coexistence, Nucleated polymerization, Protein aggregation, Protein misfolding, Strains, Subunits, Mathematical Sciences, Bioinformatics, Biological sciences, Mathematical sciences
Abstract

Prions are proteins capable of adopting misfolded conformations and transmitting these conformations to other normally folded proteins. Prions are most commonly known for causing fatal neurodegenerative diseases in mammals but are also associated with several harmless phenotypes in yeast. A distinct feature of prion propagation is the existence of different phenotypical variants, called strains. It is widely accepted that these strains correspond to different conformational states of the protein, but the mechanisms driving their interactions remain poorly understood. This study uses mathematical modeling to provide insight into this problem. We show that the classical model of prion dynamics allows at most one conformational strain to stably propagate. In order to conform to biological observations of strain coexistence and co-stability, we develop an extension of the classical model by introducing a novel prion species consistent with biological studies. Qualitative analysis of this model reveals a new variety of behavior. Indeed, it allows for stable coexistence of different strains in a wide parameter range, and it also introduces intricate initial condition dependency. These new behaviors are consistent with experimental observations of prions in both mammals and yeast. As such, our model provides a valuable tool for investigating the underlying mechanisms of prion propagation and the link between prion strains and strain specific phenotypes. The consideration of a novel prion species brings a change in perspective on prion biology and we use our model to generate hypotheses about prion infectivity.

Published
2019

11. First passage times in homogeneous nucleation: dependence on the total number of particles

Author

Yvinec, Romain, Bernard, Samuel, Hingant, Erwan, and Pujo-Menjouet, Laurent

Subjects
Quantitative Biology - Biomolecules, Mathematical Physics, Mathematics - Probability, 60H30, 60B12, 35F31, 35L50, 82C26
Abstract

Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistic of times it requires for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volume, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volume, we develop a scaling framework to study the behavior of the first assembly time as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have surprisingly a very weak dependency on the total number of particles. We highlight how the higher statistic (variance, distribution) of the first passage time may still help to infer key parameters (such as the size of the maximum cluster) from data. And last but not least, we present a framework to quantify the formation of cluster of macroscopic size, whose formation is (asymptotically) very unlikely and occurs as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory., Comment: 15 pages, 9 figures

Published
2015
Full Text
View/download PDF

13. Modeling the spatial propagation of Aβ oligomers in Alzheimer’s Disease

Author

Andrade-Restrepo Martin, Lemarre Paul, Pujo-Menjouet Laurent, Tine Leon Matar, and Ciuperca Sorin Ionel

Subjects
Applied mathematics. Quantitative methods, T57-57.97, Mathematics, QA1-939
Abstract

Recent advances in the study of Alzheimer’s Disease and the role of Aβ amyloid formation have caused the focus of biologists to progressively shift towards the smaller protein assemblies, the oligomers. These appear very early on in the disease progression and they seem to be the most infectious species for the neurons. We suggest a model of spatial propagation of Aβ oligomers in the vicinity of a few neurons, without considering the formation of large fibrils or plaques. We also include a simple representation of the oligomers neurotoxic effect. A numerical study reveals that the oligomers spatial dynamics are very sensitive to the balance between their diffusion and their replication, and that the outcome in terms of the progression of AD strongly depends on it.

Published
2020
Full Text
View/download PDF

14. Alzheimer's disease: analysis of a mathematical model incorporating the role of prions

Author

Helal, Mohamed, Hingant, Erwan, Pujo-Menjouet, Laurent, and Webb, Glenn F.

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Analysis of PDEs, 35F61, 92B05, 34L30
Abstract

We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of {\beta}-amyloid plaques based on the concentrations of A{\beta} oligomers, PrPC proteins, and the A{\beta}-x-PrPC complex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of {\beta}-amyloid is constant and also when it is described by a power law., Comment: Correction of typo in the title (paper remains unchanged)

Published
2013
Full Text
View/download PDF

15. Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation

Author

Ciuperca, Ionel Sorin, Hingant, Erwan, Palade, Liviu Iulian, and Pujo-Menjouet, Laurent

Subjects
Mathematics - Analysis of PDEs
Abstract

The Greer, Pujo-Menjouet andWebb model [Greer et al., J. Theoret. Biol., 242 (2006), 598-606] for prion dynamics was found to be in good agreement with experimental observations under no-flow conditions. The objective of this work is to generalize the problem to the framework of general polymerization-fragmentation under flow motion, motivated by the fact that laboratory work often involves prion dynamics under flow conditions in order to observe faster processes. Moreover, understanding and modelling the microstructure influence of macroscopically monitored non-Newtonian behaviour is crucial for sensor design, with the goal to provide practical information about ongoing molecular evolution. This paper's results can then be considered as one step in the mathematical understanding of such models, namely the proof of positivity and existence of solutions in suitable functional spaces. To that purpose, we introduce a new model based on the rigid-rod polymer theory to account for the polymer dynamics under flow conditions. As expected, when applied to the prion problem, in the absence of motion it reduces to that in Greer et al. (2006). At the heart of any polymer kinetical theory there is a configurational probability diffusion partial differential equation (PDE) of Fokker-Planck-Smoluchowski type. The main mathematical result of this paper is the proof of existence of positive solutions to the aforementioned PDE for a class of flows of practical interest, taking into account the flow induced splitting/lengthening of polymers in general, and prions in particular., Comment: Discrete and Continuous Dynamical Systems - Series B (2012) XX-XX

Published
2011
Full Text
View/download PDF

16. On the stability of a maturity structured model of cellular proliferation

Author

Adimy, Mostafa, Crauste, Fabien, and Pujo-Menjouet, Laurent

Subjects
Mathematics - Analysis of PDEs, Quantitative Biology - Cell Behavior, Quantitative Biology - Tissues and Organs
Abstract

We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial differential equations, with a retardation of the maturation variable and a time delay depending on this maturity. We show that the stability of this system depends strongly on the behaviour of the immature cells population. We obtain conditions for the global stability and the instability of the trivial solution.

Published
2009
Full Text
View/download PDF

19. Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia

Author

Mackey, Michael C., Ou, Chunhua, Pujo-Menjouet, Laurent, and Wu, Jianhong

Subjects
Quantitative Biology - Tissues and Organs
Abstract

We develop some techniques to prove analytically the existence and stability of long period oscillations of stem cell populations in the case of periodic chronic myelogenous leukemia. Such a periodic oscillation $p_\infty $ can be analytically constructed when the hill coefficient involved in the nonlinear feedback is infinite, and we show it is possible to obtain a contractive returning map (for the semiflow defined by the modeling functional differential equation) in a closed and convex cone containing $p_\infty $ when the hill coefficient is large, and the fixed point of such a contractive map gives the long period oscillation previously observed both numerically and experimentally., Comment: 23 pages

Published
2004

21. Toward an Early Diagnosis for Alzheimer’s Disease Based on the Perinuclear Localization of the ATM Protein

Author

Berthel, Elise, primary, Pujo-Menjouet, Laurent, additional, Le Reun, Eymeric, additional, Sonzogni, Laurène, additional, Al-Choboq, Joëlle, additional, Chekroun, Abdennasser, additional, Granzotto, Adeline, additional, Devic, Clément, additional, Ferlazzo, Mélanie L., additional, Pereira, Sandrine, additional, Bourguignon, Michel, additional, and Foray, Nicolas, additional

Published
2023
Full Text
View/download PDF

33. Est-ce par hasard s'il a le cœur qui s'égare

Author

Pujo-Menjouet, Laurent, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Subjects
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], ComputingMilieux_MISCELLANEOUS
Abstract

National audience

Published
2019

34. Alzheimer's disease and prion: An in vitro mathematical model

Author

Ciuperca, Ionel, Dumont, Matthieu, Lakmeche, Abdelkader, Mazzocco, Pauline, Pujo-Menjouet, Laurent, Rezaei, Human, Tine, Leon, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Université Djillali Liabes [Sidi Bel Abbès], Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Unité de recherche Virologie et Immunologie Moléculaires (VIM), Institut National de la Recherche Agronomique (INRA), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université Djilali Liabès [Sidi-Bel-Abbès], Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), Unité de recherche Virologie et Immunologie Moléculaires (VIM (UR 0892)), Association France-Alzheimer, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ)

Subjects
Prions, [SDV]Life Sciences [q-bio], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Alzheimer's disease, Delay equations, Advection-reaction equations, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology, Existence of solutions, Polymerization
Abstract

International audience; Alzheimer's disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation in the brain of Aβ monomers aggre-gating into oligomers and fibrils. Oligomers are amongst the most toxic structures as they can interact with neurons via membrane receptors, including PrP c proteins. This interaction leads to the misconformation of PrP c into pathogenic oligomeric prions, PrP ol. In this work, we develop a model describing in vitro Aβ polymerization process. We include interactions between oligomers and PrP c , causing the misconformation of PrP c into PrP ol. The model consists of nine equations, including size structured transport equations, ordinary differential equations and delayed differential equations. We analyse the well-posedness of the model and prove the existence and uniqueness of solutions of our model using Schauder fixed point theorem and Cauchy-Lipschitz theorem. Numerical simulations are also provided to give an illustration of the profiles that can be obtained with this model.

Published
2019

35. Analysis of mathematical model of leukemia

Author

Helal Mohamed, Adimy Mostafa, Lakmeche Abdelkader, and Pujo-Menjouet Laurent

Subjects
Information technology, T58.5-58.64
Abstract

In this paper, a model describing the dynamic of chronic myeloid leukemia is studied. By analyzing the corresponding characteristic equations, the local stability of trivial and nontrivial equilibria are discussed. By establishing appropriate Lyapunov functions, we prove the global stability of the positive constant equilibrium solutions.

Published
2015
Full Text
View/download PDF

37. Modeling the spatial propagation of Aβ oligomers in alzheimer's disease

Author

Andrade-Restrepo, Martín, Lemarre, Paul, Pujo-Menjouet, Laurent, Tine, Leon, Ciuperca, Sorin, Institut Jacques Monod (IJM (UMR_7592)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), Pujo-Menjouet, Laurent, Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2018

38. Passer notre amour à la machine

Author

Pujo-Menjouet, Laurent, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Subjects
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2019

39. Le jeu de l'amour sans le hasard Mathématiques du couple

Author

Pujo-Menjouet, Laurent, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Subjects
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
Abstract

International audience; Quelle est la clé des couples qui durent ? Leur secret si bien gardé, leur recette miracle, leur potion magique ? Bref, leur truc ? Laurent Pujo-Menjouet, docteur en mathématiques, possède une clé, peut-être même la clé. Pas d'incantation magique, non, mais une formule ou, pour être plus précis, des formules.Si la solution de nos déboires sentimentaux se trouvait dans la matière que nous détestions (peut-être) le plus à l'école ?Des premières tentatives de modélisation des relations amoureuses à ses propres recherches, Laurent Pujo-Menjouet nous invite à mettre nos sentiments en équations et à penser l'amour (moins le hasard) dans toute sa complexité.S'appuyant sur les travaux de scientifiques, d'économistes, mais aussi d'écrivains et de cinéastes, parfois aussi sur son expérience personnelle, il nous conduit à faire des mathématiques sans le savoir. Alors, prêts à vous immerger dans le cerveau des mathématiciens pour résoudre vos problèmes de cœur ?

Published
2019

40. Oscillations and asymptotic convergence for a delay differential equation modeling platelet production

Author

Boullu, Loïs, Adimy, Mostafa, Crauste, Fabien, Pujo-Menjouet, Laurent, Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Département de Mathématiques et de Statistiques [UdeM- Montréal], Université de Montréal (UdeM), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), Université Claude Bernard Lyon 1 - Faculté des sciences et technologies (UCBL FST), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, LABEX MILYON (ANR-10-LABX-0070) of Universiyé de Lyon, within the program 'Investissements d’Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR), Région Rhône-Alpes (Explo'RA Doc), France Canada Research Fund, NSERC, MITACS, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), and Université Claude Bernard Lyon 1 - Faculté des sciences (UCBL FS)

Subjects
platelet, delay, Quantitative Biology::Tissues and Organs, oscillations, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], stability, megakaryopoiesis, Quantitative Biology::Cell Behavior
Abstract

International audience; We analyze the existence of oscillating solutions and the asymptotic convergence for a nonlinear delay differential equation arising from the modeling of platelet production. We consider four different cell compartments corresponding to different cell maturity levels: stem cells, megakaryocytic progenitors, megakaryocytes, and platelets compartments, and the quantity of circulating thrombopoietin (TPO), a platelet regulation cytokine. Our initial model consists in a nonlinear age-structured partial differential equation system, where each equation describes the dynamics of a single compartment. This system is reduced to a single nonlinear delay differential equation describing the dynamics of the platelet population, in which the delay accounts for a differentiation time. After introducing the model, we prove the existence of a unique steady state for the delay differential equation. Then we determine necessary and sufficient conditions for the existence of oscillating solutions. Next we set up conditions to get local asymptotic stability and asymptotic convergence of this steady state. Finally we present a short analysis of the influence of the conditions at t < 0 on the proof for asymptotic convergence.

Published
2019

41. Stochastic model of nucleationBecker-Döring Model

Author

Yvinec, Romain, Bernard, Samuel, Chou, Tom, Deschamps, Julien, D'Orsogna, Maria R., Hingant, Erwan, Pujo-Menjouet, Laurent, Yvinec, Romain, Physiologie de la reproduction et des comportements [Nouzilly] (PRC), Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Institut Français du Cheval et de l'Equitation [Saumur]-Université de Tours-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2019

42. First passage times in homogeneous nucleation: Dependence on the total number of particles.

Author

Yvinec, Romain, Bernard, Samuel, Hingant, Erwan, and Pujo-Menjouet, Laurent

Subjects
HOMOGENEOUS nucleation, MOLECULAR physics, STOCHASTIC processes, MOLECULAR self-assembly, FINITE volume method, CLUSTER theory (Nuclear physics), FRAGMENTATION reactions
Abstract

Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory. [ABSTRACT FROM AUTHOR]

Published
2016
Full Text
View/download PDF

43. Modeling the spatial propagation of Aβ oligomers in Alzheimer's Disease.

Author

Calvez, Vincent, Grandmont, Céline, Lochërbach, Eva, Poignard, Clair, Ribot, Magali, Vauchelet, Nicolas, Andrade-Restrepo, Martin, Lemarre, Paul, Pujo-Menjouet, Laurent, Tine, Leon Matar, and Ciuperca, Sorin Ionel

Subjects
ALZHEIMER'S disease, AMYLOID beta-protein precursor, OLIGOMERS, NEUROTOXICOLOGY, DISEASE progression, COMPUTER simulation of biological systems
Abstract

Copyright of ESAIM: Proceedings & Surveys is the property of EDP Sciences and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Published
2020
Full Text
View/download PDF

44. Alzheimer's disease and prion: analysis of an in vitro mathematical model

Author

Ciuperca, Ionel Sorin, Dumont, Matthieu, Lakmeche, Abdelkader, Mazzocco, Pauline, Pujo-Menjouet, Laurent, Rezaei, Human, Tine, Léon M, Mazzocco, Pauline, Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Laboratoire de biomathématiques, Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Djillali Liabes [Sidi Bel Abbès], Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Unité de recherche Virologie et Immunologie Moléculaires (VIM), Institut National de la Recherche Agronomique (INRA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Djilali Liabès [Sidi-Bel-Abbès], Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), Unité de recherche Virologie et Immunologie Moléculaires (VIM (UR 0892)), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract

International audience; Alzheimer's disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation of Aβ monomers inside the brain, which have the faculty to aggregate into oligomers and fibrils. Oligomers are the most toxic structures as they can interact with neurons via membrane receptors, including PrP c proteins. This interaction leads to the misconformation of PrP c into pathogenic prions, PrP sc. In this work, we develop a model describing in vitro Aβ polymerization process. We include interactions between oligomers and PrP c , leading to the misconformation of PrP sc. The model consists of nine equations, including size structured transport equations , ordinary differential equations and delayed differential equations. We analyse the well-posedness of the model and prove the existence and uniqueness of solutions of our model using Schauder fixed point theorem and Cauchy-Lipschitz theorem. Numerical simulations are also provided to give an illustration of the profiles that can be obtained with this model.

Published
2018

47. Estimates and impact of lymphocyte division parameters from CFSE data using mathematical modelling

Author

Mazzocco, Pauline, Bernard, Samuel, Pujo-Menjouet, Laurent, Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
G2 Phase, CD4-Positive T-Lymphocytes, Death Rates, Immune Cells, Immunology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Synthesis Phase, Succinimides, lcsh:Medicine, CD8-Positive T-Lymphocytes, Research and Analysis Methods, Models, Biological, Animal Cells, Medicine and Health Sciences, Humans, Cell Cycle and Cell Division, lcsh:Science, Cell Analysis, Demography, Fluorescent Dyes, Cell Death, Staining and Labeling, lcsh:R, G1 Phase, Biology and Life Sciences, Cell Biology, Fluoresceins, Bioassays and Physiological Analysis, Cell Division Analysis, Cell Processes, People and Places, lcsh:Q, Cellular Types, Cell Division, Research Article
Abstract

International audience; Carboxyfluorescein diacetate succinimidyl ester (CFSE) labelling has been widely used to track and study cell proliferation. Here we use mathematical modelling to describe the kinetics of immune cell proliferation after an in vitro polyclonal stimulation tracked with CFSE. This approach allows us to estimate a set of key parameters, including ones related to cell death and proliferation. We develop a three-phase model that distinguishes a latency phase, accounting for non-divided cell behaviour, a resting phase and the active phase of the division process. Parameter estimates are derived from model results, and numerical simulations are then compared to the dynamics of in vitro experiments, with different biological assumptions tested. Our model allows us to compare the dynamics of CD4+ and CD8+ cells, and to highlight their kinetic differences. Finally we perform a sensitivity analysis to quantify the impact of each parameter on proliferation kinetics. Interestingly, we find that parameter sensitivity varies with time and with cell generation. Our approach can help biologists to understand cell proliferation mechanisms and to identify potential pathological division processes.

Published
2017

48. Étude de modèles mathématiques issus de la biologie du cycle cellulaire et de la dynamique des protéines

Author

Pujo-Menjouet, Laurent, Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Université Claude Bernard Lyon 1 - Institut Camille Jordan, Sylvie Benzoni-Gavage(benzoni@math.univ-lyon1.fr), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), Multi-scale modelling of cell dynamics : application to hematopoiesis ( DRACULA ), Centre de génétique et de physiologie moléculaire et cellulaire ( CGPhiMC ), Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique ( CNRS ) -Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ) -École Centrale de Lyon ( ECL ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ), and Institut Camille Jordan [Villeurbanne] ( ICJ )

Subjects
Biomathematics, Équations de transport, [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], Cell Cycle, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Non-linear modelling, Protein dynamics, Dynamique des protéines, Cycle cel- lulaire, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP], Equations with delays, Transport equations, Équations à retards, Prion, Alzheimer, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Biomathématiques, Modèles non-linéaires
Abstract

Discover, pass-on and disseminate. Here is the program of this manuscript summarizing my associate professor activities since my PhD defence in 2001. Within a little more than 15 years, I have been working on several mathematical models applied to biology reflecting different periods of my curriculum. In chapter 1, I summarize my analytical studies of the cell cycle models applied to blood cell production and disorders leading to related pathologies like leukaemia or anaemia. These models consist essentially of non-linear delayed differential equations arising from the integration of hyperbolic age structured partial differential equations. Chapters 2, 3 and 4 deal with my research work on protein dynamics applied to prion and Alzheimer disease. They have started while I was assistant professor in the USA and keep on being my current centre of interest. Models consist of systems of size structured polymerization-fragmentation partial differential equations coupled with non-linear differential equations. The last chapter is dedicated to my teaching, supervising and disseminating activities. I end it up with a short word on my work in progress.; Découvrir, transmettre, diffuser. Voici le programme de ce manuscrit retraçant ma carrière d’enseignant-chercheur depuis la soutenance de ma thèse de doctorat en 2001. En un peu plus de 15 années, j’ai travaillé sur plusieurs modèles mathématiques appliquées à la biologie, correspondant à différentes périodes de mon parcours. Dans le chapitre 1, je résume mes travaux d’analyse de modèles du cycle cellulaires appliqués à la production de cellules sanguines et quelques dérèglements engendrant diverses pathologies comme la leucémie ou l’anémie. Ces modèles sont principalement constitués d’équations différentielles non-linéaires à retards provenant de l’intégration d’équations aux dérivées partielles hyperboliques structurées en âge. Les chapitres 2, 3 et 4 reprennent mes travaux sur les dynamiques des protéines, appliqués aux maladies liées au prion et Alzheimer. Ils ont commencé alors que j’étais professeur assistant aux États-Unis et qui se poursuivent encore maintenant. Les modèles sont constitués de systèmes d’équations aux dérivées partielles structurés en taille de type polymérisation-fragmentation couplé à des équations différentielles non-linéaires. Le dernier chapitre fait le point sur mes activités d’enseignement, d’encadrement et de diffusion. Je termine enfin par un bref aperçu de mes projets de recherches en cours.

Published
2016

49. A unifying model for the propagation of prion proteins in yeast brings insight into the [PSI+] prion.

Author

Lemarre, Paul, Pujo-Menjouet, Laurent, and Sindi, Suzanne S.

Subjects
*PRIONS, *IMPULSIVE differential equations, *CHEMICAL processes, *YEAST, *GUANIDINIUM chlorides
Abstract

The use of yeast systems to study the propagation of prions and amyloids has emerged as a crucial aspect of the global endeavor to understand those mechanisms. Yeast prion systems are intrinsically multi-scale: the molecular chemical processes are indeed coupled to the cellular processes of cell growth and division to influence phenotypical traits, observable at the scale of colonies. We introduce a novel modeling framework to tackle this difficulty using impulsive differential equations. We apply this approach to the [PSI+] yeast prion, which is associated with the misconformation and aggregation of Sup35. We build a model that reproduces and unifies previously conflicting experimental observations on [PSI+] and thus sheds light onto characteristics of the intracellular molecular processes driving aggregate replication. In particular our model uncovers a kinetic barrier for aggregate replication at low densities, meaning the change between prion or prion-free phenotype is a bi-stable transition. This result is based on the study of prion curing experiments, as well as the phenomenon of colony sectoring, a phenotype which is often ignored in experimental assays and has never been modeled. Furthermore, our results provide further insight into the effect of guanidine hydrochloride (GdnHCl) on Sup35 aggregates. To qualitatively reproduce the GdnHCl curing experiment, aggregate replication must not be completely inhibited, which suggests the existence of a mechanism different than Hsp104-mediated fragmentation. Those results are promising for further development of the [PSI+] model, but also for extending the use of this novel framework to other yeast prion or amyloid systems. Author summary: In the study of yeast prions, mathematical modeling is a powerful tool, in particular when it comes to facing the difficulties of multi-scale systems. In this study, we introduce a mathematical framework for investigating this problem in a unifying way. We focus on the yeast prion [PSI+] and present a simple molecular scheme for prion replication and a model of yeast budding. In order to qualitatively reproduce experiments, we need to introduce a non-linear mechanism in the molecular rates. This transforms the intracellular system into a bi-stable switch and allows for curing to occur, which is a crucial phenomenon for the study of yeast prions. To the best of our knowledge, no model in the literature includes such a mechanism, at least not explicitly. We also describe the GdnHCl curing experiment, and the propagon counting procedure. Reproducing this result requires challenging hypotheses that are commonly accepted, and our interpretation gives a new perspective on the concept of propagon. This study may be considered as a good example of how mathematical modeling can bring valuable insight into biological concepts and observations. [ABSTRACT FROM AUTHOR]

Published
2020
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results