Publications HAL de Yvinec

2024

titre
Mathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data
article
2024
resume
Fat cells, called adipocytes, are designed to regulate energy homeostasis by storing energy in the form of lipids. Adipocyte size distribution is assumed to play a role in the development of obesity-related diseases. This population of cells that do not have a characteristic size, indeed a bimodal size distribution is observed in adipose tissue. We propose a model based on a partial differential equation to describe adipocyte size distribution. The model includes a description of the lipid fluxes and the cell size fluctuations and using a formulation of a stationary solution fast computation of bimodal distribution is achieved. We investigate the parameter identifiability and estimate parameter values with CMA-ES algorithm. We first validate the procedure on synthetic data, then we estimate parameter values with experimental data of 32 rats. We discuss the estimated parameter values and their variability within the population, as well as the relation between estimated values and their biological significance. Finally, a sensitivity analysis is performed to specify the influence of parameters on 1 cell size distribution and explain the differences between the model and the measurements. The proposed framework enables the characterization of adipocyte size distribution with four parameters and can be easily adapted to measurements of cell size distribution in different health conditions.
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https://hal.science/hal-04141173/file/Giacobbi_preprint_v2.pdf BibTex
titre
Modeling compartmentalization within intracellular signaling pathway
article
2024
resume
We present a novel approach to modeling receptor-activated signaling pathways that take into account the compartmentalization of receptors and their effectors, both on the cell surface and in dynamic intracellular vesicles called endosomes. The first building block of the model concerns compartment dynamics. It takes into account creation of de novo endosomes, i.e. endocytosis, and further recycling of endosomes to the cell surface or degradation, as well as fusion of endosomes via coagulation dynamics. The second building block concerns biochemical reactions on the cell surface and within intra-cellular compartments. Both building blocks are coupled by the transfer of molecules that occurs at each event that modifies the compartments. The model is formulated as a integro-partial differential equation, with transport and coagulation operators, and source terms, coupled to an integro-differential equation. In this work, we prove sufficient conditions to obtain exponential ergodicity for the size distribution of intracellular compartments. We further design a finite volume scheme to simulate our model. Finally, we show two application cases that show qualitative agreement with recently published data, proving that our model can help capture the spatio-temporal complexity of receptor-activated signaling pathway.
Accès au texte intégral et bibtex
https://hal.science/hal-04098543/file/Modeling_Compartmentalization_within_Intracellular_Signaling_Pathway_revised_vf_black.pdf BibTex

2023

titre
Some remarks about the well-posedness of lifshitz-slyozov's equations with nucleation kinetics
article
2023
resume
The Lifshitz-Slyozov model is a nonlocal transport equation that can describe certain types of phase transitions in terms of the temporal evolution of a mixture of monomers and aggregates. Most applications of this model so far do not require boundary conditions. However, there is a recent interest in situations where a boundary condition might be needed-e.g. in the context of protein polymerization phenomena. Actually the boundary condition may change dynamically in time, depending on an activation threshold for the monomer concentration. This new setting poses a number of mathematical difficulties for which the existing literature is scarce. In this contribution we construct examples of solutions for which the boundary condition becomes activated (resp. deactivated) dynamically in time; we also discuss how to approach the well-posedness problem for such situations.
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https://hal.science/hal-04099684/file/Maestro10.pdf BibTex
titre
A Lifschitz-Slyozov type model for adipocyte size dynamics : limit from Becker-Döring system and numerical simulation
article
2023
resume
Biological data show that the size distribution of adipose cells follows a bimodal distribution. In this work, we introduce a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipose cells. We prove a new convergence result from the related Becker-Döring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. Then, this result allows us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model are performed using a well-balanced scheme and compared to solutions to the transport model. Those simulations show that both bimodal and unimodal profiles can be reached asymptotically depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.
Accès au texte intégral et bibtex
https://hal.science/hal-04016144/file/articleMeyerRibotYvinec.pdf BibTex

2022

titre
Nonlinear compartmental modeling to monitor ovarian follicle population dynamics on the whole lifespan
article
2022
resume
In this work, we introduce an ODE-based compartmental model of ovarian follicle development all along lifespan. The model monitors the changes in the follicle numbers in different maturation stages with aging. Ovarian follicles may either move forward to the next compartment (unidirectional migration) or degenerate and disappear (death). The migration from the first follicle compartment corresponds to the activation of quiescent follicles, which is responsible for the progressive exhaustion of the follicle reserve (ovarian aging) until cessation of reproductive activity. The model consists of a datadriven layer embedded into a more comprehensive, knowledge-driven layer encompassing the earliest events in follicle development. The data-driven layer is designed according to the most densely sampled experimental dataset available on follicle numbers in the mouse. Its salient feature is the nonlinear formulation of the activation rate, whose formulation includes a feedback term from growing follicles. The knowledge-based, coating layer accounts for cutting-edge studies on the initiation of follicle development around birth. Its salient feature is the coexistence of two follicle subpopulations of different embryonic origins. We then setup a complete estimation strategy, including the study of theoretical identifiability, the elaboration of a relevant optimization criterion combining different sources of data (the initial dataset on follicle numbers, together with data in conditions of perturbed activation, and data discriminating the subpopulations) with appropriate error models, and a model selection step. We finally illustrate the model potential for experimental design (suggestion of targeted new data acquisition) and in silico experiments.
Accès au texte intégral et bibtex
https://hal.science/hal-03739205/file/GBFCRY-FPD.pdf BibTex