Mathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data

Anne-Sophie Giacobbi (1) , Leo Meyer (2, 3) , Magali Ribot (2, 3) , Romain Yvinec (3, 4) , Hedi Soula (5) , Chloe Audebert (1, 6)

1 LCQB-MMB - Mathematical Modeling in Biology [LCQB]
2 IDP - Institut Denis Poisson
3 MUSCA - Dynamiques de populations multi-échelles pour des systèmes physiologiques
4 PRC - Physiologie de la reproduction et des comportements [Nouzilly]
5 Nutriomics - Nutrition et obésités: approches systémiques (UMR-S 1269)
6 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions

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.

Mots clés: parameter estimation; adipocyte size distribution; parameter identifiability; partial differential equation

Domaines: Mathématiques [math]; Sciences du Vivant [q-bio]

Anne-Sophie Giacobbi, Leo Meyer, Magali Ribot, Romain Yvinec, Hedi Soula, et al.. Mathematical modeling of adipocyte size distributions: identifiability and parameter estimation from rat data. 2024. ⟨hal-04141173v3⟩