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

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. These 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 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.

[Mathematical modeling: an essential tool for the study of therapeutic targeting in solid tumors]. / La modélisation mathématique, un outil essentiel pour l'étude du ciblage thérapeutique des tumeurs solides.

Recent progress in biology has made the study of the medical treatment of cancer more effective, but it has also revealed the large complexity of carcinogenesis and cell signaling. For many types of cancer, several therapeutic targets are known and in some cases drugs against these targets exist. Unfortunately, the target proteins often work in networks, resulting in functional adaptation and the development of resilience/resistance to medical treatment. The use of mathematical modeling makes it possible to carry out system-level analyses for improved study of therapeutic targeting in solid tumours. We present the main types of mathematical models used in cancer research and we provide examples illustrating the relevance of these approaches in molecular oncobiology.

Mathematical modelling unveils the essential role of cellular phosphatases in the inhibition of RAF-MEK-ERK signalling by sorafenib in hepatocellular carcinoma cells.

The RAS-RAF-MEK-ERK cascade is a key oncogenic signal transduction pathway activated in many types of tumours in humans. Sorafenib, the medical treatment of reference against advanced stages of hepatocellular carcinoma (HCC), inhibits the RAF-MEK-ERK cascade in HCC cells. Based on previous studies suggesting that this cascade is an important target of sorafenib in HCC cells, we explored its regulation using mathematical modelling and ordinary differential equations. We analysed the dynamic regulation of the core components of the RAF-MEK-ERK cascade in three human HCC cell lines (Huh7, Hep3B and PLC/PRF5) with heterogeneous responses to sorafenib. In silico predictions derived from our mathematical model suggested that the disappearance of phosphorylated MEK and ERK proteins catalysed by cellular phosphatases is an essential mechanism underlying the anti-ERK efficacy of sorafenib in HCC cells. This prediction was experimentally validated using specific inhibitors of the phosphatases PP2A (Protein Phosphatase 2A) and DUSP1/6 (Dual-specificity phosphatases 1/6). These findings highlight an unexpected mode of action of sorafenib on the kinome of HCC cells, and open new perspectives regarding the therapeutic targeting of the RAF-MEK-ERK cascade in this context.