A model of phospholipid biosynthesis in tumor in response to an anticancer agent in vivo.

We study, in this paper, a model for the core of the system of the Glycerophospholipid metabolism in the murine cells. It comprises the simple and enzymatic reactions of PhosphatidylEthanolamine and the PhosphatidylCholine. The model's general structure is taken from a number of books and articles. We translate this model into a set of ordinary differential equations (ODEs), to propose a quantitative explanation of the experimental experiences and the observed results. In order to make it usable as a basis for simulations and mathematical analysis we need to make precise the various constants present in the equations but which are usually not directly accessible in the literature. In a first step we considered experimental data of rat's liver cells obtained by NMR spectroscopy: given the values of metabolite concentrations we find appropriate parameter values which allow us to describe the system with ODEs. We have then performed several analyses using the developed model such as stability analysis. A first interesting result is the global stability of the system which was observed by simulation and then proved by mathematical arguments. A second important result is that we observe on the diagrams that the steady state for normal cells is precisely a singular point of order two, whereas tumoral cells present different characteristics; this fact has been proved for PhosphatidylEthanolamine N-Methyl transferase (PEMT), an enzyme which seems to be identified for the first time as a crucial element in the tumoral process. In a second step we applied our model to experimental data of proton HRMAS NMR spectroscopy for solid B16 melanoma and Lewis lung (3LL) 3LL carcinoma cells treated by Chloroethyl Nitrosourea (CENU). We performed a complete comparative analysis of parameters in order to learn the predictive statements to explain increases and decreases which one can observe in concentrations.