Mathematical model for the homeostasis of alpha-macroglobulins in the rat.

Alpha-macroglobulins (AM) are proteins that inactivate proteinases. Sodium monofluorophosphate (MFP) binds to AM and transiently changes AM plasma levels. As a consequence MFP is useful to modify AM homeostasis. A mathematical model to study the homeostasis of AM is proposed in this paper. The model describes changes in plasma concentration of AM, MFP concentration in the gastrointestinal tract, MFP plasma concentration, plasma concentration of AMMFP and includes rate constants of the processes involved in AM homeostasis. Estimation of the rate constants values was achieved using experimental and mathematical resources. The homeostasis of AM after an oral dose of 80 μmol of MFP was analyzed with a simulation tool. Experimental conditions that modify the homeostasis of AM had been simulated and validated using specific drugs that change some parameter of the system. The mathematical model describes accurately the behavior of the biological model. The results allow concluding that the simplifications made did not underestimate the main processes involved in the homeostasis and, also that the assumptions made were correct.