Oscillations of phosphofructokinase in a compartmentalized system

The analysis of an allosteric model for phosphofructokinase, exhibiting an inhibition by excess substrate (ATP) shows the possibility of sustained self-oscillations. This model is described by a system of, two ordinary differential equations taking into account the coupling between metabolites diffusion (Fick's first law) and enzyme reaction. The different behavior types of the system have been studied as a function of two main parameters, rho (ration between respective permeabilities for ATP and F6P) and sigma (valuation of the diffusional constraints importance). The research for instability conditions has been carried out by normal mode analysis.