Four-Variable Model of an Enzymatic Oscillator Based on Trypsin

This paper describes a four-variable model for an enzymatic oscillator based on trypsin. Variables in this model are concentrations of the essential proteins (trypsin and trypsinogen) and small molecules (masked and active inhibitors of trypsin) within the network. Importantly, to simplify the model, non-essential side reactions are neglected and essential reactions are assumed to follow first or second order kinetics. Numerical solutions of this reduced model semi-quantitatively reproduce experimentally determined periods, amplitudes, and phase shifts of oscillations in the concentrations of several species in the network. Moreover, linear stability analysis shows that oscillations in the trypsin oscillator emerge and disappear through Hopf bifurcation. The model will be helpful in situations where simplicity is necessary such as detailed analysis of dynamics and modeling of reaction-diffusion systems.