Prediction of unstable behavior in enzymatic diffusion-reaction processes

The prediction of the behavior of biological mechanisms represents an important challenge in the comprehension of some disorders in living organisms. In this sense a better understanding of the system behavior is mandatory. In this paper we use mathematical tools and well established concepts of nonlinear dynamics and control for modeling and prediction of the biochemical behavior of an enzyme immobilized into an artificial membrane. The results are helpful to determine the causes of alterations in the enzymatic kinetic properties as well as in the prediction of complex behavior (oscillations) resulting from the catalytic activity. We first study the hydrolysis of Acetilcholine to show that it can be interpreted in terms of a coupling between the enzyme reaction and the diffusion process. The model is then extrapolated to a distributed system in order to analyze its behavior as a function of both time and space.