AN OSCILLATORY MODEL FOR GLOBALLY STABLE PROTEIN TRANSCRIPTION DYNAMICS

Oscillations appear in all levels of biological organization. Oscillatory phenomena do not always possess a simple periodic nature. In this work, we analyze a gene transcriptional network in which we assume an almost periodic input that regulates gene. We use an almost periodic input [Formula: see text] since a periodic one is very restrictive. We show that the almost periodic model proposed has a unique almost periodic attractor. Numerical simulations show that the retroactivity is highly affected when an almost periodic input is used in an upstream system that is interconnected to a downstream system. By comparison of the solutions of the model, we can conclude that when the amount of protein bound to the promoter is modeled by either a periodic function or an almost periodic one, which is denoted by [Formula: see text], the amount of protein concentration [Formula: see text] can be underestimated or overestimated depending on if [Formula: see text] is modeling by a periodic or an almost periodic function. These estimation errors can lead to an error in the quantification of retroactivity which in turn can alter the coordination between an upstream system and a downstream one.