Synthetic biology of genetic circuits

The combination of positive and negative feedback loops has been shown to increase the robustness of oscillations. Such breakthrough has enabled to understand the importance of that dual control in a few biological systems. The reason is that most biological systems are non-linear. One of the obstacles that must be overcome when dealing with non-linear systems, even if they are simple, is that the use of intuition to predict its behavior is no longer valid. The comprehension of the behavior of the system can only be achieved mathematical modeling and computational simulations This bachelor thesis aims to develop a mathematical model of the relaxoscillator, a gene regulatory network in which two genes with identical promoters are regulated by the same activator and repressor. At the same time, the binding of those depends on the concentrations of two inducers: arabinose and IPTG, which correspond to the control parameters of the system. The obtained model, derived from the chemical reactions, was simulated under different inducer concentrations in an attempt to comprehend the long term behavior of the system. The results show that varying these inducer concentrations allows to tune the period and the amplitude of the oscillations observed in the system. In order to analyze changes in the long term behavior of the system it will be required to include a third control parameter, the transcription repressor rate, so that the system displays different dynamic behaviors. The analysis of the simulations indicates the presence of a supercritical Hopf bifurcation for a given value of the transcription repressor rate that would explain the transition between damped oscillations and persistent oscillations. Nevertheless, due to the theoretical nature of the project, experimental studies as well as two-parameter bifurcation analysis should be performed in order to confirm such hypothesis and gain understanding of the behavior of the system as a function of inducers concentrations. Ingeniería Biomédica