Robustness and evolution in oscillatory systems with feedback loops

Feedback loops are major components of biochemical systems. Many systems show multiple such (positive or negative) feedback loops. Nevertheless, very few quantitative analyses address the question how such multiple feedback loops evolved. Based on published models from the mitotic cycle in embryogenesis, we build a few case studies. Using a simple core architecture (transcription, phosphorylation and degradation), we define oscillatory models having either one positive feedback or one negative feedback, or both loops. With these models, we address the following questions about evolvability: could a system evolve from a simple model to a more complex one with a continuous transition in the parameter space? How do new feedback loops emerge without disrupting the proper function of the system? Our results show that progressive formation of a second feedback loop is possible without disturbing existing oscillatory behavior. For this process, the parameters of the system have to change during evolution to maintain predefined properties of oscillations like period and amplitude.