Classical Mechanics Approach Applied to Analysis of Genetic Oscillators

Biological oscillators present a fundamental part of several regulatory mechanisms that control the response of various biological systems. Several analytical approaches for their analysis have been reported recently. They are, however, limited to only specific oscillator topologies and/or to giving only qualitative answers, i.e., is the dynamics of an oscillator given the parameter space oscillatory or not. Here, we present a general analytical approach that can be applied to the analysis of biological oscillators. It relies on the projection of biological systems to classical mechanics systems. The approach is able to provide us with relatively accurate results in the meaning of type of behavior system reflects (i.e., oscillatory or not) and periods of potential oscillations without the necessity to conduct expensive numerical simulations. We demonstrate and verify the proposed approach on three different implementations of amplified negative feedback oscillator.