Modelling Biological clocks: a study of the Repressilator

Abstract

Biological clocks are found everywhere in the natural world. From circadian rhythms to pacemakers of the heart, biological clocks are an essential part of the smooth functioning of living organisms. They are composed of microscopic clocks which operate at the cellular level. The macroscopic clock functions by synchronisation of these smaller units through intercell coupling. These clocks keep time with amazing regularity even in the face of random external fluctuating effects or internal noise which are ubiquitous in the natural world. In order to attempt to understand the robustness of such clocks against stochastic effects, a model genetic circuit called the repressilator was constructed as a simple clock. The motivation is to find generic features which underlie the operation of complex biological clocks in a simple model. This thesis reviews the previous work done on single repressilators as well as on repressilators coupled by the quorum sensing mechanism. Numerical simulations are performed to study the properties of a mathematical model of the repressilator. A new mechanism is suggested by which repressilator circuits can be coupled. Numerical simulations of two repressilators coupled by this mechanism shows attractive phase synchronisation when their natural frequencies are identical. When the natural frequencies are distinct the results rule out entrainment and seem to indicate the absence phase-locking.