Stochastic Simulation of the Entrained Circadian Rhythm

Circadian rhythms occur in almost all living things, providing an organism with a biological clock that gives an estimate of external time. The phenomenon of entrainment is a particularly interesting property of circadian rhythms in which the period of an organism’s circadian rhythm is adapted to match the natural oscillations of the environment. We applied the technique of stochastic simulation to modelling the entrainment of circadian rhythms. The biochemical processes that determine the behaviour of a circadian rhythm in nature tend to be reliant on tens to hundreds of molecules [9] With the concentrations of molecules being so low, the phenomenon of molecular noise can have a significant impact on the behaviour of the system [24]. While deterministic simulations of these processes have been used to demonstrate interesting results [15], corresponding stochastic techniques more accurately represent the mechanics of the processes due to their simulation of molecular noise [16]. Stochastic simulation of biologically incorrect models of entrainment and deterministic simulation of biologically accurate models have been carried out ([33] and [15] respectively), but the application of stochastic simulation to biologically accurate models of entrainment of circadian rhythms is demonstrated for the first time in this dissertation. Stochastic Petri Nets (SPNs) were used to implement computational models of circadian rhythms, as described in [32]. To implement models that incorporated the effects of entrainment, a new software tool was developed that was based on the extended Petri Net Kernel (PNK2e) [5]. The new version of the PNK2e described in this dissertation enables modelling and simulation of biochemical networks with time-dependent reaction rates. Its useful application is not limited to modelling biochemical networks, but extends to any system that can be effectively modelled by stochastic processes. This software will be released under the Open Source agreement like its predecessor. A series of experiments were designed to investigate the effect of modelling entrainment of circadian rhythms as a system of stochastic processes. The design of these experiments is presented in this dissertation, along with the results obtained by perfoming them. These results demonstrate that entrainment can be effectively simulated using stochastic techniques and that the predicted behaviours of such stochastic simulations agree with those of deterministic simulations and observations from laboratory experiments. It is also demonstrated that the incorporation of entrainment can result in stable oscillations in simulation of models involving so few molecules that they result in chaotic behaviour when simulated without entrainment.