A Ticking Clock: Performance Analysis of a Circadian Rhythm with Stochastic Process Algebra

We apply performance analysis techniques to a biological modelling problem, that of capturing and reproducing the Circadian rhythm. A Circadian rhythm provides cells with a clock by which to regulate their behaviour. We consider two distinct stochastic models of the Circadian rhythm – one unbounded and the other bounded. We consider a fluid approximation of the models, and, by conversion to a set of ordinary differential equations, we are able to reproduce the correct rhythm. We show that with a bounded model, the clock phase can be affected by modifying the ability to manufacture some proteins.