The paper with the Gelens lab on delay-induced oscillations is now out in Journal of the Royal Society Interface. In this paper, which was a collaboration with master student Sarah Verplaetse, we revisited a classical topic in mathematical biology: biological oscillators.

Periodic processes are present in many biological systems such as the circadian clock, the cell cycle or somitogenesis. The periodicity of these processes manifests, among others, in the repeated production and degradation of molecules. The interaction between different proteins that generates these cycles often contains a time-delayed negative feedback loop. Negative feedback can take different forms, and in this paper we compare two ways of implementing it: on the production step or on the degradation step. We show how these mechanisms impose different constraints on the rate constants that allow oscillations, and derive some mathematical results about simple delay equations that describe the system.

The picture on the left shows spirals in the complex plane, which we use to study the existence of oscillations in systems with a distributed delay.