Noise, delay and synchronisation in developmental pattern formation

Many mechanisms have been developed to explain the formation of the various emergent structures in developmental biology. Two examples are the clock-wavefront mechanism for somite segmentation, and Turing’s reaction-diffusion equations for spontaneous pattern formation. Often, the intrinsic noise associated with the individual-based nature of these models is neglected in favour of the use of simpler, deterministic equations. Such an approach can ignore important noise-induced effects such as stochastic patterns, cycles or waves, which are not captured by deterministic equations. The temptation to ignore noise becomes even greater when complicating factors such as transcriptional delays or anomalous diffusion enter into the models, giving rise to memory effects. In this talk, I will briefly discuss the path integral approach one can use to quantify the noise in individual-based systems with memory in the context of two example systems (alluded to above). I will discuss how an interplay between noise and subdiffusion can ameliorate the so-called “fine-tuning” issue associated with Turing pattern formation. I will also discuss how the combination of noise and delay can lead to the production of sustained cycles missed by deterministic models of the somite segmentation clock, and discuss the synchronisation, amplification and increase in coherence of such cycles with the strength of “delta-notch” signalling strength between cells.