Key processes in genetic regulatory networks (notably transcription and translation) are associated with irreducible time delays. Models of delayed networks operating in single cells show that delays can induce oscillatory dynamics that are not present in corresponding non-delayed models. The associated oscillatory gene expression has been observed in a number of biological settings, confirming the potential importance of delays in determining the dynamics of gene networks. These studies show that the impact of delays is particularly important when the delay occurs within a negative feedback loop, and when the magnitude of the delay is comparable to other key time scales in the network (particularly the half-lives of the regulated components). The networks underlying pattern formation during multicellular development are characterised by the presence of feedback loops and by time scales that are of the same order of magnitude as the delays expected from the processes of transcription and translation. In this talk, I will discuss the effects of time delays in some simple models of cellular pattern formation, based on intercellular signalling through proteins of the Notch and Delta families. I will show how inclusion of delays can have very striking effects on the dynamics of model solutions, resulting in a competition between oscillatory modes and spatial pattern formation. I will also discuss the potential implications of these results for the mechanisms that underlie some of the most basic patterning events in development.
- http://www.dcs.shef.ac.uk/~nmonk/vpm1.pdf - preprint with some of the work to be discussed