Joseph Baron - The role of noise and memory effects in developmental pattern formation
|Dates:||7 October 2019|
|Times:||14:00 - 14:50|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
|Who is it for:||University staff, External researchers, Current University students|
(Room 2.60 Simon Building)
Join us for this seminar by Joseph Baron (Manchester) as part of the Mathematics in the Life Sciences Series.
Many mechanisms have been developed for the purpose of explaining 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. At their heart, both of these models involve sets of discrete agents interacting with one another in a stochastic manner. Often, however, the intrinsic noise associated with the individual-based nature of the dynamics 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 and which can be non-negligible for the numbers of particles involved in biological systems.
The temptation to ignore noise becomes even greater when complicating factors such as transcriptional delays or anomalous diffusion enter into the models. Both of these complications introduce so-called memory effects into the dynamics. The interplay between these memory effects and noise presents a unique mathematical challenge.
In this talk, I will briefly discuss the path integral approach one can use to quantify the noise in individual-based systems with memory and I will discuss two examples where memory is important in a noisy system (alluded to above): delays in the gene-regulatory networks related to somite segmentation, and noise-induced pattern formation in reaction-diffusion systems with subdiffusion. 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.
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Role: PhD student
Organisation: University of Manchester
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