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<https://discovery.ucl.ac.uk/id/eprint/10158781> <http://purl.org/dc/terms/title> "Cell-cell interactions in epithelial patterning: Notch-Delta signalling and evolutionary dynamics"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10158781> <http://purl.org/ontology/bibo/abstract> "Understanding pattern formation driven by cell-cell interactions has been a significant\r\ntheme in cellular biology for many years. In particular, due to its implications on\r\nmany biological contexts, lateral-inhibition mechanisms present in the Notch-Delta\r\nsignalling pathway led to an extensive discussion between biologists and mathematicians.\r\nDeterministic and stochastic models have been developed as a consequence\r\nof this discussion, some of which address long-range signalling by considering\r\ncell protrusions reaching non-neighbouring cells. The dynamics of such signalling\r\nsystems reveal intricate properties of the coupling terms involved in these models. In\r\nthe broader context of evolutionary dynamics, signalling and patterning contribute to\r\nthe definition of phenotypes of individuals within an interacting population, whose\r\nmathematical description has been unified under various conceptual frameworks.\r\nIn this thesis, we examine the benefits and limitations of new and existing\r\nmodels of cell signalling and differentiation in a variety of contexts, including applications\r\nin general and well-studied patterning tissues in Drosophila melanogaster.\r\nUsing linear and weakly nonlinear stability analyses, we find that pattern selection\r\nrelies on nonlinear effects that are not covered by such analytical methods. The\r\ndirect application of such models on the Drosophila wing disc development and\r\npatterning of sensory organ precursor cells further shows the patterning reliance\r\non long-range signalling dynamics and the tissue’s mechanical properties. We also\r\ndevelop a theoretical framework to understand the restrictions of abstract models of\r\nevolutionary dynamics and interacting species, including a Notch-Delta application.\r\nUsing a set theory argument, we find that symmetry with respect to non-focal traits\r\nis an intrinsic requirement in well-established evolutionary models."^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10158781> <http://purl.org/dc/terms/date> "2022-11-28" .
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