Berkemeier, Francisco Pinto; (2022) Cell-cell interactions in epithelial patterning: Notch-Delta signalling and evolutionary dynamics. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to its implications on many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In the broader context of evolutionary dynamics, signalling and patterning contribute to the definition of phenotypes of individuals within an interacting population, whose mathematical description has been unified under various conceptual frameworks. In this thesis, we examine the benefits and limitations of new and existing models of cell signalling and differentiation in a variety of contexts, including applications in general and well-studied patterning tissues in Drosophila melanogaster. Using linear and weakly nonlinear stability analyses, we find that pattern selection relies on nonlinear effects that are not covered by such analytical methods. The direct application of such models on the Drosophila wing disc development and patterning of sensory organ precursor cells further shows the patterning reliance on long-range signalling dynamics and the tissue’s mechanical properties. We also develop a theoretical framework to understand the restrictions of abstract models of evolutionary dynamics and interacting species, including a Notch-Delta application. Using a set theory argument, we find that symmetry with respect to non-focal traits is an intrinsic requirement in well-established evolutionary models.

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