@phdthesis{discovery10158781,
            year = {2022},
           month = {November},
           title = {Cell-cell interactions in epithelial patterning: Notch-Delta signalling and evolutionary dynamics},
            note = {Copyright {\copyright} The Author 2022. Original content in this thesis is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) Licence (https://creativecommons.org/licenses/by-nc/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author's request.},
          school = {UCL (University College London)},
          author = {Berkemeier, Francisco Pinto},
        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.},
             url = {https://discovery.ucl.ac.uk/id/eprint/10158781/}
}