Abstract
Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to their implications within 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 this work, we examine the benefits and limitations of new and existing models of cell signalling and differentiation in a variety of contexts. Using linear and weakly nonlinear stability analyses, we find that pattern selection relies on nonlinear effects that are not covered by such analytical methods.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
Added 4 supplementary video files, missing in the first version. No further changes.
1 The quantity a1/k is the neighbour Delta activity level necessary for half-maximal Notch activation, while b−1/h is the Notch activity level necessary for half-maximal Delta inhibition.