Fig. S1 from A new mechanism for spatial pattern formation via lateral and protrusion-mediated lateral signalling

Tissue organization and patterning are critical during development when genetically identical cells take on different fates. It is well known that lateral inhibition and activation can together lead to self-organized spatial motifs in an otherwise uniform collection of cells. This can be mediated through junctional contacts between neighbouring cells, or via cellular protrusions that allow interactions between cells that are at a distance from one another. Although cellular protrusions are emerging as an exciting new means for cellular signalling with a potential role in tissue patterning, it remains unclear how they can physically contribute to the generation of complex patterns without the assistance of diffusible morphogens or the pre-existence of several cell types. In this work, we develop a model of lateral signalling based on a single receptor/ligand pair, such as that of Notch-Delta signalling. We show that allowing the signalling kinetics to differ at direct versus protrusion-mediated contacts permits individual cells to act to promote both lateral activation and lateral inhibition. This assumption is inspired by recent data which show that the cleavage of Notch in several systems requires both Delta binding and the application of mechanical force. Strikingly, under this model, in which Delta can sequester Notch, a variety of patterns resembling those typical of reaction-diffusion systems is observed, together with more unusual patterns that arise when we consider changes in signalling kinetics, and in the length and distribution of protrusions. Importantly, these patterns are self-organizing - so that local interactions drive tissue-scale patterning. Together, these data show that protrusions can, in principle, control the formation of different types of patterns in addition to their contributing to long-range signalling and to pattern refinement.