| Summary: | This thesis addresses the question of how patterning may arise through cell-to-cell communication. It combines quantitative data analysis with computational techniques to understand biological patterning processes. The first section describes an investigation into the robustness of an evolved artificial patterning system. Cellular automata rules were implemented sequentially according to the instructions in a simple `genome'. In this way, a set of target patterns could be evolved using a genetic algorithm. The patterning systems were tested for robustness by perturbing cell states during their development. This exposed how certain types of patterning rule had very different levels of robustness to perturbations. Rules that generated patterns with complex divergent patterns were more likely to amplify the effect of a perturbation. When smaller genomes, comprising less individual rules, were evolved to match certain target patterns, these were shown to be more likely to select complex patterning rules. As a result, the developmental systems based on smaller genomes were less robust than those with larger genome sizes. Section two provides an analysis of the patterning of microchaetes in the epithelial layer of the notum of Drosophila flies. It is shown that the pattern spacing is not sufficiently described by a model of lateral inhibition through Delta-Notch signalling between adjacent cells. A computational model is used to demonstrate the viability of long range signalling through a dynamic network of filopodia, observed in the basal layer of the epithelium. In-vivo experiments conrm that when filopodia lengths are effected by mutations the pattern spacing reduces in accordance with the model. In the final section the behaviour of simple asynchronous cellular automata are analysed. It is shown how these differ to the synchronous cellular automata used in the first section. A set of rules are identified whose emergent behaviour is similar to the lateral inhibition patterning process established by the Delta-Notch signalling system. Among these rules a particular subset are found to produce patterns that adjust their spacing, over the course of their development, towards a more ordered and densely packed state. A re-examination of the Delta-Notch signalling model reveals that this type of packing optimisation could take place with either dynamic filopodial signalling, or as an alternative, transient Delta signalling at each cell. Under certain parameter regimes the patterns become more densely packed over time, whilst maintaining a minimum zone of inhibition around each Delta expressing cell. The asynchronous CA are also used to demonstrate how stripes can be formed by cell-to-cell signalling and optimised, under certain conditions, so that they align in a single direction. This is presented as a possible novel alternative to the reaction-diffusion mechanism that is commonly used to model the patterning of spots and stripes.
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