We study the arrangements of recurved bristles on the anterior wing margin of wild-type and mutant Drosophila. The epidermal or neural fate of a proneural cell depends on the concentrations of proteins of the achaete-scute complex. At puparium formation, concentrations of proteins are nearly identical in all cells of the anterior wing and each cell has the potential for neural fate. In wild-type flies, the action of regulatory networks drives the initial state to one where a bristle grows out of every fifth cell. Recent experiments have shown that the frequency of recurved bristles can be made to change by adjusting the mean concentrations of the zinc-finger transcription factor Senseless and the micro-RNA miR-9a. Specifically, mutant flies with reduced levels of miR-9a exhibit ectopic bristles, and those with lower levels of both miR-9a and Senseless show regular organization of recurved bristles, but with a lower periodicity of 4. We argue that these characteristics can be explained assuming an underlying Turing-type bifurcation whereby a periodic pattern spontaneously emerges from a uniform background. However, bristle patterns occur in a discrete array of cells, and are not mediated by diffusion. We argue that intracellular actions of transmembrane proteins such as Delta and Notch can play a role of diffusion in destabilizing the homogeneous state. In contrast to diffusion, intercellular actions can be activating or inhibiting; further, there can be lateral cross-species interactions. We introduce a phenomenological model to study bristle arrangements and make several model-independent predictions that can be tested in experiments. In our theory, miRNA-9a is one of the components of the underlying network and has no special regulatory role. The loss of periodicity in its absence is due to the transfer of the system to a bistable state.
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