Determination of sensory bristles and pattern formation in Drosophila: I. A model

A model is presented to explain the formation of the pattern of sensory bristles in Drosophila. The model is based on the idea that precision and reproducibility in pattern formation can be achieved by averaging out of many moderately accurate responses to positional cues. According to this model, the determination of bristles in imaginal discs occurs in two steps. First, large numbers of imaginal cells synthesize a freely diffusible inducer, the chaetogen. Second, cells in which the concentration of this chaetogen reaches a threshold are induced to differentiate into a bristle apparatus. Induced cells prevent neighboring cells from being induced too. The synthesis of chaetogen is supposed to be a probabilistic response of cells to positional cues, so that a cell located in one region of the disc is more likely to have its chaetogen gene turned on than a cell located in another region. Various probability distributions are shown to generate the various bristle patterns observed in the adult: precisely located bristles (e.g., thoracic macrochaetes), evenly spaced bristles (e.g., tergal microchaetes), and rows of bristles (e.g., thoracic microchaetes). In the particular case of the precisely located bristles, we show that (i) the distribution of chaetogen concentration in the tissue presents a unique maximum even when a large number of contiguous cells are all engaged in the synthesis of chaetogen; (ii) the position of the maximum is largely unaffected by statistical fluctuations in the decision of each cell to synthesize or not to synthesize the chaetogen; (iii) different maxima can be reproducibly generated even when the corresponding populations of chaetogen-producing cells overlap.