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The concept of positional information is central to our understanding of howcells in a multicellular structure determine their developmental fates.Nevertheless, positional information has neither been defined mathematicallynor quantified in a principled way. Here we provide an information-theoreticdefinition in the context of developmental gene expression patterns and examinewhich features of expression patterns increase or decrease positionalinformation. We connect positional information with the concept of positionalerror and develop tools to directly measure information and error fromexperimental data. We illustrate our framework for the case of gap geneexpression patterns in the early Drosophila embryo and show how informationthat is distributed among only four genes is sufficient to determinedevelopmental fates with single cell resolution. Our approach can begeneralized to a variety of different model systems; procedures and examplesare discussed in detail.

Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework