Finding the Last Bits of Positional Information*

Small discrepancies between theory and experiment often are hints of new physics; here we provide an example in the physics of a living system, the fruit fly embryo. For the first hours of development, information about the position of cells is carried by the concentrations of a handful of molecules, all identified. These signals encode position with a precision of ~1% of the length of the embryo, smaller than the spacing between neighboring cells. But errors come from distributions, and distributions have tails. The result is that this precision, while higher than expected, is not quite enough to specify the identity of each cell uniquely. We make this “information gap” precise, in bits. We then show that the gap can be closed if positional noise is correlated over distances ~20% of the embryo length. Finally, we analyze the positions of stripes in pair rule gene expression in 100+ embryos. Correlations in positional noise are a function of distance, even though different stripes reflect the action of different transcription factors, and this dependence agrees with our prediction for what is needed to close the information gap. Direct estimates show that the total positional information, including correlations, is within ~2% of that needed for unique cellular identities.