Contributed by William Bialek, August 23, 2013 (sent for review November 21, 2012)
In a developing embryo, individual cells need to “know” where they are to do the right thing. How much do they know, and where is this knowledge written down? Here, we show that these questions can be made mathematically precise. In the fruit fly embryo, information about position is thought to be encoded by the concentration of particular protein molecules, and we measure this information, in bits. Just four different kinds of molecules are almost enough to specify the identity of every cell along the long axis of the embryo, and we argue that the way in which this information is distributed reflects an optimization principle, maximizing the information available from a limited number of molecules.
Cells in a developing embryo have no direct way of “measuring” their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for “positional information.” We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as would be expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell’s location with an error bar of 
along the anterior/posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.
↵1J.O.D. and G.T. contributed equally to this work.
This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2012.
Author contributions: This work is a close collaboration between theorists (G.T. and W.B.) and experimentalists (J.O.D., E.F.W., and T.G.). All authors contributed to all aspects of the work.
The authors declare no conflict of interest.
See QnAs on page 16288.
Freely available online through the PNAS open access option.
