Positional information, in bits
Julien O. Dubuis, Gasper Tkacik, Eric F. Wieschaus, Thomas Gregor and William Bialek, PNAS 110, 16301-16308 (2013).
Abstract
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 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 ∼1% 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.
Significance: In a developing embryo, individual cells need to “know” where they are in order to do the right thing. But 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.
For earlier version see arXiv, or Julien Dubuis’ PhD thesis.