INAUGURAL ARTICLE by a Recently Elected Academy Member:Positional information,in bits

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.Building a complex, differentiated body requires that individual cells in the embryo make decisions, and ultimately adopt fates, that are appropriate to their position. There are wildly diverging models for how cells acquire this “positional information” (1), but there is general consensus that they encode positional information in the expression levels of various key genes. A classic example is provided by anterior/posterior patterning in the fruit fly, Drosophila melanogaster, where a small set of gap genes and then a larger set of pair rule and segment polarity genes are involved in the specification of the body plan (2). These genes have expression levels that vary systematically along the body axis, forming a blueprint for the segmented body of the developed larva that we can “read” within hours after the start of development (3).Although there is consensus that particular genes carry positional information, less is known quantitatively about how much information is being represented by the expression levels in individual cells. Do the broad, smooth expression profiles of the gap genes, for example, provide enough information to specify the exact pattern of development, cell by cell, along the anterior/posterior axis? How much information does the whole embryo use in making this pattern? Answering these questions is important, in part, because we know that crucial molecules involved in the regulation of gene expression are present at low concentrations and even low absolute copy numbers, so that expression is noisy (4–10), and this noise must limit the transmission of information (11–14). Is it possible, as suggested theoretically (15–18), that the information transmitted through these regulatory networks is close to the physical limits set by the irreducible randomness of counting individual molecular events? To answer this and other questions, we need to measure positional information quantitatively, in bits. We do this here using the gap genes in Drosophila as an example.There are many ways in which positional information could be represented during the process of development. Cells could make decisions based on the integration of signals over time or by comparing their internal states with those of their neighbors. Eventually, the internal state of each individual cell must carry enough information to specify that cell’s fate, but it is not clear at what point in development this happens. Thus, when we look at the gap genes during the 14th nuclear cycle after fertilization, there is no guarantee that their expression levels will carry all the information that cells eventually will acquire, either from maternal inputs or via communication with their neighbors. Because our experimental methods give us access to snapshots of gene expression levels, however, we will start by asking how much positional information is carried by local measurements in individual cells at a moment in time. These expression levels themselves reflect an integration of many inputs over space and time (9, 19), but these molecular mechanisms do not influence the definition or measurement of the information that the expression levels carry.