  Information of relevance to the organism often is represented by the
concentrations of particular molecules inside a cell. As outside observers we
can now measure these concentrations precisely, but the cell's own mechanisms
must be noisier. We show that, in certain limits, there is a universal tradeoff
between the information capacity of these concentration measurements and the
amount of relevant information that is captured, a version of the information
bottleneck problem. This universal tradeoff is confirmed, quantitatively, in an
analysis of the positional information encoded by the gap genes in the
developing fly embryo.
