Trading bits in the readout of positional information

Expression levels of gap genes, crucial for fly development, have been shown to be precise, matching the spatial precision in the expression of downstream genes. If the transcriptional machinery can read these gap expression levels only imprecisely, subsequent precision could not be reproduced. Yet, assuming that levels can be read with infinite precision is unrealistic. Reading expression levels with limited precision can be phrased mathematically by limiting the number of bits which are available for each measurement. The question of how to use these bits to capture the maximum positional information is an instance of the information bottleneck problem. We show that to capture ~90% of the available information, we need more bits than intuitively biologically reasonable. We can allow for an increased number of bits per measurement by having molecules bind to multiple sites. This is a generalization of the information bottleneck problem. We show that one can capture almost all the available information with multiple “low precision” encodings, which may correspond physically to multiple binding sites or even enhancers.