In multicellular organisms, the initial patterns of gene expression are regulated by spatial gradients of biochemical factors, known as morphogen gradients. Because of biochemical noise in the morphogen gradients there are associated spatial errors in the positions of target gene patterns. Using a simple single morphogen and/or single target gene model, we use propagation of error analysis to derive a condition on the amount of morphogen that needs to be produced in order to have precise spatial patterning of the target. We find that there is an optimal morphogen gradient profile that requires the least amount of morphogen to be produced. Experimental results for the Bicoid-Hunchback system in early Drosophila development are consistent with the predictions of this analysis. We also discuss our results in the context of recent work that analyzed this system using mutual information as an organizing principle, and show that minimizing the amount of morphogen produced also leads to a near optimal flow of information between input and target.

• Received 19 October 2007

DOI:https://doi.org/10.1103/PhysRevE.77.041903