Role of spatial averaging in the precision of gene expression patterns

During embryonic development, differentiating cells respond via gene expression to positional cues from morphogen gradients. While gene expression is often highly erratic, embryonic development is precise. We show by theory and simulations that diffusion of the expressed protein can enhance the precision of its expression domain. While diffusion lessens the sharpness of the expression boundary, it also reduces super-Poissonian noise by washing out bursts of gene expression. Balancing these effects yields an optimal diffusion constant maximizing the precision of the expression domain.