  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.
