  We study by simulation the effect of the diffusive motion of repressor
molecules on the noise in mRNA and protein levels in the case of a repressed
gene. We find that spatial fluctuations due to diffusion can drastically
enhance the noise in gene expression. For a fixed repressor strength, the noise
due to diffusion can be minimized by increasing the number of repressors or by
decreasing the rate of the open complex formation. We also show that the effect
of spatial fluctuations can be well described by a two-step kinetic scheme,
where formation of an encounter complex by diffusion and the subsequent
association reaction are treated separately. Our results also emphasize that
power spectra are a highly useful tool for studying the propagation of noise
through the different stages of gene expression.
