  Information transmission in cells occurs quite accurately even when
concentration changes are "read" by individual target molecules. In this Letter
we study molecule number fluctuations when molecules diffuse and react. We show
that, for immobile binding sites, fluctuations in the number of bound molecules
are averaged out on a relatively fast timescale due to correlations. This
result can explain the observed co-existence of highly fluctuating
instantaneous transcriptional activities and of relatively stable protein
concentrations shortly after the beginning of transcription. We also show that
bound molecule numbers fluctuate with one or two characteristic timescales
depending on the concentration of free molecules. This transition can explain
changes in enzyme activity observed at the single molecule level.
