Fluctuations, correlations and the estimation of concentrations inside cells

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.