Figure 1.

(A) Effect of the transport step on the noise in mRNA levels. A gene, G, is activated only when a TF is localized at the gene locus and produces mRNA molecules, M, at rate k. The TFs, of copy number n, are assumed to diffuse in a nucleus or cell of volume V. The space accessible to TFs is depicted in yellow and the space made inaccessible due to crowding effects in red. T denotes the random waiting time between successive production events of M, whose distribution, $f_n\left(T\right)$, is governed by successive returns of TFs to the locus. The mRNA molecules are degraded at rate ${\lambda }_d$. We will consider here both cases of eukaryotes (for which degradation generally occurs outside the nucleus) and prokaryotes. (B) Schematic TF trajectory when crowding effects are weak: the typical number of fast returns of a TF to a given site is small and the exploration of the cellular or nuclear environment is called noncompact. The production of mRNA is then shown to follow classical first-order kinetics. (C) Schematic TF trajectory when crowding effects are important, as in the case of a fractal organization of DNA: the typical number of fast returns of a TF to a given site is very large and the exploration is called compact. We show that the geometry of compact trajectories induces large correlated bursts of mRNA.