Intrinsic gene-expression noise (${\eta }_{\mathrm{int}}^2=⟨(x-y{)}^2⟩/2$)

Fluctuations due to individual random events in an expression process, conditional on shared cellular conditions. In a matched dual-reporter measurement, independent reporter fluctuations produce scatter perpendicular to the equal-expression diagonal. For mean-normalized reporters $x,y$, the intrinsic squared noise is $⟨(x-y{)}^2⟩/2$ when reporter-specific measurement noise has been accounted for.

For linear RNA removal and protein production driven by independent additive white noises, the stationary RNA variance is $q_R/(2{\gamma }_R)$ and the protein variance is the displayed expression. Steady count birth-and-death intensities $q_R=2{\gamma }_R⟨R⟩$, $q_P=2{\gamma }_P⟨P⟩$ give the protein Fano factor $1+k_P/({\gamma }_R+{\gamma }_P)$. This specializes arbitrary noise strengths; it is not an identity valid for every additive-noise model.