Two-stage linear gene-expression covariance (source code)

= Two-stage linear gene-expression covariance
{title2=$\operatorname{var}P=q_P/(2\gamma_P)+k_P^2q_R/[2\gamma_R\gamma_P(\gamma_R+\gamma_P)]$}

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 $q_R=2\gamma_R\langle R\rangle$, $q_P=2\gamma_P\langle P\rangle$ 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.