Figure 1.

Reporter accuracy depends upon regulatory context. Identical alleles of the same gene produce mRNA molecules M₁ and M₂. Alleles 1 and 2 behave independently when there is no common upstream regulator or regulator concentration (x) is constant, yet become coupled if the upstream regulator fluctuates. (Top panels) Shown here are fluctuations of upstream regulator concentration. Panels show constant x (A) and x ∼ Gamma(r,θ), for low regulator dispersion θ = 0.02 (B) and high regulator dispersion θ = 0.5 (C). (Bottom panels) Shown here are joint and marginal distributions for m₁ and m₂. Joint distributions are the product of two Poisson distributions (A, Eq. 2) and bivariate negative binomials, BNB(r,p), with p = q for identical alleles (B and C; Eq. 4). All distributions use λ = 50 for both alleles and contours show probabilities: 0.0001 inner, 0.0003 middle, and 0.0005 outer. NB(r,p/(1−p)) denotes “negative binomial”. Scatter plots, histograms, and MI (in nats) are shown for a random sample of 1000 draws. The same scales apply to all comparable plots. To see this figure in color, go online.