Figure 1: Decoding in a genetic network.

(A) In the early Drosophila embryo, maternally provided morphogens (bcd, nos, tor) regulate the expression of gap genes (kni, kr, gt, hb), which is visualized here in a mid-sagittal slice through an embryo during n.c. 14 (scale bars, 100 μm). Enhancers (schematically depicted as circles) respond to combinations of gap protein concentrations to drive pair-rule gene expression that occurs in a precise and reproducible striped pattern (Gregor et al., 2014). (B) Schematic depiction of the decoding problem. Positional information is supplied by three morphogens primarily acting in the anterior A, posterior P, or terminal T domains. The network can be viewed as an input/output device that encodes physical location x in the embryo using concentrations {g₁, g₂, g₃, g₄} of the gap gene proteins. Optimal decoding is a well-posed mathematical problem, whose solution is found in the posterior distribution P(x*∣{g_i}) (Equation 3); results can be visualized as a decoding map, P(x*∣x) (Equation 4 and Figure 2). The posterior distribution is constructed from measurements (average gap gene expressions, $\{{\stackrel{‒}{g}}_i(x)\}$ and their covariability, C_ij(x), and contains no arbitrary parameters. (C) Testable predictions from optimal decoding. Pair-rule stripes are expected wherever decoding a combination of concentrations yields an implied position, X*, associated with a pair-rule stripe, $X_{\text{str}}^{\ast }$, in WT.