Bicoid Morphogen Gradient — Drosophila Embryo Patterning

Turing's Gradient and Positional Information

Christiane Nüsslein-Volhard (Nobel 1995) discovered that Bicoid protein forms a smooth exponential gradient along the anterior-posterior axis of the Drosophila embryo, providing positional information to downstream genes. Bicoid mRNA is deposited at the anterior pole by the mother; protein diffuses posteriorly and is degraded uniformly.

The steady-state solution of the 1D diffusion-degradation PDE ∂c/∂t = D ∂²c/∂x² − λc + J(x) is exponential: c(x) = c₀ exp(−x/λ_scale) where λ_scale = √(D/λ) sets the gradient length scale. The hunchback gap gene threshold response converts this graded signal into a sharp boundary at ~50% egg length. The colored bands show approximate domains of segmentation genes (hunchback, Krüppel, knirps, giant).