Morphogen Gradient — Bicoid Exponential Patterning

Bicoid morphogen diffuses from anterior and degrades throughout the Drosophila embryo. Concentration threshold crossings define segment boundaries — reaction-diffusion with positional information.

Morphogen Concentration Profile

Gene Expression Domains

Parameters

∂C/∂t = D∇²C − μC + J·δ(x)
Steady state: C(x) = C₀ exp(−x/λ)
λ = √(D/μ), threshold → boundary
λ = 1.000
C₀ = 1.000

Noise Robustness

Many embryos with 5% noise on D,μ. Blue lines = individual profiles; spread shows boundary precision.