Bicoid Morphogen Gradient

Drosophila positional information · Diffusion-degradation · Threshold patterning

Production rate J: 1.0

Diffusion D: 0.5

Degradation λ: 0.8

Hunchback threshold θ_hb: 0.30

Knirps threshold θ_kn: 0.12

Gene dosage (copies): 2

Decay length λ⁻¹—

hb boundary—

kn boundary—

Robustness—

Bicoid (Bcd) is a transcription factor produced at the anterior pole of the Drosophila egg. It diffuses posteriorly and is degraded uniformly.
Steady-state profile: C(x) = C₀ exp(−x/λ), where λ = √(D/λ_deg) is the decay length.
Positional information: downstream genes like hunchback are activated where Bcd > θ_hb. This sets the head/trunk boundary.
Robustness: because C₀ ∝ gene-copy-number, changing dosage shifts the entire profile. The relative boundary position x/L ≈ λ·log(J/(κθ)) depends logarithmically on dosage — robust to 2-fold changes.