Wolpert's French flag model: cells read a morphogen gradient and differentiate based on local concentration thresholds. See how decay length, noise, and opposing gradients shape tissue patterning.
Model
Decay length λ0.30
Threshold 1 (T₁)0.60
Threshold 2 (T₂)0.25
Noise σ0.02
Number of cells80
Wolpert (1969): The positional information (PI) framework separates the generation of a morphogen gradient from how cells interpret it. A cell's "position" is encoded in local concentration; thresholds gate identity. Robustness: Boundary sharpness ~ 1/(σ × |∂C/∂x|⁻¹). Steeper gradient → sharper boundaries → more robust to noise. Opposing gradients (gap genes): Bicoid activates anterior; Nanos/Caudal suppresses Hunchback posteriorly. Cross-repression creates sharp, stable boundaries.