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A simple model of Nodal diffusion and capture reproduces experimental observations.(A) Schematic of Nodal diffusion-capture model. Simulations were performed on a two-dimensional tissue of 100 μm x 300 μm. Nodal molecules are secreted at a constant rate from a localized source at one boundary of the tissue (i.e. 0 < x < 5 μm) and diffuse freely until capture by cell surface receptors (‘Oep’). Ligand-receptor complexes are removed from the system by internalization. To track signaling activity, Smad2 phosphorylation is simulated with rate proportional to the concentration of receptor-ligand complexes. (B-D) Simulation of transplant experiments. In each simulation, the behavior of sensor cells (white outlines) is compared with the behavior of the host embryo (remainder of tissue). Parameters were independently set for host and sensor regions, allowing for simulation of experiments with mutations and overexpression. Signaling activity (i.e. [pSmad2]) is plotted in magenta. Upper panels present representative simulations with randomly-positioned sensor cells. Lower panels depict quantified signaling intensities for sensor cells from the panel above (blue points) and average intensities derived from replicate simulations (red curves). (B) Wild-type gradient simulation. Sensor cells with normal Oep levels are transplanted into a host with normal Oep levels. A stable gradient forms, and signaling is identical in sensor cells and neighboring regions. (C) Gradient expansion in MZoep mutants. Sensor cells contain normal Oep levels, but host cells lack Oep. Sensor cells detect ligand throughout the tissue. (D) Gradient contraction with oep overexpression. Sensor cells contain normal Oep levels, whereas host cells lack Smad2, but overexpress oep. Signaling is absent in the host tissue—due to lack of Smad2—but elevated receptor expression restricts Nodal spread to the sensors.
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