Reaction wavefront theory of notochord segment patterning

The vertebrate axis is segmented into repetitive structures, the vertebrae. In fish, these segmented structures are thought to form from the paraxial mesoderm and the adjacent notochord. Recent work revealed an autonomous patterning mechanism in the zebrafish notochord, with inputs from the segmented paraxial mesoderm. The notochord pattern is established in a sequential manner, progressing from anterior to posterior. Building on this previous work, here, we propose a reaction wavefront theory describing notochord patterning in zebrafish. The pattern is generated by an activator-inhibitor reaction-diffusion mechanism. Cues from the paraxial mesoderm are introduced as a profile of inhibitor sinks. Reactions are turned on by a wavefront that advances from anterior to posterior. We show that this reaction wavefront ensures that a pattern is formed sequentially, in register with the cues, despite the presence of fluctuations. We find that the velocity and shape of the reaction wavefront can modulate the prevalence of defective patterns. Normal patterning is supported in a wide range of sink profile wavelengths, while a minimum sink strength is required for the pattern to follow the cues. The theory predicts that distinct defect types occur for small or large wavelengths. Thus, the reaction wavefront theory provides a possible scenario for notochord patterning, with testable predictions that prompt future experiments.