Periodic spatial patterning with a single morphogen

Abstract

Multicellular development employs periodic spatial patterning to generate repetitive structures such as digits, vertebrae, and teeth. Turing patterning has long provided a key paradigm for understanding such systems. The simplest Turing systems are believed to require at least two signals, or morphogens, that diffuse and react to spontaneously generate periodic patterns. Here, using mathematical modeling, we show that a minimal circuit comprising an intracellular positive feedback loop and a single diffusible morphogen is sufficient to generate stable, long-range spatially periodic cellular patterns. The model considers cells as discrete entities as a key feature, and incorporates transient boundary conditions. Linear stability analysis reveals that this single-morphogen Turing circuit can support a broad range of spatial wavelengths, including fine-grain patterns similar to those generated by classic lateral inhibition systems. Further, signals emanating from a boundary can initiate and stabilize propagating modes with a well-defined spatial wavelength. Once formed, patterns are self-sustaining and robust to noise. Finally, while noise can disrupt patterning in pre-patterned regions, its disruptive effect can be overcome by a bistable intracellular circuit loop, or by considering patterning in the context of growing tissue. Together, these results show that a single morphogen can be sufficient for robust spatial pattern formation, and should provide a foundation for engineering pattern formation in the emerging field of synthetic developmental biology.