Collective Space-Sensing Coordinates Pattern Scaling in Engineered Bacteria

• A synthetic gene circuit generates robust scale invariance in bacteria
• Scaling is mediated by integral feedback and incoherent feedforward control
• Scaling occurs through modulation of temporal dynamics of diffusible molecules
• The mechanism is applicable for examining pattern formation and scaling in nature

SummaryScale invariance refers to the maintenance of a constant ratio of developing organ size to body size. Although common, its underlying mechanisms remain poorly understood. Here, we examined scaling in engineered Escherichia coli that can form self-organized core-ring patterns in colonies. We found that the ring width exhibits perfect scale invariance to the colony size. Our analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop. The integral feedback is implemented by the accumulation of a diffusive chemical produced by a colony. This accumulation, combined with nutrient consumption, sets the timing for ring initiation. The incoherent feedforward is implemented by the opposing effects of the domain size on the rate and duration of ring maturation. This mechanism emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.

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