Decaying and expanding Erk gradients process memory of skeletal size during zebrafish fin regeneration

Regeneration of an amputated salamander limb or fish fin restores pre-injury size and structure, illustrating the phenomenon of positional memory. Although appreciated for centuries, the identity of position-dependent cues and how they control tissue growth are not resolved. Here, we quantify Erk signaling events in whole populations of osteoblasts during zebrafish fin regeneration. We find that osteoblast Erk activity is dependent on Fgf receptor signaling and organized into millimeter-long gradients that extend from the distal tip to the amputation site. Erk activity scales with the amount of tissue amputated, predicts the likelihood of osteoblast cycling, and predicts the size of regenerated skeletal structures. Mathematical modeling suggests gradients are established by the transient deposition of long-lived ligands that are transported by tissue growth. This concept is supported by the observed scaling of expression of the essential epidermal ligand fgf20a with extents of amputation. Our work provides evidence that localized, scaled expression of pro-regenerative ligands instructs long-range signaling and cycling to control skeletal size in regenerating appendages.