Dynamic gradient scaling as a critical point of growth control

A fundamental question in Biology is to understand how large numbers of cells collectively coordinate their behavior by chemical signals when tissues form and how tissues grow to a finite size. In several organisms, chemical patterns scale with tissue size. We demonstrate how such scaling can arise as a feature of a critical point in growth control, which demarcates regimes of infinite growth and growth arrest. As an application to this theory, we find that homogenous growth and scaling behaviors, as quantified in the wing disc of the fruit fly, reflects signatures of criticality. Our work provides a generic mechanism by which homogeneous self-organized growth and pattern scaling can be robustly achieved in biochemical feedback systems.