Growth instabilities and margin patterns in an active solid tissue

During morphogenesis, tissues coordinate growth to create complex, spatially patterned organs. While much work has elucidated self-organized mechanisms for patterning fluid-like animal tissues, how such processes can pattern the bulk and boundary of solid-like plant tissues is less explored. Motivated by observations of margin patterns in leaves, we develop an active solid model for a growing tissue that minimally couples tissue growth with biochemical regulation and mechanical feedback. Growth is dictated by a diffusible chemical (Auxin) which in turn is actively transported in a polarized fashion along the leaf margin. This polarity dependent coupling can spontaneously generate chemical patterns, whose transition and properties are controlled by mechanical feedback. We identify instability mechanisms distinct to solid tissues, and determine the conditions for a freely growing tissue to develop boundary instabilities, suggesting a self-organized scenario for the origin of leaf serrations.