Differential growth and shape formation in plant organs.

Morphogenesis is a phenomenon by which a wide variety of functional organs are formed in biological systems. In plants, morphogenesis is primarily driven by differential growth of tissues. Much effort has been devoted to identifying the role of genetic and biomolecular pathways in regulating cell division and cell expansion and in influencing shape formation in plant organs. However, general principles dictating how differential growth controls the formation of complex 3D shapes in plant leaves and flower petals remain largely unknown. Through quantitative measurements on live plant organs and detailed finite-element simulations, we show how the morphology of a growing leaf is determined by both the maximum value and the spatial distribution of growth strain. With this understanding, we develop a broad scientific framework for a morphological phase diagram that is capable of rationalizing four configurations commonly found in plant organs: twisting, helical twisting, saddle bending, and edge waving. We demonstrate the robustness of these findings and analyses by recourse to synthetic reproduction of all four configurations using controlled polymerization of a hydrogel. Our study points to potential approaches to innovative geometrical design and actuation in such applications as building architecture, soft robotics and flexible electronics.