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.

形态发生是生物系统中形成多种功能器官的现象。在植物中，形态发生主要是由组织的差异生长驱动的。人们付出了大量的努力来确定遗传和生物分子途径在调节细胞分裂和细胞扩张以及影响植物器官形状形成中的作用。然而，决定差异生长如何控制植物叶子和花瓣中复杂 3D 形状形成的一般原理仍然很大程度上未知。通过对活体植物器官的定量测量和详细的有限元模拟，我们展示了生长应变的最大值和空间分布如何决定生长叶子的形态。有了这种认识，我们为形态相图开发了一个广泛的科学框架，该框架能够合理化植物器官中常见的四种配置：扭曲、螺旋扭曲、鞍形弯曲和边缘波动。我们通过使用水凝胶的受控聚合来合成所有四种配置，证明了这些发现和分析的稳健性。我们的研究指出了在建筑、软机器人和柔性电子等应用中创新几何设计和驱动的潜在方法。