Abstract
A fundamental question in developmental biology is how spatial patterns are self-organized from homogeneous structures. In 1952, Turing proposed the reaction-diffusion model in order to explain this issue. Experimental evidence of reaction-diffusion patterns in living organisms was first provided by the pigmentation pattern on the skin of fishes in 1995. However, whether or not this mechanism plays an essential role in developmental events of living organisms remains elusive. Here we show that a reaction-diffusion model can successfully explain the shoot apical meristem (SAM) development of plants. SAM of plants resides in the top of each shoot and consists of a central zone (CZ) and a surrounding peripheral zone (PZ). SAM contains stem cells and continuously produces new organs throughout the lifespan. Molecular genetic studies using Arabidopsis thaliana revealed that the formation and maintenance of the SAM are essentially regulated by the feedback interaction between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction, incorporating cell division and the spatial restriction of the dynamics. Our model explains the various SAM patterns observed in plants, for example, homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in clv mutants, and initiation of ectopic secondary meristems from an initial flattened SAM in wus mutant. In addition, the model is supported by comparing its prediction with the expression pattern of WUS in the wus mutant. Furthermore, the model can account for many experimental results including reorganization processes caused by the CZ ablation and by incision through the meristem center. We thus conclude that the reaction-diffusion dynamics is probably indispensable for the SAM development of plants.
Highlights
A major subject of developmental biology is how stationary patterns are generated from homogeneous fields
Basic Model for shoot apical meristem (SAM) Dynamics We developed as simple a mathematical model as possible because we aimed to understand the essential dynamics that underlie the proliferation and patterning of the SAM in plants
The diffusible peptide CLV3 corresponds to the inhibitor, and CLV1, CLV2-CRN, and RECEPTOR-LIKE PROTEIN KINASE 2 (RPK2) are involved in its downstream pathway for repressing the activator
Summary
A major subject of developmental biology is how stationary patterns are generated from homogeneous fields. In 1952, in order to account for this issue, Turing proposed the reaction-diffusion model in which stable patterns are self-organized by diffusible components interacting with each other [1]. Whereas this Turing model has been extensively studied by mathematical biologists [2,3,4], until recently it has not been widely accepted by experimental biologists. Following the description in 1995 of a Turing pattern in the skin pigmentation of marine angelfish [5], the Turing model has attracted attention from developmental and molecular biologists. It would be difficult to verify whether or not the reaction-diffusion pattern plays essential roles in morphogenesis processes in animals [6,7]
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