A mathematical model for understanding synergistic regulations and paradoxical feedbacks in the shoot apical meristem

The shoot apical meristem (SAM) is the primary stem cell niche in plant shoots. Stem cells in the SAM are controlled by an intricate regulatory network, including negative feedback between WUSCHEL (WUS) and CLAVATA3 (CLV3). Recently, we identified a group of signals, Epidermal Patterning Factor-Like (EPFL) proteins, that are produced at the peripheral region and are important for SAM homeostasis. Here, we present a mathematical model for the SAM regulatory network. The model revealed that the SAM uses EPFL and signals such as HAIRY MERISTEM from the middle in a synergistic manner to constrain both WUS and CLV3. We found that interconnected negative and positive feedbacks between WUS and CLV3 ensure stable WUS expression in the SAM when facing perturbations, and the positive feedback loop also maintains distinct cell populations containing WUS ^on and CLV3 ^on cells in the apical-basal direction. Furthermore, systematic perturbations of the parameters revealed a tradeoff between optimizations of multiple patterning features. Our results provide a holistic view of the regulation of SAM patterning in multiple dimensions. They give insights into how Arabidopsis integrates signals from lateral and apical-basal axes to control the SAM patterning, and they shed light into design principles that may be widely useful for understanding regulatory networks of stem cell niche.