A robust mathematical model of adaxial–abaxial patterning

Abstract

Abstract Biological development results from intricate and dynamic interactions between members of gene regulatory networks. This is exemplified by the production of flat leaf architecture. Leaves flatten by driving growth along the boundary between their adaxial (top) and abaxial (bottom) domains. These domains are generated by interactions between a complex network of transcription factors and small RNAs. Despite its complexity, flat leaf production is robust to genetic and environmental noise. To identify factors contributing to this robustness, we mathematically modelled the determinants and interactions that pattern the adaxial–abaxial axis in leaves of Arabidopsis thaliana. Model parameters were estimated almost exclusively using experimental data. Our model recapitulates observations of adaxial–abaxial patterning and small RNA-target interactions. Positioning of the adaxial–abaxial boundary is stable across a wide range of small RNA source values and is highly robust to noise in the model. The successful application of our one-dimensional spatial model will enable higher-dimension modelling of the complex and mechanistically challenging process of flat leaf production.