Flat leaf formation realized by cell-division control and mutual recessive gene regulation

Most of the land plants generally have dorsoventrally flat leaves, maximizing the surface area of both upper (adaxial) side and lower (abaxial) side. The former is specialized for light capturing for photosynthesis and the latter is specialized for gas exchange. From findings of molecular genetics, it has been considered that the coupled dynamics between tissue morphogenesis and gene regulation for cell identity is responsible for making flat leaves. The hypothesis claims that a flat leaf is generated under two assumptions, (i) two mutually recessive groups of genes specify adaxial and abaxial sides of a leaf, (ii) cell divisions are induced at the limited region in the leaf margin where both of two groups are expressed. We examined the plausibility and possibility of this hypothesis from the dynamical point of view. We studied a mathematical model where two processes are coupled, tissue morphogenesis induced by cell division and deformation, and dynamics of gene regulations. From the analysis of the model we found that the classically believed hypothesis is not sufficient to generate flat leaves with high probability. We examined several different modifications and revision of the model. Then we found that a simple additional rule of polarized cell division facilitates flat leaf formation. The result of our analysis gives prediction of possible mechanism, which can be easily verified in experiments.