A Developmental Model for Branching Morphogenesis of Lake Cress Compound Leaf

Abstract

Lake cress, Rorippa aquatica (Brassicaceae), is a semi-aquatic plant that exhibits a variety of leaf shapes, from simple leaves to highly branched compound leaves, depending on the environment. Leaf shape can vary within a single plant, suggesting that the variation can be explained by a simple model. In order to simulate the branched structure in the compound leaves of R. aquatica, we implemented reaction-diffusion (RD) patterning onto a theoretical framework that had been developed for serration distribution in the leaves of Arabidopsis thaliana, with the modification of the one-dimensional reaction-diffusion domain being deformed with the spatial periodicity of the RD pattern while expanding. This simple method using an iterative pattern could create regular and nested branching patterns. Subsequently, we verified the plausibility of our theoretical model by comparing it with the experimentally observed branching patterns. The results suggested that our model successfully predicted both the qualitative and quantitative aspects of the timing and positioning of branching in growing R. aquatica leaves.

Regulation of the KNOX-GA Gene Module Induces Heterophyllic Alteration in North American Lake Cress

“…Therefore, the extensive knowledge on leaf development accumulated from these compound-and simple-leafed model species may help to reveal the molecular mechanism regulating heterophylly in R. aquatica. Indeed, studies on submergence tolerance in Rorippa species have been successfully performed based on comparisons with Arabidopsis (Akman et al, 2012;Sasidharan et al, 2013), and phylogenetic and modeling-based analyses have also been reported (Nakamasu et al, 2014;Nakayama et al, 2014). These features make R. aquatica an excellent model species to investigate the mechanism regulating heterophylly.…”

Asymmetries in leaf branch are associated with differential speeds along growth axes: A theoretical prediction

“…According to our previous study (Nakamasu et al, 2014), the number of higher-orders of axes on each secondary axis were predicted to increase intermittently. For example, the n th newest secondary axis would have C n ¼ 2C nÀ2 þ C nÀ1 ðn !…”

“…In the previous model for divaricate-leaf morphogenesis (Nakamasu et al, 2014), a 1D boundary domain on a 2D plane ( ¼ leaf DEVELOPMENTAL DYNAMICS …”

“…According to the model, the distribution of axes along the primary axis could be estimated by a recurrence formula (Nakamasu et al, 2014), as mentioned above. According to the model, the distribution of axes along the primary axis could be estimated by a recurrence formula (Nakamasu et al, 2014), as mentioned above.…”

“…Previous studies have defined leaf formation as a deformation of a boundary of the 2D field depending on a spatially periodic pattern (Bilsborough et al, 2011;Nakamasu et al, 2014). Previous studies have defined leaf formation as a deformation of a boundary of the 2D field depending on a spatially periodic pattern (Bilsborough et al, 2011;Nakamasu et al, 2014).…”