A developmental model for branching morphogenesis of lake cress compound leaf

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

Spatiotemporal plot and growth profiles for the BPM rings by pattern dependent expansion.

<p>A: Schematic of the modeling. B: Spatiotemporal plot for peak doubling by insertion. The value of reactant is represented by the gray scale. Each panel shows the first (C), second (D), third (E), and fourth (F) insertion. Each point indicate the middle point of segmented cell, then the color of points indicate the value of reactant <i>u</i>. Solid arrowheads indicate the points of peak insertion, and empty arrowheads are points of side branch generation.</p

Spatiotemporal plot and growth profiles for the BPM rings by Expansion inhibition.

<p>A: Spatiotemporal plot for peak doubling by splitting. The value of reactant is represented by the gray scale. Each panel shows the first (B), second (C), third (D), and fourth (E) splitting. Each point indicate the middle point of segmented cell, then the color of points indicate the value of reactant <i>u</i>. Solid arrowheads indicate the points of peak splitting, and empty arrowheads are points of side branch generation.</p

The numbers of leaflet primordia of each primary leaflet.

<p>A: Schematic of the branched structure of one half of a <i>R</i>. <i>aquatica</i> compound leaf. Circled numbers indicate the positions of primary leaflet (the horizontal axis in B), and theoretically derived recurrence formulas of each primary leaflet are shown by . The red numbers represent the numbers of leaflets formed on the 4^th primary leaflet (the vertical axis in B). B: A comparison between the experimentally observed data in actual plants and theoretically estimated numbers derived from mathematical formulae of leaflet on each primary leaflet. The magenta dots show the data from mature leaves. The number of leaflets at each stage was plotted as aligned at the center. The theoretical estimations are represented on a yellow planar graph, and the actual data in developing leaves as blue dots with columns.</p

Morphogenesis of <i>Rorippa aquatica</i> leaves.

<p>A, B: Mature leaf morphology of the simple leaf that was developed at 30°C (A) and the highly branched compound leaf that was developed at 20°C (B). Scale bar: 1 cm. C: Dissected shoot apex of a plant grown at 20°C, showing the nested group of leaf primordia with indented blade. D–F: Dissected primordial of a plant grown at 20°C for about 2 months. Each primodium has the 32th (D), 35th (E), and 39th (F) leaf primordium from the oldest (i.e. outermost) leaf of a plant. The larger leaf position numbers indicate younger leaves. Scale bar: 1 mm (C) and 200 µm (D–F). G: Comparison of the total number of leaflet primordial between experimentally observed and the theoretically estimated value.</p

Simulations of leaf primordia and branches.

<p>Each panel shows the simulated whole leaves (A–C) and primary leaflets (D–H). The simulated branches were crossover. Each branch was independently formed nested regular branches. The inserted number shows the time of iterative calculations (), and the arrowheads indicate each leaflet; filled, flamed, and dotted arrow heads represent the first, second, and third primary leaflet respectively.</p