Quantitative phenotyping of leaf margins in three dimensions, demonstrated on KNOTTED and TCP trangenics in Arabidopsis

Abstract

The geometry of leaf margins is an important shape characteristic that distinguishes among different leaf phenotypes. Current definitions of leaf shape are qualitative and do not allow quantification of differences in shape between phenotypes. This is especially true for leaves with some non-trivial three-dimensional (3D) configurations. Here we present a novel geometrical method novel geometrical methods to define, measure, and quantify waviness and lobiness of leaves. The method is based on obtaining the curve of the leaf rim from a 3D surface measurement and decomposing its local curvature vector into the normal and geodesic components. We suggest that leaf waviness is associated with oscillating normal curvature along the margins, while lobiness is associated with oscillating geodesic curvature. We provide a way to integrate these local measures into global waviness and lobiness quantities. Using these novel definitions, we analysed the changes in leaf shape of two Arabidopsis genotypes, either as a function of gene mis-expression induction level or as a function of time. These definitions and experimental methods open the way for a more quantitative study of the shape of leaves and other growing slender organs.

Keywords: Arabidopsis; curvature; differential geometry; growth; leaf shape; lobes; waviness..

Fig. 1.

Decomposition of leaf margin local curvature. (A) A 3D measurement of an Arabidopsis KAN>>miR319 leaf. Both surface topography (axes and colour bar in mm) and the edge curve (black line) are obtained. (B) At each point, s, along the margins we obtain the local tangent vector to the margins curve, $\widehat{t}$ , and the local normal to the surface, $\widehat{N}$ . The local curvature vector, $\overrightarrow{k}$ , is decomposed into its normal component${\kappa }_n$ and geodesic component ${\kappa }_g$ . The local tangent plane is depicted as a shaded square. (This figure is available in colour at JXB online.)

Fig. 2.

Arabidopsis leaf shape phenotypes. (A) 35S:kn1-GR leaves, sprayed with increasing dexamethasone concentrations (as indicated). Bar, 5mm. (B) A KAN>>miR319 leaf at different ages. Bar, 5mm. (This figure is available in colour at JXB online.)

Fig. 3.

Waviness and lobiness of synthetic surfaces and common leaves. The images (top panels) show the surface topography from two different viewpoints. Surface colour represents the z coordinate in arbitrary units. The plots (bottom panels) display local curvature components ${\kappa }_n$ (dashed blue) and ${\kappa }_g$ (solid red) as functions of arc-length coordinate along the perimeter, s. (A) A mathematical wavy surface of constant radius (measured along the surface). (B) A mathematical wavy surface with oscillating radius. (C) A wavy Pittosporum leaf. (D) A flat and lobate tomato leaflet. Bars, 5mm. The measured values of w and l (see main text for definitions) are shown below the plots. (This figure is available in colour at JXB online.)

Fig. 4.

Waviness and lobiness of Arabidopsis 35S:Kn1-GR leaves. (A–C) Leaves treated with DEX at different concentrations (from left to right: 0, 2×10^–7, and 1×10^–6 mol l^–1). The variation in the geometry of leaf margins is captured quantitatively by ${\kappa }_n(s)$ (dashed blue) and${\kappa }_g(s)$ (solid red). The letters on the top and bottom panels show the close correlations between specific features on the leaf and the local measurements of ${\kappa }_g(s)$ and${\kappa }_n(s)$ . Bar, 5mm. (This figure is available in colour at JXB online.)

Fig. 5.

Changes in leaf geometry of Arabidopsis 35S:Kn1-GR. (A) The overall leaf area as a function of DEX concentration. (B) The ratio,$R$ , between leaf perimeter and diameter as a function of DEX concentration. (C) The waviness, w (squares), and lobiness, l (triangles), as functions of DEX concentration. (D) The waviness and lobiness in (C) as functions of R. Each data point is the averaged result over nine leaves. (This figure is available in colour at JXB online.)

Fig. 6.

Changes in a single leaf marginal shape during growth: comparison between wild-type (open symbols) and KAN1>>miR319 (filled symbols) leaves. (A) Leaf areas versus time. (B) Excess length ratios, R, versus time (C) The waviness, w (squares), and lobiness, l (triangles), as functions of time. (D) The waviness and lobiness as in (C) as functions of R. (This figure is available in colour at JXB online.)