Quantitative modeling of Arabidopsis development

Abstract

We present an empirical model of Arabidopsis (Arabidopsis thaliana), intended as a framework for quantitative understanding of plant development. The model simulates and realistically visualizes development of aerial parts of the plant from seedling to maturity. It integrates thousands of measurements, taken from several plants at frequent time intervals. These data are used to infer growth curves, allometric relations, and progression of shapes over time, which are incorporated into the final three-dimensional model. Through the process of model construction, we identify the key attributes required to characterize the development of Arabidopsis plant form over time. The model provides a basis for integrating experimental data and constructing mechanistic models.

Figure 1.

Schematic diagram of Arabidopsis (not to scale). Metamers of the main axis and on some of the lateral branches are labeled. The branching angle (β) and leaf insertion angle (α) are shown for m8 and m9, respectively.

Figure 2.

Internode length (int l) plotted against time on a linear scale (A) and on a logarithmic scale (B). The Boltzmann function on a linear scale (C) and on a logarithmic scale (D). All lengths are in millimeters.

Figure 3.

Leaf width (leaf w) of the main-stem metamers plotted against time (hfs) and fitted with the Boltzmann function.

Figure 4.

A, Four dissected leaves at widths of 1 mm, 3 mm, 6 mm, and the maximum leaf width for each metamer normalized by height. B, The mature leaf of m5, with an eight-point B-spline fitted to its outline, and the resulting outline curve.

Figure 5.

Mature leaf shapes of the m4 to m10 lateral branches. Rows refer to leaves from the same branch of index n, while columns refer to leaves at the same position along each branch. Thus, the leaf in the bottom left corner is the first leaf of branch m4 (i.e. m4-0).

Figure 6.

Flower measurements from a single plant taken at daily intervals and plotted against time (hfs). A, Bud width fitted with an exponential function. B, Pedicel length fitted with the Boltzmann function.

Figure 7.

Organ measurements from dissected flowers aligned with the time course of flower 1 using bud width (▪) or pedicel length (□) data. In A to D, data are fitted with the Boltzmann function: A, sepal width (sep w); B, petal width (pet w); C, anther width (ant w); D, carpel length (car l). In E and F, data are fitted with an exponential function during the early phase of growth and the Boltzman function during the later phase. E, Pedicel length (ped l); F, filament length (fil l). The switch point between phases is shown with a black arrow. Time of flower opening is indicated by white arrow.

Figure 8.

Petals and sepals dissected and flattened at four stages of development with a spline curve fitted to the left half of the shape.

Figure 9.

Average plastochron (▪) and angle (□) between successive metamers plotted against metamer interval. Dotted line shows the golden angle of approximately 137.5°.

Figure 10.

Comparison of sample Arabidopsis plants (A, C, E) with the model (B, D, F). A and B, at 264 hfs; C and D, at 417 hfs; E and F, at 491 hfs. Scale bar = 1 cm.