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 threedimensional 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.Plant development is a dynamic process in which the topology and geometry change over time in a seemingly complex manner. This changing form provides the context of gene action while at the same time being under the control of gene action. To understand this process quantitatively, we first need to identify and measure the key attributes of plant form needed to specify the observed growth pattern. This can be achieved by coupling data acquisition with the construction of a model. The needs of the model guide the process of data acquisition, and the choice of parameters is eventually validated by the final appearance of the model (Bell, 1986).We present such a model for Arabidopsis (Arabidopsis thaliana), one of the key organisms used in the study of plant biology. Measurements and staging of wild-type Arabidopsis growth have been described previously to provide standards for comparisons with mutants (e.g. Smyth et al., 1990; Meicenheimer, 2000a, 2002b). Arabidopsis models have previously been constructed by De Visser et al. (2003) for the purpose of simulating a number of flowering mutants, and by Chenu et al. (2004) for the purpose of simulating light acquisition by rosette leaves. We present a more detailed model of the wild-type plant, intended to serve as a stepping stone for the integration of developmental and molecular genetic data, and for the incorporation of developmental mechanisms.Models of plant development can be implemented using a variety of methods (Prusinkiewicz, 1998). We chose the formalism of L-systems (Lindenmayer, 1968;Prusinkiewicz and Lindenmayer, 1990;Karwowski and Prusinkiewicz, 2003), which provides a programming language for describing the models and a convenient method for visualizing the results as growing three-dimensional structures. According to this formalism, a plant is viewed as a developing assembly of individual units, or modules. These modules are characterized by parameters such as length, width, and age, as well as parameters characterizing shape. A methodology for constructing L-system models based on empirical estimates of such parameters has been introduced by Prusinkiewicz et al. (1994).Here we adapt this methodology to model a developing Arabidopsis (Landsberg erecta) plant from seedling to maturity. We cons...

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