Towards mechanistic models of plant organ growth

Abstract

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.

Leaf development: a cellular perspective

“…The efflux carriers orient the transport of auxin toward neighboring cells with a higher auxin concentration, leading to the formation of accumulation patterns across the cell population. Several mathematical modeling studies (reviewed in De Vos et al, 2012) have simulated phyllotactic patterning based on feedback interactions between auxin and PIN distribution. Some models postulate that AUX1 creates auxin accumulation mainly in L1 layer cells, whereas PIN1 is initially localized in the protodermal (L1) layer cells and causes drainage of auxin toward the base of the shoot by inducing vascular strand differentiation in L2/3 layer cells of the SAM (Reinhardt et al, 2003; de Reuille et al, 2006; Figure 3 ).…”

“…Next to the molecular mechanism regulating vascular development that has been extensively investigated (Scarpella et al, 2006), knowledge of the regulation of these processes by spatial signals such as growth hormones in order to explain the establishment of their spatial distribution in simulation models is also emerging. Various mathematical models were constructed to explore the role of auxin in vasculature development (Scarpella et al, 2006; De Vos et al, 2012). However, a model proposed by Cano-Delgado et al (2004) highlights the role of BRs in vascular patterning in Arabidopsis .…”

Synthetic Botany

“…The past decade has seen the emergence of increasingly effective models for plant growth in which the software describes the genetic, cellular, and biophysical properties of growing tissues (Jönsson and Krupinski 2010;De Vos et al 2012;Prusinkiewicz and Runions 2012). Although these models have been developed primarily to provide insight into plant develop-C.R.…”

Quantifying Shape Changes and Tissue Deformation in Leaf Development

“…For instance, cell vertices were used as landmarks by Kuchen et al (2012) to track growth in three leaf samples at early developmental stages, and the resulting growth data were used to build a simulation model of early leaf morphogenesis. Simulation models need to be validated experimentally and quantitatively (De Vos et al, 2012) and refined in an iterative fashion through feedback between modeling and the quantitative analysis of experimental data, following systems biology and computational morphodynamics approaches (Roeder et al, 2011). The method we propose here makes it possible to compute tissue deformations from experimental growth data and, therefore, could be used to build and/or quantitatively validate simulation models of leaf morphogenesis.…”