Available online at www.sciencedirect.com Modeling plant growth and pattern formation Henrik Jo ¨ nsson and Pawel Krupinski Abstract Plants continue to grow and generate new organs in symmetric patterns throughout their lives. This development requires an interconnected regulation of genes, hormones, and anisotropic growth, which in part is guided by environmental cues. Recently, several studies have used a combination of experiments and mathematical modeling to elucidate the mechanisms behind different growth and molecular patterns in plants. The computational models were used to investigate the often non-intuitive consequences of different hypotheses, and the in silico simulations of the models inspired further experimentation. Address Computational Biology and Biological Physics, Lund University, Sweden Corresponding author: Jo ¨ nsson, Henrik (henrik@thep.lu.se) Current Opinion in Plant Biology 2010, 13:5–11 This review comes from a themed issue on Growth and Development Edited by Dominique C. Bergmann and Andrew J. Fleming Available online 11th November 2009 1369-5266/$ – see front matter # 2009 Elsevier Ltd. All rights reserved. DOI 10.1016/j.pbi.2009.10.002 Introduction Plant development can be described as a dynamic system of molecular patterning, resulting from biochemical reac- tions and molecular transport [1,2], combined with a regulated growth, resulting from an isotropic turgor pres- sure and anisotropic mechanical properties of the cell walls [3]. The coordination between molecular patterning and morphogenesis suggests the existence of feedback between the two systems. Recent increase in the amount of available molecular data together with in vivo measure- ments of the cytoskeleton has enhanced the possibility to investigate the interactions between genes, hormones, and growth as a single system. Computational modeling provides an important tool for examining the hormonal patterning, the genetic network modules that control differentiation, and the possibility of mechanical properties driving patterning. In this review we will discuss recent progress in modeling these pro- cesses including efforts combining molecular patterning with mechanical changes that alter growth dynamics. The examples given show that different modeling techniques can be successful and that the models in iterative com- bination with experiments present a powerful approach toward a more comprehensive understanding of plant development. Modeling hormonal control of development Phytohormones regulate many aspects of plant growth and development [2]. A prominent example investigated in many modeling studies is auxin. Auxin is fundamental to multiple physiological processes at different scales in the plant including embryonic patterning, phyllotaxis, tropism, and the development of leaf veins and root hairs [4]. Critical for auxin patterning is its polar movement between cells facilitated by membrane-bound influx and efflux mediators — AUX and PIN family of proteins, respectively. In roots the transport mediators are expressed in a static pattern, which has been adopted in models using a pre- defined localization of transport mediators to predict auxin distribution. PIN efflux mediators are localized basally (toward the root tip) in internal tissues and apically in epidermal cells, with some lateral inward localization in outer cell layers suggesting a ‘reflux’ of auxin that creates a maximum at the root tip. Grieneisen et al. [5  ] imple- mented these PIN patterns in a two-dimensional model showing that this was sufficient to create the experimen- tally verified stable auxin maximum at the root apex, and also predicted several perturbations and auxin-regulated growth (Figure 1a). A similar model was used to argue that changes in auxin concentration due to a geometric trans- formation could be responsible for the initiation of the lateral root [6]. Swarup et al. [7] used a three-dimensional model of the outer cell layers of the root to demonstrate the importance of the epidermally expressed AUX1 for apical transport of auxin and maintenance of the asym- metry in auxin localization caused by gravitropic response. Using a similar model, Jones et al. [8  ] found that differentially expressed AUX1 in root-hair versus non-hair cells promotes a more uniform and long-ranged distribution of auxin (Figure 1b). These root models are examples of successful approaches where the models have been developed and challenged with direct com- parisons with experiments. It would be interesting to compare predictions of a model including both internal tissue and influx mediators with increasingly resolved quantitative measurements of auxin in the root (e.g. [9]). Other aspects of auxin patterning show dynamic expres- sion and localization of transport mediators. Molecular models of leaf venation rely on the prevailing idea of canalization introduced by Sachs [10] and first www.sciencedirect.com Current Opinion in Plant Biology 2010, 13:5–11