BioSystems 109 (2012) 488–497 Contents lists available at SciVerse ScienceDirect BioSystems jo ur nal homep age : www.elsevier.com/locate /biosystems Dynamic regulation of growing domains for elongating and branching morphogenesis in plants Lionel G. Harrison a , Richard J. Adams a , David M. Holloway b,∗ a Chemistry Department, University of British Columbia, Vancouver, B.C., Canada b Mathematics Department, British Columbia Institute of Technology, Burnaby, B.C., Canada a r t i c l e i n f o Article history: Received 7 December 2011 Received in revised form 6 March 2012 Accepted 21 March 2012 Keywords: Plant morphogenesis Reaction diffusion Turing pattern formation Growth Tip growth Branching a b s t r a c t With their continuous growth, understanding how plant shapes form is fundamentally linked to under- standing how growth rates are controlled across different regions of the plant. Much of a plant’s architecture is generated in shoots and roots, where fast growth in tips contrasts with slow growth in supporting stalks. Shapes can be determined by where the boundaries between fast- and slow-growing regions are positioned, determining whether tips elongate, branch, or cease to grow. Across plants, there is a diversity in the cell wall chemistry through which growth operates. However, prototypical morpholo- gies, such as tip growth and branching, suggest there are common dynamic constraints in localizing chemical growth catalysts. We have used Turing-type reaction-diffusion mechanisms to model this spa- tial localization and the resulting growth trajectories, characterizing the chemistry-growth feedback necessary for maintaining tip growth and for inducing branching. The mechanism defining the bound- aries between fast- and slow-growing regions not only affects tip shape, it must be able to form new boundaries when the pattern-forming dynamics break symmetry, for instance in the branching of a tip. In previous work, we used an arbitrary concentration threshold to switch between two dynamic regimes of the growth catalyst in order to define growth boundaries. Here, we present a chemical dynamic basis for this threshold, in which feedback between two pattern-forming mechanisms controls the extent of the regions in which fast growth occurs. This provides a general self-contained mechanism for growth control in plant morphogenesis (not relying on external cues) which can account for both simple tip extension and symmetry-breaking branching phenomena. © 2012 Elsevier Ireland Ltd. All rights reserved. 1. Introduction Many plant structures and organs are generated by the exten- sion of simple tips and by branching. Generating these shapes requires growth to be localized to active centres, for example at the tips of shoots or roots. Maintenance of the active centre sizes, i.e. regulation of the boundaries between the fast-growing regions (e.g. tips) and slow-growing regions (e.g. stalks), is critical to shape control. Fine control of these boundaries during growth selects among different morphological outcomes. For example, a contin- uously growing tip requires the boundary between the growing tip and the supporting stalk to move with the tip (Fig. 1A – parts I and II). Slower boundary movement relative to the tip enlarges the actively growing region, flaring the tip (Fig. 1A – part III), which can, as discussed below, allow for branching; whereas faster ∗ Corresponding author at: Mathematics Department, B.C. Institute of Technology, 3700 Willingdon Ave., Burnaby, B.C., Canada V5G 3H2. Tel.: +1 604 456 8199; fax: +1 604 432 9173. E-mail address: David Holloway@bcit.ca (D.M. Holloway). movement reduces the active region, narrowing the tip and cutting off growth. It is an open question how the sizes of growing domains are intrinsically regulated to select these different morphologies. Here, we present a chemically controlled growth mechanism which can account for extending tip growth and branching. Actively growing regions are chemically distinct from inactive regions, having, for instance, localized gene expression or hor- mone accumulation which can specify tissue identity (e.g. for new organs, such as lateral branches), cell division and growth. These localized chemical patterns have been characterized in a num- ber of systems, at the molecular level and in terms of developing dynamic models for pattern formation (e.g. de Reuille et al., 2006; Jönsson et al., 2006; Smith et al., 2006; Fujita et al., 2011). For localized chemical catalysis of growth, there is a great molecular diversity across plants: for instance, many higher plants extend by localized relaxation of cell wall polymers (for example, expansin catalyzed surface outgrowth – Cosgrove, 1996; Fleming et al., 1997 – linked to the auxin hormone pattern); while many lower plants (e.g. chlorophyte algae) extend by localized addition of cell wall material (intussusception – Bonner, 1934; for example, via tip- localized membrane-bound proteins which ‘dock’ vesicles carrying 0303-2647/$ – see front matter © 2012 Elsevier Ireland Ltd. All rights reserved. http://dx.doi.org/10.1016/j.biosystems.2012.03.004