Review
Tansley review Computational models of plant development and form
Author for correspondence: Przemyslaw Prusinkiewicz and Adam Runions Przemyslaw Prusinkiewicz Tel: +1 403 220 5494 Department of Computer Science, University of Calgary, Calgary, AB T2N 1N4, Canada Email: [email protected] Received: 6 September 2011 Accepted: 17 November 2011
Contents
Summary 549 V. Molecular-level models 560
I. A brief history of plant models 549 VI. Conclusions 564
II. Modeling as a methodology 550 Acknowledgements 564
III. Mathematics of developmental models 551 References 565
IV. Geometric models of morphogenesis 555
Summary
New Phytologist (2012) 193: 549–569 The use of computational techniques increasingly permeates developmental biology, from the doi: 10.1111/j.1469-8137.2011.04009.x acquisition, processing and analysis of experimental data to the construction of models of organisms. Specifically, models help to untangle the non-intuitive relations between local Key words: growth, pattern, self- morphogenetic processes and global patterns and forms. We survey the modeling techniques organization, L-system, reverse/inverse and selected models that are designed to elucidate plant development in mechanistic terms, fountain model, PIN-FORMED proteins, with an emphasis on: the history of mathematical and computational approaches to develop- auxin. mental plant biology; the key objectives and methodological aspects of model construction; the diverse mathematical and computational methods related to plant modeling; and the essence of two classes of models, which approach plant morphogenesis from the geometric and molecular perspectives. In the geometric domain, we review models of cell division pat- terns, phyllotaxis, the form and vascular patterns of leaves, and branching patterns. In the molecular-level domain, we focus on the currently most extensively developed theme: the role of auxin in plant morphogenesis. The review is addressed to both biologists and computa- tional modelers.
I. A brief history of plant models have twelve or twenty, and some a great many more than these’. Although this observation appears to be off by one (Fibonacci How far mathematics will suffice to describe, and physics numbers of petals, 13 and 21, are more likely to occur than 12 to explain, the fabric of the body, no man can foresee. and 20), it represents the longest historical link between observa- D’Arcy Wentworth Thompson (1942, p. 13) tions and a mathematically flavored research problem in develop- mental plant biology. Numerical canalization, or the surprising In Book VI of the Enquiry into Plants, Theophrastus (1948; c. tendency of some plant organs to occur preferentially in some spe- 370–285 BCE) wrote: ‘most [roses] have five petals, but some cific numbers (Battjes et al., 1993), was described quantitatively