, provides an intuitively plausible interpretation of the data, but raises questions of whether the proposed mechanism is, in fact, capable of producing the observed temporal and spatial patterns, is robust, can start de novo, and can account for phyllotactic transitions, such as the frequently observed transition from decussate to spiral phyllotaxis. To answer these questions, we created a computer simulation model based on data described previously or in this paper and reasonable hypotheses. The model reproduces, within the standard error, the divergence angles measured in Arabidopsis seedlings and the effects of selected experimental manipulations. It also reproduces distichous, decussate, and tricussate patterns. The model thus offers a plausible link between molecular mechanisms of morphogenesis and the geometry of phyllotaxis.active transport ͉ auxin ͉ PIN ͉ polarity ͉ computer simulation W ithin the variety of phyllotactic patterns found in nature, the most intriguing and, at the same time, the most prevalent is the spiral phyllotactic pattern characterized by the arrangement of organs into conspicuous spirals (parastichies), where the numbers of parastichies are consecutive elements of the Fibonacci series. This pattern is related to the divergence angle between organs approximating the golden angle of 137.5°. In the entire world of developmental biology, phyllotaxis is perhaps the most striking example of a phenomenon that can only be described by using quantitative notions of geometry.The regularity and mathematical properties of spiral phyllotaxis have attracted the attention of biologists and mathematicians since the early 19th century. They proposed conceptual, mathematical, and computational models, which elucidated the geometric properties of spiral phyllotactic arrangements (1) and the emergence of phyllotactic patterns during plant development. This latter category of models was pioneered by Hofmeister (2) and Snow and Snow (3), who hypothesized that the creation of new primordia is inhibited by the proximity of older primordia. New primordia, therefore, can be formed only at a certain minimal distance from the old ones. This general hypothesis has subsequently been refined into a number of computational models, postulating and exploring different types of inhibitory mechanisms such as geometric spacing (4), physical forces (5, 6), and chemical signals (7,8).In the absence of molecular data, the proposed mechanisms were more or less abstract. Recent experiments, however, provided an insight into the molecular processes involved in phyllotaxis, pointing to the central role of active transport of the plant hormone auxin. When shoot apices were cultivated in the presence of auxin transport inhibitors, the induction of lateral organs was blocked, and the apices grew vigorously as radially symmetric structures. Application of the natural auxin indole-3-acetic acid (IAA) to such pin-shaped meristems induced lateral primordia, with the size and position depending on the concentration and the position o...

The plant hormone auxin mediates developmental patterning by a mechanism that is based on active transport. In the shoot apical meristem, auxin gradients are thought to be set up through a feedback loop between auxin and the activity and polar localization of its transporter, the PIN1 protein. Two distinct molecular mechanisms for the subcellular polarization of PIN1 have been proposed. For leaf positioning (phyllotaxis), an ''up-the-gradient'' PIN1 polarization mechanism has been proposed, whereas the formation of vascular strands is thought to proceed by ''with-the-flux'' PIN1 polarization. These patterning mechanisms intersect during the initiation of the midvein, which raises the question of how two different PIN1 polarization mechanisms may work together. Our detailed analysis of PIN1 polarization during midvein initiation suggests that both mechanisms for PIN1 polarization operate simultaneously. Computer simulations of the resulting dual polarization model are able to reproduce the dynamics of observed PIN1 localization. In addition, the appearance of high auxin concentration in our simulations throughout the initiation of the midvein is consistent with experimental observation and offers an explanation for a long-standing criticism of the canalization hypothesis; namely, how both high flux and high concentration can occur simultaneously in emerging veins.[Keywords: Auxin; transport; PIN1; phyllotaxis; vein; computer simulation] Supplemental material is available at http://www.genesdev.org.

Morphogenesis emerges from complex multiscale interactions between genetic and mechanical processes. To understand these processes, the evolution of cell shape, proliferation and gene expression must be quantified. This quantification is usually performed either in full 3D, which is computationally expensive and technically challenging, or on 2D planar projections, which introduces geometrical artifacts on highly curved organs. Here we present MorphoGraphX (www.MorphoGraphX.org), a software that bridges this gap by working directly with curved surface images extracted from 3D data. In addition to traditional 3D image analysis, we have developed algorithms to operate on curved surfaces, such as cell segmentation, lineage tracking and fluorescence signal quantification. The software's modular design makes it easy to include existing libraries, or to implement new algorithms. Cell geometries extracted with MorphoGraphX can be exported and used as templates for simulation models, providing a powerful platform to investigate the interactions between shape, genes and growth.DOI: http://dx.doi.org/10.7554/eLife.05864.001