Adam Runions

Model for the regulation of Arabidopsis thaliana leaf margin development

Biological shapes are often produced by the iterative generation of repeated units. The mechanistic basis of such iteration is an area of intense investigation. Leaf development in the model plant Arabidopsis is one such example where the repeated generation of leaf margin protrusions, termed serrations, is a key feature of final shape. However, the regulatory logic underlying this process is unclear. Here, we use a combination of developmental genetics and computational modeling to show that serration development is the morphological read-out of a spatially distributed regulatory mechanism, which creates interspersed activity peaks of the growth-promoting hormone auxin and the CUP-SHAPED COTYLEDON2 (CUC2) transcription factor. This mechanism operates at the growing leaf margin via a regulatory module consisting of two feedback loops working in concert. The first loop relates the transport of auxin to its own distribution, via polar membrane localization of the PINFORMED1 (PIN1) efflux transporter. This loop captures the potential of auxin to generate self-organizing patterns in diverse developmental contexts. In the second loop, CUC2 promotes the generation of PIN1-dependent auxin activity maxima while auxin represses CUC2 expression. This CUC2-dependent loop regulates activity of the conserved auxin efflux module in leaf margins to generate stable serration patterns. Conceptualizing leaf margin development via this mechanism also helps to explain how other developmental regulators influence leaf shape.

Modeling and visualization of leaf venation patterns

We introduce a class of biologically-motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree-like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.

Self-organizing tree models for image synthesis

We present a method for generating realistic models of temperate-climate trees and shrubs. This method is based on the biological hypothesis that the form of a developing tree emerges from a self-organizing process dominated by the competition of buds and branches for light or space, and regulated by internal signaling mechanisms. Simulations of this process robustly generate a wide range of realistic trees and bushes. The generated forms can be controlled with a variety of interactive techniques, including procedural brushes, sketching, and editing operations such as pruning and bending of branches. We illustrate the usefulness and versatility of the proposed method with diverse tree models, forest scenes, animations of tree development, and examples of combined interactive-procedural tree modeling.

Computational models of plant development and form

The use of computational techniques increasingly permeates developmental biology, from the 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 morphogenetic processes and global patterns and forms. We survey the modeling techniques and selected models that are designed to elucidate plant development in mechanistic terms, with an emphasis on: the history of mathematical and computational approaches to developmental 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 patterns, 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 computational modelers.

Modeling trees with a space colonization algorithm

We extend the open leaf venation model by Runions et al. [RFL*05] to three dimensions and show that it generates surprisingly realistic tree structures. Model parameters correspond to visually relevant tree characteristics identified in landscaping, offering convenient control of tree shape and structure.

A Division in PIN-Mediated Auxin Patterning during Organ Initiation in Grasses

The hormone auxin plays a crucial role in plant morphogenesis. In the shoot apical meristem, the PIN-FORMED1 (PIN1) efflux carrier concentrates auxin into local maxima in the epidermis, which position incipient leaf or floral primordia. From these maxima, PIN1 transports auxin into internal tissues along emergent paths that pattern leaf and stem vasculature. In Arabidopsis thaliana, these functions are attributed to a single PIN1 protein. Using phylogenetic and gene synteny analysis we identified an angiosperm PIN clade sister to PIN1, here termed Sister-of-PIN1 (SoPIN1), which is present in all sampled angiosperms except for Brassicaceae, including Arabidopsis. Additionally, we identified a conserved duplication of PIN1 in the grasses: PIN1a and PIN1b. In Brachypodium distachyon, SoPIN1 is highly expressed in the epidermis and is consistently polarized toward regions of high expression of the DR5 auxin-signaling reporter, which suggests that SoPIN1 functions in the localization of new primordia. In contrast, PIN1a and PIN1b are highly expressed in internal tissues, suggesting a role in vascular patterning. PIN1b is expressed in broad regions spanning the space between new primordia and previously formed vasculature, suggesting a role in connecting new organs to auxin sinks in the older tissues. Within these regions, PIN1a forms narrow canals that likely pattern future veins. Using a computer model, we reproduced the observed spatio-temporal expression and localization patterns of these proteins by assuming that SoPIN1 is polarized up the auxin gradient, and PIN1a and PIN1b are polarized to different degrees with the auxin flux. Our results suggest that examination and modeling of PIN dynamics in plants outside of Brassicaceae will offer insights into auxin-driven patterning obscured by the loss of the SoPIN1 clade in Brassicaceae.

TreeSketch: interactive procedural modeling of trees on a tablet

TreeSketch is a system for modeling complex trees that look natural yet are creatively designed. The system integrates procedural tree generation with a multi-touch tablet interface that provides detailed control of tree form. The procedural component is based on the concept of tree self-organization and simulates competition of branches for space and light as the tree develops from a seedling. The modeler can control this process by directing growth with a procedural brush, changing parameters as the tree grows, interleaving controlled and autonomous growth, and editing generated forms. Complex trees can be created in a matter of seconds.

A common developmental program can produce diverse leaf shapes

Summary Eudicot leaves have astoundingly diverse shapes. The central problem addressed in this paper is the developmental origin of this diversity. To investigate this problem, we propose a computational model of leaf development that generalizes the largely conserved molecular program for the reference plants Arabidopsis thaliana, Cardamine hirsuta and Solanum lycopersicum. The model characterizes leaf development as a product of three interwoven processes: the patterning of serrations, lobes and/or leaflets on the leaf margin; the patterning of the vascular system; and the growth of the leaf blade spanning the main veins. The veins play a significant morphogenetic role as a local determinant of growth directions. We show that small variations of this model can produce diverse leaf shapes, from simple to lobed to compound. It is thus plausible that diverse shapes of eudicot leaves result from small variations of a common developmental program.

Auxin-driven patterning with unidirectional fluxes

Highlight The key modes of auxin-driven patterning— the formation of convergence points and canals—depend on whether auxin efflux and influx feed back on polar auxin transport synergistically or antagonistically.

Computational Models of Auxin-Driven Development

Auxin plays a key regulatory role in plant development. According to our current understanding, the morphogenetic action of auxin relies on its polar transport and the feedback between this transport and the localization of auxin transporters. Computational models complement experimental data in studies of auxin-driven development: they help understand the self-organizing aspects of auxin patterning, reveal whether hypothetical mechanisms inferred from experiments are plausible, and highlight differences between competing hypotheses that can be used to direct further experimental studies. In this chapter we present the state of the art in the computational modeling of auxin patterning and auxin-driven development in plants. We first discuss the methodological foundations of model construction: computational representations of tissues, cells, and molecular components of the studied systems. On this basis, we present mathematical models of auxin transport and the essential properties of pattern formation mechanisms involving auxin. We then review some of the key areas that have been investigated with the use of models: phyllotactic patterning of lateral organs in the shoot apical meristem, determination of leaf shape and vasculature, long-distance signaling and apical control of development, and auxin patterning in the root. The chapter is concluded with a brief review of current open problems.