Przemyslaw Prusinkiewicz

Visual models of plants interacting with their environment

Interaction with the environment is a key factor affecting the development of plants and plant ecosystems. In this paper we introduce a modeling framework that makes it possible to simulate and visualize a wide range of interactions at the level of plant architecture. This framework extends the formalism of Lindenmayer systems with constructs needed to model bi−directional information exchange between plants and their environment. We illustrate the proposed framework with models and simulations that capture the development of tree branches limited by collisions, the colonizing growth of clonal plants competing for space in favorable areas, the interaction between roots competing for water in the soil, and the competition within and between trees for access to light. Computer animation and visualization techniques make it possible to better understand the modeled processes and lead to realistic images of plants within their environmental context.

A plausible model of phyllotaxis

A striking phenomenon unique to the kingdom of plants is the regular arrangement of lateral organs around a central axis, known as phyllotaxis. Recent molecular-genetic experiments indicate that active transport of the plant hormone auxin is the key process regulating phyllotaxis. A conceptual model based on these experiments, introduced by Reinhardt et al. [Reinhardt, D., Pesce, E. R., Stieger, P., Mandel, T., Baltensperger, K., et al. (2003) Nature 426, 255–260], 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.

Realistic modeling and rendering of plant ecosystems

Modeling and rendering of natural scenes with thousands of plants poses a number of problems. The terrain must be modeled and plants must be distributed throughout it in a realistic manner, reflecting the interactions of plants with each other and with their environment. Geometric models of individual plants, consistent with their positions within the ecosystem, must be synthesized to populate the scene. The scene, which may consist of billions of primitives, must be rendered efficiently while incorporating the subtleties of lighting in a natural environment. We have developed a system built around a pipeline of tools that address these tasks. The terrain is designed using an interactive graphical editor. Plant distribution is determined by hand (as one would do when designing a garden), by ecosystem simulation, or by a combination of both techniques. Given parametrized procedural models of individual plants, the geometric complexity of the scene is reduced by approximate instancing, in which similar plants, groups of plants, or plant organs are replaced by instances of representative objects before the scene is rendered. The paper includes examples of visually rich scenes synthesized using the system.

The use of positional information in the modeling of plants

We integrate into plant models three elements of plant representation identified as important by artists: posture (manifested in curved stems and elongated leaves), gradual variation of features, and the progression of the drawing process from overall silhouette to local details. The resulting algorithms increase the visual realism of plant models by offering an intuitive control over plant form and supporting an interactive modeling process. The algorithms are united by the concept of expressing local attributes of plant architecture as functions of their location along the stems.

Synthetic topiary

The paper extends Lindenmayer systems in a manner suitable for simulating the interaction between a developing plant and its environment. The formalism is illustrated by modeling the response of trees to pruning, which yields synthetic images of sculptured plants found in topiary gardens.

Evolution and Development of Inflorescence Architectures

To understand the constraints on biological diversity, we analyzed how selection and development interact to control the evolution of inflorescences, the branching structures that bear flowers. We show that a single developmental model accounts for the restricted range of inflorescence types observed in nature and that this model is supported by molecular genetic studies. The model predicts associations between inflorescence architecture, climate, and life history, which we validated empirically. Paths, or evolutionary wormholes, link different architectures in a multidimensional fitness space, but the rate of evolution along these paths is constrained by genetic and environmental factors, which explains why some evolutionary transitions are rare between closely related plant taxa.

Development models of herbaceous plants for computer imagery purposes

In this paper we present a method for modeling herbaceous plants, suitable for generating realistic plant images and animating developmental processes. The idea is to achieve realism by simulating mechanisms which control plant growth in nature. The developmental approach to the modeling of plant architecture is extended to the modeling of leaves and flowers. The method is expressed using the formalism of L-systems.

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.

Control of bud activation by an auxin transport switch.

In many plant species only a small proportion of buds yield branches. Both the timing and extent of bud activation are tightly regulated to produce specific branching architectures. For example, the primary shoot apex can inhibit the activation of lateral buds. This process is termed apical dominance and is dependent on the plant hormone auxin moving down the main stem in the polar auxin transport stream. We use a computational model and mathematical analysis to show that apical dominance can be explained in terms of an auxin transport switch established by the temporal precedence between competing auxin sources. Our model suggests a mechanistic basis for the indirect action of auxin in bud inhibition and captures the effects of diverse genetic and physiological manipulations. In particular, the model explains the surprising observation that highly branched Arabidopsis phenotypes can exhibit either high or low auxin transport.