Modeling Xylem Functionality Aspects.

Depending on the questions to be answered, water flow in the xylem can be modelled following different approaches with varying spatial and temporal resolution. When focussing on the influence of hydraulic architecture upon flow dynamics, distribution of water potentials in a tree crown or questions of vulnerability of the hydraulic system, functional-structural plant models, which link representations of morphological structure with simulated processes and with a virtual environment, can be a promising tool. Such a model will then include a network of idealized xylem segments, each representing the conducting part of a stem or branch segment, and a numerical machinery suitable for solving a system of differential equations on it reflecting the hydrodynamic laws, which are the basis of the broadly accepted cohesion-tension theory of water flow in plants. We will discuss functional-structural plant models, the simplifications that are useful for hydraulic simulations within this framework, the deduction of the used differential equations from basic physical conservation laws, and their numerical solution, as well as additional necessary models of radiation, photosynthesis, and stomatal conductance. In some supplementary notes, we are shortly addressing some related questions, for example, about root systems or about the relation between macro-scale hydraulic parameters and fine-grained (anatomical) xylem structure.

An approach to multiscale modelling with graph grammars.

BACKGROUND AND AIMS: Functional-structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs. METHODS: A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL. KEY RESULTS: Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas. CONCLUSIONS: The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.

A functional-structural model of rice linking quantitative genetic information with morphological development and physiological processes.

BACKGROUND AND AIMS: Although quantitative trait loci (QTL) analysis of yield-related traits for rice has developed rapidly, crop models using genotype information have been proposed only relatively recently. As a first step towards a generic genotype-phenotype model, we present here a three-dimensional functional-structural plant model (FSPM) of rice, in which some model parameters are controlled by functions describing the effect of main-effect and epistatic QTLs. METHODS: The model simulates the growth and development of rice based on selected ecophysiological processes, such as photosynthesis (source process) and organ formation, growth and extension (sink processes). It was devised using GroIMP, an interactive modelling platform based on the Relational Growth Grammar formalism (RGG). RGG rules describe the course of organ initiation and extension resulting in final morphology. The link between the phenotype (as represented by the simulated rice plant) and the QTL genotype was implemented via a data interface between the rice FSPM and the QTLNetwork software, which computes predictions of QTLs from map data and measured trait data. KEY RESULTS: Using plant height and grain yield, it is shown how QTL information for a given trait can be used in an FSPM, computing and visualizing the phenotypes of different lines of a mapping population. Furthermore, we demonstrate how modification of a particular trait feeds back on the entire plant phenotype via the physiological processes considered. CONCLUSIONS: We linked a rice FSPM to a quantitative genetic model, thereby employing QTL information to refine model parameters and visualizing the dynamics of development of the entire phenotype as a result of ecophysiological processes, including the trait(s) for which genetic information is available. Possibilities for further extension of the model, for example for the purposes of ideotype breeding, are discussed.

A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction.

BACKGROUND AND AIMS: Functional-structural plant models (FSPM) constitute a paradigm in plant modelling that combines 3D structural and graphical modelling with the simulation of plant processes. While structural aspects of plant development could so far be represented using rule-based formalisms such as Lindenmayer systems, process models were traditionally written using a procedural code. The faithful representation of structures interacting with functions across scales, however, requires a new modelling formalism. Therefore relational growth grammars (RGG) were developed on the basis of Lindenmayer systems. METHODS: In order to implement and test RGG, a new modelling language, the eXtended L-system language (XL) was created. Models using XL are interpreted by the interactive, Java-based modelling platform GroIMP. Three models, a semi-quantitative gibberellic acid (GA) signal transduction model, and a phytochrome-based shade detection and object avoidance model, both coupled to an existing morphogenetic structural model of barley (Hordeum vulgare L.), serve as examples to demonstrate the versatility and suitability of RGG and XL to represent the interaction of diverse biological processes across hierarchical scales. KEY RESULTS: The dynamics of the concentrations in the signal transduction network could be modelled qualitatively and the phenotypes of GA-response mutants faithfully reproduced. The light model used here was simple to use yet effective enough to carry out local measurement of red:far-red ratios. Suppression of tillering at low red:far-red ratios could be simulated. CONCLUSIONS: The RGG formalism is suitable for implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, their ensuing complexity requires careful design. On the positive side, such an FSPM displays knowledge gaps better thereby guiding future experimental design.

The rule-based language XL and the modelling environment GroIMP illustrated with simulated tree competition.

The programming language XL ('eXtended L-system language') is an extension of Java, which supports the specification and execution of relational growth grammars, a variant of parallel graph grammars. XL is a powerful generalisation of the well-known L-system approach to functional-structural plant modelling. Some features of XL are discussed that are particularly useful for combining structure and function and for querying plant architectural data, and an exemplary functional-structural plant model of young beech trees is presented that is implemented in XL and includes PAR distribution, assimilate allocation and morphological plasticity. Together with a simpler model of spruce trees, this beech model is included in a virtual landscape with a mixed-species forest stand where competition for light occurs. The open-source platform GroIMP was used for the complete model development process and for visualising the results.

Barley morphology, genetics and hormonal regulation of internode elongation modelled by a relational growth grammar.

A multiscaled ecophysiological model of barley (Hordeum vulgare) development is presented here. The model is based on the new formalism of relational growth grammars (RGG), an extension of L-systems, and implemented using the new modelling language XL. It is executable in the interactive modelling platform GroIMP. The model consists of a set of morphogenetic rules, combined with a metabolic regulatory network, which simulates the biosynthesis of gibberellic acid (GA1). GA1 and two of its metabolic precursors are transported along the developing simulated structure. Local concentrations of GA1 determine internode elongation. Furthermore, virtual barley individuals are chosen interactively from a population, based on genotype, and (sexual or asexual) reproduction is simulated. Genotype and phenotype of the population are visualized. Seven Mendelian genes have been implemented in the model so far; some of these directly influence the GA-regulation network. The model exemplifies and validates the new formalism and modelling language. RGG have the capability to represent genetic, metabolic and morphological aspects of plant development and reproduction, all within the same framework.

A graph grammar approach to artificial life.

We present the high-level language of relational growth grammars (RGGs) as a formalism designed for the specification of ALife models. RGGs can be seen as an extension of the well-known parametric Lindenmayer systems and contain rule-based, procedural, and object-oriented features. They are defined as rewriting systems operating on graphs with the edges coming from a set of user-defined relations, whereas the nodes can be associated with objects. We demonstrate their ability to represent genes, regulatory networks of metabolites, and morphologically structured organisms, as well as developmental aspects of these entities, in a common formal framework. Mutation, crossing over, selection, and the dynamics of a network of gene regulation can all be represented with simple graph rewriting rules. This is demonstrated in some detail on the classical example of Dawkins' biomorphs and the ABC model of flower morphogenesis: other applications are briefly sketched. An interactive program was implemented, enabling the execution of the formalism and the visualization of the results.