AOBPreview originally published online on August 31, 2007
Annals of Botany 2008 101(8):1109-1123; doi:10.1093/aob/mcm172
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A Rule-based Model of Barley Morphogenesis, with Special Respect to Shading and Gibberellic Acid Signal Transduction
1 Crop and Weed Ecology Group, Wageningen UR, Haarweg 333, 6709 RZ Wageningen, The Netherlands
2 Department of Computer Science, Brandenburg University of Technology at Cottbus, PO Box 101344, 03013 Cottbus, Germany
3 Institute of Forest Biometry and Computer Science, University of Göttingen, Büsgenweg 4, 37077 Göttingen, Germany
* For correspondence. E-mail gerhard.buck-sorlin{at}wur.nl
Received: 31 January 2007 Returned for revision: 21 March 2007 Accepted: 21 June 2007 Published electronically: 31 August 2007
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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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.
Key words: Barley, Hordeum vulgare L., functional-structural plant model (FSPM), extended L-System language, relational growth grammars, morphogenesis, gibberellic acid, plant hormone, signal transduction, shade detection, object avoidance, computer graphics
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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Plant models that cover several levels of organization (genetic, metabolic, physiological, architectural) usually require complex design and calibration. If they are implemented in a standard programming language such as C or Java, their computer code is long and obscure. So there is the need for a model-specification formalism or language that would be specifically adapted to the needs of botany and could assist in creating and running multi-scaled models and facilitate communication about them among scientists. A first approach towards such a formalism consists of the L-systems, introduced by Lindenmayer (1968) and applied to higher plants by Prusinkiewicz and Lindenmayer (1990). With several extensions, they are to date the most widely used rule-based formalism for structural plant models (e.g. Fournier et al., 2003; Mündermann et al., 2005). Other formal tools employed for this purpose are multi-scaled tree graphs (Godin and Caraglio, 1998), Markov chains (Barczi et al., 1997) and dual-scale automata (Zhao et al., 2001). However, all these formalisms in their ‘pure form’ lack the capacity to take into account environmental effects. Therefore, ‘open L-systems’ were introduced by M
ch and Prusinkiewicz (1996) and, independently, ‘sensitive growth grammars’ (L-systems with functions that act as sensors perceiving information about the local environment) by Kurth (1994). Both extensions of the L-system concept enable a connection with simulation models specified for external processes (using a code in a classical, imperative programming language) and have been used particularly for simulating photosynthetically active radiation interception and competition of plants for light (Kurth and Sloboda, 1999). As an alternative to more time-demanding ray tracing or Monte Carlo simulations, a sensitive function can check a virtual cone, which points from the sky to the leaf or shoot under consideration, for shading obstacles (an approximation for radiation conditions taken from Pfreundt and Sloboda; 1996). A similar technique for the object avoidance model was used but a dedicated, Monte-Carlo ray tracer-based light model was also developed, since it was found that the virtual cone model was not precise enough, especially for the determination of local light qualities. The division between procedural and rule-based model parts in open L-systems and sensitive functions is somewhat artificial and can sometimes make the models obscure. The programming languages L + C (Karwowski and Prusinkiewicz, 2003) and XL (eXtended L-system) (Kniemeyer, 2004) were developed to enable a more flexible integration of both modelling paradigms. Particularly, XL combines rule-based replacement with the object-oriented, platform-independent language Java. Furthermore, in XL, L-systems were generalized to the more powerful relational growth grammars (RGG), which extend the replacement mechanism from strings to graphs thus allowing, for example, an intuitive graphical specification of genetic processes like crossing-over, which is not possible with L-systems (Kniemeyer et al., 2004).
Barley (Hordeum vulgare), the organism chosen for this modelling study, has a long tradition of research in plant physiology (e.g. Kirby and Faris, 1970; Kirby and Jones, 1977; Kirby et al., 1982, 1994). Particularly the action of the plant hormone gibberellic acid (GA) has been well investigated (Chandler and Robertson, 1999; Chandler et al., 2002; Fu et al., 2002). Barley model modules implemented in RGG/XL so far include an ecophysiological model, which combines morphogenetic rules with a hormone biosynthesis network (GA) controlling internode elongation and a simplified genotype, as well as the model BarleyBreeder which allows the sexual and asexual reproduction of individuals based on user selection, thereby faithfully simulating genetic recombination and mutation (Buck-Sorlin et al., 2005, 2007).
In the present paper, an extension of the barley model is shown, which simulates (a) the transduction of the GA signal from bioactive GA1 to resulting internode elongation and (b) recognizes objects and detects shade using information on the local distribution of radiation of certain wavelengths.
There are two main reasons for modelling shading of leaves by other leaves or stems in a plant canopy: (1) shading affects photosynthetic performance; and (2) shading modifies plant morphogenesis. The plant reacts to shade by carrying out a shade avoidance reaction, e.g. apical growth and elongation of internodes and petioles, suppression of lateral branching, suppression of leaf expansion, early flowering (Srivastava, 2002), or reduction of tillering in cereals (Skinner and Simmons, 1993; Evers et al., 2006). Shading by green plants reduces light quantity and changes light quality. In particular, the ratio of red to far-red light is reduced (Holmes and Smith, 1977). Shade avoidance responses are mediated by photoreceptors. For instance, suppression of leaf blade expansion and increase of petiole elongation in thale cress (Arabidopsis thaliana) are mediated by phytochrome and cryptochromes (Kozuka et al., 2005). Phytochrome photoreceptors perceive the red : far-red ratio in daylight, and mediate an important part of shade avoidance responses (Smith, 1982). Photoreceptors regulate morphogenetic and physiological processes via signalling pathways involving plant hormones (Srivastava, 2002).
Furthermore, there exists the phenomenon of object avoidance, which can be a simple change in orientation of leaf blades in order to evade collision with another blade or stem. In the model presented below, such a simple object avoidance mechanism, based on object detection within a restricted field of perception, has been implemented. In contrast to the shade avoidance model, no attempt was made to represent a physiological basis for this object detection capability of the plant in the model.
Growth and elongation of leaf blades and internodes are regulated by a host of hormones (amongst them auxins and brassinosteroids), in particular GA, through the stimulation of cell elongation and sometimes cell division in young tissues (Srivastava, 2002). GA is also involved in the control of male flower formation in dioecious plants, seed germination (by the induction and de novo synthesis of enzymes), fruit set and growth, and embryo development (Srivastava, 2002). Shade avoidance reactions in plants are subject to complex hormonal regulation by auxin, brassinosteroids and GA (Srivastava, 2002). Toyomasu et al. (1998) report direct control of GA biosynthesis by phytochromes during seed germination in lettuce (Lactuca sativa). Reports of such a direct control are still lacking for cereals.
The ecophysiological barley model presented here can be considered as a first step towards the long-term effort for a generalized mechanistic representation of interactions at different hierarchical levels (regulatory network, organ, individual, population) and across functional domains (genetic, physiological, morphological). Here, the aim is to demonstrate the suitability of the RGG approach to model the whole sequence from shading via signal transduction to morphological reaction, thus covering several scales in one and the same formal framework. Of course, the barley model itself still has shortcomings. Taking its current state as an example, the problems and possibilities of rule-based multi-scaled functional–structural plant models are discussed.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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Some elements of the barley model have already been presented elsewhere (Buck-Sorlin et al., 2005, 2007). These are the morphogenetic rules determining the observable architectural development of the plant, the incorporation of genotypic information (as virtual genomes) and rules for recombination and mutation, and the representation of a GA biosynthesis network. However, the entire source code has been completely refactored into a set of eight submodels, which facilitate the combination of different sets of modules with each other as well as the addition of future extensions. The complete model, including source code, will be made available for download at www.grogra.de.
Relational growth grammars and extended L-systems
Relational growth grammars are a recent effort to address the needs of functional–structural plant modelling. They extend the proven L-system formalism which has been widely used for plant modelling. The underlying fundamental idea of RGG and L-systems is the rule-based approach to in silico modelling. The development of a plant is modelled as a set of rules which are in a natural correspondence to the observed behaviour, and it is the task of the computer to apply the set of rules to the virtual plant. As an example, consider the following rule:
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This expresses the observed behaviour (at a simplified view) of plant growth. Meristems produce internodes, thereby reinstating themselves at the shoot apex, i.e. on top of the produced internode. Having specified such a rule, the computer has to search for every occurrence of a meristem in the current set of virtual plants, and has to apply the rule at these locations.
Of course, meristems, internodes and other entities of the model have to be represented internally in a way that is suitable for processing by a computer. For this purpose, RGG use a representation as a graph, where entities are represented by nodes and their relations by edges. These relations cover simple topological relations (e.g. the succession of entities along an axis), but also functional relations (e.g. cyclic relations in signal transduction networks) and finally arbitrary user-defined relations. As a simple example consider a ramification, where the development of the current axis is continued and the development of an additional lateral axis is initiated:
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)*). Then for every internode on this path, take its length and sum up. Although such an operation would be possible within L-systems, too, it would become very inefficient for branched structures, because the complete string starting at the meristem and including all branches up to the meristem location, has to be scanned in reverse, thereby counting bracket symbols in order to skip the consideration of internodes in branches. Graph queries can move locally along the structure in any direction and can be based on any relationship, or globally jump to some specified location, thus equipping the modeller with unlimited global sensitivity.
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While the type of rules stated above is suitable for structural growth, the implementation of functional aspects can often be implemented more adequately by another type, namely execution rules. This second type does not modify the topology of the structure on its own, it just performs computations (e.g. allocation, transport, metabolism) on the current structure (the results of such computations may have an influence on subsequent structural development). A simple example of such an execution rule is
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The programming language XL is an implementation of RGG which properly extends the complete programming language Java. Thus, top-level Java concepts like classes, methods and variables are inherited. Equally, within imperative code control statements like if and loops can be used. In addition to Java, one can specify rule statements like the given examples which apply the rules to the current graph, and one can use graph queries everywhere as part of expressions in order to examine the current structure. This combination of the rule-based approach with a mature multi-purpose language allows modellers to retain the structural botanical view, while at the same time not being limited by a restrictive string data structure or a fixed, pre-defined set of programmes dealing with functional aspects. The language XL is integrated in the interactive modelling platform GroIMP which provides the building blocks for plant modelling. A rich set of geometry and algorithms based on the geometry, visualization of the 3D outcome and its graph structure, visualization of datasets in terms of function plots, structural analysis functions, and some other features are provided. GroIMP is open-source software. It is available for download at http://www.grogra.de
GA-signal transduction network
A simplified model covering the last three steps of GA biosynthesis – which are considered most important – from GA19 over GA20 to bioactive GA1, and from there to the catabolite, GA8, had been implemented previously in XL (Buck-Sorlin et al., 2005, 2007) as a biosynthesis network of nodes that represented the three substances, and a set of rules and functions representing the actual turnover (production, decay) according to principles of enzyme kinetics (Bisswanger, 2000).
Once bioactive GA1 is available, subsequent GA signalling essentially functions as a derepression system moderated by DELLA-domain proteins, the latter acting as negative transcriptional regulators (Fleet and Sun, 2005; Hartweck and Olszewski, 2006). In the case of internode elongation – the process which is the focus of the present model – the DELLA protein SLN1 represses LUE1, a katanin-like microtubule-severing protein which is involved in microtubule organization (Bouquin et al., 2003). The actual derepression process is a GA-mediated destabilization, in which SLN1 is ubiquitinated for proteasome-dependent degradation (Fu et al., 2002; Fleet and Sun, 2005). Recent experimental evidence from rice (Oryza sativa) (Sasaki et al., 2003; Ueguchi-Tanaka et al., 2005) suggests that GA is not acting directly upon SLR1 (corresponding to SLN1 in barley) but via the soluble receptor GID1 (GID2 in barley). Put differently, only when GID1 binds to GA1, can it interact with SLR1 to label the latter for degradation (Sasaki et al., 2003; Ueguchi-Tanaka et al., 2005).
The signal transduction model implemented in XL using the information from the references stated above is illustrated in Fig. 2 and Tables 1 and 2. The four different elements (one hormone and three proteins), GA1, GID2, SLN1 and LUE1, are declared as XL modules of type Substance (with one parameter, concentration). In the morphogenetic model, the four new substances are inserted as branched nodes after each module of type Meristem and Internode, respectively, thereby initiating a transduction network for all meristems and internodes formed during a simulation (cf. node ‘Meristem’ in Fig. 1). This is an extension of the principle used in Buck-Sorlin et al. (2005), where the three substances of type GA19, GA20 and GA1 were associated with each Meristem module only. The XL rule is shown for Meristem (the rule is analogous for Internode):
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For simplicity, all interactions between substances are modelled as if they were of the Michaelis–Menten type, i.e. with two parameters, KM (specificity of reaction) and vmax (maximum turnover rate), and with the first substance, S, being the substrate for the reaction, the second substance, P, the product of the reaction. Further assumptions had to be made during the calibration process in order to obtain a stable system with numerically reasonable output (Fig. 2), namely a constant production of LUE1 and a concentration-dependent decay of GID2, using a Michaelis–Menten type equation for catabolism. An abridged version of the XL rules used in the signal transduction network is shown in Table 1, and their parameterization in Table 2. The rules used for the dynamics of GA biosynthesis are documented elsewhere (Buck-Sorlin et al., 2005).
Simple object avoidance and shade detection model
A first version of the object avoidance model is based on an earlier model by Kurth (1994) and Kurth and Sloboda (1999). Here, a sensor which is attached to a simulated leaf blade and pointing upwards, is regularly checking for objects inside a virtual cone with a given opening angle. In a previous version of the barley model, leaf blades had just been represented as Bézier surfaces with a fixed shape. In order to allow object avoidance using a number of sensors, this concept had to be abandoned. A blade is now represented as a chain of vertices of a NURBS (non-uniform rational B-splines; Foley et al., 1996) surface, in which each vertex acts as a sensor detecting other leaves in its vicinity. The blade grows by adding new vertices with the help of the meristem and extending the distance between two vertices until a maximum size is reached. A sizing parameter in the blade meristem determines the maximum blade length (currently a function of the genotype). If there are no other vertices in the way (i.e. within a cone with a certain opening angle, e.g. 30°) at a certain distance of the sensing vertex, then the leaf blade grows straight. Otherwise it carries out small evasive movements before placing a new vertex (e.g. swaying sideways or bending up/down in a random manner) to avoid the obstacle.
Ray tracer-based radiation model
The measurement of local red:far-red ratios for shade avoidance reactions via phytochromes (see below) required the development of a high-precision radiation model. The model that is presented in this paper is described below in summary.
The radiation model is fully embedded into GroIMP and thus makes use of the platform's native scene description. A scene in GroIMP represents a virtual world containing (amongst other elements) sources of radiation and visible objects. It thus suffices to invoke one instance of the radiation model per scene. It is then the task of the radiation model to compute how much of the radiation created by the sources, of which an arbitrary number can be inserted into the scene, is received by the objects in the scene. The amount of radiation received by an object may be queried at any stage in the application model proper.
Several types of sources of radiation are supported, among them point radiation, spot radiation and directional radiation. These sources of radiation can be selected interactively in GroIMP and their parameters set manually (e.g. spectral composition, power). A number of rays is generated by the sources and traced along their paths through the scene. Direct input parameters of the radiation model are (apart from the number and type of sources) the number of rays to be created at each step. The higher the number of rays, the more reliable the computation of the local light conditions will be. For the simulations, a directional source was used at a distance of 50 cm, emitting 200 000 rays of white light with a radiant power density of 100 W m–2.
A phytochrome model
The model assumes that the leaf blades have different reflection (R), transmittance (T) and absorption (A) properties for two types of radiation considered, red (640 ± 5 nm) and far-red (730 ± 5 nm). This was achieved by providing the blade surface objects in the model with a material, which possesses (amongst others) the properties of diffuse reflectance and diffuse transparency. R and T values characteristic for a barley canopy for these two wavebands were derived from Vohland et al. (2006, their figure 2). The fraction of absorbed light is then computed as 1 – (R + T). The values for R, T and A in the red band are 0·123, 0·23 and 0·647, respectively, and 0·323, 0·623 and 0·054 in the far-red band. A similar approach has been used by Gautier et al. (2000). White light produced by a light source in the scene is thus changed in composition when passing through the simulated canopy. While about 60% of the red light is absorbed by the blade surfaces, >95% of the far-red band is either diffusely transmitted or reflected, thereby accumulating in the shade. Light sensors, which are distributed along the simulated structure, are then used to sense local light conditions in the red and far-red part of the spectrum. Of these local light values, the characteristic red:far-red ratio is computed, which is referred to as 
. Small values of indicate shade, larger ones unshaded conditions.
Phytochrome photoreceptors have two isoforms, Pr and Pfr, that can convert into each other upon the absorption of a photon. The abundances of Pr and Pfr depend on this photochemical reaction but also on the rates of synthesis and breakdown of the isoforms. If the light intensity is sufficiently high, the photochemical reaction is driven to an equilibrium. Daylight is more than sufficient to induce the equilibrium. In daylight the equilibrium settles quickly, i.e. within 10–30 s (Smith and Holmes, 1977; Smith 1982). The state of the photoequilibrium can be described by the fraction of phytochrome present in the Pfr isoform: Pfr/Ptotal, also referred to as 
. Under a wide range of natural and artificial light regimes, the state of the photoequilibrium is closely related to the red:far-red ratio of the intercepted light (Smith and Holmes, 1977). The relationship between and was modelled with a formula by Burema (2007).
In order to obtain an impression of the interaction of the radiation, the phytochrome and the GA biosynthesis and signal transduction models, the models were finally combined by making the production of GA19 in the regulatory network a linear function of the local value of , thereby using the observation by Toyomasu et al. (1998) for lettuce. An overview of the combined model is given in Fig. 3.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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Biosynthesis and signal transduction network
For the purposes of calibration and in order to test the principal suitability of the GA biosynthesis and signal transduction network, the network model was first of all uncoupled from the morphological model. This uncoupled model was able to predict qualitatively the time courses of the concentrations of the six substances involved in the network (the three GA hormones, GID2, SLN1 and LUE1) (Fig. 4A), i.e. the decline in SLN1 concentrations and the synchronous increase in GID2 and LUE1. By setting the initial concentrations of SLN1 and GID2 to zero one at a time or both at the same time, the effect of the loss-of-function mutants gid2 and sln1, as well as that of the double mutant sln1-gid2 could be simulated qualitatively (Fig. 4B–D). sln1 is the GA-insensitive Slender mutant which is lacking the repressing SLN1 protein. Accordingly, LUE1 accumulates (Fig. 4B), leading to uncontrolled growth and extension to a long and slender appearance in the Slender mutant. The GA-insensitive dwarf gid2, on the other hand, is lacking the GID2-receptor (Chandler and Robertson, 1999). Here, SLN1 protein is accumulating despite normal GA production (Fig. 4C), whereas LUE1 concentrations remain too low for noticeable growth, resulting in dwarfism. Furthermore, as a result of the absence of the GID2-receptor, GA1 accumulates in the simulation, a phenomenon which is also observed in the mutant (Hartweck and Olszewski, 2006).
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The calibrated signal transduction model was then coupled again with the morphogenetic model to visualize the integrated outcome of several networks at the individual level (Fig. 5). Again, the composite model was able to predict the overall visual appearance of the two mutants (double mutant not shown but in appearance quite similar to the Slender mutant) reasonably well. However, compared with the simpler version presented in Buck-Sorlin et al. (2005), in which internode length was made a direct function of local GA1 concentration, the prediction of internode length distribution along the culm was worse in the extended model (Fig. 6A), which was particularly visible at the reduced simulated lengths in the uppermost ranks. As can be seen in Fig. 6B, this was probably due to much too regularly simulated internode extension speeds and equal phyllochrons. Actually, in winter barley, the phyllochron shortens and the slope of the internode extension curve becomes steeper with increasing rank (authors' observation).
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The dynamics of average hormone concentrations per simulated phytomer are illustrated in Fig. 7. After heavy fluctuations in especially the concentrations of GA1 and SLN1 during the first 15 steps, the oscillations quickly become smaller and smooth out to relatively stable values. This phenomenon is certainly due to the rapidly increasing number of phytomers, reaching 123 by the end of the simulation (112 steps). Overall, an increase in the average amount of GID2 and a decrease in SLN1 are observed, whilst the three GAs decrease to zero before the end of the simulation and LUE1 remains stable.
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The pleiotropic effects seen in the simulated sln1 and gid2 mutants (reduced size and number of grains) were implemented as empirical rules rather than as a result of the network, due to lack of information on the exact mechanisms leading to these effects.
Shade detection and object avoidance
To explore the scope and sensitivity of the present radiation model, tentative simulation studies were conducted. First of all, the effect of the object avoidance rules can be clearly seen in all simulated barleys (Fig. 5), namely a distinct curling or turning of leaf blades as well as a relatively rare mutual intersection of blades, overall conveying a more realistic impression to the simulations.
Meristems and internodes were equipped with sensors (see Materials and methods), which detected local values of within a radius of 0·5 cm in all directions (Fig. 8). This sensitivity was chosen in order to minimize overlap with neighbouring sensors and to allow enough light to be captured by the sensor. The sensors were thus used for measurements of the local amount and quality of incident light. Furthermore, the formation of lateral apical meristems (forming tillers subsequently) was made dependent upon the condition that the local value of be above a certain threshold. This is based on the observation that tillering in cereals is suppressed in the shade (Skinner and Simmons, 1993; Gautier et al., 1999; Evers et al., 2006).
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To get a general impression of the reliability of the radiation model, local values of
and were captured at each step of vegetative development (112 steps) by virtual sensors that were attached to the internodes (Fig. 8). The simulated values reliably reproduced the entire range of values encountered in nature (Smith and Holmes, 1977). One-way analysis of variance for and with the topological factors phytomer rank and branching order clearly yielded that both (Fig. 9) and were significantly different for both factors. More specifically, decreased from rank 1 (mean 0·8) to rank 10 (0·3) and then increased slightly (F = 20·57, P < 0·0001), whilst it decreased with increasing order (F = 20·67, P < 0·0001). The same trend was observed for (F = 24·69, P < 0·0001 for rank; F = 13·98, P < 0·0001 for order). Since in the present model the rank of the first phytomer of a new tiller was given the rank of its mother shoot, these results also suggest that higher-order tillers have a tendency to be more shaded than the main stem, simply because they appear later, and that, vice versa, the lower ranks and orders (early phytomers) of the main stem capture higher (and thus ) values whilst they are still growing in ‘open conditions’.
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Next, the effect of different plant spacings and threshold values for
on tillering were tested. In the model it was assumed that a local threshold value of has to be reached (i.e. measured as and then instantly converted into ) at least once during a fixed window of opportunity lasting an arbitrary ten steps. Previous simulations carried out by us had shown that at plant spacings between 3 cm and 7 cm, values for in the range between 0·5 and 0·55 seemed to contain the turning point below which all meristems grew out into tillers and above which no tillering took place (Fig. 10). Figure 11 gives the simulation results of some of the data points of Fig. 10, as obtained for a small canopy consisting of nine individuals.
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All simulations so far had been done with a directional light shining vertically downwards. This situation is only realistic for crops grown in the tropics or in a greenhouse with an artificial light source. However, tillering in winter cereals occurs when the sun is at a much lower elevation (about 16–37° during autumn and winter in central Europe). Therefore a couple of simulations were carried out with the same settings for
and spacing, but with the directional light source at an elevation of 28° (mean value of solar elevation in autumn and winter). At the lower elevation, fewer tillers were formed (difference on average two or three; results not shown), but there was no marked margin effect towards the direction of incident light, with respect to both morphology (Fig. 12A) and sensed light (Fig. 12B).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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GA signal transduction model
Though the present model was able to qualitatively predict the time courses of the substances involved in signal transduction, the lack of a correlated data set of hormone concentrations for different mutations and the wild type makes it currently unsuitable for predictive quantitative modelling. Furthermore, despite the relatively good chain of evidence for the model as presented in Fig. 1, an integral model for internode elongation would also require the consideration of at least the auxins and ethylene as the stability of the DELLA-protein SLN1 seems to be affected also by these two hormones and not only by the combined action of GID2 and GA1, indicating that SLN1 might act as an integrator for multiple hormonal signals (Hartweck and Olszewski, 2006).
The central issue when trying to do up-scaling from the level of the regulatory network to that of the organ or individual is that of the temporal and spatial distribution of such up-scaled processes. In the case of the GA biosynthesis and the signal transduction network, several questions thus come up: When and where is a component produced? Is it transported subsequently? Where to and when? So far, the following assumptions have been implemented into the present model. All meristems and internodes are locations of GA synthesis and signal transduction, furthermore, GA19 is transported basipetally, GA1 acropetally. There exists evidence for long-distance transport of GAs in the xylem and phloem (cited in Kaneko et al., 2003). However, these model assumptions probably need careful revision or considerable refinement in future model versions. With regard to locations of biosynthesis and signalling, there is some evidence that this is taking place where needed, i.e. in rapidly growing and extending tissues (Kaneko et al., 2003). Chandler et al. (2002) report that the bases of growing leaf blades of barley exhibit high concentrations of SLN1 and that its concentration diminished quickly towards the tip of the blade. Furthermore, the current morphogenetic model also includes generative development yet neglects the role of GA in seed formation and embryo development where GA seems to be involved in the switching between vegetative and post-fertilization development (Fleet and Sun, 2005).
The often considerable lack of knowledge about the information fluxes at lower hierarchical scales actually forbids carrying out integration modelling of (part of) these phenomena at a higher level, e.g. the organ or individual scale. However, we regard our approach as a true experimental tool alongside wet experiments. This justifies in our opinion the attempt to combine partial and highly fragmented representations of reality from different scientific disciplines into a single model, even if it only helps to falsify or question current hypotheses. Luquet et al. (2007) investigated the Phyllo rice mutant using simulation as a tool alongside experiments in the climate chamber. Though they acknowledged that their systems analysis approach (by modelling) did not succeed in telling cause from effect, their overall conclusion is that model-assisted, physiological analysis of different developmental mutants can at least provide useful insights into the complexity of developmental and physiological feedbacks. We agree with this view as we have come to a similar conclusion in the present study as well as in previous studies dealing with similar topics and applications.
Use and limitations of the shade detection and object avoidance model
The simulation studies which were conducted with the shade detection model were of a preliminary and exploratory nature and were aimed at testing its principal suitability in the context of a complex functional–structural plant model (FSPM). Calculations of the radiation regime can be done in an FSPM at different degrees of closeness to physical reality. Whereas in older process-oriented models of crop plant stands or forests often a rather coarse simplification of canopy optical structure was applied, namely, the assumption of homogeneity and of exponential extinction of incoming light (Lambert-Beer law; cf. Monsi and Saeki, 1953), later models employed techniques from engineering and computer graphics to get high-precision estimates of light interception of single plant organs in a 3D stand model. Variants of ray tracing (e.g. Blaise, 1991; Takenaka, 1994) or radiosity calculation (Chelle and Andrieu, 1998; Soler et al., 2003) have been used for this purpose. Although these physically based approaches naturally require high costs in terms of CPU load and computer memory, such an approach and a simpler model based on Pfreundt and Sloboda (1996) for obstacle avoidance have been used here.
Radiation and phytochrome model
In order to estimate quantitatively the amount of assimilate produced in different parts of a plant, here the previously described radiation model has been applied and some promising first results regarding one of the aspects of shade avoidance, reduction of tillering at low values, have been achieved.
The combination of numerous shade detection sensors with multiple instances of a GA biosynthesis and signal transduction network in one individual plant or a small stand yielded a visually realistic output. However, the integration at the organ and individual scale plus visual validation are as yet insufficient tools to test current hypotheses on the potential connection between the quality of incident light at the sites of GA biosynthesis and morphology (internode elongation, tillering) in different scenarios of stand structure (row spacing). The light sources and lighting scenarios used in the present simulations were probably too primitive, and especially a representation of integrated daily sunlight, in both quality and spatial distribution, would be necessary to simulate special plant responses such as LFR (low fluence response), which only occur during certain periods of the day. Furthermore, the influence of diffusely scattered light from the sky should be simulated. The sensitive thresholds for that were found to be inductive for tillering might be too specific for the chosen lighting scenario and completely meaningless in other scenarios. Also, the influence of different row or inter-plant distances and plant arrangements on tillering has not been tested here. The differences in plant emergence after germination might have a huge effect on plant development in general, and tillering in particular, since a late-germinating plant might already sense considerable shading by more advanced neighbours. Finally, the reduction in tiller number is not the only shade avoidance reaction in barley. Kirby and Faris (1970) found that with increasing planting density (range of 50–1600 plants m–2, corresponding to an average spacing of 2·5–14 cm) the number of leaves was reduced, internode elongation started earlier and at lower nodes, and final stem length was reduced because stem growth ceased earlier. Furthermore, with decreased spacing, blade and sheath lengths of lower ranks were increased, whilst blade widths were smaller compared with normal planting densities. This nicely illustrates the enormous plasticity and range of potential physiological reactions to shading, the surface of which has hardly been scratched with the model presented here.
Here a first attempt at a largely descriptive connection between the light surrounding the plant and its morphology or physiology has been made, making a number of sensible assumptions as has also been done by other authors (Gautier et al., 2000). However, this simple approach ignores the plant's complex sensory mechanisms by which responses to ambient light are mediated.
Phytochrome photoreceptors are known to mediate shade avoidance responses and induction of flowering in long-day plants (Srivastava, 2002). The mechanism of their sensory function is quite well understood. Two isoforms (Pr and Pfr) are converted into each other by a photochemical reaction. In daylight, the fraction of phytochrome in the Pfr form () depends on the ratio of red and far-red light, . The relation between the local value of and (in daylight) can be described with a simple equation (Smith and Holmes, 1977; Burema, 2007), which has been employed in the present model. Furthermore the state of phytochrome, , is linearly related to multiple shade avoidance responses in several weed species (Morgan and Smith, 1979). Hence phytochrome function can be included easily in a functional–structural plant model as has been shown here, making an instance of a local phytochrome pool for each ‘light sensor point’ (as demonstrated in this study and by Burema, 2007). In a similar way, the function of other photoreceptors could be included in future models.
The next step would then be to include (elements of) the signalling pathways controlled by the photoreceptors, e.g. plant hormones. For lettuce seeds (Lactuca sativa) there is strong evidence that phytochrome regulates germination by controlling the synthesis of GA1 (Toyomasu et al., 1998). Phytochrome regulates the expression of a 3β-hydroxylase gene, which is involved in GA1 synthesis (Kamiya and García-Martinez, 1999). In the present model, the level of has been provisionally connected with this reaction of the metabolic pathway, as it has been modelled explicitly (Buck-Sorlin et al., 2005).
Shade avoidance is a complex syndrome involving multiple photoreceptors (including multiple phytochromes) (Smith and Whitelam, 1997), hormones and other signalling molecules (Srivastava, 2002; Kim et al., 2005). Many questions about relative importance and interaction of signalling pathways are unanswered. Hypotheses about this complex issue could be incorporated in an FSPM and tested at the theoretical level, which could save a lot of experiments. In particular, a great potential is seen for the use of virtual sensors for environmental cues, as part of general models simulating some aspect of the microclimate, as has been shown here with the radiation model: Such combinations of general, versatile and transparent environment model modules and local virtual sensors could be used for all kinds of purposes, e.g. the detection of relative humidity or leaf temperature in a virtual canopy.
Calibration and validation of an increasingly complex FSPM
Even with large correlated datasets at hand (Costa et al., 2001; Buck-Sorlin, 2002) it seems that the path to ‘virtual barley’, i.e. a physiologically consistent, calibrated ecophysiological barley model with predictive power, is still very long and cumbersome. In the following, some of the main problems will be discussed and an attempt will be made to provide tentative solutions. To begin with, a virtual plant, if one is taking the definition seriously, is no longer a simple plant model but ideally both a combined multi-scaled representation of several essential and interrelated aspects of physiology, morphological development and genetics, and at the same time a database of parameters and biological processes implemented as a collection of modules describing basic functions (such as photosynthesis or genetic recombination). Establishing all necessary model parameters is most often not feasible due to lack of resources, lack of time, or simply methodological deficiencies. Using literature data seems to be a good alternative to your own measurements but only at first glance. The data found in this source is often heterogeneous, unadapted to the model one has in mind, uncorrelated with data already used in the model, or, in the worst case, completely or partially contradictory in itself or in conflict with already established model parameters/functions. Furthermore, calibration and validation of a multi-parametric, multi-scaled model becomes increasingly difficult, as the number of parameters and their mutual dependencies increase, as could be shown once more in the present study. This does not merely seem to be a linear increase in complexity but an almost exponential one. Lastly, there is a purely technical issue, namely that of a highly problematic run-time behaviour, which makes debugging of such a model ever more time-consuming.
Working with multi-scaled FSPMs, one sooner or later becomes painfully aware of the provisional character of the scales chosen. Whereas the scales used for the representation of morphology/morphogenesis (organ and individual scale) seem to be more or less appropriate – thereby neglecting or simplifying the fact that the origins of basic morphogenetic rules lie in the hormonal/genetic gradients found at the cellular scale inside the shoot apical meristem – this is not the case for the lower scales (tissue, cell, organelle, biochemical).
Given the ever more complex and intricate nature of virtual plants, further modularization into submodels is imperative. At the same time, a generalization of biological phenomena in models would be advisable as it would markedly increase reusability of code as well as acceptance in the community of experimental biologists potentially looking for alternative, in silico approaches. A promising initiative in this respect, ALEA (Pradal et al., 2004), is aimed at providing a homogenous software platform, integrating various tools and models within the FSPM domain. RGG models written in XL can already be distributed over different classes, thereby considerably improving readability and reusability of code. Knowing that one formalism or language can in practise not cover each and every biological circumstance, it would furthermore be a good parallel strategy to interface XL models with appropriate database tools. Plant data warehouse and text mining tools are already quite advanced and will allow/facilitate in future parameterization and calibration of models, using data from the literature. The success rate of the latter is, of course, above all a function of the quality of the published data as no search tool will be able to improve that quality by itself.
Ultimately, one could envisage an automatic generation of rules within XL. This could be set up as a scheme of correlated datasets and scientific reasoning written down as sets of conditions and restrictions which are then parsed into a set of rules. A similar approach called constraint programming has been applied for the modelling of dynamic biological systems by Bockmayr and Courtois (2002).
In conclusion, it has been shown that the RGG formalism is principally suitable for the implementation of multi-scaled FSPM of plants interacting with their environment via hormonal control. However, the inevitable increase in model complexity is a serious issue and this requires more careful, modular, design and probably also new techniques for calibration that go beyond standard parameter fitting. On the positive side, such an FSPM displays knowledge gaps better, thereby guiding future experimental design.
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We thank the two anonymous reviewers for their constructive criticism of a first version of the manuscript. This research was funded by the DFG under grants Ku 847/5-1/Ku 847/6-1 to W.K. and 446 CHV 111/15/06 to G.B.-S, which allowed his participation in the PMA'06 symposium in Beijing, P.R. China, to present a preliminary version of this paper. All support is gratefully acknowledged. G.B.-S. and B.B. thank the IPK, in particular Dr Patrick Schweizer, for discussions and for providing office facilities at the institute.
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