Quantitative genetics and functional-structural plant growth models: simulation of quantitative trait loci detection for model parameters and application to potential yield optimization

BACKGROUND AND AIMS: Prediction of phenotypic traits from new genotypes under untested environmental conditions is crucial to build simulations of breeding strategies to improve target traits. Although the plant response to environmental stresses is characterized by both architectural and functional plasticity, recent attempts to integrate biological knowledge into genetics models have mainly concerned specific physiological processes or crop models without architecture, and thus may prove limited when studying genotype x environment interactions. Consequently, this paper presents a simulation study introducing genetics into a functional-structural growth model, which gives access to more fundamental traits for quantitative trait loci (QTL) detection and thus to promising tools for yield optimization. METHODS: The GREENLAB model was selected as a reasonable choice to link growth model parameters to QTL. Virtual genes and virtual chromosomes were defined to build a simple genetic model that drove the settings of the species-specific parameters of the model. The QTL Cartographer software was used to study QTL detection of simulated plant traits. A genetic algorithm was implemented to define the ideotype for yield maximization based on the model parameters and the associated allelic combination. KEY RESULTS AND CONCLUSIONS: By keeping the environmental factors constant and using a virtual population with a large number of individuals generated by a Mendelian genetic model, results for an ideal case could be simulated. Virtual QTL detection was compared in the case of phenotypic traits--such as cob weight--and when traits were model parameters, and was found to be more accurate in the latter case. The practical interest of this approach is illustrated by calculating the parameters (and the corresponding genotype) associated with yield optimization of a GREENLAB maize model. The paper discusses the potentials of GREENLAB to represent environment x genotype interactions, in particular through its main state variable, the ratio of biomass supply over demand.     

Rhythms and alternating patterns in plants as emergent properties of a model of interaction between development and functioning

BACKGROUND AND AIMS: To model plasticity of plants in their environment, a new version of the functional-structural model GREENLAB has been developed with full interactions between architecture and functioning. Emergent properties of this model were revealed by simulations, in particular the automatic generation of rhythms in plant development. Such behaviour can be observed in natural phenomena such as the appearance of fruit (cucumber or capsicum plants, for example) or branch formation in trees. METHODS: In the model, a single variable, the source-sink ratio controls different events in plant architecture. In particular, the number of fruits and branch formation are determined as increasing functions of this ratio. For some sets of well-chosen parameters of the model, the dynamical evolution of the ratio during plant growth generates rhythms. KEY RESULTS AND CONCLUSIONS: Cyclic patterns in branch formation or fruit appearance emerge without being forced by the model. The model is based on the theory of discrete dynamical systems. The mathematical formalism helps us to explain rhythm generation and to control the behaviour of the system. Rhythms can appear during both the exponential and stabilized phases of growth, but the causes are different as shown by an analytical study of the system. Simulated plant behaviours are very close to those observed on real plants. With a small number of parameters, the model gives very interesting results from a qualitative point of view. It will soon be subjected to experimental data to estimate the model parameters.     

Characterization of the interactions between architecture and source-sink relationships in winter oilseed rape (Brassica napus) using the GreenLab model

Background and Aims

This study aimed to characterize the interaction between architecture and source–sink relationships in winter oilseed rape (WOSR): do the costs of ramification compromise the source–sink ratio during seed filling? The GreenLab model is a good candidate to address this question because it has been already used to describe interactions between source–sink relationships and architecture for other species. However, its adaptation to WOSR is a challenge because of the complexity of its developmental scheme, especially during the reproductive phase.

Methods

Equations were added in GreenLab to compute expansion delays for ramification, flowering of each axis and photosynthesis of pods including the energetic cost of oil synthesis. Experimental field data were used to estimate morphological parameters while source–sink parameters of the model were estimated by adjustment of model outputs to the data. Ecophysiological outputs were used to assess the sources/sink relationships during the whole growth cycle.

Key Results

First results indicated that, at the plant scale, the model correctly simulates the dynamics of organ growth. However, at the organ scale, errors were observed that could be explained either by secondary growth that was not incorporated or by uncertainties in morphological parameters (durations of expansion and life). Ecophysiological outputs highlighted the dramatic negative impact of ramification on the source–sink ratio, as well as the decrease in this ratio during seed filling despite pod envelope photosynthesis that allowed significant biomass production to be maintained.

Conclusions

This work is a promising first step in the construction of a structure–function model for a plant as complex as WOSR. Once tested for other environments and/or genotypes, the model can be used for studies on WOSR architectural plasticity.     

The hepatic adrenergic receptors

Summary The presence of both alpha- and beta-adrenergic receptors in liver designated the hepatic plasma membrane as a useful tool for the elucidation of the mechanisms by which the hormonal signal is transfered through the membrane via a coupling system to an amplifying entity. This process is well documented for the beta-adrenergic receptor which is linked to adenylate cyclase, whereby it modulates the cyclic AMP level. Much less is known about the alpha-adrenergic receptor.Recently, two factors have contributed to a renewed interest in alpha- and beta-adrenergic receptors in liver: i) The fact that activation of glycogenolysis in isolated liver parenchymall cells by epinephrine may be mediated by either alpha- or beta-adrenergic receptors, depending on the species or on the state of nutrition, and not only by beta-adrenergic receptors as previously thought. ii) The existence of specific adrenergic agonists and antagonists radiolabeled to a high specific activity which has permitted the characterization of adrenergic receptors in terms of nature, number, affinity and regulation.The present review will be devoted to the recent progress made in the physiological, pharmacological and biochemical characterization of alpha- and beta-adrenergic receptors in the liver.     

NEMA, a functional-structural model of nitrogen economy within wheat culms after flowering. II. Evaluation and sensitivity analysis

Background and Aims

Simulating nitrogen economy in crop plants requires formalizing the interactions between soil nitrogen availability, root nitrogen acquisition, distribution between vegetative organs and remobilization towards grains. This study evaluates and analyses the functional–structural and mechanistic model of nitrogen economy, NEMA (Nitrogen Economy Model within plant Architecture), developed for winter wheat (Triticum aestivum) after flowering.

Methods

NEMA was calibrated for field plants under three nitrogen fertilization treatments at flowering. Model behaviour was investigated and sensitivity to parameter values was analysed.

Key Results

Nitrogen content of all photosynthetic organs and in particular nitrogen vertical distribution along the stem and remobilization patterns in response to fertilization were simulated accurately by the model, from Rubisco turnover modulated by light intercepted by the organ and a mobile nitrogen pool. This pool proved to be a reliable indicator of plant nitrogen status, allowing efficient regulation of nitrogen acquisition by roots, remobilization from vegetative organs and accumulation in grains in response to nitrogen treatments. In our simulations, root capacity to import carbon, rather than carbon availability, limited nitrogen acquisition and ultimately nitrogen accumulation in grains, while Rubisco turnover intensity mostly affected dry matter accumulation in grains.

Conclusions

NEMA enabled interpretation of several key patterns usually observed in field conditions and the identification of plausible processes limiting for grain yield, protein content and root nitrogen acquisition that could be targets for plant breeding; however, further understanding requires more mechanistic formalization of carbon metabolism. Its strong physiological basis and its realistic behaviour support its use to gain insights into nitrogen economy after flowering.     

Characterization of the effects of inter-tree competition on source–sink balance in Chinese pine trees with the GreenLab model

We investigate the characteristics of individual tree response to competition on source–sink balance through the functional–structural plant model GreenLab. Four Chinese pine (Pinus tabulaeformis Carr.) trees were destructively sampled and were divided into two groups: high-density group and low-density group. First, the effects of density on organ dimensions and on organ relative mass were analysed based on experimental measurements. These were primary indicators of the plant response to competition. Second, the hidden parameters of the GreenLab model, as well as a tree-specific characteristic surface, were estimated using the data of total tree biomass for needle and wood compartments, for each of the four trees in parallel. The quality of the fitting is finally validated using data of individual organ mass at shoot level for the sampled branches. The Mann–Whitney Student’s t test showed that there were significant differences between the shoot attributes of the two groups for shoot diameter, shoot biomass and needle biomass. No significant difference was found for current year shoot lengths of the two groups. The parametric identification of the model allowed estimating and comparing the amount of biomass that was allocated to primary growth and to secondary growth in the two density conditions. It showed that biomass allocated to secondary growth (ring compartment) was the most strongly affected by density, and that the organ demand satisfaction ratio profiles of each of these trees were a relevant, integrated indicator of the tree state.     

Computing competition for light in the GREENLAB model of plant growth: a contribution to the study of the effects of density on resource acquisition and architectural development

BACKGROUND AND AIMS: The dynamical system of plant growth GREENLAB was originally developed for individual plants, without explicitly taking into account interplant competition for light. Inspired by the competition models developed in the context of forest science for mono-specific stands, we propose to adapt the method of crown projection onto the x-y plane to GREENLAB, in order to study the effects of density on resource acquisition and on architectural development. METHODS: The empirical production equation of GREENLAB is extrapolated to stands by computing the exposed photosynthetic foliage area of each plant. The computation is based on the combination of Poisson models of leaf distribution for all the neighbouring plants whose crown projection surfaces overlap. To study the effects of density on architectural development, we link the proposed competition model to the model of interaction between functional growth and structural development introduced by Mathieu (2006, PhD Thesis, Ecole Centrale de Paris, France). KEY RESULTS AND CONCLUSIONS: The model is applied to mono-specific field crops and forest stands. For high-density crops at full cover, the model is shown to be equivalent to the classical equation of field crop production (Howell and Musick, 1985, in Les besoins en eau des cultures; Paris: INRA Editions). However, our method is more accurate at the early stages of growth (before cover) or in the case of intermediate densities. It may potentially account for local effects, such as uneven spacing, variation in the time of plant emergence or variation in seed biomass. The application of the model to trees illustrates the expression of plant plasticity in response to competition for light. Density strongly impacts on tree architectural development through interactions with the source-sink balances during growth. The effects of density on tree height and radial growth that are commonly observed in real stands appear as emerging properties of the model.