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author:("andreu, Bruno")
1.  Multiple pathways regulate shoot branching 
Shoot branching patterns result from the spatio-temporal regulation of axillary bud outgrowth. Numerous endogenous, developmental and environmental factors are integrated at the bud and plant levels to determine numbers of growing shoots. Multiple pathways that converge to common integrators are most probably involved. We propose several pathways involving not only the classical hormones auxin, cytokinins and strigolactones, but also other signals with a strong influence on shoot branching such as gibberellins, sugars or molecular actors of plant phase transition. We also deal with recent findings about the molecular mechanisms and the pathway involved in the response to shade as an example of an environmental signal controlling branching. We propose the TEOSINTE BRANCHED1, CYCLOIDEA, PCF transcription factor TB1/BRC1 and the polar auxin transport stream in the stem as possible integrators of these pathways. We finally discuss how modeling can help to represent this highly dynamic system by articulating knowledges and hypothesis and calculating the phenotype properties they imply.
PMCID: PMC4292231  PMID: 25628627
axillary bud outgrowth; apical dominance; polar auxin transport; strigolactone; cytokinins; shade avoidance; flowering; modeling
2.  Rose bush leaf and internode expansion dynamics: analysis and development of a model capturing interplant variability 
Rose bush architecture, among other factors, such as plant health, determines plant visual quality. The commercial product is the individual plant and interplant variability may be high within a crop. Thus, both mean plant architecture and interplant variability should be studied. Expansion is an important feature of architecture, but it has been little studied at the level of individual organs in rose bushes. We investigated the expansion kinetics of primary shoot organs, to develop a model reproducing the organ expansion of real crops from non-destructive input variables. We took interplant variability in expansion kinetics and the model's ability to simulate this variability into account. Changes in leaflet and internode dimensions over thermal time were recorded for primary shoot expansion, on 83 plants from three crops grown in different climatic conditions and densities. An empirical model was developed, to reproduce organ expansion kinetics for individual plants of a real crop of rose bush primary shoots. Leaflet or internode length was simulated as a logistic function of thermal time. The model was evaluated by cross-validation. We found that differences in leaflet or internode expansion kinetics between phytomer positions and between plants at a given phytomer position were due mostly to large differences in time of organ expansion and expansion rate, rather than differences in expansion duration. Thus, in the model, the parameters linked to expansion duration were predicted by values common to all plants, whereas variability in final size and organ expansion time was captured by input data. The model accurately simulated leaflet and internode expansion for individual plants (RMSEP = 7.3 and 10.2% of final length, respectively). Thus, this study defines the measurements required to simulate expansion and provides the first model simulating organ expansion in rosebush to capture interplant variability.
PMCID: PMC3807087  PMID: 24167509
Rosa hybrida L.; individual plant; phytomer; model; elongation kinetics; leaflet size; internode length; growth
3.  NEMA, a functional–structural model of nitrogen economy within wheat culms after flowering. I. Model description 
Annals of Botany  2011;108(6):1085-1096.
Background and Aims
Models simulating nitrogen use by plants are potentially efficient tools to optimize the use of fertilizers in agriculture. Most crop models assume that a target nitrogen concentration can be defined for plant tissues and formalize a demand for nitrogen, depending on the difference between the target and actual nitrogen concentrations. However, the teleonomic nature of the approach has been criticized. This paper proposes a mechanistic model of nitrogen economy, NEMA (Nitrogen Economy Model within plant Architecture), which links nitrogen fluxes to nitrogen concentration and physiological processes.
A functional–structural approach is used: plant aerial parts are described in a botanically realistic way and physiological processes are expressed at the scale of each aerial organ or root compartment as a function of local conditions (light and resources).
Key Results
NEMA was developed for winter wheat (Triticum aestivum) after flowering. The model simulates the nitrogen (N) content of each photosynthetic organ as regulated by Rubisco turnover, which depends on intercepted light and a mobile N pool shared by all organs. This pool is enriched by N acquisition from the soil and N release from vegetative organs, and is depleted by grain uptake and protein synthesis in vegetative organs; NEMA accounts for the negative feedback from circulating N on N acquisition from the soil, which is supposed to follow the activities of nitrate transport systems. Organ N content and intercepted light determine dry matter production via photosynthesis, which is distributed between organs according to a demand-driven approach.
NEMA integrates the main feedbacks known to regulate plant N economy. Other novel features are the simulation of N for all photosynthetic tissues and the use of an explicit description of the plant that allows how the local environment of tissues regulates their N content to be taken into account. We believe this represents an appropriate frame for modelling nitrogen in functional–structural plant models. A companion paper will present model evaluation and analysis.
PMCID: PMC3189836  PMID: 21685431
Rubisco turnover; remobilization; functional–structural plant model; nitrogen; light acclimation; senescence; wheat; Triticum aestivum; root uptake; common pool
4.  NEMA, a functional–structural model of nitrogen economy within wheat culms after flowering. II. Evaluation and sensitivity analysis 
Annals of Botany  2011;108(6):1097-1109.
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.
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.
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.
PMCID: PMC3189838  PMID: 21685429
Rubisco turnover; remobilization; functional–structural plant model; nitrogen; light acclimation; senescence; wheat; Triticum aestivum; root uptake; common pool
5.  Modelling the effect of wheat canopy architecture as affected by sowing density on Septoria tritici epidemics using a coupled epidemic–virtual plant model 
Annals of Botany  2011;108(6):1179-1194.
Background and Aims
The relationship between Septoria tritici, a splash-dispersed disease, and its host is complex because of the interactions between the dynamic plant architecture and the vertical progress of the disease. The aim of this study was to test the capacity of a coupled virtual wheat–Septoria tritici epidemic model (Septo3D) to simulate disease progress on the different leaf layers for contrasted sowing density treatments.
A field experiment was performed with winter wheat ‘Soissons’ grown at three contrasted densities. Plant architecture was characterized to parameterize the wheat model, and disease dynamic was monitored to compare with simulations. Three simulation scenarios, differing in the degree of detail with which plant variability of development was represented, were defined.
Key Results
Despite architectural differences between density treatments, few differences were found in disease progress; only the lower-density treatment resulted in a slightly higher rate of lesion development. Model predictions were consistent with field measurements but did not reproduce the higher rate of lesion progress in the low density. The canopy reconstruction scenario in which inter-plant variability was taken into account yielded the best agreement between measured and simulated epidemics. Simulations performed with the canopy represented by a population of the same average plant deviated strongly from the observations.
It was possible to compare the predicted and measured epidemics on detailed variables, supporting the hypothesis that the approach is able to provide new insights into the processes and plant traits that contribute to the epidemics. On the other hand, the complex and dynamic responses to sowing density made it difficult to test the model precisely and to disentangle the various aspects involved. This could be overcome by comparing more contrasted and/or simpler canopy architectures such as those resulting from quasi-isogenic lines differing by single architectural traits.
PMCID: PMC3189839  PMID: 21724656
Crop architecture; modelling; Septoria tritici; wheat; Triticum aestivum; sowing density; 3-D virtual plant model; plant–pathogen interaction
6.  A comparative analysis of leaf shape of wheat, barley and maize using an empirical shape model 
Annals of Botany  2010;107(5):865-873.
Background and Aims
The phenotypes of grasses show differences depending on growth conditions and ontogenetic stage. Understanding these responses and finding suitable mathematical formalizations are an essential part of the development of plant and crop models. Usually, a marked change in architecture between juvenile and adult plants is observed, where dimension and shape of leaves are likely to change. In this paper, the plasticity of leaf shape is analysed according to growth conditions and ontogeny.
Leaf shape of Triticum aestivum, Hordeum vulgare and Zea mays cultivars grown under varying conditions was measured using digital image processing. An empirical leaf shape model was fitted to measured shape data of single leaves. Obtained values of model parameters were used to analyse the patterns in leaf shape.
Key Results
The model was able to delineate leaf shape of all studied species. The model error was small. Differences in leaf shape between juvenile and adult leaves in T. aestivum and H. vulgare were observed. Varying growth conditions impacted leaf dimensions but did not impact leaf shape of the respective species.
Leaf shape of the studied T. aestivum and H. vulgare cultivars was remarkably stable for a comparable ontogenetic stage (leaf rank), but differed between stages. Along with other aspects of grass architecture, leaf shape changed during the transition from juvenile to adult growth phase. Model-based analysis of leaf shape is a method to investigate these differences. Presented results can be integrated into architectural models of plant development to delineate leaf shape for different species, cultivars and environmental conditions.
PMCID: PMC3077976  PMID: 20929895
Leaf shape; model; model-based analysis; ontogeny; image processing; Triticum aestivum; Hordeum vulgare; Zea mays
7.  Onset of Sheath Extension and Duration of Lamina Extension are Major Determinants of the Response of Maize Lamina Length to Plant Density 
Annals of Botany  2006;98(5):1005-1016.
• Background and Aims Plants regulate their architecture strongly in response to density, and there is evidence that this involves changes in the duration of leaf extension. This questions the approximation, central in crop models, that development follows a fixed thermal time schedule. The aim of this research is to investigate, using maize as a model, how the kinetics of extension of grass leaves change with density, and to propose directions for inclusion of this regulation in plant models.
• Methods Periodic dissection of plants allowed the establishment of the kinetics of lamina and sheath extension for two contrasting sowing densities. The temperature of the growing zone was measured with thermocouples. Two-phase (exponential plus linear) models were fitted to the data, allowing analysis of the timing of the phase changes of extension, and the extension rate of sheaths and blades during both phases.
• Key Results The duration of lamina extension dictated the variation in lamina length between treatments. The lower phytomers were longer at high density, with delayed onset of sheath extension allowing more time for the lamina to extend. In the upper phytomers—which were shorter at high density—the laminae had a lower relative extension rate (RER) in the exponential phase and delayed onset of linear extension, and less time available for extension since early sheath extension was not delayed.
• Conclusions The relative timing of the onset of fast extension of the lamina with that of sheath development is the main determinant of the response of lamina length to density. Evidence is presented that the contrasting behaviour of lower and upper phytomers is related to differing regulation of sheath ontogeny before and after panicle initiation. A conceptual model is proposed to explain how the observed asynchrony between lamina and sheath development is regulated.
PMCID: PMC3292240  PMID: 16926228
Co-ordination; emergence; leaf extension; kinetics; lamina; leaf; ligule; ontogeny; plant architecture; primordium; sheath; Zea mays; RER; LER
8.  Cessation of Tillering in Spring Wheat in Relation to Light Interception and Red : Far-red Ratio 
Annals of Botany  2006;97(4):649-658.
• Background and Aims The production of axillary shoots (tillering) in spring wheat (Triticum aestivum) depends on intraspecific competition. The mechanisms that underlie this competition are complex, but light within the wheat canopy plays a key role. The main objectives of this paper are to analyse the effects of plant population density and shade on tillering dynamics of spring wheat, to assess the canopy conditions quantitatively at the time of tillering cessation, and to analyse the relationship between the tiller bud and the leaf on the same phytomer.
• Methods Spring wheat plants were grown at three plant population densities and under two light regimes (25 % and 100 % light). Tiller appearance, fraction of the light intercepted, and red : far-red ratio at soil level were recorded. On six sampling dates the growth status of axillary buds was analysed.
• Key Results Tillering ceased earlier at high population densities and ceased earlier in the shade than in full sunlight. At cessation of tillering, both the fraction of light intercepted and the red : far-red ratio at soil level were similar in all treatments. Leaves on the same phytomer of buds that grew out showed more leaf mass per unit area than those on the same phytomer of buds that remained dormant.
• Conclusions Tillering ceases at specific light conditions within the wheat canopy, independent of population density, and to a lesser extent independent of light intensity. It is suggested that cessation of tillering is induced when the fraction of PAR intercepted by the canopy exceeds a specific threshold (0·40–0·45) and red : far-red ratio drops below 0·35–0·40.
PMCID: PMC2803660  PMID: 16464875
Triticum aestivum; wheat; tiller; bud; plant population density; shade; PAR; red : far-red ratio; functional–structural model
9.  Maximum Likelihood Inference and Bootstrap Methods for Plant Organ Growth via Multi-phase Kinetic Models and their Application to Maize 
Annals of Botany  2005;96(1):137-148.
• Background and Aims Fitting the parameters of models of plant organ growth is a means to investigate how environmental conditions affect plant architecture. The aim of this article is to evaluate some non-linear methods for fitting the parameters of multi-phase models of the kinetics of extension of plant organs such as laminae, sheaths and internodes.
• Methods A set of computational procedures was developed allowing parameter-fitting of multi-phase models, using the maximum likelihood criterion, in which phases are identified with reference to ontogenic processes. Two bootstrap methods were compared to assess the precision of the estimates of fitted parameters, and of functions of these parameters such as the final leaf length, and the duration and rate of the rapid extension phase. Methods were applied to an experimental dataset, representing the kinetics of laminae, sheaths and internodes along the maize shoot, for two contrasting densities.
• Key Results A set of multi-phase models was proposed to describe the extension of laminae, sheaths and internodes along the shoot. The distinguishable phases differed between laminae, sheaths and internodes. For sheaths and laminae, but not for internodes, the same model could be fitted to all phytomers along the shoot. The variation of parameters along the shoot and between density treatments, as well as derived functions such as the durations of the phases of extension, are presented for laminae. It was the duration of the fast extension period, rather than its rate, which determined the difference in final length between treatments.
• Conclusions Such methods permit a large degree of objectivity and facilitate the analysis of such rather complicated but co-ordinated datasets. The work also illustrates some natural limitations of maximum likelihood methods, and viable ways of overcoming them by including a priori knowledge in the model fitting method are discussed.
PMCID: PMC4246818  PMID: 15911541
Zea mays; maximum likelihood; bootstrap; architectural model; maize; multi-phase kinetic model; extension

Results 1-9 (9)