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1.  Influence of the variation of geometrical and topological traits on light interception efficiency of apple trees: sensitivity analysis and metamodelling for ideotype definition 
Annals of Botany  2014;114(4):739-752.
Background and Aims
The impact of a fruit tree's architecture on its performance is still under debate, especially with regard to the definition of varietal ideotypes and the selection of architectural traits in breeding programmes. This study aimed at providing proof that a modelling approach can contribute to this debate, by using in silico exploration of different combinations of traits and their consequences on light interception, here considered as one of the key parameters to optimize fruit tree production.
Methods
The variability of organ geometrical traits, previously described in a bi-parental population, was used to simulate 1- to 5-year-old apple trees (Malus × domestica). Branching sequences along trunks observed during the first year of growth of the same hybrid trees were used to initiate the simulations, and hidden semi-Markov chains previously parameterized were used in subsequent years. Tree total leaf area (TLA) and silhouette to total area ratio (STAR) values were estimated, and a sensitivity analysis was performed, based on a metamodelling approach and a generalized additive model (GAM), to analyse the relative impact of organ geometry and lateral shoot types on STAR.
Key Results
A larger increase over years in TLA mean and variance was generated by varying branching along trunks than by varying organ geometry, whereas the inverse was observed for STAR, where mean values stabilized from year 3 to year 5. The internode length and leaf area had the highest impact on STAR, whereas long sylleptic shoots had a more significant effect than proleptic shoots. Although the GAM did not account for interactions, the additive effects of the geometrical factors explained >90% of STAR variation, but much less in the case of branching factors.
Conclusions
This study demonstrates that the proposed modelling approach could contribute to screening architectural traits and their relative impact on tree performance, here viewed through light interception. Even though trait combinations and antagonism will need further investigation, the approach opens up new perspectives for breeding and genetic selection to be assisted by varietal ideotype definition.
doi:10.1093/aob/mcu034
PMCID: PMC4156120  PMID: 24723446
Silhouette to total area ratio; STAR; functional–structural growth modelling; leaf area; branching; sensitivity analysis; apple; ideotype; Malus × domestica
2.  A functional–structural modelling approach to autoregulation of nodulation 
Annals of Botany  2010;107(5):855-863.
Background and Aims
Autoregulation of nodulation is a long-distance shoot–root signalling regulatory system that regulates nodule meristem proliferation in legume plants. However, due to the intricacy and subtleness of the signalling nature in plants, molecular and biochemical details underlying mechanisms of autoregulation of nodulation remain largely unknown. The purpose of this study is to use functional–structural plant modelling to investigate the complexity of this signalling system. There are two major challenges to be met: modelling the 3D architecture of legume roots with nodulation and co-ordinating signalling-developmental processes with various rates.
Methods
Soybean (Glycine max) was chosen as the target legume. Its root system was observed to capture lateral root branching and nodule distribution patterns. L-studio, a software tool supporting context-sensitive L-system modelling, was used for the construction of the architectural model and integration with the internal signalling.
Key Results
A branching pattern with regular radial angles was found between soybean lateral roots, from which a root mapping method was developed to characterize the laterals. Nodules were mapped based on ‘nodulation section’ to reveal nodule distribution. A root elongation algorithm was then developed for simulation of root development. Based on the use of standard sub-modules, a synchronization algorithm was developed to co-ordinate multi-rate signalling and developmental processes.
Conclusions
The modelling methods developed here not only allow recreation of legume root architecture with lateral branching and nodulation details, but also enable parameterization of internal signalling to produce different regulation results. This provides the basis for using virtual experiments to help in investigating the signalling mechanisms at work.
doi:10.1093/aob/mcq182
PMCID: PMC3077977  PMID: 20826439
Legume; soybean; soya bean; virtual plant; L-system; root reconstruction; synchronization; nodulation
3.  Computational Complementation: A Modelling Approach to Study Signalling Mechanisms during Legume Autoregulation of Nodulation 
PLoS Computational Biology  2010;6(2):e1000685.
Autoregulation of nodulation (AON) is a long-distance signalling regulatory system maintaining the balance of symbiotic nodulation in legume plants. However, the intricacy of internal signalling and absence of flux and biochemical data, are a bottleneck for investigation of AON. To address this, a new computational modelling approach called “Computational Complementation” has been developed. The main idea is to use functional-structural modelling to complement the deficiency of an empirical model of a loss-of-function (non-AON) mutant with hypothetical AON mechanisms. If computational complementation demonstrates a phenotype similar to the wild-type plant, the signalling hypothesis would be suggested as “reasonable”. Our initial case for application of this approach was to test whether or not wild-type soybean cotyledons provide the shoot-derived inhibitor (SDI) to regulate nodule progression. We predicted by computational complementation that the cotyledon is part of the shoot in terms of AON and that it produces the SDI signal, a result that was confirmed by reciprocal epicotyl-and-hypocotyl grafting in a real-plant experiment. This application demonstrates the feasibility of computational complementation and shows its usefulness for applications where real-plant experimentation is either difficult or impossible.
Author Summary
Endogenous signals, such as phytohormones, play a vital role in plant development and function, controlling processes such as flowering, branching, disease response, and nodulation. However, the signalling mechanisms are so subtle and so complex that details about them remain largely unknown. In this study, we develop a “Computational Complementation” approach for the investigation of long-distance signalling networks during legume autoregulation of nodulation (AON). The key idea is to use computational modelling to complement the deficiency of an empirical model of an AON deficient mutant with hypothesised AON components. If the complementation restores a wild-type nodulation phenotype, the modelled hypotheses would be supported as reasonable. To evaluate the feasibility of this approach, we tested whether wild-type soybean cotyledons participate in AON, commonly controlled by “real” leaves. The test gave an affirmative result (i.e., cotyledons do have AON activity), which was subsequently confirmed by a graft experiment on real plants. Future applications of this approach may be to test candidate AON signals such as auxins, flavones, and CLE peptides, and other plant signalling networks.
doi:10.1371/journal.pcbi.1000685
PMCID: PMC2829028  PMID: 20195551

Results 1-3 (3)