MuSCA: a multi-scale source-sink carbon allocation model to explore carbon allocation in plants. An application to static apple tree structures.

BACKGROUND AND AIMS: Carbon allocation in plants is usually represented at a topological scale, specific to each model. This makes the results obtained with different models, and the impact of their scales of representation, difficult to compare. In this study, we developed a multi-scale carbon allocation model (MuSCA) that allows the use of different, user-defined, topological scales of a plant, and assessment of the impact of each spatial scale on simulated results and computation time. METHODS: Model multi-scale consistency and behaviour were tested on three realistic apple tree structures. Carbon allocation was computed at five scales, spanning from the metamer (the finest scale, used as a reference) up to first-order branches, and for different values of a sap friction coefficient. Fruit dry mass increments were compared across spatial scales and with field data. KEY RESULTS: The model was able to represent effects of competition for carbon assimilates on fruit growth. Intermediate friction parameter values provided results that best fitted field data. Fruit growth simulated at the metamer scale differed of ~1 % in respect to results obtained at growth unit scale and up to 60 % in respect to first order branch and fruiting unit scales. Generally, the coarser the spatial scale the more predicted fruit growth diverged from the reference. Coherence in fruit growth across scales was also differentially impacted, depending on the tree structure considered. Decreasing the topological resolution reduced computation time by up to four orders of magnitude. CONCLUSIONS: MuSCA revealed that the topological scale has a major influence on the simulation of carbon allocation. This suggests that the scale should be a factor that is carefully evaluated when using a carbon allocation model, or when comparing results produced by different models. Finally, with MuSCA, trade-off between computation time and prediction accuracy can be evaluated by changing topological scales.

Analysis of transcripts differentially expressed between fruited and deflowered 'Gala' adult trees: a contribution to biennial bearing understanding in apple.

BACKGROUND: The transition from vegetative to floral state in shoot apical meristems (SAM) is a key event in plant development and is of crucial importance for reproductive success. In perennial plants, this event is recurrent during tree life and subject to both within-tree and between-years heterogeneity. In the present study, our goal was to identify candidate processes involved in the repression or induction of flowering in apical buds of adult apple trees. RESULTS: Genes differentially expressed (GDE) were examined between trees artificially set in either 'ON' or 'OFF' situation, and in which floral induction (FI) was shown to be inhibited or induced in most buds, respectively, using qRT-PCR and microarray analysis. From the period of FI through to flower differentiation, GDE belonged to four main biological processes (i) response to stimuli, including response to oxidative stress; (ii) cellular processes, (iii) cell wall biogenesis, and (iv) metabolic processes including carbohydrate biosynthesis and lipid metabolic process. Several key regulator genes, especially TEMPRANILLO (TEM), FLORAL TRANSITION AT MERISTEM (FTM1) and SQUAMOSA PROMOTER BINDING PROTEIN-LIKE (SPL) were found differentially expressed. Moreover, homologs of SPL and Leucine-Rich Repeat proteins were present under QTL zones previously detected for biennial bearing. CONCLUSIONS: This data set suggests that apical buds of 'ON' and 'OFF' trees were in different physiological states, resulting from different metabolic, hormonal and redox status which are likely to contribute to FI control in adult apple trees. Investigations on carbohydrate and hormonal fluxes from sources to SAM and on cell detoxification process are expected to further contribute to the identification of the underlying physiological mechanisms of FI in adult apple trees.

Deciphering the genetic determinism of bud phenology in apple progenies: a new insight into chilling and heat requirement effects on flowering dates and positional candidate genes.

The present study investigates the genetic determinism of bud phenological traits using two segregating F(1) apple (Malus × domestica) progenies. Phenological trait variability was dissected into genetic and climatic components using mixed linear modeling, and estimated best linear unbiased predictors were used for quantitative trait locus (QTL) detection. For flowering dates, year effects were decomposed into chilling and heat requirements based on a previously developed model. QTL analysis permitted the identification of two major and population-specific genomic regions on LG08 and LG09. Both 'chilling requirement' and 'heat requirement' periods influenced flowering dates, although their relative impact was dependent on the genetic background. Using the apple genome sequence data, putative candidate genes underlying one major QTL were investigated. Numerous key genes involved in cell cycle control were identified in clusters within the confidence interval of the major QTL on LG09. Our results contribute towards a better understanding of the interaction between QTLs and climatic conditions, and provide a basis for the identification of genes involved in bud growth resumption.

Insights into secondary growth in perennial plants: its unequal spatial and temporal dynamics in the apple (Malus domestica) is driven by architectural position and fruit load.

BACKGROUND AND AIMS: Secondary growth is a main physiological sink. However, the hierarchy between the processes which compete with secondary growth is still a matter of debate, especially on fruit trees where fruit weight dramatically increases with time. It was hypothesized that tree architecture, here mediated by branch age, is likely to have a major effect on the dynamics of secondary growth within a growing season. METHODS: Three variables were monitored on 6-year-old 'Golden Delicious' apple trees from flowering time to harvest: primary shoot growth, fruit volume, and cross-section area of branch portions of consecutive ages. Analyses were done through an ANOVA-type analysis in a linear mixed model framework. KEY RESULTS: Secondary growth exhibited three consecutive phases characterized by unequal relative area increment over the season. The age of the branch had the strongest effect, with the highest and lowest relative area increment for the current-year shoots and the trunk, respectively. The growth phase had a lower effect, with a shift of secondary growth through the season from leafy shoots towards older branch portions. Eventually, fruit load had an effect on secondary growth mainly after primary growth had ceased. CONCLUSIONS: The results support the idea that relationships between production of photosynthates and allocation depend on both primary growth and branch architectural position. Fruit load mainly interacted with secondary growth later in the season, especially on old branch portions.

Shaping the shoot: the relative contribution of cell number and cell shape to variations in internode length between parent and hybrid apple trees.

Genetic control of plant size and shape is a promising perspective, particularly in fruit trees, in order to select desirable genotypes. A recent study on architectural traits in an apple progeny showed that internode length was a highly heritable character. However, few studies have been devoted to internode cellular patterning in dicotyledonous stems, and the interplay between the two elementary cell processes that contribute to their length, i.e. cell division and elongation, is not fully understood. The present study aimed at unravelling their contributions in the genetic variation of internode length in a selection of F(1) and parent genotypes of apple tree, by exploring the number of cells and cell shape within mature internodes belonging to the main axes. The results highlighted that both the variables were homogeneous in samples collected either along a sagital line or along the pith width, and suggest that cell lengthening was homogeneous during internode development. They allowed the total number of cells to be estimated on the internode scale and opened up new perspectives for simplifying tissue sampling procedures for further investigations. Differences in internode length were observed between the genotypes, in particular between the parents, and partly resulted from a compensation between cell number and cell length. However, genetic variations in internode length primarily involved the number of cells, while cell length was more secondary. These results argue for an interplay between cellular and organismal control of internode shape that may involve the rib meristem.

Contributions of foliage distribution and leaf functions to light interception, transpiration and photosynthetic capacities in two apple cultivars at branch and tree scales.

Both the spatial distribution of leaves and leaf functions affect the light interception, transpiration and photosynthetic capacities of trees, but their relative contributions have rarely been investigated. We assessed these contributions at the branch and tree scales in two apple cultivars (Malus x domestica Borkh. 'Fuji' and 'Braeburn') with contrasting architectures, by estimating their branch and tree capacities and comparing them with outputs from a radiation absorption, transpiration and photosynthesis (RATP) functional-structural plant model (FSPM). The structures of three 8-year-old trees of each cultivar were digitized to obtain 3-D representations of foliage geometry. Within-tree foliage distribution was compared with shoot demography, number of leaves per shoot and mean individual leaf area. We estimated branch and tree light interception from silhouette to total leaf area ratios (STAR), transpiration from sap flux measurements and net photosynthetic rates by the branch bag method. Based on a set of parameters we previously established for both cultivars, the outputs of the RATP model were tested against STAR values, sap fluxes and photosynthetic measurements. The RATP model was then used to virtually switch foliage distribution or leaf functions (stomatal and photosynthetic properties), or both, between cultivars and to evaluate the effects on branch and tree light interception, transpiration and photosynthetic capacities in each cultivar. 'Fuji' trees had a higher proportion of leaf area borne on long shoots, fewer leaves per unit shoot length and a larger individual leaf area than 'Braeburn' trees. This resulted in a lower leaf area density and, consequently, a higher STAR in 'Fuji' than in 'Braeburn' at both branch and tree scales. Transpiration and photosynthetic rates were significantly higher in 'Fuji' than in 'Braeburn'. Branch heterogeneity was greater in 'Braeburn' than in 'Fuji'. An analysis of the virtual switches of foliage distribution or leaf function showed that differences in leaf spatial distribution and functions had additive effects that accounted for the lower transpiration and photosynthetic rates of branches and trees of 'Braeburn' compared with 'Fuji'. Leaf distribution had a more important role at the branch scale than at the tree scale, but the leaf function effect exceeded the leaf distribution effect at both scales. Our study demonstrated the potential of FSPM to disentangle physiological differences between cultivars through in silico scenarios.

Clarifying the effects of dwarfing rootstock on vegetative and reproductive growth during tree development: a study on apple trees.

BACKGROUND AND AIMS: Despite the widespread use of dwarfing rootstocks in the fruit-tree industry, their impact on tree architectural development and possible role in the within-tree balance between growth and flowering are still poorly understood, in particular during the early years of growth. The present study addressed this question in apple trees, through a detailed analysis of shoot populations, i.e. both vegetative and flowering shoots, during tree development. METHODS: Architectural databases were constructed for trees of two cultivars that were either own-rooted or grafted on dwarfing rootstock. Within-tree shoot demographics and annual shoot characteristics, i.e. their dimensions, number of laterals and flowering, were observed from the first to the fifth year of growth and compared among scion/root system combinations. KEY RESULTS: Differences in axis demographics appeared among scion/root system combinations after the second year of growth. Differences were found (a) in the number of long axes and (b) the number of medium axes. Dwarfing rootstock reduced the total number of axes developed in a tree, and this reduction resulted from proportionally more medium axes and spurs than long axes. The life span of spurs was also shortened. These phenomena appeared after an increase in flowering that started in the second year of growth and involved both axillary and terminal positions. Flowering regularity was also increased in grafted trees. CONCLUSIONS: These results confirm that the number of long shoots and flowering potential depend on the cultivar. They indicate that tree architectural plasticity in response to its root system mainly derives from the number of medium shoots developed and follows priorities within the whole tree axis population. There was also evidence for dwarfing rootstock involvement in adjusting the flowering abundance and that differences in flowering occurrence take precedence over those regarding vegetative growth during tree development.

Wide range QTL analysis for complex architectural traits in a 1-year-old apple progeny.

The present study aimed at investigating the genetic determinisms of architectural traits in a 1-year-old apple (Malus x domestica Borkh.). F1 progeny. A precise phenotyping including both tree topology and geometry was performed on 123 offspring. For a wide range of developmental traits, broad-sense heritability was estimated and quantitative trait loci (QTLs) were investigated. Several loci controlling geometry were identified (i) for integrated traits, such as tree surface and volume; (ii) for traits related to the form of long sylleptic axillary shoots (LSAS), such as bending and basis angle; and (iii) for traits of finer components, such as internode length of the trunk and LSAS. Considering topology, 4 QTLs were mapped for the total number of sylleptic branching in the tree, suggesting a strong and complex genetic control that was analysed through colocalisations between QTLs mapped for the different shoot types (long, medium, short). Two QTLs were also mapped for a phenological trait (date of bud break). When several QTLs were detected for a trait, a linear model was built to test epistatic effects and estimate the whole percentage of variability explained. The discussion focuses on particular colocalisations and on the relevance of traits to further tree development.

Co-ordinated growth between aerial and root systems in young apple plants issued from in vitro culture.

BACKGROUND AND AIMS: In several species exhibiting a rhythmic aerial growth, the existence of an alternation between root and shoot growth has been demonstrated. The present study aims to investigate the respective involvement of the emergence of new organs and their elongation in relation to this phenomenon and its possible genotypic variation in young apple plants. METHODS: Two apple varieties, X6407 (recently named 'Ariane') and X3305 ('Chantecler' x 'Baujade'), were compared. Five plants per variety, issued from in vitro culture, were observed in minirhizotrons over 4 months. For each plant, root emergence and growth were observed twice per week. Growth rates were calculated for all roots with more than two segments and the branching density was calculated on primary roots. On the aerial part, the number of leaves, leaf area and total shoot length were observed weekly. KEY RESULTS: No significant difference was observed between varieties in any of the final characteristics of aerial growth. Increase in leaf area and shoot length exhibited a 3-week rhythm in X3305 while a weaker signal was observed in Ariane. The primary root growth rate was homogeneous between the plants and likewise between the varieties, while their branching density differed significantly. Secondary roots emerged rhythmically, with a 3-week and a 2-week rhythm, respectively, in X3305 and 'Ariane'. Despite a high intra-variety variability, significant differences were observed between varieties in the secondary root life span and mean length. A synchronism between leaf emergence and primary root growth was highlighted in both varieties, while an opposition phase was observed between leaf area increments and secondary root emergence in X3305 only. CONCLUSION: A biological model of dynamics that summarizes the interactions between processes and includes the assumption of a feedback effect of lateral root emergence on leaf emergence is proposed.

Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models.

Plant architecture is the result of repetitions that occur through growth and branching processes. During plant ontogeny, changes in the morphological characteristics of plant entities are interpreted as the indirect translation of different physiological states of the meristems. Thus connected entities can exhibit either similar or very contrasted characteristics. We propose a statistical model to reveal and characterize homogeneous zones and transitions between zones within tree-structured data: the hidden Markov tree (HMT) model. This model leads to a clustering of the entities into classes sharing the same 'hidden state'. The application of the HMT model to two plant sets (apple trees and bush willows), measured at annual shoot scale, highlights ordered states defined by different morphological characteristics. The model provides a synthetic overview of state locations, pointing out homogeneous zones or ruptures. It also illustrates where within branching structures, and when during plant ontogeny, morphological changes occur. However, the labelling exhibits some patterns that cannot be described by the model parameters. Some of these limitations are addressed by two alternative HMT families.

Comparison methods for branching and axillary flowering sequences.

Comparing branching and axillary flowering patterns accurately is a major issue both in botany and in various agronomic contexts. Data take the form of sequences which naturally represent the underlying structural information of branching and axillary flowering patterns. Various comparison methods are proposed based either on sequence alignment or on the computation of dissimilarity measures between (hidden) Markovian models built from sets of sequences. Sequence alignment is a natural complement to the exploratory tools and statistical models proposed in Guédon et al. (J. Theor. Biol. 212 (2001) 481) with the distinctive feature of applying to individual sequences. Comparison methods may also be used to reveal some grouping within a set of sequences or to evaluate the strength of a predefined grouping of sequences. The proposed approach is illustrated by examples corresponding to different plant species and different biological or agronomic objectives.

Winter bud content according to position in 3-year-old branching systems of 'Granny Smith' apple.

An investigation was made of the number of preformed organs in winter buds of 3-year-old reiterated complexes of the 'Granny Smith' cultivar. Winter bud content was studied with respect to bud position: terminal buds were compared on both long shoots and spurs according to branching order and shoot age, while axillary buds were compared between three zones (distal, median and proximal) along 1-year-old annual shoots in order 1. The percentage of winter buds that differentiated into inflorescences was determined and the flowers in each bud were counted for each bud category. The other organ categories considered were scales and leaf primordia. The results confirmed that a certain number of organs must be initiated before floral differentiation occurred. The minimum limit was estimated at about 15 organs on average, including scales. Total number of lateral organs formed was shown to vary with both bud position and meristem age, increasing from newly formed meristems to 1- and 2-year-old meristems on different shoot types. These differences in bud organogenesis depending on bud position, were consistent with the morphogenetic gradients observed in apple tree architecture. Axillary buds did not contain more than 15 organs on average and this low organogenetic activity of the meristems was related to a low number of flowers per bud. In contrast, the other bud categories contained more than 15 differentiated organs on average and a trade-off was observed between leaf and flower primordia. The ratio between the number of leaf and flower primordia per bud varied with shoot type. When the terminal buds on long shoots and spurs were compared, those on long shoots showed more flowers and a higher ratio of leaf to flower primordia.

Application of architectural analysis and AMAPmod methodology to study dwarfing phenomenon: the branch structure of 'Royal Gala' apple grafted on dwarfing and non-dwarfing rootstock/interstock combinations.

Architectural analysis was applied to study branch development of 'Royal Gala' apple trees grafted with dwarfing and non-dwarfing rootstock/interstock combinations, which had been chosen to produce trees with a wide range of vigour. Using AMAPmod methodology, the structure of 3-year-old branches was described at four levels of representation: branch; annual shoot; growth unit; and node. Three types of growth units were distinguished: extension growth unit (vegetative unit with internode extension); vegetative spur with minimal internode extension; and fruiting spur or bourse. The aim of the analysis was to describe exactly how the rootstock/interstock combinations affected the structure building process. The number of extension growth units, vegetative spurs and fruiting spurs per annual shoot changed over the years, but this was not affected by rootstock/interstock combination. Compared with MM.106 rootstock, M.9 rootstock reduced the number of nodes per extension growth unit. In most cases, rootstock/interstock combination had no effect on the linear relationship between extension growth unit length and node number (R(2) = 0.88). Average internode length depended on unit node number, with internodes being shorter for units with fewer nodes. Thus the difference in apple branch size induced by the rootstock/interstock combinations was mainly due to a reduction in the length and number of neoformed nodes produced on extension growth units. As percentage budbreak of axillary buds on extension growth units was not affected by rootstock/interstock combination, differences in numbers of axillary annual shoots per branch were entirely due to differences in the total numbers of nodes extended during the previous year.

Exploring within-tree architectural development of two apple tree cultivars over 6 years.

The present study addresses the prediction of apple tree development, taking into account both the number and within-tree position of tree components. The architectural development of two trees per scion cultivar, 'Fuji' and 'Braeburn', was studied by describing all shoots over 6 years. Flowering and fruiting were observed over 3 years. The description included different scales [entire trees, axes, growth units (GUs) and metamers], and the analysis compared all axes of the trees as a function of their branching order and age. Three main aspects of vegetative development were investigated: the quantity of primary growth; the number and nature of developing axillary shoots; and meristem death. Results confirm the existence of within-tree morphological gradients, and show that the decrease in growth was comparable in magnitude for all axes and GUs, irrespective of their position. This decrease results from a reduction in the number of metamers per GU, which was modelled by an exponential function. The decrease in growth involved changes in the number and nature of the axillary shoots, which could be described by simple functions. The probability of spur death was constant over the years but differed according to cultivar and type of bearing shoot. The within-tree probability of flowering and fruiting was predictable for 'Braeburn' because axes, regardless of their position and type, had a high probability of flowering and a low probability of fruit set which led to a regular bearing habit. In contrast, 'Fuji' had an alternating bearing behaviour that was more complex to predict. This appeared to result from a synchronized increase in the probability that all GUs at tree scale are floral, combined with a high probability of fruit set. The consequences of these results for both yield prediction and architectural simulations are discussed.

Optimisation of the coagulation-flocculation process of raw water by optimal design method.

In the present paper, a systematic study of the influence of raw water quality and operating conditions on the effectiveness of the coagulation-flocculation process using aluminium sulphate (AS) is presented. The influence of raw water composition is studied at two levels, fractional factorial designs and a Doehlert uniform shell design to determine the influence of the operating conditions. The analysis of the experimental responses (residual turbidity and minimally AS dose are denoted as (Tu(m)) and (AS(m)), respectively) shows that the parameters which have the greatest influence change depending on the response. It is not always possible, for a given water composition, to obtain simultaneously low residual turbidity and minimally AS dose. However, under the conditions of this study, the search for a criterion of optimisation must bear the minimisation of residual turbidity, because it remains the principal criterion of effectiveness of the process, even, if in a few cases, it results in an increase in the cost of treatment.

Modelling branching patterns on 1-year-old trunks of six apple cultivars.

The structure resulting from branching on 1-year-old apple tree trunks was analysed in a set of apple cultivars with diverse branching and fruiting habits. Four different lateral types borne on successive nodes were observed when vegetative and flowering fates, as well as sylleptic and proleptic branching, were taken into account. The location and grouping of lateral types along the trunk were analysed for all cultivars, but are detailed for one cultivar only. This cultivar showed a succession of zones, each zone being characterized by its composition of lateral types. Statistical models-hidden semi-Markov chains-were built to take this structure into account and to characterize the cultivar's specific branching pattern. The models showed that most of the branching zones had a similar location in the different cultivars, even though zone composition and zone length differed among cultivars. On a more detailed scale, the nodes bearing a lateral, regardless of its type, were frequently followed by latent buds. The validity of the models and their biological interpretation are discussed with respect to parent shoot dynamics, hormonal gradients and competition between neighbouring buds.

Pattern analysis in branching and axillary flowering sequences.

In the architectural approach to the study of plants, a major issue is to analyse branching and axillary flowering patterns. Due to the structured expression of the branching process and the noisy character of the observed patterns, we propose an analysis framework which is both structural and probabilistic. Data take the form of sequences which naturally represent the underlying structural information of branching and axillary flowering patterns and allow the application of a large number of methods ranging from exploratory analysis to stochastic modeling. The primary aim of the proposed analysis methods is to reveal patterns not directly apparent in the data, and thus to deepen our biological understanding of the underlying mechanisms that control the branching and the axillary flowering of plants over time and space. The proposed approach is illustrated using a set of examples corresponding to different plant species and different biological or agronomic objectives.

Use of mixed perfluorinated ion-pairing agents as solvents in ion-pair high-performance liquid chromatography for the preparative purification of aminoglycoside antibiotics.

The possibility of using mixed ion-pair reversed-phase high-performance liquid chromatography for the preparative purification of aminoglycoside antibiotics was investigated. Retention can be satisfactorily defined in aqueous conditions but efficiency is critical. The analysis of a polynominal model allowed ion-pairing agents compositions to be designed leading to improved efficiency. Inexpensive aqueous mobile phases using volatile buffers can be defined for the satisfactory ion-pair preparative chromatography of aminoglycosides.