Model-assisted comparison of sugar accumulation patterns in ten fleshy fruits highlights differences between herbaceous and woody species

BACKGROUND AND AIMS

Sugar concentration is a key determinant of fruit quality. Soluble sugars and starch concentrations in fruits vary greatly from one species to another. The aim of this study was to investigate similarities and differences in sugar accumulation strategies across ten contrasting fruit species using a modelling approach.

METHODS

We developed a coarse-grained model of primary metabolism based on the description of the main metabolic and hydraulic processes (synthesis of compounds other than sugar and starch, synthesis and hydrolysis of starch, and water dilution) involved in the accumulation of soluble sugars during fruit development.

KEY RESULTS

Statistical analyses based on metabolic rates separated the species into six groups according to the rate of synthesis of compounds other than sugar and starch. Herbaceous species (cucumber, tomato, eggplant, pepper and strawberry) were characterized by a higher synthesis rate than woody species (apple, nectarine, clementine, grape and kiwifruit). Inspection of the dynamics of the processes involved in sugar accumulation revealed that net sugar importation, metabolism and dilution processes were remarkably synchronous in most herbaceous plants, whereas in kiwifruit, apple and nectarine, processes related to starch metabolism were temporally separated from other processes. Strawberry, clementine and grape showed a distinct dynamic compared with all other species.

CONCLUSIONS

Overall, these results provide fresh insights into species-specific regulatory strategies and into the role of starch metabolism in the accumulation of soluble sugars in fleshy fruits. In particular, inter-specific differences in development period shape the co-ordination of metabolic processes and affect priorities for carbon allocation across species. The six metabolic groups identified by our analysis do not show a clear separation into climacteric and non-climacteric species, possibly suggesting that the metabolic processes related to sugar concentration are not greatly affected by ethylene-associated events.

Reducing a model of sugar metabolism in peach to catch different patterns among genotypes

Several studies have been conducted to understand the dynamic of primary metabolisms in fruit by translating them into mathematics models. An ODE kinetic model of sugar metabolism has been developed by Desnoues et al. (2018) to simulate the accumulation of different sugars during peach fruit development. Two major drawbacks of this model are (a) the number of parameters to calibrate and (b) its integration time that can be long due to non-linearity and time-dependent input functions. Together, these issues hamper the use of the model for a large panel of genotypes, for which few data are available. In this paper, we present a model reduction scheme that explicitly addresses the specificity of genetic studies in that: (i) it yields a reduced model that is adapted to the whole expected genetic diversity (ii) it maintains network structure and variable identity, in order to facilitate biological interpretation. The proposed approach is based on the combination and the systematic evaluation of different reduction methods. Thus, we combined multivariate sensitivity analysis, structural simplification and timescale-based approaches to simplify the number and the structure of ordinary differential equations of the model. The original and reduced models were compared based on three criteria, namely the corrected Aikake Information Criterion (AIC_C), the calibration time and the expected error of the reduced model over a progeny of virtual genotypes. The resulting reduced model not only reproduces the predictions of the original one but presents many advantages including a reduced number of parameters to be estimated and shorter calibration time, opening new promising perspectives for genetic studies and virtual breeding. The validity of the reduced model was further evaluated by calibration on 30 additional genotypes of an inter-specific peach progeny for which few data were available.

Model-based QTL detection is sensitive to slight modifications in model formulation

Classical crop models have been developed to predict crop yield and quality, and they are based on physiological and environmental inputs. After molecular discoveries, models should integrate genetic variation to allow predictions that are more genotype-dependent. An interesting approach, Quantitative Trait Locus (QTL)-based ecophysiological modeling, has shown promising results for the design of ideotypes that are adapted to biotic and abiotic stresses, but there are still limitations to attaining a fully integrated model. The aim of this case study is to clarify the impact of choosing different model equations (closely related and with different numbers of parameters) and optimization methods on the detection of QTLs controlling the parameters of crop growth. Different growth equations were parameterized based on a genetic population by following different approaches. The correlations between parameters were analyzed, and two different strategies were adopted to address the correlation issue. QTL analysis was performed on the optimized values of the parameters of the growth equations and on the observed dry mass (DM) data to validate the QTLs detected. Overall, models and strategies resulted in different QTLs being detected. Similar LOD profiles but with peaks of different heights were observed, some of which were significant, resulting in different numbers of QTLs. In some cases, peaks had slightly different positions or were absent. Even closely related growth models led to the detection of different QTLs. The goodness of fit and complexity of the growth models were found to be insufficient to select the best model. Calculating parameters independently of observed data may not be a good strategy, whereas setting parameters independent of the genotype is recommended. Given the large-scale global optimization problem and the strong correlations between parameters, the two algorithms tested showed poor performance. Currently, the lack of effective algorithms is the main obstacle to answering the question posed. The authors therefore suggest testing different model formulations and comparing the QTLs detected before choosing the best formulation to use in an ecophysiological modeling approach based on QTLs.