Recent advances in the understanding of the physiology of berry growth and in modelling allow simulation of fruit growth and sugar accumulation from the perspective of water and carbon balance. This review summarises present knowledge on the modelling and molecular physiology of carbon and water fluxes related to grape berry growth and quality. It focuses principally on the effects of environmental factors and cultural practices on fruit quality through their consequences on water and carbon fluxes during fruit growth. Together with ecophysiological and molecular approaches, process-based models show promising ability to aid in integrating physiological results, generating novel hypotheses and consequently providing a full picture of the control of berry growth and quality development. In the future, nitrogen and sulfur fluxes, necessary for the synthesis of secondary metabolites important for quality, should also be integrated. Modelling at the organ level should extend to metabolic content and metabolite fluxes (metabolomic and fluxomic studies). Genotypes naturally or artificially affected on a key gene or function will also be helpful to validate modelling hypotheses.
The quality of grape berries for winemaking is affected by genotype, environment and agricultural management. The typicity of wine, which depends on berry content and is controlled by the determinants mentioned above, may be negatively impacted by global climate change. The recent progresses made in the molecular physiology of berry growth and ripening, genome sequencing and modelling approaches offer new perspectives to elaborate predictive models that would be very valuable for a perennial plant that may take many years to reach optimal fruit quality.
Why model ripening of the grape berry?
Grape quality is a complex concept that mainly refers to berry chemical composition, including sugars, acids, phenolics and other aroma compounds (Lund and Bohlmann 2006, Conde et al. 2007). At harvest, the sugar and acid concentration of the berries should be around 150–250 g/L (Ribéreau-Gayon et al. 2006) and 6.5–8.5 g/L, respectively (Ruffner 1982). Low sugar levels are detrimental to grape and wine quality, but high sugar content leads to a high level of alcohol, which may be detrimental for the health of wine consumers. The challenge for grape growers is to maintain the sugar level in an optimal range for a given type of wine. Acid concentration is another determinant for grape and wine quality (Ruffner 1982). It plays an important role in controlling the wine stability, ageing potential and wine balance. A low level of acid results in a flat and dull wine, while high acid content leads to tart and sour wine.
The composition and concentration of chemical compounds in the berry dynamically change with development and can be affected by many factors (Coombe 1992). Acids mainly accumulate during the early stages of berry growth while sugars predominantly accumulate during the late stages. Intrinsic factors, such as berry seed number (Cawthon and Morris 1982, Ristic and Iland 2005, Walker et al. 2005, Friend et al. 2009) and berry position within a bunch (Gray 2002, Tarter and Keuter 2005), affect berry growth and composition. Environmental parameters and management practices (pruning, fertilisation and fruit thinning) also dramatically impact berry growth and content. For example, fruit thinning modifies the source-to-sink ratio and, consequently, the import of carbon, which provides precursors for the synthesis of secondary metabolites essential for wine quality (Keller et al. 2005, Santesteban and Royo 2006, Keller et al. 2008). Water supply may modify the sugar concentration by altering sugar import, sugar metabolism and/or water import (Conde et al. 2007). The effects of assimilate and water supply on berry growth and composition must be further clarified, especially in terms of berry carbon and water balances. The higher temperature and stronger water deficit expected in the context of global warming will act simultaneously on berries (Bindi et al. 1996, Schultz 2000, Jones et al. 2005, Webb et al. 2007). Grapevine growers will have to face these new challenges, requiring in-depth understanding of the mechanisms that regulate berry growth and quality development, especially in terms of the interactive effects of multifactors (Schultz 2000).
The skin, flesh and seed, respectively, account for about 15, 80 and 5% of total berry fresh weight (Roby and Matthews 2004), although this distribution is genotype dependent. Berry growth follows a double-sigmoid curve with three distinct growth phases, namely, the first rapid growth phase, lag phase and the second rapid growth phase (Coombe 1992).
During the first rapid growth phase, cell division continues for several weeks, in a genotype-dependent manner (Ojeda et al. 1999, Schlosser et al. 2008). The intensity of cell division is positively related to the number of seeds per berry, probably because of hormones synthesised in the seeds (Coombe 1960, Ristic and Iland 2005). The cell number after cessation of cell division defines the potential size of many fruits, such as peach (Quilot and Génard 2008), tomato (Bertin 2005) and grapes (Considine 1981, Coombe and Iland 2004). While berry size per se is not a major quality feature for wine grapes, it might have profound effects on berry chemical composition (Roby et al. 2004, Walker et al. 2005, Matthews and Nuzzo 2007). Assuming that the berry shape is approximately spherical, then the surface area : volume ratio decreases with berry size by a factor of 3/radius. Therefore, in small berries, there will be lower dilution caused by inner mesocarp cell sap on secondary metabolites contained in the skin (Gladstone 1992, Hardie et al. 1997). During the first rapid growth phase, berries are relatively susceptible to temperature (Ebadi et al. 1996), water availability (Ojeda et al. 2001) or assimilate supply (Ollat and Gaudillere 1998), the perturbation of which usually leads to irreversible influences on berry growth. Despite its potential effect on growth and quality, cell division has not been modelled for grape berries. Indeed, few attempts have been made to simulate fruit cell division in response to different growth circumstances. One noticeable exception is the work of Bertin et al. (2003, 2007), who simulated cell division during the development of tomato fruit. This may provide a useful framework for modelling cell division in the winegrape.
During the lag phase of grape berry development, berry size changes very little, while seed size and fresh weight reach their maximum value at the end of the lag phase (Ristic and Iland 2005). The transition between the lag phase and the second rapid growth phase (veraison) corresponds to major and rapid changes in berry physiology. Berries become soft, show skin colour change for red varieties and accumulate high levels of sugars (Robinson and Davies 2000).
During the second rapid growth phase, berries normally double their size exclusively because of cell expansion, which is predominantly driven by sugar and water accumulation (Coombe 1992). In addition, a further period with berry weight loss is observed in some specific varieties such as Shiraz (Tilbrook and Tyerman 2008, 2009, Greer and Rogiers 2009). The integrative roles of water and sugar influx into and out of berries in controlling berry growth will be discussed separately in the following sections.
Effect of water and assimilate supply on berry growth and sugar concentration
Despite the ample information collected on gene expression throughout berry development in the last decade (Robinson and Davies 2000, Terrier et al. 2005, Deluc et al. 2007), there is no report concerning the effects of fruit load or water stress on gene expression in grape berries. Castellarin et al. (2007) recently studied the effect of water stress on the flavonoid biosynthesis pathway. They showed that increased anthocyanin accumulation under water limitation did not only result from berry growth reduction, but also from earlier and greater expression of the genes controlling the anthocyanin pathway. However, this work was performed in the field where water deficit may induce many secondary effects (leaf drop and enhanced exposure of bunches). These examples recorded at the plant or gene level underline the complexity of the effect of environment and viticultural practice on vine physiology, and the issue of multiple stresses. In order to get accurate information for modelling, careful experimental design, taking into account factors including environmental conditions and whole plant status monitoring, and/or controlled stress application are essential, especially for molecular analysis.
Water fluxes to and from grape berry
Grape berries normally contain 75–85% of water, which is the main solvent of solutes including sugars, acids and phenolic compounds (Ribéreau-Gayon et al. 2006). Water can be imported into the berry via both xylem and phloem (Lang and Thorpe 1989, Greenspan et al. 1994, 1996, Ollat et al. 2002, Matthews and Shackel 2005, Tilbrook and Tyerman 2009). The relative contribution of xylem and phloem to water influx, however, depends on berry developmental stages. Thus, before veraison, berry water is mainly provided by xylem tracheids, whereas phloem constitutes the preferential pathway in post-veraison berries (Creasy and Lombard 1993, Greenspan et al. 1994). The most common hypotheses proposed in grape for this shift of water supply is that the growth of the berry stretches and breaks the peripheral xylem. However, several recent studies showed that xylem appears functional and connected between the vine and the berries after veraison (Rogiers et al. 2001, 2006, Bondada et al. 2005, Keller et al. 2006, Tilbrook and Tyerman 2009). These findings are supported by direct observations of the xylem network in the berry, showing that the vast majority of the xylem tracheary elements remains intact despite the growth of the berry (Chatelet et al. 2008b). Thus, Bondada et al. (2005) and Keller et al. (2006) proposed that a lack of an appropriate driving force because of the solute partitioning between fruit symplast and apoplast after veraison may explain the decline in xylem water influx into ripening berries. Interestingly, and despite the fact that xylem network remains functional after veraison, Tyerman et al. (2004) reported a 10-fold reduction of the whole berry hydraulic conductance between the veraison and harvest stages. This result points to the possible intervention of water channels, or aquaporins, in the regulatory mechanisms of berry hydraulic conductance. Indeed, a decrease of membrane hydraulic conductance can be linked to a decrease of aquaporin activity by post-transcriptional modifications and/or to a modification of aquaporin abundance in the membrane (Hachez et al. 2006).
When investigating aquaporin gene expression in developing berries, Fouquet et al. (2008) observed a global decrease in the amount of transcripts encoding plasma membrane aquaporins after veraison, which could explain, at least in part, the reduction of the berry hydraulic conductance observed by Tyerman et al. (2004) and Tilbrook and Tyerman (2009). Moreover, aquaporin expression was also detected in xylem parenchyma cells where water channels are likely to facilitate transcellular water flow (Fouquet et al. 2008). As suggested by Tyerman et al. (2004) and Tilbrook and Tyerman (2009), a decrease of aquaporin abundance and/or activity in these particular cells after veraison may be an important component of the reduction of berry hydraulic conductance.
where U is the total flow through a membrane of area A, with the hydraulic conductivity coefficient L and membrane reflection coefficient (σ) under the control of differences between turgor pressure (P) and osmotic pressure (π) between transport pathway (1) and fruit cells (2). In more detail, σ provides a measure of the impermeability of the interactant biomembrane to the solute, with σ = 1 representing a membrane for which the solute permeability is zero, and σ = 0 representing a membrane having no selectivity for the given solute. This equation indicates that the water transport flow depends on driving force (water gradient), hydraulic conductivity of the pathway and the available surface of the pathway. This equation has been successfully used to simulate water uptake in roots (Hsiao and Xu 2000), developing seeds (Zhang et al. 2007) and sweet cherry fruit (Beyer et al. 2005). In grape, a water potential gradient between the bunch and the vine stem has been shown to facilitate water transport between these two compartments (Greenspan et al. 1994, 1996). A similar result was reported in tomato fruit (Johnson et al. 1992). However, it should be noted that in the previous function, the pathway's anatomy structure such as length and diameter is not included, because these features can be embedded in the parameter hydraulic conductivity (L) as demonstrated in a tomato water import model (Bussiéres 2002).
In addition to fruit transpiration, water backflow from the berry to the vine may also impact the fruit water balance. Many authors have suggested water backflow in different varieties of grape berries including Shiraz (Tyerman et al. 2004), Italia (Lang and Thorpe 1989) and Cabernet Sauvignon (Greenspan et al. 1994, 1996). Theoretically, xylem water backflow can only occur if (i) the xylem is functionally connected to the berry apoplast and (ii) there is an appropriate gradient to drive water flow from the berries to the parent vine (Tyerman et al. 2004). The effective connection of the xylem has been demonstrated by several studies (Keller et al. 2006, Chatelet et al. 2008a,b, Tilbrook and Tyerman 2008). However, the pressure gradients that drive xylem backflow from the berry to the parent vine will depend on the water potentials of the two compartments and the hydraulic conductivity between the two compartments (Tyerman et al. 2004, Tilbrook and Tyerman 2008, 2009). The hydraulic conductivity between the berry and the vine has been shown to change during berry development with varietal differences (Tyerman et al. 2004, Tilbrook and Tyerman 2009). Despite recent advances, obtaining an in situ value for possible backflow in intact organs remains a challenging task. Most previous investigations are based on a pedicel-girdling approach, comparing the water variations in fruits connected to plants, excised from plants or connected to plants but with girdled phloem (Lang and Thorpe 1989). This method relies on the assumption that fluxes in phloem and xylem are independent, and modification of one pathway has no effect on the other. The assumption may not be valid in natural plant organs, as there is evidence that removing phloem decreases xylem water conductance (Zwieniecki et al. 2004). Recently, the backflow from the berry to the parent vine has been proven to occur in a genotype-dependent manner with stylar loading of dyes and quantitative measurements of xylem hydraulic conductivity and water potential gradients (Tilbrook and Tyerman 2008, 2009).
where Af denotes skin surface area, Mw is the molecular mass of water, P* is the saturation vapour pressure, ρ is the skin water permeability, Hf and Ha are, respectively, the relative humidity in fruit free space and in the atmosphere, R is the gas constant and T is the temperature. In particular, the change of skin water permeability during the development can be represented by a function of the parameter ρ. This equation has been used successfully to simulate transpiration in peach (Fishman and Génard 1998, Lescourret et al. 2001, Gibert et al. 2005), mango (Lechaudel et al. 2007), citrus (Ben-Yehoshua et al. 1985) and tomato fruits (Leonardi et al. 2000).
Regarding the model simulating water backflow, Daudet et al. (2002) provided some preliminary attempts but without validation by comparison with experimental results. More modelling efforts are needed to involve this process in a fruit growth model (Génard et al. 2007). Recently, Tilbrook and Tyerman (2009) determined the hydraulic conductivities for backflow in grape, providing the essential information to mechanically model this process.
Carbon fluxes to and from grape berry
Figure 1 summarises carbon metabolism and compartmentation in the grape berry. At harvest, carbon accounts for about 40–50% of berry dry weight among different varieties (Ollat and Gaudillere 2000, Vivin et al. 2003). This carbon pool comprises not only a high level of soluble sugars, but also structural carbohydrates and other compounds such as protein and amino acids (Coombe 1992, Vivin et al. 2003). Together with the yeast strains used during vinification, the berry sugar concentration determines the alcohol level and shapes the flavour profile in the wine, and it is of high commercial importance (Sinton et al. 1978). In addition to their nutritive role, sugars also function as signals regulating gene expression (Conde et al. 2006) and controlling the production of quality-related secondary compounds, such as anthocyanins (Vitrac et al. 2000). Therefore, the overview of carbon balance in berry will focus principally on sugar import, partitioning and accumulation, and the available model frameworks on these processes.
Sugar composition and dynamics of accumulation in grape berry
Sugars can be transported via an apoplasmic and/or symplasmic pathway from the phloem to the cytoplasm of mesocarp cells. Sugars then cross the tonoplast membrane to be finally stored in the vacuole (Conde et al. 2007). The shift of the sugar unloading pathway from symplasmic to apoplasmic (Zhang et al. 2006) indicates transmembrane transport of sugars during the main sugar accumulation stage. Consequently, the transport processes can involve passive diffusion, turgor-driven mass flow or active transport facilitated by sugar transporters (Davies and Robinson 1996, Hayes et al. 2007). Passive diffusion is known to be efficient only for short distances and can be represented with Fick's first law:
where A is the membrane area between phloem (p) and fruit (f), Ps is the solute permeability coefficient that measures how easily solutes move through a particular medium (Venâncio and Teixeira 1997), and Cp and Cf are the sugar concentrations in phloem and fruit cells, respectively. This process has been elucidated in tomato, and a Ps value of 3.6 × 10−5 g/cm2/h was estimated for phloem membrane in relation to sucrose uptake (Ruan and Patrick 1994). No direct estimation has been reported in grape.
Mass flow may contribute to sugar accumulation when the membrane between two compartments has a reflection coefficient (σ) for sugar (Eqn 1) smaller than 1. In this case, sugar imported through mass flow can be described as:
where U and σ are the same as in Eqn 1, and Cp and Cf are the same as defined in Eqn 3. As discussed in the section on water import, this mechanism relies on a favourable water potential gradient between phloem and fruit. Because the hexose sugars accumulated in berry cells are osmotically active solutes, they can modify the cell osmotic potential and consequently influence the water gradient, which in turn regulates sugar import. This mechanism is also known as the Münch theory and has been applied extensively in many plant systems (Tyree and Fensom 1970, Daudet et al. 2002, Thompson and Holbrook 2003, 2004, Gould et al. 2005, Lacointe and Minchin 2008). An alternative hypothesis, called the ‘turgor-regulated translocation hypothesis’ and close to the Münch theory, has been proposed and applied in grape (Lang 1983, Lang and Düring 1991). This hypothesis emphasises the role of apoplasmic osmotic pressure gradients, which is ignored in most formulations of the Münch theory (Lang and Thorpe 1986). To explain the dramatic increase in sugar accumulation, this hypothesis assumes that cell membrane integrity declines and results in a loss of subcellular compartmentation at veraison. Although the authors provided some evidence that compartmentation breakdown does occur in grape berry after veraison, the conclusion is based on indirect measurements and extrapolations (Lang and Düring 1991). In contrast, recent direct observations showed that berry cells maintain considerable cell membrane integrity throughout berry development (Thomas et al. 2006, Krasnow et al. 2008, Tilbrook and Tyerman 2008), at least until about 90–100 days after flowering, suggesting that the turgor-regulated transport hypothesis on berry sugar translocation needs further reassessment.
or with the presence of an inhibitor such as a full non-competitive inhibitor:
where Vm is the maximum uptake rate, Km is the Michaelis constant, Cp is sugar concentration in the phloem, and CI and KI are the concentration and Michaelis constant for the inhibitor, respectively. So far, three sucrose transporters have been identified from Shiraz and Cabernet Sauvignon grapes, including VvSUC11, VvSUC12 and VvSUC27. VvSUC11 and VvSUC12 are intermediate affinity sucrose transporters (Km = 0.9 and 1.4 mM, respectively) (Ageorges et al. 2000, Manning et al. 2001), whereas VvSUC27 is a low affinity sucrose transporter with a Km of about 10 mM (Zhang et al. 2008). However, the subcellular localisation of these sucrose transporters is controversial, making it difficult to define their roles in sugar transport between phloem and berry cells in grape.
In grape, 59 putative hexose transporters can be identified from the 8 x genome sequence presently available (Jaillon et al. 2007). Six hexose transporters named from VvHT1 to VvHT6 (V. vinifera hexose transporter) have been cloned from Pinot Noir, Ugni Blanc, Chardonnay, Cabernet Sauvignon and Syrah berries (Fillion et al. 1999, Vignault et al. 2005, Hayes et al. 2007). When expressed in yeasts, VvHT1, VvHT4 and VvHT5 are high affinity, H+-dependent transporters mediating the uptake of radiolabelled D-[U-14C]glucose according to saturable Michaelis-Menten kinetics. They are localised in the plasma membrane (Vignault et al. 2005, Hayes et al. 2007). VvHT1 exhibits the highest affinity for glucose (Km of 70 µM, Vmax of about 14 µmol/min g/FW), compared with VvHT4 and VvHT5 (Km about 150 and 100 µM, respectively, Vmax of about 5 and 0.15 µmol min−1 g FW−1, respectively), and is the only one able to restore the growth on glucose of a yeast deficient in hexose transport. Until now, attempts to confirm the transport activity of VvHT2, VvHT3 and VvHT6 in yeast have been unsuccessful.
Fructose does not significantly affect glucose uptake rates in the mutant yeast expressing VvHT1, whereas it behaves as a competitive inhibitor in grape cell suspensions (Vignault et al. 2005, Conde et al. 2006, Hayes et al. 2007). Furthermore, uptake of radiolabelled D-[U-14C]fructose by grape cells also displayed Michaelis-Menten kinetics with a Vmax similar to that measured for glucose uptake, although the Km for fructose was much higher (Conde et al. 2006). No tonoplast sugar transporter has yet been identified in grapevine.
VvHT1, VvHT2 and VvHT3 are highly expressed compared with the other VvHTs at all developmental stages. VvHT1 transcripts and protein levels (Conde et al. 2006) are much higher at pre-veraison stages, whereas VvHT5 is expressed during late ripening. VvHT3 mRNA levels are sharply reduced at veraison but high at both green and ripening stages (Hayes et al. 2007), whereas VvHT6 transcripts accumulate from veraison onwards, suggesting that this transporter may be responsible for early import of hexose at the inception of ripening (Terrier et al. 2005, Vignault et al. 2005, Deluc et al. 2007).
The diversity of hexose transporter genes expressed during berry development is consistent with the shift from a symplasmic to an apoplasmic phloem unloading pathway prior to veraison, the latter being the dominant mechanism of sugar import into cells at ripening stages (Bondada et al. 2005, Zhang et al. 2006).
Until further details of the biological characteristics of sugar transporters are available, a composite virtual transporter can be incorporated into model framework as applied in the Fishman and Génard (1998) model for peach fruit, and in a similar model for tomato fruit (Liu et al. 2007a).
Carbon efflux – respiration
The respiration rate of grape berry cv. Cabernet Sauvignon decreases from 45 µmol C/g FW/h at 10 days after anthesis to 15 µmol C/g FW/h at veraison, and stays relatively stable thereafter (Palliotti and Cartechini 2001). A similar decline was also observed by Ollat and Gaudillere (2000), who reported a range from 5 µmol to 45 µmol C/g DW/h for grape berry. As in other plant tissues, the respiration rate of the berry is temperature dependent and follows the Arrhenius equation (Koch and Alleweldt 1977, Palliotti et al. 2005). The temperature effect is usually described using Q10, defined as the ratio of respiration rate at T+10°C divided by respiration rate at T°C. Q10 values range from 2.3 to 2.6 for different varieties, including Rielsing, Optima and Bacchus (Koch and Alleweldt 1977). To model the process of respiration (Rf), it can be dissected into growth respiration and maintenance respiration as (Thornley and Johnson 1990):
where qg and qm are the coefficients for growth and maintenance respirations, respectively, GR is berry growth rate in dry mass (DW) and T is berry temperature. This equation has been used and validated in many plant materials (Cannell and Thornley 2000, Thornley and Cannell 2000). It has been applied to analyse carbon balance in kiwi fruits (Walton and DeJong 1990), in peach (DeJong and Goudriaan 1989) and grape berries (Ollat and Gaudillere 2000). From the results of Ollat and Gaudillere (2000), it is possible to calculate the qg and qm for Cabernet Sauvignon grape berries. Their values are calculated to be 84 × 10−4 gC/g DW for qg and 2.5 × 10−4 gC/g DW/h for qm during the post-veraison growth phase (Figure 2). The qg value is much smaller than those reported for other species, such as peach where qg equals 0.12 gC/g DW (DeJong and Goudriaan 1989), while the qm value (1.13 × 10−4 gC/g DW/h) is comparable with that of peach. This difference might reflect a common species-dependent feature between nonclimacteric and climacteric fruits.
Although INV activities were considered to be non-limiting (Davies and Robinson 1996), recent reports by Zhang et al. (2006) and Hayes et al. (2007) clearly indicate that expression and activity of cwINV are induced just prior to veraison. Similar expression patterns were found for cwINV and some monosaccharide transporters in young grape leaves but not in grape berries (Hayes et al. 2007). Furthermore, cwINV enzyme activity in berry represents only 4% of total INV activity (Davies and Robinson 1996), and microarray results showed a constant level of both cwINV and nINV mRNAs throughout berry development (Deluc et al. 2007). This suggests that cwINV alone cannot be responsible for the increase of monosaccharide concentration in the ripening berry. Acidic vINV activity occurs too early to trigger by itself hexose accumulation at ripening inception (Davies and Robinson 1996, Patrick 1997, Dreier et al. 1998). However, vINV activity is important to drive the import of sugars during ripening, as its natural reduction in the Steuben grapevine hybrid contributes to an increase of the relative proportion of sucrose in the ripening berry (Takayanag and Yokotsuka 1997).
Sucrose can also be converted into uridine di-phosphate (UDP)-glucose and fructose by sucrose synthases in the presence of UDP. In grape, 6–9 genes encoding putative sucrose synthases are expected based on recent genome sequencing. However, the activity of sucrose synthases in grape berry is relatively constant and is not conclusively linked to changes in the soluble sugar concentration (Zhang et al. 2006). The resulting glucose and fructose can be either accumulated in the flesh, be partly used to synthesise non-carbohydrate compounds (organic acids, cellulose, proteins, etc.) or be used for respiration.
Models of sugar accumulation and metabolism
Despite the economic and physiological importance of sugar concentration, attempts to mechanistically model it are rare (Struik et al. 2005). In grape, Dreier et al. (2000) examined the effect of transpiration on sugar concentration, with a physical model assuming that no metabolic process is involved in sugar accumulation. However, this assumption, based on the breakdown of compartmentation at veraison (Lang and Düring 1991), is questionable because of new evidence that berry cells maintain considerable viability throughout berry development (Krasnow et al. 2008). Recently, Sadras and McCarthy (2007) proposed an allometric approach to assess the relative rate of sugar and water accumulation, which jointly determines the sugar concentration (measured as soluble solids) during berry development. Sadras et al. (2008) also presented an empirical function (a three-parameter sigmoid function) to fit the variation in berry sugar concentration in different varieties. However, these two frameworks did not take into account the regulatory mechanisms of sugar transport or metabolism. Thus, it would be of great interest to integrate all the processes discussed above for a full evaluation of the controlling network of sugar accumulation. Metabolic control analysis (MCA) could be a good candidate to fulfil this purpose (Fell 1992).
MCA is an approach based on steady-state analysis used to identify which steps of a metabolic pathway are the most significant for the control of a given biochemical process, providing rational insights into metabolic regulation (Fell 1992, Bost et al. 1999). For example, sucrose accumulation in sugar cane, a crop that can store high sucrose concentrations, has been studied with a kinetic model according to MCA (Rohwer and Botha 2001, Uys et al. 2007). To do this, all the chemical reactions involved in sucrose metabolism are represented, and the corresponding parameters of enzyme activities are described with a proper rate equation. After model analysis and control coefficient estimation, increases in fructose or glucose transporter or the vacuolar sucrose importer, as well as decreases in cytosolic and neutral INVs are identified to be the most critical steps to increase sucrose concentration in sugar cane (Rohwer and Botha 2001, Uys et al. 2007). Based on the results derived from the MCA, specific genetic manipulation aiming at modifications of the target biochemical cycle can be designed accordingly (Bost et al. 1999, Weselake et al. 2008). Despite its powerful performance in metabolism analysis, the MCA of a biochemical process needs a large set of parameters that are not often available in the literature or even easy to measure simultaneously. For instance, there are up to 50 parameters for 11 reactions in the kinetic model of sucrose accumulation (Rohwer and Botha 2001). This may be one of the reasons why the MCA method has not yet been used on fruits. With the constant progress in metabolomics and fluxomics, the MCA might be more extensively used to study or simulate the regulation and control of metabolism.
Keeping model complexity to a relative low level while reflecting the major mechanic control of sugar metabolism, the SUGAR model (Génard and Souty 1996) developed for peach, provides a valuable framework to simulate sugar accumulation in fruits. This model simulates sugar content in relation to fruit carbon balance and partitioning, and also integrates water accumulation to model the dynamics of sugar concentration. This model was later updated to analyse the effects of assimilate import, metabolism and water dilution on changes in sugar concentration (Génard et al. 2003). In addition, it has also been used to dissect genotype-dependent variations in sugar concentration (Quilot et al. 2004) and to simulate fruit soluble solid concentration as measured by refractometric index (Grechi et al. 2008) in peach, indicating its efficiency for sugar modelling. After refinement with considerations of specific features of sugar metabolism in grape berry, the SUGAR model has been adapted to simulate sugar accumulation in grape berry (Dai et al. 2009b). This SUGAR-vitis model correctly simulated the negative effect of lowered source-to-sink ratio and the positive effect of water shortage on sugar concentration.
Models of fruit growth
To simulate fruit growth and its responses to environmental and management conditions, both empirical growth functions and process-based mechanistic models are used (Thornley and Johnson 1990, Génard et al. 2007, Sadras et al. 2008, Seleznyova 2008). These two approaches have their own advantages and shortcomings: growth functions generally have a limited number of parameters that can be easily estimated by fitting the selected function to the observed data. However, parameter stability can only be kept when the plants are grown under the same growth conditions as the plants used for parameter estimation. Therefore, growth functions have a low capability to predict fruit growth under various growth conditions. In contrast, process-based models using biochemical or biophysical equations to describe the main biological processes involved in fruit growth can largely take into account the effects of growth conditions, such as source–sink ratio and/or environmental factors. However, the process-based models are not easy to develop and are generally based on many parameters. Moreover, parameter estimation of process-based models sometimes turns out to be a challenging task (Thornley and Johnson 1990). Depending on the objectives of the model, researchers can choose growth functions and process-based models to simulate fruit growth.
The frequently used growth functions include logistic, Gompertz, exponential and monomolecular growth functions, and combinations of these (Figure 3) (Thornley and Johnson 1990). For example, the Gompertz function has been used to fit fruit growth of tomato (Bertin 2005) and kiwi fruit (Lescourret et al. 1998a,b), while a combination of monomolecular and logistic functions was used for peach fruit (Génard et al. 1991, 1999). In addition, the Gompertz function has been used to simulate effects of seed number and fruit load on fruit growth of kiwi fruit (Lescourret et al. 1998a,b). Recently, an approach has been proposed to simulate temperature effects on logistic-based growth function (Seleznyova 2008). For grape, a bi-logistic growth function has been used to fit berry size (Fanizza and Colonna 1996), and the combination of monomolecular and logistic functions has recently been applied to analyse the association among the function parameters and berry quality features (Dai et al. 2009a). Although the growth function method can well represent the growth curve of some specific fruits, it offers very limited, if any, information about the underlying biological processes determining fruit growth, such as cell expansion because of water and dry mass accumulation.
After cessation of cell division, fruit growth depends on cell expansion with water and dry mass accumulation. These biological processes can be described using process-based models in order to simulate fruit growth. Cell volume changes can result from irreversible plastic growth and/or reversible elastic variation (Proseus et al. 1999). Plastic growth can be described using Lockhart's equation (Lockhart 1965), and elastic volume variation can be described as indicated by Ortega (1985). Accordingly, the volume (V) changes of a cell can be represented as (Lechaudel et al. 2007):
where Pf is turgor pressure, φ is cell wall extensibility, Y is a threshold value of turgor pressure below which no cell plastic growth occurs, and ε is the elastic modulus. Scaling up this growth theory from a single cell to a multicellular system by considering the latter system as a big cell has been successfully applied to the analysis of volume changes of roots (Steudle et al. 1993 for maize, Génard et al. 2001 for peach), stems (Génard et al. 2001 for peach) and leaves (Matthews et al. 1984 for sunflower, Hohl and Schopfer 1992 for maize, Serpe and Matthews 2000 for Begonia argenteo-guttata). Recalling that the term of turgor pressure (Pf) is also presented in Eqn 1, which describes water import, the two equations (Eqns 1 and 8) can be combined to track the feedback between water import and volume changes of a plant organ. This framework has been used to develop a biophysical growth model to simulate fruit growth by integrating processes of water balance and sugar balance (Fishman and Génard 1998). In this model (Figure 4), a fruit is simplified as a big cell separated by a composite membrane between the parent vine and the outside environment. At each run step, water accumulation was calculated through the water balance between xylem and phloem water influx and transpirational water loss, controlled by water potential gradient between the berry and the parent plant. Meanwhile, dry mass accumulation was simulated with the balance between phloem sugar import and respired carbon depletion. The accumulated sugar changes the fruit osmotic potential and consequently the turgor potential, offering a feedback control on fruit growth in the next step. This growth model was first validated for peach fruit grown under different assimilate supply and water supply (Fishman and Génard 1998) and was later used to simulate fruit growth of tomato (Liu et al. 2007a) and mango (Lechaudel et al. 2007) with appropriate modification, indicating its generic compatibility for fleshy fruits.
In grape berry, the existing models for berry growth generally only focus on dry mass accumulation and work at the bunch level (Gutierrez et al. 1985, Vivin et al. 2002). Modelling berry development after cell division with a process-based model has the potential to enhance our understanding of how environmental changes during the ripening phase impact on berry size and composition. Recently, Dai et al. (2008) have obtained preliminary results on simulating the response of berry growth to source-to-sink ratio by adapting Fishman and Génard's (1998) growth model. The refined growth model also exhibits promising capability to simulate diurnal changes in berry water balance and fresh mass.
Grape quality is a pivotal determinant of the quality of wine and will continue to be a major research topic in the future. Advances in our understanding of the physiological basis of quality control may help to develop novel viticultural practices or strategies in order to obtain the desired quality.
First, variation in berry size within a bunch in relation to seed number and differences in the mean berry size per bunch between bunches in relation to assimilate supply can be further investigated in terms of source competition with a multilevel competition model (Lescourret and Génard 2003, Quilot and Génard 2008). At the bunch level, berry number per bunch will, at least to some extent, determine competition for source supply between berries. Similarly, at the berry level, the flesh fraction corresponding to each seed can act as a unit to compete for source supply. Therefore, three levels, including bunch, berry and pulp corresponding to each seed, can be considered. More detailed examination of the data available with model selection approaches (Johnson and Omland 2004, Quilot and Génard 2008) and further data collection through new experiments are required to identify the potential effects of competition at different organism levels on berry size.
Second, the growth model (Dai et al. 2008) has the potential to identify the underlying reasons that trigger the rapid growth transition from the lag phase to the second rapid growth at veraison. Although many previous investigations attempted to clarify the factors causing the resumed growth at veraison, this process is still poorly understood (Terrier et al. 2005, Lund et al. 2008, Wada et al. 2008). Based on the theory that expansive cell growth is associated with cell turgor and rate of cell wall loosening (Lockhart 1965, Cosgrove 1993, 2000), Matthews and Shackel (2005) proposed several hypotheses to explain the resumption of berry growth at veraison. Rapid berry growth is driven by an increase in berry cell turgor that might result from (i) solute accumulation without any change in cell wall loosening; (ii) weakening of the cell wall without a turgor change; or (iii) solute accumulation together with cell wall loosening. As pointed out by these authors, each of the above possibilities would lead to different consequences for whole fruit water potential, and consequently, in differences in water transport between plants and berries. These three possibilities can be experimentally measured and quantitatively elucidated with the assistance of the growth model, which simulates berry growth as a function of turgor pressure and cell wall features (both cell wall extensibility and elastic modulus). To this end, turgor pressure, whole berry water potential and berry volume changes can be measured simultaneously (Lechaudel et al. 2007), and then model analysis can be conducted. The hypotheses under which the model simulation fits the observed results well will pinpoint the likely reasons for berry growth transition at veraison.
Third, the sugar model (Dai et al. 2009b) and the growth model can be used to dissect differences among genotypes of grape berry. Developing new varieties is one of the most promising approaches to improve berry quality. To efficiently reach the breeding aims, complex traits, such as fruit size and chemical composition, must be decomposed into elementary biological processes and traits that are independent of the environment. The incorporation of ecophysiological models into breeding programs would pave the way for trait decomposition (Yin and Struik 2008). This kind of integration between ecophysiological models and marker-assisted breeding has been reported for peach (Quilot et al. 2004, 2005), maize (Welcker et al. 2007) and barley (Yin et al. 1999, Yin and Struik 2008), but not for grape. The process-based sugar and growth models can be applied to breeding populations or distinct grape genotypes in order to identify the processes and parameters accounting for the observed differences (Rajasingh et al. 2008).
Fourth, the growth model would be useful to assess the effect of temperature on berry growth, with additional extensions. Temperature can affect many processes in grapevine, such as leaf photosynthesis, rate of sugar accumulation and synthesis of anthocyanins, etc (Ebadi et al. 1996, Schultz 2000, Bergqvist et al. 2001, Webb et al. 2007). When the temperature is higher than ideal at harvest, sugar ripeness may be reached earlier, while acids are depleted via increased respiration, causing unbalanced wines (Jones et al. 2005). This trend will present a new challenge for grapevine growers in the context of global climate change. To predict the effects of climate change on grapevine production, several models have been proposed (Bindi et al. 1996, Webb et al. 2007). However, these models consider all fruits as a global sink compartment and do not address berry growth at a berry level and berry quality. To obtain a realistic prediction of plant response to climate change, appropriate functional equations linking biological responses to climate factors must be identified.
The present growth model can be extended by using climate scenarios obtained from models predicting climate change. Possible feedback regulation between source and sink under changing climate conditions is not included in the present growth model. This can be taken into account in a model describing the interaction between source and sink in grapevine (Quereix et al. 2001). Another limitation concerning the effects of temperature is that the input of berry temperature in the present version of the growth model was assumed to be equal to the air temperature, which may not be accurate. This limitation can be overcome by incorporating temperature models that simulate the diurnal changes in fruit temperature (Mariani et al. 2007, Saudreau et al. 2007). As a result, the updated growth model would be more effective to simulate the effects of microclimate on berry growth and chemical composition (Pereira et al. 2006).
In summary, recent advances in the physiology of berry growth and in modelling allow simulation of fruit growth and sugar accumulation from the perspective of water and carbon balance. These biological processes interact with each other and respond actively to environmental conditions, making it a challenge to evaluate the outcome of multifactorial interplay. Together with ecophysiological and molecular approaches, process-based models show promise for incorporating physiological results, generating novel hypotheses and consequently providing a fuller picture of the control of berry growth and quality development. In the future, nitrogen and sulfur fluxes, necessary for the synthesis of secondary metabolites important for quality, should also be incorporated. Modelling at the organ level should extend to modelling of metabolic content and fluxes (metabolomic and fluxomic studies). Natural and artificial mutants affected on a key gene or function will also be helpful to validate modelling hypotheses.
We thank Dr Michel Génard, UR1115 Plantes et Système de Culture Horticoles, INRA Avignon, for the helpful discussions and comments on the manuscript.