Tree Physiology 23, 373–385
© 2003 Heron Publishing—Victoria, Canada
Changes in fruit sugar concentrations in response to assimilate supply,
metabolism and dilution: a modeling approach applied to peach fruit
(Prunus persica)
M. GÉNARD,1,2 F. LESCOURRET,1 L. GOMEZ1 and R. HABIB1
1
Unité Plantes et Systèmes de culture Horticoles, Institut National de la Recherche Agronomique, Domaine Saint-Paul, Site Agroparc, 84914 Avignon
Cedex 9, France
2
Author to whom correspondence should be addressed ([email protected])
Received March 15, 2002; accepted September 6, 2002; published online March 17, 2003
Summary The influence of assimilate supply, metabolism
and dilution on sugar concentrations in the mesocarp of peach
(Prunus persica (L.) Batsch) fruit during the main stage of fruit
enlargement was analyzed with the SUGAR model of Génard
and Souty (1996). The model predicts the partitioning of carbon into sucrose, sorbitol, glucose and fructose in the mesocarp
of peach fruit. Based on measured data and the model, we
determined values for the relative rates of sugar transformation. These rates were constant, varied with time or varied with
relative fruit growth rate, depending on the type of sugar. Equations were derived to describe these rates and incorporated into
the SUGAR model. The model simulated the effects of changing assimilate supply and fruit volume on sugar concentrations.
The set of equations for the SUGAR model was rewritten to include the three components influencing sugar concentrations:
assimilate supply, metabolism and dilution. The sugar types
differed in sensitivity to these components. Sucrose was highly
sensitive to changes in assimilate supply and to the dilution effect; it was not subject to intense metabolic transformation.
Sorbitol was the most important carbohydrate in fruit metabolism, which explains why the sorbitol concentration was always low despite the strong positive effect of assimilate supply.
The reducing sugars constituted a transitory storage pool and
their concentrations were closely related to metabolism.
Keywords: fructose, glucose, irrigation, leaf:fruit ratio, sorbitol, sucrose, SUGAR model.
Introduction
Fruit sweetness is an important aspect of fruit quality. The
sweetness of fruit mesocarp is highly dependent on its sugar
composition, because sugars differ in sweetness (Kulp et al.
1991). Sucrose, glucose and fructose are the main sugars
found in fruits of commercial importance (Wrolstad and Shallenberger 1981). Sorbitol, which is a sugar alcohol, is also
present and is important in some fruits (Wrolstad and Shallenberger 1981) such as pear (Pyrus communis L.), cherry (Prunus avium L.) and plum (Prunus domestica L.). Fructose is 3,
2.3 and 1.7 times sweeter than sorbitol, glucose and sucrose,
respectively (Kulp et al. 1991). Peach fruits deemed to be of
good quality contain large amounts of fructose and low quantities of glucose and sorbitol (Brooks et al. 1993).
Numerous studies have examined changes in sugar composition during fruit growth (Ishida et al. 1971, Chapman et
al. 1991, Ackerman et al. 1992). Génard et al. (1999) found
strong correlations between sugar composition and growth
rate of peach fruit. Sugar concentrations vary throughout fruit
development according to the supply of phloem sugars,
changes in fruit metabolism, and dilution caused by increases
in fruit volume. The effect of sugar supply has been studied indirectly by analyzing the effect of leaf:fruit ratios on fruit quality. Seager et al. (1995) compared leaf:fruit ratio treatments
and showed that total sugar and starch concentrations were
higher in kiwifruit (Actinidia deliciosa Chev.) in the high
leaf:fruit ratio treatment than in the low leaf:fruit ratio treatment. In peach fruit, sucrose concentration increases with increasing leaf:fruit ratio, whereas concentrations of reducing
sugars seem to be invariable (Weinberger 1931, Souty et al.
1999). The effect of leaf:fruit ratio on sorbitol, which is found
in the phloem sap of rosaceous plants (Escobar-Gutiérrez and
Gaudillère 1996), has not been studied in detail.
Studies of mechanisms involved in sugar metabolism in sink
tissues have been conducted (Keener et al. 1979, Ho 1996).
The main enzymatic reactions responsible for sugar synthesis
have been identified for several fleshy fruits (Moriguchi et al.
1990, 1992), but little is known about the relative importance
of these processes and their regulation. The effect of dilution
as a result of increasing fruit size has been studied indirectly
by analyzing the effect of plant irrigation on fruit quality. Soluble solid and sugar concentrations usually increase in response
to reduced irrigation (Li et al. 1989, Crisosto et al. 1994, Kilili
et al. 1996), but irrigation results in both dilution and metabolic effects on fruit sugar concentrations (Mills et al. 1997).
We have used the SUGAR model developed by Génard and
Souty (1996) to study the relative importance of assimilate
supply, metabolism and dilution on sugar concentrations in
peaches during the main stage of mesocarp enlargement. The
374
GÉNARD, LESCOURRET, GOMEZ AND HABIB
inputs of this model are daily fresh and dry masses and temperature. The model predicts carbon partitioning into sucrose,
sorbitol, glucose and fructose in peach fruit mesocarp by calculating the rates of sugar transformation, and then computing
the concentrations of these sugars. The model was initially
used to study the effect of fruit growth on sugar concentrations
in peach fruits (Génard and Souty 1996). The model has also
been linked to a model of fresh mass growth in order to simulate the effect of water supply on fruit sugar concentrations
(Génard and Huguet 1997). More recently, the SUGAR model
was linked to a simulation model of carbon acquisition and
partitioning to simulate the effects of light interception and
fruit thinning on peach sweetness (Génard et al. 1999).
We measured sugar concentrations and dry mass of peach
fruits, calculated the rates of sugar transformation and examined their variation. We then derived equations to describe
these rates and incorporated them into the SUGAR model. We
also developed equations to distinguish the effects of assimilate supply, dilution and metabolism. Experiments were performed to examine effects of varying assimilate supply and
fruit volume on fruit sugar concentrations.
Materials and methods
Plant material and experimental design
Experiments were performed on peach trees planted in 1981 in
the orchard at the INRA Avignon Centre. The cultivar was the
late-maturing ‘Suncrest’/GF 677 (fruits are ready to harvest at
the beginning of August). Trees were goblet-trained and received routine horticultural care.
The first experiments in 1993 and 1996 varied assimilate
supply to the fruits. Treatments were applied to fruit-bearing
shoots located on the southern part of each tree and isolated
from the tree by girdling. Three treatments set leaf:fruit ratios
at 6, 18 and 30 leaves per fruit to obtain minimum, mean and
maximum growth curves that were representative of the ‘Suncrest’ cultivar. Shoots with 6 or 18 leaves per fruit were thinned
to four fruits, and shoots with 30 leaves per fruit were thinned
to two or three fruits. In 1993 and 1996, 240 fruit-bearing
shoots were prepared on 64 and 36 trees, respectively, to provide 80 sets of three neighboring shoots with leaf:fruit ratios of
6, 18 and 30. Fruits were harvested from five replicates per
treatment each week from June 8, 1993 and May 25, 1996 to
the beginning of fruit maturation. A replicate was made up of
fruits from two shoots when fruits were small and from one
shoot later in the season. The last harvests were on August 16,
1993 and August 16, 1996.
Experiment 2, performed in 1994, suppressed assimilate
supply to the fruit by girdling the shoot on both sides of the
fruit pedicel. Fifty-eight fruit-bearing shoots on 13 trees were
selected on June 27, to provide 29 pairs of neighboring shoots
with either girdled or control fruits. Five to nine fruits were
harvested per treatment on four dates from June 27 to August 1.
Experiment 3, performed in 1997, varied both assimilate
and water supply to the fruits. The treatments were applied in
mid-May to 240 fruit-bearing shoots isolated from 40 trees by
girdling and located on the southern part of each tree. Half of
the trees were irrigated (I) in June and July, whereas irrigation
was withheld from the remaining trees (D). For each irrigation
treatment, leaf:fruit ratio of the selected fruit-bearing shoots
was 10 or 30. Sixty pairs of neighboring shoots with leaf:fruit
ratios of 10 and 30 were prepared for each irrigation treatment.
Fruits from five replicates per treatment were harvested each
week from May 27 to fruit maturation (July 15–24).
Field and biochemical measurements
At each harvest and for each replicate, the fresh mass of fruit
mesocarp was measured; a subsample was weighed, and dry
mass was determined after drying at 70 °C for 72 h. The remaining mesocarp tissue was frozen in liquid nitrogen and
pulverized with a Dangoumill 300 ball-crusher for 2 min.
Twenty grams of this powder were homogenized in 80 ml of
distilled water with a Polytron homogenizer. The slurry was
centrifuged for 10 min at 2500 g and the supernatant stored at
–20 °C for evaluation of sugars by high performance liquid
chromatography (HPLC).
For HPLC analysis, thawed supernatant was filtered on a
Sep-Pak Plus C18 column (55–105 µm particle size; Waters,
Milford, MA) and on a 0.45-mm Acrodisc cartridge (Jasco,
Nantes, France, Part TR200102). The HPLC analyses were
performed on a Varian Chromatograph (9010 Pump with a
7125 Reodyne valve; Varian, Sunnydale, CA) in 1993 and
1994 and on a Waters Chromatograph (510 Pump with a Reodyne valve) in 1996 and 1997. A Sugar Pack I column (6.5 ×
300 mm; Waters) was used at 85 °C. Sugars were detected with
a refractive index detector (Model RI-4, Varian, in 1993 and
1994; Model 410, Waters, in 1996 and 1997). External standard solutions of sucrose, sorbitol, glucose and fructose were
used to quantify eluted peaks.
Daily mean temperature was recorded by the INRA meteorological station located close to the experiment fields.
Statistical and model analysis
To study the effects of assimilate supply (i.e., leaf:fruit ratio or
girdling treatments), water supply, fruit age, year and the twoor three-way interactions on observed fresh and dry mass and
sugar concentrations, we used analyses of variance with assimilate supply, water supply and year as factors and fruit age
as a quantitative covariate. Because the leaf:fruit ratio and the
girdling treatments were set up per tree, each tree was treated
as a block. We separately analyzed data from 1993 and 1996
(leaf:fruit ratio treatments equal to 6, 18 or 30), data from 1994
(suppression of assimilate supply versus control) and data
from 1997 (leaf:fruit ratio of 10 or 30 and well-watered versus
dry conditions). When there were more than two leaf:fruit ratio treatments and the effect was significant, we used multiple
comparison Tukey tests.
Daily dry and fresh masses, which were inputs of the model,
were estimated from our measurements by local regression
(Chambers and Hastie 1992).
A computer program was written in Advanced Continuous
Simulation Language (ACSL; MGA Software, Concord, MA,
1995). The differential equations were solved numerically by
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CHANGES IN FRUIT SUGAR CONCENTRATIONS
375
the first-order Runge-Kutta method with a time step of 1 day.
Parameters were estimated using ACSL Optimize (MGA
Software 1996). The data to be fitted included the amounts of
carbon in the fruit mesocarp in the form of sucrose, sorbitol,
glucose, fructose and other compounds (Figure 1) from the
leaf: fruit ratios experiment of 1993. The parameters were estimated by maximizing likelihood by the Generalized Reduced
Gradient method. To minimize errors in parameter estimation
caused by heterogeneity of the variance of the model variables
(carbon content in the form of sucrose, sorbitol, glucose, fructose and other compounds), the error variance was defined as
recommended by Huet et al. (1996):
s2 = ω2 f γ
where s is the standard deviation of the modeled variable, f is
the predicted value, ω is a proportionality factor and γ is an
adjustable heteroscedacity parameter. The heteroscedacity parameter was set to 2.
Goodness-of-fit criteria were computed to evaluate (i) the
goodness-of-fit of the model, on the basis of data used for
parameterization, and (ii) the predictive quality of the model,
for independent data. The calculation was made separately for
each sugar concentration curve and each (year) × (Factor 1) ×
(Factor 2) combination (where Factors 1 and 2 are the assimilate and water supply factors, respectively). In each case, observed data were available for several dates distributed over
the fruit development period (ni data at each date ti, and N
dates). One simulation series was obtained starting from date
t0 with the averaged observed data at t0 as the initial conditions.
The adopted criterion was the root mean squared error
(RMSE), a common criterion to quantify the mean difference
between simulation and measurement (Kobayashi and Us
Salam 2000), here defined as:
N
RMSE =
∑n i (x i − y i) 2
i =1
N
∑n i
i =1
where xi is the simulation result and yi is the mean of observed
data at date ti.
The smaller the RMSE in comparison with measurements,
the better the goodness-of-fit, which can be represented
through relative RMSE (RRMSE):
RRMSE = RMSE / y
where y =
N
N
i =1
i =1
∑n i yi ∑n i , the mean of all observed values.
Description and implementation of model
Formulation of model
The SUGAR model, which is summarized in Figure 1, simulates the partitioning of carbon from phloem to sucrose, sor-
Figure 1. Diagram of the SUGAR model. Arrows and boxes represent
carbon fluxes and carbon components, respectively. The two ellipses
represent carbon supply and losses by respiration. The proportion of
sucrose in the phloem-sourced sugar pool (λ ph ) and the relative rates
of sugar transformation k1(t), k2(t), k3(t) and k 4(t) for each arrow are
indicated.
bitol, glucose, fructose, other compounds and CO2 produced
through respiration. The model focuses on changes in sugar
composition, given the amount of sugar unloaded. The unloading of sugars was deduced directly from field measurements of
fruit dry mass growth, which is the main input of the model.
For simplicity, we assumed that the fruit behaves as a single
metabolic compartment with all sugars present available for
metabolism.
The model is based on eight assumptions: (i) the proportion
of phloem carbon unloaded as sucrose is constant; (ii) carbon
present in the fruit as sucrose and sorbitol is partially converted to glucose and fructose; (iii) conversion of sucrose
yields equal quantities of glucose and fructose; (iv) carbon
used for synthesizing compounds other than sugars comes either from glucose or fructose; (v) carbon used for maintenance
and growth respiration comes from glucose and fructose in
proportion to their quantity in the fruit; (vi) maintenance respiration depends on mesocarp dry mass and temperature; (vii)
growth respiration depends on growth rate in terms of dry matter; and (viii) apart from respiration, the carbon flux between
two compounds is proportional to the quantity of carbon in the
source compound.
The model is defined by the following set of differential
equations:
dM ph
dM su
= λ ph
− k1(t )M su
dt
dt
dM ph
dM so
= (1 − λ ph)
− (k2(t ) + k3(t )) M so
dt
dt
dM gl
dt
=
M gl
k1(t)
dM re
M su + k2(t ) M so − k4(t ) M gl −
2
M gl + M fr dt
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GÉNARD, LESCOURRET, GOMEZ AND HABIB
dM fr k1(t)
M fr
dM re
M su + k3(t ) M so − k4(t ) M fr −
=
dt
M gl + M fr dt
2
where Msu, Mso, Mgl and Mfr are the amounts of carbon (g) in
the form of sucrose, sorbitol, glucose and fructose, respectively; λ ph is the proportion of sucrose in the phloem-sourced
sugar pool resulting from plant metabolism; and k1(t), k2(t),
k 3(t) and k 4(t) (day –1) are, respectively, the relative rates of
sugar transformation for net sucrose transformation to glucose
and fructose, net sorbitol transformation to glucose, net
sorbitol transformation to fructose, and the synthesis of compounds other than sugars from glucose and fructose.
Respiration flux of carbon (g day –1) from the fruit is:
dWdry
dM re
= qg
+ qmWdry Q10( T − 20)/10
dt
dt
(2)
where Wdry is mesocarp dry mass (g), qg (g C per gram of dry
mass) is the growth respiration coefficient, qm (g C per gram of
dry mass per day) is the maintenance respiration coefficient at
20 °C, Q10 is the temperature ratio of maintenance respiration
(dimensionless) and T is temperature (°C).
Phloem flux of carbon into the fruit (dMph /dt) is used for
fruit growth and respiration. Fruit growth was measured and
respiration was estimated by Equation 2. It was then possible
to estimate carbon flux as the sum of carbon used for respiration and growth:
dM ph
dt
= σ fl
dWdry
dt
+
dM re
dt
(3)
where σfl is the carbon concentration of the mesocarp (g C per
gram of dry mass).
Daily mean temperature and daily mesocarp dry masses
were the inputs of the SUGAR model. Sugar concentrations at
the beginning of the simulation were measured values. The
carbon concentration (σfl) was taken from Génard and Souty
(1996) and values of qg, qm and Q10 were taken from DeJong et
al. (1987), Pavel and DeJong (1993) and Grossman and
DeJong (1994).
Evaluation of metabolic activities
Equations describing the relative rates of sugar transformation
were derived from Equation 1, assuming that the proportion of
phloem carbon unloaded as sucrose (λ ph) was constant. Temporal variation of carbon fluxes and amounts of carbon in the
compartments of the system depicted in Figure 1 were known.
k1(t) =
k2(t) =
dM ph dM su 
1 
−
 λ ph

M su 
dt
dt 
k3(t) =
dM ph dM so 
1 
−
(1 − λ ph )
 − k2(t)
M so 
dt
dt 
k4(t) =
1
dM total
M gl + M fr dt
where Mtotal (amount of carbon (g) as other compounds) =
σflWdry – Msu – Mso – Mgl – Mfr.
Based on Equation 4, the values of the relative rates were
calculated using the data from the 1993 experiment. The input
variables were calculated daily from seasonal measurements
of sugar concentrations and fruit mass by local regression
(Chambers and Hastie 1992). We set λ ph to 0.54, based on
measurements for phloem sap of a peach rootstock (GF 305)
by Moing et al. (1992). Analysis of the variation of the relative
rates of sugar transformation indicated that this variation was
not sensitive to the value chosen for λ ph (results not shown).
The value of λ ph for the ‘Suncrest’ cultivar was estimated by a
fitting procedure (see Results).
Because metabolic processes vary with fruit developmental
stage in many fruits, including apple (Malus domestica
Borkh., Yamaki and Ishikawa 1986), tomato (Lycopersicon
esculentum Mill., Robinson et al. 1988), peach (Moriguchi et
al. 1990) and pear (Pyrus communis L., Moriguchi et al. 1992),
Lelièvre et al. (1997) suggested that the expression of many
genes implicated in these metabolic processes is developmentally controlled. To analyze this possible effect of development, variations in k1(t), k2(t), k3(t) and k 4(t) with days after
bloom were analyzed. The effect of temperature on the variation in k1(t), k2(t), k3(t) and k 4(t) was also analyzed. A possible
link between relative rates and sugar concentrations was investigated. The rates were also plotted against relative mesocarp
growth rate because of the link between fruit growth, sugar
concentration and the activity of carbohydrate-metabolizing
enzymes (Génard et al. 1991, 1999, Lo Bianco et al. 1999b).
Renormalization and application of the model
The objective of the model renormalization was to analyze the
effects of assimilate supply, metabolism and dilution on sugar
concentrations. The effect of fruit sugar concentrations on water and assimilate supply has been analyzed previously (Fishman and Génard 1998, Bruchou and Génard 1999) and was not
considered here. In the present approach, assimilate supply
and changes in fruit volume were based on field measurements
of dry and fresh mass.
The amount of carbon as a sugar i (Mi) depends on the concentration of i within the fruit (Ci) according to the following
equation:
(4)
M i = σi C i Wfresh
M gl
1  dM gl k1(t)
dM re 


M su + k4(t) M gl +
−
M so  dt
2
M gl + M fr dt 
(5)
where σi is the carbon concentration of sugar i and Wfresh is the
fresh mass of fruit mesocarp.
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CHANGES IN FRUIT SUGAR CONCENTRATIONS
dC gl
Differentiation of Equation 5 leads to:
dt
dC i
dMi
dWfresh
1
1
Ci
=
−
dt
Wfresh
dt
σiWfresh dt
(6)
Equation 6 can be combined with Equation 1 to introduce
the three components causing change in sugar concentrations:
assimilate supply {s}, metabolism {m} and dilution attributable to the change in fruit volume {d}. Each component is
expressed per unit of fresh mass. The dilution component describes the effect of a change in fresh mass on the concentrations of sugars.
Equations for sucrose (Csu ) and sorbitol (Cso) concentrations
(g (100 gFM) –1) are similar. They involve three components:
λ ph dM ph
dC su
1
dWfresh
=
− k1(t)Csu −
C su
σsuWfresh dt
dt
Wfresh
dt
{s}
{m.su}
(7)
{d}
1 − λ ph dM ph
1
dWfresh
dC so
=
− (k2(t) + k3(t))C so −
Cso
dt
dt
Wfresh
σsoWfresh dt
{s}
{m.so}
{d}
where σsu and σso are the carbon concentrations of sucrose and
sorbitol, respectively.
The equations for glucose (Cgl ) and fructose (Cfr) concentrations depend only on metabolism and dilution:
=
377
k1(t)
C su + k2(t) Cso − k4(t) Cgl −
2
{m.su}
{m.so}
{m.gl}
C gl
(σ gl C gl + σfrC fr )Wfresh
1
dM re
dWfresh
−
C gl
dt
Wfresh
dt
{m.re}
(8)
{d}
dC fr k1(t)
C su + k3(t)Cso − k4(t)C fr −
=
dt
2
{m.su}
{m.so}
{m.fr}
C fr
dM re
dWfresh
1
C fr
−
Wfresh
dt
(σ gl C gl + σfrC fr )Wfresh dt
{m.re}
{d}
where σgl and σfr are the carbon concentrations of glucose and
fructose, respectively.
Fresh mass, which appears in Equations 7 and 8, is an input
of the renormalized model, calculated from field measurements. Temporal variations in components {s}, {m} and {d}
for each sugar were analyzed for the treatments comprising the
1997 experiment.
Figure 2. Seasonal variations
in fresh mass, dry mass and
sugar concentrations (% fresh
mass) for each experiment.
Symbols and abbreviations:
symbols 6, 10, 18 and 30 indicate the leaf:fruit ratio; I and D
indicate the irrigated and dry
treatments; and G and C indicate the girdled and control
treatments. All curves have
been smoothed by local regression (cf. Chambers and Hastie
1992).
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GÉNARD, LESCOURRET, GOMEZ AND HABIB
Results
Effects of changing assimilate and water supply on sugar
concentrations: statistical analysis
Seasonal trends in biomass and sugar concentrations are
shown in Figure 2 and the statistical analysis of experimental
data is summarized in Table 1. Harvest dates were earlier for
fruits in the higher leaf:fruit ratio treatments in 1993. There
was almost always a significant block effect. Fresh and dry
masses and sucrose concentration increased significantly with
both fruit age and number of leaves per fruit. There was also a
year effect for fresh and dry fruit mass and, to a lesser extent,
for sucrose concentration. Suppression of assimilate supply to
the fruit by girdling decreased fresh and dry fruit mass and sucrose concentration. Withholding irrigation in 1997 had no effect on dry mass or sucrose concentration, but had a minor
negative effect on fresh mass. Interactions between fruit age
and number of leaves per fruit or girdling were evident, with
the effects of number of leaves and girdling on mesocarp mass
and sucrose concentration increasing with fruit age. The other
interaction terms explained only a small proportion of the total
sum of squares (results not shown). Sorbitol concentration varied with fruit age, following a bell-shape curve. Sorbitol concentration increased significantly with number of leaves per
fruit and decreased when assimilate supply was suppressed by
girdling. Number of leaves per fruit had no significant effect
on concentrations of glucose and fructose, but concentrations
of both reducing sugars decreased significantly with fruit age.
Suppression of assimilate supply had a significant effect on
glucose concentration. Withholding irrigation in 1997 resulted
in a slight but significant increase in the concentrations of
sorbitol and reducing sugars. The difference between years
was significant for fructose only. The interaction terms for sorbitol, glucose and fructose were sometimes significant but explained only a small proportion of the total sum of squares
(results not shown).
Equations describing the metabolic processes
Based on sugar concentrations and fruit dry mass measured in
1993 and assuming that λ ph = 0.54, we used Equations 4 to assign values to the relative rates of sugar transformation and to
analyze their variation (Figures 3 and 4). In every case, there
was no clear effect of mean daily temperature (Figure 3) or of
sugar concentrations (Figure 4), although these variables fluctuated considerably during the season (Figures 2 and 5). The
relative rate of sucrose transformation to glucose and fructose
(k1(t)) was mainly dependent on days after bloom (DAB), decreasing exponentially from 0.25 day –1 at 80 days after bloom
Table 1. Analysis of variance for fresh mass, dry mass and sugar concentrations of peach fruit. Abbreviation: df = degrees of freedom. *** = Significant at P < 0.001; ** = significant at P < 0.01; * = significant at P < 0.05; and ns = not significant.
Year and
factors
1993–96
Block
Leaf:fruit ratio
Age
Year
Leaf:fruit ratio × age
Leaf:fruit ratio × year
Year × age
Leaf:fruit ratio × year × age
Residuals
1994
Block
Girdling
Age
Girdling × age
Residuals
1997
Block
Leaf:fruit ratio
Irrigation
Age
Leaf:fruit ratio × irrigation
Leaf:fruit ratio × age
Age × irrigation
Leaf:fruit ratio × age × irrigation
Residuals
Mean square and F significance
df
Fresh mass
(g)
Dry mass
(g)
Sucrose
(g (100 g)–1)
Sorbitol
(g (100 g)–1)
Glucose
(g (100 g)–1)
Fructose
(g (100 g)–1)
550 ***
79166 ***
432331 ***
45858 ***
31311 ***
4455 ***
982 *
458 ns
244
14 ***
2212 ***
5493 ***
338 ****
721 ***
55 ***
40 *
5 ns
7
1 ***
85 ***
286 ***
3*
17 ***
2*
2 ns
1 ns
0.5
0.03 ***
1.44 ***
1.12 ***
0.00 ns
0.02 ns
0.03 ns
0.05 *
0.06 **
0.01
0.06 ***
0.04 ns
6.21 ***
0.04 ns
0.04 ns
0.25 ***
0.38 ***
0.02 ns
0.03
0.09 ***
0.05 ns
0.55 ***
1.34 ***
0.22 ***
0.33 ***
0.27 **
0.02 ns
0.03
1369 ns
44926 ***
23807 **
13083 **
603
26 ns
1022 ***
412 **
240 *
15
0.6 ns
43.8 ***
3.2 **
3.8 **
0.2
0.02 ns
0.67 **
0.00 ns
0.01 ns
0.02
0.02 ns
0.23 **
0.14 **
0.00 ns
0.01
0.03 *
0.04 *
0.03 ns
0.02 ns
0.01
895 ***
119711 ***
12653 ***
537189 ***
2913 **
57085 ***
1173 ns
728 ns
349
23 **
3294 ***
18 ns
6759 ***
46 ns
1619 ***
9 ns
8 ns
13
1.7 **
55.9 ***
3.1 ns
88.9 ***
1.9 ns
8.5 **
7.0 **
0.2 ns
1.0
0.04 **
0.20 **
0.29 ***
0.88 ***
0.05 ns
0.00 ns
0.04 ns
0.00 ns
0.02
0.24 ns
0.40 ns
1.94 **
34.95 ***
0.95 *
0.22 ns
0.80 *
1.37 *
0.19
0.29 ns
0.07 ns
1.56 **
26.87 ***
0.98 *
0.57 ns
0.50 ns
1.26 *
0.20
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2
1
1
2
2
1
2
175
6
1
1
1
5
38
1
1
1
1
1
1
1
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Figure 3. Variations in calculated relative rates (day –1) of
sucrose transformation to glucose and fructose (k1(t)),
sorbitol transformation to glucose and fructose (k2(t) and
k3(t)), and synthesis of compounds other than sugars from
glucose and fructose (k4(t)) depending on days after bloom,
mean daily temperature and
relative growth rate of dry
mass. These values were calculated using Equations 4 and
the data of treatments 6, 18
and 30 leaf:fruit from the 1993
experiment.
to almost 0 at harvest, regardless of the leaf:fruit ratio (Figure 3). The relative rates of sorbitol transformation to glucose
and fructose (k2(t) and k3(t)) were high and variable (0.1–1.6
day –1), but there were no evident trends (Figure 3). The relative rate of synthesis of compounds other than sugars from glucose and fructose (k 4(t)) varied from 0 to 0.25 day –1; and was
generally positively dependent on relative mesocarp growth
rate (Figure 3). Relative mesocarp growth rate was highly variable, ranging from almost 0 to 0.09 day –1 in response to a sudden accumulation of dry matter as shown in the 30 leaf:fruit
ratio treatment of 1993 at about 125 DAB (Figure 5).
Based on these observations and measurements, the following equations were chosen to describe the metabolic process:
k1(t) = k1,3 e
– k 1 ,1 ( t − k 1, 2 )
k2(t) = k2
k3(t) = k3
k4(t) = k4
1 dWdry
Wdry dt
(9)
where k1,3 is a constant equal to 1 day –1, and k1,1 (day –1), k1,2
(day), k2 (day –1), k 3 (day –1) and k 4 are parameters.
Implementation and sensitivity analysis
The SUGAR model (Equations 2, 3, 7, 8 and 9) was fitted to
the 18 leaf:fruit data of the 1993 experiment (Figure 6) and parameters λ ph, k1,1, k1,2, k2, k3 and k4 (Equation 9) were estimated
(Table 2). The mean measured concentrations of sucrose, sorbitol, glucose and fructose were 3.4, 0.25, 1.21 and 1.39 g
(100 g) –1, respectively. The corresponding RMSE values (a
measure of the mean difference between simulated and measurement values) were 0.47, 0.12, 0.15 and 0.14 g (100 g) –1.
The RMSE values were acceptable for sucrose, glucose and
fructose (RRMSE = 0.10 to 0.14), but not for sorbitol
(RRMSE = 0.50). However, the model successfully represented the very small amounts of sorbitol present in peach
fruit. The proportion of carbon as sucrose in the phloem sap
(λ ph) was estimated to be 0.35. The relative rate of decrease in
k1(t) was estimated at k1,1 = 0.12 day –1 and k1(t) was equal to
1 day –1 at time k1,2 = 63 days. The relative rate of sorbitol transformation to glucose was k2 = 0.44 day –1, which is a little less
than the relative rate of sorbitol transformation to fructose, k3 =
0.51 day –1. The ratio of the relative rate of glucose and fructose transformation into compounds other than sugars to the
relative growth rate was estimated to be k4 = 2.56 (Table 2).
A sensitivity analysis was performed to determine the relative importance of the metabolic processes (Figure 7). The relative rates of sugar transformation were varied by ± 20%.
Sucrose was mainly sensitive to λ ph (i.e., proportion of phloem
carbon unloaded as sucrose, which depends on the metabolism
of the plant). When λ ph increased, the sucrose concentration
increased and sorbitol, glucose and fructose concentrations
decreased. Variation in k1(t) had no major effect on sugar concentrations. A large variation in k1(t) (± 110%, data not shown)
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380
GÉNARD, LESCOURRET, GOMEZ AND HABIB
Figure 5. Seasonal variations in 1993 temperature and relative growth
rate of mesocarp dry mass of treatments 6, 18 and 30 leaf:fruit from
the 1993 experiment.
and had a strong effect on the concentrations of glucose and
fructose. An increase in k 4(t) (i.e., the transformation of glucose and fructose to non-sugar compounds) decreased reducing sugar concentrations. The parameters qg and qm were
varied by ± 20% to vary growth and maintenance respiration
by the same factor and there was almost no effect on sugar concentrations.
Testing the model
Figure 4. Variations in calculated relative rates (day –1) of sucrose
transformation to glucose and fructose (k1(t)), sorbitol transformation
to glucose and fructose (k2(t) and k3(t)), and synthesis of compounds
other than sugars from glucose and fructose (k4(t)) according to sucrose, sorbitol, glucose and fructose concentrations. The ki(t) values
were calculated using Equations 4 and the data of treatments 6, 18 and
30 leaf:fruit from the 1993 experiment.
was needed to obtain a variation in sugar concentrations equivalent to that obtained when λ ph varied by ± 20%. Increases in
k2(t) and k3(t) (i.e., the transformation of sorbitol to glucose
and fructose, respectively) decreased sorbitol concentrations
When we excluded the 18 leaf:fruit data from the 1993 experiment, the model was able to simulate the order-of-magnitude
and seasonal variations in concentrations of the four sugars in
all treatments and years (Figure 8). The mean measured concentration and RMSE value were calculated for each sugar and
each treatment × year combination, and compared by RRMSE
(Table 3). The RRMSE values varied, with 32, 50 and 18% of
values in the ranges 0.05–0.20, 0.20–0.40 and 0.40–0.64, respectively. The RRMSE values were larger for sorbitol than
for other sugars.
The treatment effects were well reproduced by the model.
The model adequately simulated the positive effect of leaf:
fruit ratio on sucrose and sorbitol concentrations, the negative
effect of suppressed assimilate supply on sucrose and sorbitol
concentrations and the virtual lack of leaf:fruit ratio and girdling effects on glucose and fructose concentrations. The minor positive effect of water deficit on sugars was also well
reproduced. The main discrepancies between measured and
modeled data concerned the predictions for the 18 and 30
TREE PHYSIOLOGY VOLUME 23, 2003
CHANGES IN FRUIT SUGAR CONCENTRATIONS
381
and treatment considered. The variation in sucrose concentration resulted mainly from a positive effect of assimilate supply
and a negative dilution effect, except in the early stages of fruit
development where the metabolic transformation of sucrose to
reducing sugars (m.su) had a considerable negative effect on
sucrose concentration. Dilution as a result of increasing fruit
size had almost no effect on the variation in sorbitol concentration. Assimilate supply and metabolic transformation (m.so)
were the main determinants of changes in sorbitol concentration, having a positive and a negative effect, respectively. Variations in glucose and fructose concentrations were positively
related to the metabolic transformation of sorbitol (m.so) and,
to a much lesser extent, to the hydrolysis of sucrose (m.su) in
the early stages of fruit development. The metabolic transformation of glucose and fructose for the synthesis of compounds
other than sugars (m.gl and m.fr) had a stronger negative effect
than respiration (m.re) and dilution. The treatments had a considerable impact on the results, with an increase in the effects
of the three components (s, m, d) when irrigation was withheld, particularly for the high leaf:fruit ratio.
Discussion and conclusions
Figure 6. Mean observed (circles) and simulated (lines) sugar concentrations for the 18 leaf:fruit treatments of the 1993 experiment.
leaf:fruit ratios in 1996 and the effect of girdling in 1994 on sucrose concentration.
Effects of assimilate supply, metabolism and dilution on
sugar concentrations
Seasonal variations in the three components (s, m, d; Equations 7 and 8) influencing sugar concentrations were analyzed
using the conditions of the 1997 experiment in which leaf:fruit
ratio and water supply varied (Figure 9). Most of the effects
decreased in absolute value with time, regardless of the sugar
Much is known about the metabolic pathways involved in
sugar accumulation in plants and conceptual frameworks are
available to analyze them. Metabolic control theory (Kacser
and Burns 1981) has been used successfully for theoretical genetic studies of metabolism (Bost et al. 1999). However, the
regulation of metabolic fluxes in response to environmental
factors (such as temperature or sugar availability) are too
poorly understood to allow these conceptual frameworks to be
used as tools for analyzing causes of variability in sugar concentration in fruits. As an alternative approach, we used the
SUGAR model of Génard and Souty (1996) as the basis of our
analysis. We assumed, for simplicity, that the fruit behaves as a
single compartment with all sugars present being available for
metabolism. Thus the model implicitly considers that an equilibrium exists between the sugar concentrations in the different compartments of the fruit. The results of Yamaki and Ino
(1992) on cellular compartmentation and sugar concentrations
in immature and mature apple fruits show that sucrose, sorbitol, glucose and fructose concentrations increase from the immature to the mature stage in the same proportion in the free
space, cytoplasm and vacuole. The modified SUGAR model
Table 2. Estimation of parameter values.
Parameter
Description
Unit
Estimation
Standard error
λ ph
k1,1
k1,2
k2
k3
k4
Proportion of carbon as sucrose in the phloem sap
Relative rate of decrease of k1(t)
Time at which k1(t) = 1 day –1
Relative rate of sorbitol transformation to glucose
Relative rate of sorbitol transformation to fructose
Ratio of the relative rate of glucose and fructose transformation
to the relative growth rate
–
day –1
day
day –1
day –1
–
0.35
0.12
63
0.44
0.51
2.56
0.0036
0.0051
1.02
0.0051
0.0051
0.0204
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382
GÉNARD, LESCOURRET, GOMEZ AND HABIB
Figure 7. Sensitivity analysis
of the model to relative rates
of sugar transformation and
respiration coefficients (headings shown above graphs). The
outputs are seasonal variations
of sugar concentrations. The
analysis was performed using
the mesocarp growth curves of
treatment 18 of the 1993 experiment. Two simulations are
presented in each subplot,
which correspond to a variation of +20% (thick line) and
–20% (thin line) in the relative
rates and respiration coefficients.
was able to account for the main effects of water and assimilate
supply on seasonal variations in sugar concentrations, even in
the extreme case of no assimilate supply.
Sensitivity analysis showed that an important parameter determining sugar concentrations in peach fruit mesocarp was
the proportion of sucrose in the phloem-sourced sugar pool
(Figure 7), which was estimated to be 0.35. This value is in the
range (0.23–0.54) reported for phloem sap of peach seedlings
(Moing et al. 1992, Escobar-Gutiérrez et al. 1998). We considered this parameter to be constant, but direct evidence of its
variation, at least with water supply, has been shown
(Escobar-Gutiérrez et al. 1998). Variation in the sucrose:sorbitol ratio in peach leaves has been studied extensively. It is dependent on water supply (Escobar-Gutiérrez et al. 1998, Lo
Bianco et al. 2000), photosynthesis (Escobar-Gutiérrez and
Gaudillère 1997) and genotype (Escobar-Gutiérrez and
Gaudillère 1994). If we assume that there is a link between the
sucrose:sorbitol ratio in leaves and in phloem sap (cf.
Escobar-Gutiérrez et al. 1998), it is clear that these factors will
have to be considered in future modeling investigations. Omission of these considerations might explain some discrepancies
between the measured data and our model prediction for sucrose concentration in 1996. The year 1996 was marked by unusually high photosynthetically active radiation until 120 days
after flowering, which would have resulted in greater photosynthesis compared with the other years studied. According to
the results of Escobar-Gutiérrez and Gaudillère (1997), the
year 1996 would be characterized by a high proportion of sucrose in the phloem-sourced sugar pool. A value of 0.45 (instead of 0.35) improves agreement between the model predictions and measured sucrose concentrations in 1996.
The relative rates of sucrose transformation to glucose and
fructose decreased during the fruit growth period, reaching almost 0 at harvest (Figure 3). Vizzoto et al. (1996) and Lo Bianco et al. (1999a) concluded that storage of sucrose in peach
fruit was mainly related to decreased activities of sucrose-hydrolyzing enzymes (insoluble acid invertase, soluble acid invertase, neutral invertase, sucrose synthase), which could
mean that relative rates of net sucrose transformation essentially describe the metabolic activities of sucrose-hydrolyzing
enzymes. In contrast to the results of several studies (Moriguchi et al. 1990, Hubbard et al. 1991, Kobashi et al. 1999),
Vizzoto et al. (1996) found no increase in the activities of sucrose-synthesizing enzymes during fruit development, suggesting that sucrose may, at least for some peach cultivars,
enter the cell carbohydrate pool directly as was assumed in our
model formulation.
The model was sensitive to the relative rates of sorbitol conversion to glucose and fructose (Figure 7). These relative rates
were high and reflected the activities of sorbitol oxidase,
which converts sorbitol to glucose, and sorbitol dehydrogenase, which converts sorbitol to fructose. The rates were as-
TREE PHYSIOLOGY VOLUME 23, 2003
CHANGES IN FRUIT SUGAR CONCENTRATIONS
383
Figure 8. Mean observed
(symbols) and simulated
(lines) sugar concentrations for
each treatment, except the 18
leaf:fruit treatment of the 1993
experiment.
sumed to be constant because no clear trends were found to
explain their seasonal variations (Figure 3), and no clear patterns of seasonal variation in sorbitol oxidase or sorbitol dehydrogenase have been reported. To improve our model, more
knowledge about the control of these enzymes is needed.
Moriguchi et al. (1990) and Kobashi et al. (1999) suggested
that most sorbitol is converted to glucose by sorbitol oxidase in
peach fruit; however, the conversion of sorbitol to fructose by
sorbitol dehydrogenase was recently observed in peach fruits
(Lo Bianco et al. 1999a). In our study, relative rates of sorbitol
conversion to glucose and fructose were similar (0.44 and
0.51 day –1, respectively).
The relative rate of synthesis of compounds other than sugars from glucose and fructose increased with increasing relative mesocarp growth rate (Figure 3). A likely explanation for
this relationship is that the periods of intense relative growth
are marked by the synthesis of new structures such as cell
walls, whereas the periods of low relative growth such as
the ripening period are marked by low cell wall synthesis
(Bouranis and Niavis 1992, Fishman et al. 1993).
Table 3. Mean measured sugar concentrations (C; g (100 g) –1), root mean squared error between observed and simulated values (RMSE; g
(100 g) –1) and relative RMSE (RRMSE) values for four sugars and 11 year × treatment combinations.
Year
1993
1996
1994
1997
Treatment
6
30
6
18
30
G
C
I10
I30
D10
D30
Sucrose
Sorbitol
Glucose
Fructose
C
RMSE
RRMSE
C
RMSE
RRMSE
C
RMSE
RRMSE
C
RMSE RRMSE
2.38
1.08
1.64
3.05
3.77
2.25
4.33
1.73
2.99
2.20
3.14
0.48
0.76
0.26
0.77
1.10
1.26
0.47
0.51
0.97
0.45
1.09
0.20
0.18
0.16
0.25
0.29
0.56
0.11
0.30
0.32
0.20
0.25
0.14
0.43
0.16
0.33
0.39
0.35
0.61
0.27
0.37
0.40
0.42
0.09
0.16
0.08
0.13
0.12
0.11
0.16
0.12
0.10
0.13
0.12
0.64
0.37
0.50
0.40
0.32
0.33
0.27
0.44
0.27
0.32
0.30
1.28
1.23
1.21
1.26
1.33
1.28
1.43
1.03
1.01
1.35
1.06
0.36
0.16
0.26
0.14
0.14
0.59
0.07
0.21
0.40
0.42
0.49
0.28
0.13
0.21
0.11
0.10
0.46
0.05
0.20
0.40
0.31
0.47
1.51
1.40
1.25
1.31
1.38
1.58
1.52
1.09
1.12
1.41
1.18
0.48
0.19
0.34
0.20
0.16
0.35
0.71
0.28
0.51
0.55
0.62
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0.32
0.14
0.27
0.15
0.11
0.22
0.05
0.25
0.45
0.39
0.53
384
GÉNARD, LESCOURRET, GOMEZ AND HABIB
Figure 9. Simulated seasonal variations in the components (Equations 7 and 8) of sugar concentrations. Abbreviations: s = assimilate supply; d =
dilution due to the change in fruit volume; m.i = metabolic transformation of sugar i into other sugars or compounds (su = sucrose, so = sorbitol,
gl = glucose, fr = fructose); and m.re = respiration.
We attempted to model the effects of sugar importation, dilution by water and metabolism on sugar concentrations in
peach fruits. We demonstrated that sugars differ in their sensitivity to assimilate supply and dilution (Figure 9). According
to our model, sucrose did not undergo metabolic transformation and was subject to a strong dilution effect. Sorbitol was
the most important carbohydrate used for metabolism in peach
fruit. Its concentration was always low and was linked to
phloem importation and to metabolism. Reducing sugars constituted a transitory storage pool and their concentrations were
closely related to metabolism.
Acknowledgments
We gratefully acknowledge R. Laurent and J. Hostallery for their assistance during the field experiments, and D. Dumont, E. Rubio and
M. Reich for their assistance in the sugar analyses. We thank AnneMarie Wall (INRA Translation Unit, Unité Centrale de Documentation, Jouy-en-Josas) and Gail Wagman for revising the manuscript.
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