Production Practices and Quality Assessment of Food Crops. Vol. 1

56 M. Génard and F. Lescourret
1991; Ackerman et al., 1992). The conversion of phloem sugars within the fruit
has been studied by Hansen (1970). The main enzymes involved in the sugar
metabolism of fleshy fruits have been identified (Yamaki and Ishikawa, 1986;
Moriguchi et al., 1992), but little is known about their regulation. Use of carbohydrates
by the fruit and changes in sugar contents are probably strongly correlated,
which may explain the strong correlations usually noted between sugar content at
harvest and the size of fruit from a same tree (Génard et al., 1991 and 1999b).
These results were used in the SUGAR model which will be presented in the
following section (see Génard and Souty, 1996 for more details). This model is a
dynamic deterministic model of carbon use that includes sugar accumulation and
synthesis in fruit flesh. The model was designed for peach, but the main principles
can be used for other fruit.
4.1.2.1. Main knowledge in the case of peach and model principles
Sucrose and sorbitol are the only sugars founds in the phloem sap of trees from
the Prunus species such as peach trees (Escobar-Gutierrez and Gaudillère, 1996).
In the peach flesh, sucrose is the main sugar, glucose and fructose are present in
similar quantities and can reach about 25% each of the total sugar content, and
sorbitol content is always low (Souty and André, 1975; Brooks et al., 1993). This
suggests that sorbitol is almost totally metabolised into reducing sugars when sucrose
is only partly hydrolysed into fructose and glucose. But as sucrose accumulates in
the fruit, a seasonal decrease in conversion of the sucrose into reducing sugars
was assumed. Glucose and fructose are used as substrates for synthesize compounds
other than sugars. As more and more soluble sugars accumulate with fruit
development (i.e. when the relative growth rate of the fruit decreases), we assumed
that this synthesis decreases with the decrease in relative growth rate. Indeed, the
periods of low relative growth, such as the ripening period are characterized by
low cell wall synthesis (Bouranis and Niavis, 1992; Fishman et al., 1993).
Glucose and fructose are used as substrates for respiration and both sugars are
assumed to be used in proportion to their quantity in the fruit. Respiration is
calculated as in the SWAF model. Apart from respiration, the carbon flow between
two compounds is proportional to the quantity of carbon in the source compound.
The system is represented by the following set of differential equations
dM su
dt
dM so
dt
dMgl dt
dMfr dt
= λ ph
dM ph
dt
– k 1(t)M su
dM ph
= (1 – λph) – [k
dt
2(t) + k3(t)]Mso k
= 1(t)
Msu + k
2
2(t)Mso – k4(t)Mgl –
k
= 1(t)
Msu + k
2
3(t)Mso – k4(t)Mgl –
dM re
dt
where M su, M so, M gl and M fr are the amounts of carbon as sucrose, sorbitol, glucose,
M gl
M gl + M fr
M fr
M gl + M fr
dM re
dt
(1)