Tansley review
Modelling the size and composition of
fruit, grain and seed by process-based
simulation models
Author for correspondence: Pierre Martre
Tel: +33 473 624 351
Email: [email protected] Received: 3 March 2011
Accepted: 29 March 2011
Pierre Martre
1,2, Nadia Bertin
3, Christophe Salon
4,5and Michel Ge´nard
31INRA, UMR 1095 Genetics, Diversity, and Ecophysiology of Cereals (GDEC), 234 Avenue du
Brezet, F-63100 Clermont-Ferrand, France;2Blaise Pascal University, UMR 1095 GDEC, F-63177
Aubie`re, France;3INRA, UR 1115 Plantes et Syste`mes de Culture Horticoles, F-84914 Avignon,
France;4INRA, UMR 102 Ge´ne´tique et Ecophysiologie des Le´gumineuses (LEG), BP 86510,
F-21065 Dijon, France;5AgroSup Dijon, UMR102 LEG, F-21065 Dijon, France
New Phytologist (2011)191: 601–618 doi: 10.1111/j.1469-8137.2011.03747.x
Key words: cereals, end-use value, fleshy fruits, grain legumes, growth, metabolism, oilseeds, quality.
Summary
Understanding what determines the size and composition of fruit, grain and seed
in response to the environment and genotype is challenging, as these traits result
from several linked processes controlled at different levels of organization, from
the subcellular to the crop level, with subtle interactions occurring at or between
the levels of organization. Process-based simulation models (PBSMs) implement
algorithms to simulate metabolic and biophysical aspects of cell, tissue and organ
behaviour. In this review, fruit, grain and seed PBSMs describing the main phases
of growth, development and storage metabolism are discussed. From this
concur-rent work, it is possible to identify generic storage organ processes which can be
modelled similarly for fruit, grain and seed. Spatial heterogeneity at the tissue and
whole-plant level is found to be a key consideration in modelling the effects of the
environment and genotype on fruit, grain and seed end-use value. In the future,
PBSMs may well become the main link between studies at the molecular and
whole-plant levels. To bridge this phenotype-to-genotype gap, future models need
to remain plastic without becoming overparameterized.
I. Introduction
Over the past 50 yr, global crop yields have steadily
increased by between 0.5 and 2% yr
–1(Calderini & Slafer,
1998; Cassman, 1999, 2001). However, with the world
population projected to reach nearly nine billion in 2050,
an estimated 40% higher rate of yield increase needs to be
sustained for most crop species to ensure food security (e.g.
Contents
Summary 601
I. Introduction 601
II. Modelling the morphogenesis and growth of fruit, grain and seed
602
III. Modelling fruit, grain and seed composition 605 IV. Next steps in modelling the size and composition
of fruit, grain and seed
610
Tester & Langridge, 2010). Past yield increases have been
accompanied by large and, in terms of quality, generally
negative modifications in the oil content of oilseeds (Triboi
& Triboi-Blondel, 2002; Aguirreza´bal et al., 2009), the
sugar and organic acid content of fleshy fruits (Ge´nard
et al., 1999; Causse et al., 2003), and the protein content of
cereals (Oury et al., 2003; Aguirreza´bal et al., 2009) and
grain legumes (Weber & Salon, 2002; Graham & Vance,
2003). How can the relationship between the yield and
composition of fruit, grain and seed crops be managed
when the objective is to optimize the level and stability of
both?
For fruit, grain and seed, the size and composition at
har-vest are complex traits resulting from many processes at
both the plant and organ levels that show large
geno-type · environment
interactions
(Aguirreza´bal
et al.,
2009). Thus the broad-sense heritability of these traits is
generally low (< 0.2), and respective quantitative trait loci
(QTLs) usually explain < 10% of the variation observed
(Blanco et al., 2002; Chaı¨b et al., 2006; Dudley et al.,
2007). Ecophysiological process-based simulation models
(PBSMs) are increasingly used to help unravel this
complex-ity, to identify relevant traits and processes and further
analyse the degrees of genetic and environmental
determin-ism (e.g. Quilot et al., 2005a,b; Yin et al., 2005; Chenu
et al., 2009; Semenov et al., 2009). PBSMs are built on
evi-dence-based or otherwise justifiable hypotheses about
interrelationships among processes and how they are
affected by environmental variations (Loomis et al., 1979).
They can be used to quantify how a plant responds to
genetic, environmental and management factors by
dynamic mathematical simulation of the biophysical and
physiological processes involved, with parameters that are
relatively independent of the environment, yet characteristic
of one or several genotypes (Mavromatis et al., 2002; Boote
et al., 2003).
The objective of this Tansley review is to present and
dis-cuss models developed over the last decade of how fleshy
fruits, grains and seeds grow. Grain ⁄ seed and fruit
model-ling have developed quite independently. In fruit
modelling, the emphasis has been on processes occurring in
cells or tissues, whereas in grain and seed modelling,
emphasis has been at the level of the organ or the whole
crop. However, the size and composition of both fruit,
grain and seed are determined through successive phases of
development: intensive cell division; rapid cell expansion
with endoreduplication and accumulation of nitrogen and
carbon storage components; and then maturation (Gillaspy
et al., 1993; Olsen, 2001; Weber et al., 2005). Analysis of
current models reveals that the approaches taken in
model-ling fruit growth in terms of water relations or cell division,
for example, are relatively generic and could be used as a
basis for modelling these processes in grain and seed too.
The mechanisms and environmental regulation of the
simu-lated processes are only covered here in any detail where
necessary to illustrate ways in which modelling may
develop. Whole-plant models of carbon and nitrogen
allo-cation among organs are outside the scope of this review
but are reviewed in depth elsewhere (Marcellis et al., 1998;
Lacointe, 2000; Marcellis & Heuvenlink, 2007; Minchin,
2007; Prusinkiewicz et al., 2007).
II. Modelling the morphogenesis and growth of
fruit, grain and seed
1. Cell division
The initial phase of fruit, grain and seed development is
characterized by a high mitotic activity in storage tissues
(i.e. the mesocarp in fleshy fruits, the endosperm in cereal
grains and the cotyledons in dicotyledonous seeds). The
number of cells produced during this stage of development
is a key determinant of the potential final size (both volume
and mass) of fruit (Cong et al., 2002; Bertin et al., 2003a;
Liu et al., 2003; Quilot & Ge´nard, 2008) and grain or seed
(Munier-Jolain & Ney, 1998; Lemontey et al., 2000;
Vilhar et al., 2002; Ishimaru et al., 2003).
A phenomenological simulation model of cell division
has also been developed to describe cell dynamics during
the early growth of tomato fruit (Lycopersicon esculentum
Mill.) under nonlimiting conditions (Bertin et al., 2003b).
The model assumes that the fruit develops from a single
mother cell by asynchronous binary cell fission. After a first
period of exponential cell division at a constant rate, the
mitotic activity (i.e. the proportion of dividing cells) is
assumed to decrease after each cell cycle. A next step would
be to introduce environmental factors into this model. One
way to do so would be to couple this cell division model to
a biophysical model of cell or tissue expansion. As far as we
know, no model of grain endosperm or seed cotyledon cell
division has been developed, but an approach similar to that
developed for tomato fruit may be applicable for simulating
the kinetics of cell division in grain and seed.
Mechanistic models based on comprehensive knowledge
of the molecular control of the cell cycle have been
proposed (Gardner et al., 1998; Ciliberto & Tyson, 2000;
Yang et al., 2006). These models have many (from 30 to
90) parameters, which is of limited value in analysing
geno-type · environment interactions. A much simpler model
coupling cell cycle regulation and cell expansion has also
been proposed (Beemster et al., 2006), based on the
con-cept that availability of a growth factor drives cell
expansion, presumably through an effect on protein
synthe-sis. Cells start to divide when they reach a certain ratio of
the amount of DNA to the cell volume, then progression
through the cell cycle being triggered by the accumulation
of cell cycle regulators (cyclin-dependent kinases). This
generic model qualitatively simulates the effect of
over-expressing a cell cycle inhibitor on cell expansion and the
rate of mitosis during the cell proliferation phase of leaf
development in the model species Arabidopsis thaliana (L.)
Heynh. This kind of approach is promising because it is
well suited to analysing the effect of mutations on growth
and may form the basis to develop mechanistic models of
cell division for fruit, grain and seed.
2. Endoreduplication
The initial phase of cell division in the storage tissues of
most fruit, grain and seed is followed by a sharp increase in
the average DNA content per nucleus as a result of somatic
polyploidization, through endoreduplication. This is thought
to be a mechanism to increase cell size and enhance
gene expression in highly active metabolic cells (Edgar &
Orr-Weaver, 2001; Sugimoto-Shirasu & Roberts, 2003;
Barow, 2006). The number of rounds of endoreduplication
has been correlated with increases in the cell size and storage
capacity of fruit, grain and seed (Engelen-Eigles et al.,
2000; Lemontey et al., 2000; Cheniclet et al., 2005). The
endocycles (i.e. DNA replication without cytokinesis) do
not require reorganization of the cytoskeleton and may
therefore allow for faster growth, especially of storage
tissues, than cell proliferation (Kondorosi & Kondorosi,
2004). While the number of endocycles is not always
corre-lated to cell volume (Gendreau et al., 1998; Leiva-Neto
et al., 2004; Bertin, 2005; Inze & De Veylder, 2006; Nafati
et al., 2011), in grain endosperm or seed cotyledons
endoreduplication is tightly associated with large spatial
heterogeneity in cell size (Vilhar et al., 2002) and starch
(Kladnik et al., 2006) and protein content (Le Gal et al.,
1984; Cavallini et al., 1995; Knake-Sobkowicz & Marciniak,
2005). This suggests that the degree of ploidy determines
the potential for cell expansion and the accumulation of
storage compounds. To understand environmental and
genetic effects on the size and composition of fruit, grain
and seed, it is therefore important to model differences in
endoreduplication in storage tissues.
The molecular mechanisms underlying
endoreduplica-tion remain poorly understood, making it difficult to
develop a mechanistic model in terms of environmental
and endogenous variables. Instead, a phenomenological
model describing the dynamics of endoreduplication during
maize (Zea mays) endosperm development has been
devel-oped (Schweizer et al., 1995). It accounts for the kinetics
of endoreduplication observed under field conditions in
maize endosperm (Schweizer et al., 1995) and in orchid
(Phalaenopsis aphrodite ssp. formosana, P. equestris and
Oncidium varicosum) flower tissues (Lee et al., 2004, 2007).
The main hypotheses of this model are that: the rate of
change of nuclei going from a lower to a higher ploidy is
proportional to the number of nuclei at the lower ploidy;
the rate constant of change in ploidy decreases over
developmental time in a predictable way; and for
endoredu-plicating nuclei, the duration of one endocycle increases
with the ploidy value. A drawback of this model is its
over-parameterization. It has as many parameters as the number
of DNA classes, each representing the transition rate from
one C value to the next. To overcome this limitation, a
model coupling cell division and endoreduplication was
proposed (Bertin et al., 2007), which describes the
phenomenological development of mitotic cycles, the
transition from mitotis to endoreduplication, and further
endoreduplication cycles. It predicts reasonably well the
number of cells and their distribution according to their C
value during the development of tomato pericarp, a highly
polyploid tissue. When the model was applied to
contrast-ing genotypes (cherry tomato and large-fruited tomato), it
was found that the switch from the mitotic cycle to the
endocycle and the duration of fruit development appeared
to be the main genetically determined differences between
these two genotypes, whereas the process of
endoreduplica-tion itself was regulated similarly in both genotypes (Bertin
et al., 2007).
3. Cell and tissue expansion and water flux
After cell division ceases, cells in tissues expand. This
requires processes that drive the flux of water and solutes
into the expanding tissues, including transport through the
pedicel and epidermis, phloem unloading, and regulation of
the osmotic and hydrostatic pressure of cells and bio
rheological properties of cell walls (Cosgrove, 1993; Boyer
& Silk, 2004).
Several PBSMs of fleshy fruit expansion based on water
and carbon fluxes have been published. Most of these
models link water influx into the fruit to the water potential
difference between the stem and the fruit and the hydraulic
conductivity of the water pathways (Lee, 1990; Bussie`res,
1995, 2002; Fishman & Ge´nard, 1998). The model
pro-posed by Fishman & Ge´nard (1998) takes into account the
main biophysical processes and how they are affected by the
maternal plant physiology and environmental signals, by
assuming that fruit mesocarp behaves as a single cell
(Fig. 1a). This model links water and carbohydrate uptake
by the fruit using thermodynamic concepts derived from
the root composite transport model (Steudle, 2000). Tissue
expansion is related to mesocarp turgor pressure and cell
wall biorheological properties through the Lockhart
equa-tion (Lockhart, 1965).
This model has been used to predict seasonal and diurnal
increases in the fresh and dry mass of peach fruit (Prunus
persica (L.) Batsch) at different leaf-to-fruit ratios
(Fig. 1b,c) and tree water statuses (Fishman & Ge´nard,
1998). The model has been extended to account for
devel-opmental changes in the total fruit surface conductance to
water vapour (Lescourret et al., 2001) and its components –
stomata, the cuticle and cracks (Gibert et al., 2005).
Developmental changes in elastic and plastic cell wall
properties have also been considered for mango (Mangifera
indica L.) fruit (Le´chaudel et al., 2007). The developmental
shift of phloem unloading from the symplastic to the
apo-plastic pathway and competition between mesocarp cells for
sucrose during tomato fruit development have been
incor-porated in the model (Liu et al., 2007). The latter
refinement meant that the interaction between sink strength
(i.e. cell number) and active carbon accumulation could be
analysed, the result explaining the known negative
correla-tion between fruit cell number and cell size (Bertin, 2005;
Quilot & Ge´nard, 2008).
Although several data suggest that the water status of the
grain and seed itself plays an important regulatory role in
their development and growth (Bradford, 1994; Zhang
et al., 2007; Zhou et al., 2007), this aspect has yet to be
modelled. In addition to the integrated and quantitative
view that a PBSM of water flux during grain and seed
development could provide, it would also give an insight
into how processes determining grain and seed quality are
regulated. For example, in bread wheat (Triticum aestivum
L.) the kinetics of water loss during the maturation stage
plays an important role in determining the rheological
properties of storage proteins, the percentage of damaged
starch granules, and grain texture (Carceller & Aussenac,
1999, 2001; Sabino et al., 2006). For maize, low grain
water content at harvest, which is correlated to the grain
drying rate in the field (Kang & Zuber, 1987), is very
important because it reduces both yield loss in the field and
the cost of postharvest drying.
There is experimental evidence to support the concept that
grain growth is regulated by the pericarp in maize (Kiniry
et al., 1990; Hood et al., 1993; Sala et al., 2007) and wheat
(Millet & Pinthus, 1984). Likewise, genetic and molecular
studies of A. thaliana have demonstrated that the seed coat
regulates seed growth (Garcia et al., 2005; Schruff et al.,
2006) and shape (Le´on-Kloosterziel et al., 1994). Several
authors have thus hypothesized that the biorheological
prop-erties of the outer tissues regulate overall grain and seed
expansion, while tissue expansion is driven by tissue pressure
generated in the endosperm (Haughn & Chaudhury, 2005;
Berger et al., 2006). In the Fishman & Ge´nard (1998) model,
it is assumed that the fruit pericarp behaves as a single cell, so
physical restraint by outer tissues is accounted for as for cell
wall biorheological parameters (Le´chaudel et al., 2007).
Therefore, it may be possible to adapt this fruit model to
sim-ulate grain and seed water relations and expansion to test the
hypothesis that their expansion is controlled by the
biorheo-logical properties of the outer tissues.
Tissues surrounding grains (floret bracts) and seeds (seed
pods) physically restrain their overall expansion in soybean
(Glycine max (L.) Merr.; Bravo et al., 1980; Fraser et al.,
1982; Egli et al., 1987), barley (Hordeum vulgare L.; Scott
et al., 1983), oats (Avena sativa L.; Grafius, 1978), rice
(Oryza
sativa
L.;
Matsushima,
1967;
Murata
&
Matsushima, 1975; Song et al., 2007), and even in wheat,
which has nonadhering floret bracts (Grafius, 1978; Millet
& Pinthus, 1984; Millet, 1986). If subtending organs,
which cease expansion before fertilization, are physical
restraints on grain and seed expansion, modelling their
development
and
growth
will
also
be
important.
Constraints exerted by neighbouring florets may affect the
shape and size of wheat grains (Boshankian, 1918; Millet &
Pinthus, 1984), meaning that the architectural and
mechan-ical constraints within the whole inflorescence may need to
be considered as well.
FC ψstem Leaf : fruit Dry matter : Total C = Soluble C (sugars) +Structural C (cell walls)
+ π
P
ψfruit=
Dilution Extension Fresh matter: Water VPD, T T dV =V .φ.(P – Y) dt (a) 200 50 100 150 1993Time after bloom (d)
80 100 120 140 160
Simulated FW (g per fruit)
0 (b) 150 200 250 r 2 = 0.96 Slope = 0.87 RRMSE = 7% 1:1
Observed FW (g per fruit)
50 100 150 200 250
Simulated FW (g per fruit)
50 (c)
100
Leaf : fruit ratio 6 10 18 30 1993 1996 1997 Respiration Transpiration • •
Fig. 1 Fruit growth and water relations model. (a) Schematic representation of the model (modified from Bertin et al., 2006). Broken lines indicate information flow and solid lines indicate water and carbon fluxes. (b) Simulated (lines) and observed (symbols) fruit FW vs time after bloom (circles, thin line, six leaves per fruit; triangles, medium line, 18 leaves per fruit; squares, thick line, 30 leaves per fruit). (c) Simulated vs observed fruit FW at maturity for peach cv Suncrest grown in 1993, 1996 and 1997 in an orchard in Avignon, France, with different leaf-to-fruit ratios (adapted from Lescourret & Ge´nard, 2005, by permission of Oxford University Press). This dataset was not used for model development or calibration. FC, flux of sucrose import to the fruit; P, turgor pressure;
T, average daily air temperature; VPD, vapour pressure deficit; V, fruit volume; Y, threshold value of turgor pressure below which no irreversible cell expansion occurs; /, cell wall extensibility; Wstem,
stem water potential; Wfruit, fruit water potential; p, fruit osmotic
III. Modelling fruit, grain and seed composition
1. Carbohydrate concentration and composition
The organoleptic quality of fleshy fruits is determined by
subtle sugar–acid balances (Stevens et al., 1979), which vary
throughout fruit development according to the supply of
carbohydrate by the phloem, changes in the metabolic
activ-ity of the fruit, and dilution owing to fruit expansion
(Chapman et al., 1991; Ackerman et al., 1992). Sugars also
have important signalling roles and control the expression
of genes involved in the synthesis of quality-related
second-ary metabolites (Vitrac et al., 2000). In most grains, the
major form of carbon and energy storage is starch, which is
the primary source of carbohydrate in the human diet. At
maturity, starch accounts for 50–70% of cereal grain dry
mass and is responsible for most of the year-to-year and
site-to-site variation in grain dry mass and protein
concen-tration (Triboi & Triboi-Blondel, 2002).
Sugar accumulation has been modelled empirically in
grape (Vitis vinifera) berry using an allometric-type
approach (Sadras & McCarthy, 2007; Sadras et al., 2007).
This approach can take into account ontogenetic drift and
size-dependent variations in berry sugar concentration or
analyse the phenotypic plasticity in concentrations of fruit
compounds in terms of rate and duration of accumulation
(Sadras et al., 2007, 2008). However, it gives only limited
insight into the physiological processes causing the observed
variations in fruit sugar concentration. A more mechanistic
approach has been taken in constructing the peach fruit
model SUGAR. This model simulates the partitioning of a
given amount of carbon unloaded from the phloem into
sucrose, sorbitol, glucose, fructose, other compounds
(starch and structural carbohydrates) and respiratory CO
2(Fig. 2; Ge´nard & Souty, 1996; Ge´nard et al., 2003), from
which a fruit sweetness index can be calculated (Lescourret
& Ge´nard, 2005). In SUGAR, the fruit is modelled as a
sin-gle metabolic compartment and, apart from respiration, the
enzymatic reactions involved in the sugar metabolism are
described in chemical kinetics terms (Chang, 2000), where
the rate of a reaction is proportional to the amount of
reac-tant. SUGAR has been coupled to a fruit model of fresh
mass accumulation to simulate environmental effects on
peach fruit sugar composition (Ge´nard & Huguet, 1997),
and then to a model of carbon acquisition and partitioning
to simulate the effects of light interception and fruit
thin-ning on peach fruit sweetness (Ge´nard et al., 1999).
More recently, a modified version of SUGAR simulating
developmental, growth and temperature-related variations
in the relative rates of different sugar transformations has
been developed for peach (Ge´nard et al., 2003), and then
adapted for tomato (Prudent et al., 2011) and grape (Dai
et al., 2009). This shows the versatility of the approach
when applied to fleshy fruit. This version of SUGAR
quan-tifies the relative contribution of sucrose supply, metabolic
activity (incorporating carbon into compounds other than
carbohydrates) and dilution (resulting from changes in fruit
volume) to fruit sugar concentration and composition. This
has then been extended to consider how the same three
fac-tors contribute to the genetic variability in the total sugar
concentration in fruit flesh within peach (Quilot et al., 2004)
and tomato (Prudent et al., 2011) mapping populations.
Detailed kinetic models have been proposed for the
reac-tion network of glycolysis and the oxidative pentose
phosphate pathway in developing rapeseed embryos
(Brassica napus L.; Schwender et al., 2003), for sucrose
metabolism in sugarcane culms (Saccharum officinarum L.;
Rohwer & Botha, 2001; Uys et al., 2007), and for the
C supply Sucrose Glucose Fructose
( )
( ( )) 1 = e t–k1,2 –k1,1 k t lphl 2 k 1 – lphl Sorbitol Other C compounds CO2 3 k 2 k (a) 5 1993 0 1 2 3 4 1993 Glucose Fructose Sucrose SorbitolTime after bloom (d)
80 100 120 140 160 S ugar con cen trat io n (g per 100 g FW) (b) 7 8 9 10 r2 = 0.87 Slope = 0.88 RRMSE = 7.8% 1:1
Observed sweetness index (%)
5 6 7 8 9 10 Sim ula ted s w e e tne s s in de x ( % ) 5 6 Leaf to fruit ratio 6 18 30 1993 1996 (c) (t) = dry 4 4,1 dry 1 dW k k W dt
Fig. 2 The SUGAR model of fruit sugar metabolism. (a) Schematic representation of the model (adapted from Ge´nard et al., 2003, by permission of Oxford University Press). (b) Simulated (lines) and observed (symbols) quantity of sucrose, glucose, fructose and sorbitol per fruit vs time after bloom; (c) simulated (lines) vs observed (symbols) sweetness index at maturity for peach cv Suncrest grown in 1993 and 1996 in an orchard in Avignon, France, with different leaf : fruit ratios (adapted from Lescourret & Ge´nard, 2005, by permission of Oxford University Press). This dataset was not used for model development or calibration. kphl, proportion of
sucrose in the phloem sap; k1, k2, k3, and k4, relative rates of sugar
transformation for net transformation of sucrose to glucose and fructose, sorbitol to glucose, sorbitol to fructose, and glucose and fructose to nonsugar compounds, respectively; t, time after bloom (d). kphl, k1,1, k1,2, k2, k3and k4,1are estimated parameters. The
sweetness index (g of equivalent sucrose per 100 g of flesh FW) was computed as a linear combination of sugar concentrations, with the sweetness ratings of each sugar as coefficients. RRMSE, relative root mean squared error.
starch-to-sucrose transition in potato tubers (Solanum
tuberosum L.; Junker, 2004). When the steady-state
meta-bolic control of the 11 reactions of the sugarcane model
were analysed, the fructose and glucose transporters, the
vacuolar sucrose importer, and the cytosolic neutral
invert-ase activity were identified as the most critical steps in
determining the rate of sucrose accumulation in sugarcane
culms (Rohwer & Botha, 2001; Uys et al., 2007). Neutral
invertase activity was predicted to be a key determinant of
the sucrose-to-hexose ratio and the sucrose concentration,
and this was demonstrated experimentally in transgenic
sugarcane cell culture and regenerated plants in which the
neutral invertase was down-regulated (Rossouw et al., 2010).
Despite the considerable advances made in the
topologi-cal and stoichiometry analysis of metabolic pathways, the
development of kinetic models of metabolic networks is
hampered by the numerous parameters required to describe
the enzyme kinetics rate laws, often difficult to determine
experimentally (Schallau & Junker, 2010). In flux balance
analysis, steady-state fluxes are calculated by applying mass
balance constraints to stoichiometric models, with the
advantage that knowledge of the kinetic parameters is not
required (Orth et al., 2010). Recently, flux balance analysis
has been applied to a model describing 256 biochemical
and transport reactions of central metabolism (glycolysis,
oxidative pentose phosphate pathway, citrate cycle), amino
acid metabolism, starch synthesis and some minor pathways
in developing barley endosperm (Grafahrend-Belau et al.,
2009). The major limitation of this approach is that it
can-not accommodate regulatory events and it can only predict
optimal behaviour. Nevertheless, the barley metabolic
model was able to qualitatively reproduce the growth rate
and metabolic pathway patterns of developing endosperm
in response to oxygen availability or enzyme deletion
(Grafahrend-Belau et al., 2009). These in silico experiments
highlighted the capacity of the primary metabolism of cereal
endosperm to compensate for oxygen depletion and
enzy-matic perturbations and the importance of subcellular
compartmentalization for network robustness.
The size distribution of starch granules is an important
factor for cereal grain milling yield, rheological properties
and starch digestibility (Casey et al., 1997; Edwards et al.,
2008). Whereas maize produces starch granules of only one
size class, wheat, oat and barley endosperm produce two or
three size classes, which are initiated at specific times during
endosperm development (Bechtel & Wilson, 2003). The
mechanisms of initiation of polysaccharide synthesis and
nucleation that lead to the formation of new starch granules
are not fully understood, so the development of a PBSM of
starch granule initiation and growth is still elusive.
However, a phenomenological model of the waves of starch
granule protrusion and growth could probably be built
based on current knowledge. Such a model would help in
analysing and understanding the basis of genotype ·
envi-ronment interactions for the number and size distribution
of starch granules and would make it possible to test new
hypotheses regarding their formation.
2. Organic acid concentration and composition
To understand how fruit acidity is determined requires
knowledge of the mechanisms involved in the accumulation
of both malic and citric acids, the major organic acids in
most fruits (Tucker, 1993). PBSMs of citrate (Lobit et al.,
2003; Wu et al., 2007) and malate (Lobit et al., 2006)
metabolism have been developed to predict whole fruit
cit-rate and malate concentration during the period of rapid
fruit growth.
Like most organic acids, citrate is stored in the vacuoles
of mesocarp cells where it is continuously exchanged
between the vacuole and the cytosol. Its biosynthesis
involves a set of mitochondrial enzymes. Lobit et al. (2003)
proposed a model to describe the synthesis of citrate,
assum-ing that vacuolar storage is not limitassum-ing. It is based on
analysis of citrate metabolism at the cellular level, but
instead of exhaustively representing the kinetics and
regula-tion of individual enzymatic reacregula-tions, variaregula-tions in fluxes
relative to a reference state were represented as linear
combi-nations of regulating factors (temperature, energy status and
metabolite concentrations). The system was further
simpli-fied by assuming that some series of reactions could be
modelled as single reactions (Fig. 3a,b). The result is a
unique equation relating the rate of net citrate production
in a fruit to its initial DW, temperature and respiration rate
(Lobit et al., 2003). The parameters of this equation are
closely related to the properties of mitochondrial transport
systems and enzymes, and it is assumed that genotypic
differences in these parameters reflect differences in the
underlying metabolic properties of the fruit (Wu et al.,
2007). This model has been successfully evaluated for
com-binations of years, leaf-to-fruit ratios, assimilate availability
and cultivars (Fig. 3c,d; Lobit et al., 2003; Wu et al., 2007).
The lack of relationship between malate accumulation
and the activity of the enzymes involved in its metabolism
in peach fruit (Moing et al., 1998) suggests that malate
accumulation is controlled, not by metabolism, but by its
transport to the vacuole of mesocarp cells. Thus, in contrast
to the citrate model, Lobit et al. (2006) proposed modelling
malate accumulation based on the thermodynamic
charac-teristics of its transport through the tonoplast. This led to
the development of a PBSM describing interactions
between acid–base reactions in the vacuole, proton
trans-port across the tonoplast and malate accumulation, with
parameters essentially describing the functioning of
tonoplast proton pumps (Lobit et al., 2006). The model
was further simplified by considering changes in vacuolar
composition as a succession of stationary states, in which
the malate concentration, pH and electrical potential can be
considered as constant. This approach avoided the need to
describe all fluxes across the tonoplast, which would have
led to an unwieldy number of unknowns and parameters.
Solving the resulting system of three equations made it
pos-sible for the malic acid content of the fruit to be predicted
as a function of other acid and potassium concentrations
and temperature. Despite the complex regulation of malate
accumulation, this model succeeded in integrating
physio-logical knowledge in a manner compatible with its use in
analysing genotype · environment · management
interac-tions. This is because the driving variables can be easily
measured at the tissue level and only five parameters need to
be estimated.
The citrate and malate accumulation PBSMs have been
linked to a physicochemical model of titratable acidity and
pH based on relationships between organic acid and
salify-ing cation content (Lobit et al., 2002). This integrated
model was used to simulate the effects of nitrogen and
potassium supply on titratable acidity and sourness of peach
fruit (Habib, 2000; Lobit et al., 2006). Since citrate and
malate metabolisms are similar in different fruit species,
these PBSMs might be applicable to other fruit crops
with-out much modification.
3. Oil concentration and composition
The value of oilseed crops for human and animal food and
industrial applications is mainly determined by seed oil
con-centration and composition in terms of saturated and
unsaturated fatty acids (Kris-Etherton & Yu, 1997; Dyer
et al., 2008). Here we discuss the main assumption made in
building a PBSM of seed oil concentration and composition
for sunflower (Helianthus annuus L; Pereyra-Irujo &
Aguirreza´bal, 2007), and possible ways of developing this
model based on our knowledge of how metabolic pathways
of fatty acid biosynthesis are regulated.
Seed oil concentration In contrast to other oilseed species
(Green, 1986; Piper & Boote, 1999; Thomas et al., 2003),
in sunflower (Helianthus annuus L.) both the quantity of oil
per seed and seed oil concentration are largely independent
of temperature for daily average temperatures below 30C
(Izquierdo et al., 2002; Rondanini et al., 2003, 2006). In
the field, sunflower seed oil concentration is usually
deter-mined by the amount of radiation intercepted per plant
during the seed-filling period (Aguirreza´bal et al., 2003),
mainly because of its effect on the duration of seed filling
(Izquierdo et al., 2008). These results were used to establish
a simple PBSM of variation in seed oil concentration
for field-grown sunflower (Fig. 4a; Pereyra-Irujo &
Aguirreza´bal, 2007). The model simulated variations in seed
oil concentration for a wide range of environmental
condi-tions, including several sites, years, sowing dates and sowing
Pyruvate
Oxalo-acetate Citrateth Citrate
Pyruvate dehydrogenase Acetyl-CoA Cytosol Malic NADH NAD+ CO2 NADH NAD+ CO2 CoA-SH Citrate Malate Cis-aconitate Fumarate Aconitase Isocitrate dehydrogenase Malate dehydrogenase Aconitase synthase Mitochondria Isocitrate
Succinate Succinate dehydrogenase NADH NAD+ enzyme NAD+ NADH Oxalosuccinate FAD+ FADH α-Ketoglutarate Succinyl-CoACoA-SH CO2 NAD + NADH GDP GTP CO 2 Pyruvate ϕ4 Resp = ϕ1+ 2ϕ2+ ϕ3 ϕ6 ϕ1 Malate Citrate ϕ3 5 ϕ2 ϕ1 ϕ5 40 1993 Citrate concentration (mol g –1 FW) 0 5 10 15 20 25 30 35 10 15 20 25 80 100 120 140 160 r2 = 0.52 Slope = 0.51 RRMSE = 38.6% 1:1
Simulated citrate concentration (mol g–1 FW)
0 5 10 15 20 25
Simulated citrate concentration
(mol g –1 FW) 0 5 Leaf to fruit ratio 6 18 30 1993 1996
Time after bloom (d) (c)
(b) (a)
(d)
Fig. 3 Citrate model of fruit citrate metabolism. (a) Schematic representation of the citrate cycle. Enzymes are indicated in italics. (b) Simplified representation adopted in the citrate model where chains of reactions involved in the conversion of malate and pyruvate into citrate are represented as unique reactions. u1, all
reactions involved in the synthesis of citrate from pyruvate and malate; u2, all reactions involved in citrate degradation; u3, flux
through the malic enzyme; u4, u5and u6, transport of pyruvate,
malate and citrate, respectively, between cytosol and mitochondria. Respiration (Resp) is the total amount of CO2released by all
reactions (reproduced from Lobit et al., 2003, by permission of Oxford University Press). (c) Simulated (lines) and observed (symbols) fruit citrate concentration vs time after bloom (circles, thin line, six leaves per fruit; triangles, medium line, 18 leaves per fruit; squares, thick line, 30 leaves per fruit). (d) Simulated vs observed citrate concentration at maturity for the peach cv Suncrest grown in 1993 and 1996 in an orchard in Avignon, France (adapted from Wu et al., 2007, by permission of Oxford University Press). This dataset was not used for model development or calibration.
densities (Fig. 4b). The simulated results confirmed that
environmental variation in seed oil concentration is mostly
the result of variation in seed mass and not in oil content
per seed.
Although the metabolic pathways for storage lipid
forma-tion are known along with the genes coding for most of the
enzymes involved (Mekhedov et al., 2000; Voelker &
Kinney, 2001), the mechanisms that control and regulate
fatty acid synthesis are only beginning to be understood
(Shen et al., 2006; Wang et al., 2007; Baud & Lepiniec,
2010). Top-down metabolic control analysis, where
meta-bolic pathways are simplified by dividing them into blocks
of reactions (Brand, 1996), has been used to quantify the
regulation of fatty acid and lipid biosynthesis in tissue
cul-tures of olive (Olea europaea L.) and oil palm (Elaeis
guineensis Jacq.). For this, the overall rate of lipid
biosynthe-sis was modified by changing the temperature or by
introducing oleate to alter the amount of intermediates in
the experimental system (Ramli et al., 2002a,b). The
com-plete pathway of lipid biosynthesis was summarized as two
blocks of reactions, the pathway of fatty acid synthesis in
the plastid and the Kennedy pathway of lipid assembly in
the endoplasmic reticulum, connected by a single
interme-diate pool of cytosolic acyl-coenzyme A. These studies
provided an overview of the control structure of the whole
pathway and gave quantitative information on the control
exerted by large blocks of the complex lipid biosynthesis
pathway (Ramli et al., 2005, 2009). A similar top-down
approach has been used to analyse the metabolic control of
lipid biosynthesis in rapeseed (Weselake et al., 2008).
In oil palm fruits, a statistical learning approach has also
been used to infer a Boolean lipid–metabolite network
using measurements of labelled metabolites after adding
[1-
14C] acetate (Quek et al., 2005). This approach allowed
the interactions between major lipid metabolites to be
ranked so as to discover control points in the pathway and
how they are modified by environmental change
(tempera-ture). The drawback of both this approach and top-down
metabolic control analysis is their limited predictive power
because of the lack of information on regulation, but they
clearly suggest that simplifying approaches, considering
large sections of lipid biosynthesis pathways as ‘blocks’,
52 42 44 46 48 50 52 Si m u la te d g rai n oil (% o f DM) 42 44 46 48 50 r 2 = 0.68 Slope = 0.90 RRMSE = 3.3% Degree-day accumulation Sowing date Phenology Leaf area growth Daily radiation interception Intercepted radiation
during critical periods
Minimum temp.
during critical periods
Mean temperature Plant density Incident radiation Grain number Grain weight Grain yield Grain yield
Observed grain oil (% of DM)
40 50 60 70 Slope = 1.03 RRMSE = 7.6% Minimum temperature Intermediate variables Oleic acid Oil % Tocopherol Tocopherol Linoleic acid
Grain and oil quality
Linoleic acid
Observed linoleic : oleic acid ratio (%) 20 30 40 50 60 70 Si m u la ted l inoleic : olei c ac id r a ti o ( % ) 20 30 GW IR OP = min 36.4 + 0.5 ,50 PD LA = 84.575 – 0.938 × OA min OA = min –23.1+ 3.4 + 0.9 ,54.2 OP OP –0.125 × GW 100 TC = 563 +1451 × e (a) (c) (b) r2 = 0.98 0.9 0.6 0.7 0.8 0.9 Si m u la ted toc oph er ol ( m g g –1 oil ) 0.6 0.7 0.8 Slope = 1.04 RRMSE = 5.5%
Observed tocopherol (mg g–1oil)
r2 = 0.84
Fig. 4 Sunflower model of seed yield and oil composition. (a) Schematic representation of the model (reproduced from Pereyra-Irujo & Aguirreza´bal, 2007, with permission from Elsevier). Input variables (outside the dashed lines), intermediate variables, output variables (seed yield, seed number m–2, average seed dry mass and seed oil quality) and their relationships are represented. (b) Simulated (lines) vs observed (symbols) oil concentration (OP), linoleic (LA) : oleic (OA) acid ratio, and tocopherol concentration (TC) for mature sunflower seed obtained in the field at Balcarce, Argentina, with different sowing dates and plant density treatments. This dataset was not used for model development or calibration. (c) Model formula to calculate OP, LA, OA and TC are shown. DM, dry mass; IRGW, intercepted irradiance between 250 and 450
degree-days (Cd) after anthesis; PD, plant density; Tmin, mean daily minimum temperature between 100 and 300Cd after anthesis; GW, seed
might allow the simulation of lipid biosynthesis more
mechanistically than in the current sunflower model of
Pereyra-Irujo & Aguirreza´bal (2007).
Seed oil composition In sunflower, seed oil composition is
relatively unaffected by light intensity or nitrogen supply
(Tre´molie`res et al., 1982; Steer & Seiler, 1990), but it is
modified by temperature during the seed-filling period
(Rondanini et al., 2003; Sobrino et al., 2003; Thomas et al.,
2003). When grown in the field or in growth chambers with
different day–night temperature regimes, the relative
pro-portion of oleic (C18:1) and linoleic (C18:2) acids, which
account for c. 90% of the total fatty acid content of mature
seeds, is linearly related to the minimum night temperature,
but not to daily minimum or average temperatures
(Izquierdo et al., 2002, 2006). Moreover, seed oil
composi-tion is most sensitive to night temperature during the early
seed growth period (between 100 and 300 degree-days
(Cd) after anthesis), before a significant amount of oil
accu-mulates in the seed (Izquierdo et al., 2006). Based on these
data, a PBSM of seed oil composition was developed and
coupled to the sunflower PBSM of seed dry mass and oil
concentration (Fig. 4; Pereyra-Irujo & Aguirreza´bal, 2007).
Studies of the genetic variability of the model parameters
showed that the percentage of oleic acid varies with
tempera-ture within a specific temperatempera-ture range and that this range is
under genetic control (Izquierdo & Aguirreza´bal, 2008).
The rate of change in the percentage of oleic acid with
tem-perature was negatively correlated with the difference
between the minimum and maximum temperatures. More
recently Echarte et al. (2010) proposed an equation to
account for the additive effect of temperature and
inter-cepted radiation on the percentage of oleic acid for
sunflower.
A more mechanistic way of modelling seed oil
composi-tion would be to model the activity of fatty acid desaturases,
which are responsible for the effect of temperature on the
oleic : linoleic ratio (Sarmiento et al., 1998; Tang et al.,
2005; Byefield & Upchurch, 2007). Two types of
desatur-ase are expressed in the seed of most oilseed species. It has
been proposed that one contributes to a basal, constitutive
rate of fatty acid desaturation occurring at high
temper-atures, whereas the second is responsible for the high rate of
fatty acid desaturation at low temperatures when it is
induced (Williams et al., 1992; Sarmiento et al., 1998).
The microsomal and oil body fractions of fatty acids should
also be considered since temperature has different effects on
the desaturation of these two pools (Sarmiento et al.,
1998). Besides the direct effect of temperature on fatty acid
desaturase regulation, changes in O
2solubility with
temper-ature can indirectly affect the activity of the fatty acid
desaturases (Garcia-Diaz et al., 2002; Martinez-Rivas et al.,
2003; Esteban et al., 2004). Different approaches to
model-ling O
2exchange have been reported (e.g. Ge´nard &
Gouble, 2005; Ho et al., 2011). Izquierdo et al. (2009)
suggested that the effect of intercepted radiation on fatty
acid desaturation may be the result of its effect on seed
car-bon availability, which modulates the amount of the
rate-limiting fatty acid desaturases. Simulation of fatty acid
de-saturation at the biochemical level might help to elucidate
how observed effects come about and allow further testing
of hypotheses, while analysing possible ways of genetically
modifying the response of seed oil composition to
environ-mental factors.
Seed tocopherol concentration Tocopherols (vitamin E)
are fat-soluble antioxidants which act as membrane
stabiliz-ers and are important for human health (Munne´-Bosch &
Falk, 2004; Traber & Atkinson, 2007). They are produced
only by photosynthetic organisms and accumulate to high
concentrations in the seeds of most oilseed crops and in the
pericarp and embryo of cereal grains. Although the
path-ways, including the genes and the enzymes they encode, of
tocopherol biosynthesis are known in A. thaliana, very little
is known about the enzymes controlling the
availabil-ity ⁄ production of the major precursors of tocopherol and
how they are regulated by environmental and endogenous
signals (DellaPenna & Last, 2006). So it is not possible to
develop a mechanistic PBSM of tocopherol concentration
and composition. However, a unique relationship,
indepen-dent of environment and genotype, between the quantity of
oil per seed and the tocopherol concentration in oil has
been reported for sunflower (Nolasco et al., 2004;
Izquierdo et al., 2007) and this was incorporated into the
sunflower PBSM described earlier (Fig. 4). This has allowed
fairly accurate simulation of the variations in tocopherol
concentration observed in the field (Pereyra-Irujo &
Aguirreza´bal, 2007).
4. Protein concentration and composition
Grain and seed protein concentration Most of the
nitro-gen in mature grains and seeds (typically between 50 and
80% for cereals) is already assimilated by the plant before
grain or seed filling begins. Under most conditions, grain
and seed nitrogen content is determined by the availability
of endogenous and soil nitrogen to the plant, and not by
the capacity of the grain or seed to assimilate nitrogen
(Lhuillier-Soundele et al., 1999; Martre et al., 2003).
Several whole-plant models simulating seed (Boote et al.,
1998) or grain (Yin & van Laar, 2005; Martre et al., 2006;
Hammer et al., 2010) yield also simulate crop nitrogen
dynamics primarily because crop nitrogen status greatly
influences canopy photosynthesis, respiration and leaf
expansion and senescence, all pivotal processes for
simulat-ing environmental variations in crop biomass and grain or
seed yield. For the same reason, remobilization of nitrogen
from vegetative organs to grains, which causes
photo-synthetic capacity to decline and enhances leaf senescence,
is considered in most crop models. Some models also
describe nitrogen dynamics with the aim of simulating grain
nitrogen concentration (Sexton et al., 1998a; Asseng et al.,
2002; Martre et al., 2006). To the best of our knowledge,
no fruit nitrogen concentration PBSM has been developed
as yet. Whole-plant models of nitrogen economy are
beyond the scope of this review and have been reviewed
pre-viously (Jeuffroy et al., 2002; Priesack & Gayler, 2009).
Grain and seed protein composition Storage proteins
account for 70–80% of the total quantity of reduced
nitro-gen in mature grains of cereals and seeds of grain legumes,
and their composition greatly influences processing and
nutritional quality. Environmentally induced changes in
protein composition are the result of the altered expression
of genes encoding storage proteins, in response to signals
that indicate the relative availability of nitrogen and sulphur
(Bevan et al., 1993; Peak et al., 1997; Chiaiese et al., 2004;
Hernandez-Sebastia et al., 2005). These signals trigger
transduction pathways in developing grains or seeds that, in
general, balance the storage of nitrogen and sulphur to
maintain homeostasis of the total amount of protein per
grain or seed (Tabe et al., 2002; Islam et al., 2005).
Molecular aspects of the signal transduction pathways are
still largely unknown (Shewry et al., 2001; Tabe et al.,
2002). However, it has been shown that, in both cereals
and grain legumes, the amount of the different storage
pro-tein classes scales with the total amount of nitrogen per
grain (Sexton et al., 1998b; Landry, 2002). It has been
hypothesized that these allometric relationships are
emer-gent properties of a nutritional transcriptional regulatory
network (Martre et al., 2003; Ravel et al., 2009). These
relationships are independent of nitrogen and water supply
and temperature during grain or seed filling and are similar
for developing and mature grains or seeds (Daniel &
Triboi, 2001; Triboi et al., 2003). Therefore, the regulatory
network controlling expression of storage protein genes is
coordinated so that the grain or seed reacts in a predictable
manner to nitrogen availability, yielding a metamechanism
at the grain or seed level.
These allometric relationships between the total amount
of nitrogen per grain and the amount of the different storage
protein fractions have been used to develop a simulation
model of gliadin and glutenin accumulation in developing
wheat grain (Martre et al., 2003). This model has been
implemented in the wheat simulation model SiriusQuality1
and has been evaluated against a wide range of values for
nitrogen supply, post-anthesis temperature and water supply
(Martre et al., 2006). Considered in this model is
accumula-tion of structural proteins and carbon during the stage of
endosperm cell division and endoreduplication, and of
stor-age proteins and starch after the end of endosperm cell
division. Accumulation of structural proteins and carbon
(per grain) is assumed to be sink-driven and is determined
by temperature. By contrast, accumulation of storage
pro-teins and starch is assumed to be source-driven (i.e.
independent of the number of grains per unit ground area)
and is set daily to be proportional to the current amount of
nonstructural (i.e. transferable) shoot nitrogen.
Nitrogen supply determines the degree of protein
accu-mulation in the grain or seed and its gross allocation
between storage protein fractions, but at a given
concentra-tion of nitrogen, sulphur supply fine-tunes the composiconcentra-tion
of protein fractions by regulating the expression of
individ-ual storage protein genes (Hagan et al., 2003; Chiaiese
et al., 2004). The next step would thus be to model the
effect of sulphur availability on the allocation of storage
proteins and how this interacts with nitrogen availability
(Aguirreza´bal et al., 2009).
IV. Next steps in modelling the size and
composition of fruit, grain and seed
1. Towards integrated process-based simulation
models
Developing the PBSMs reviewed here represents an
impor-tant step towards the integration of multiple quality traits
defining fruit, grain and seed end-use value. Such
integra-tion needs to consider complex interacintegra-tions and feedback
regulation across the various organizational levels. A first
step towards this goal is the integrated peach fruit model
(Lescourret & Ge´nard, 2005) that predicts the size, dry
matter concentration and sugar concentration and
composi-tion of peach fruit by coupling three PBSMs. A carbon
PBSM, which calculates daily carbon availability and
allo-cates carbon among vegetative and reproductive organs
(Lescourret et al., 1998), determines the daily carbon flux
to any average fruit on the stem. The SUGAR model
described earlier (Ge´nard & Souty, 1996; Ge´nard et al.,
2003) uses this daily influx of carbon as the input for
simu-lating the metabolic transformations between individual
sugars. The model of fruit expansion and water fluxes
(Fishman & Ge´nard, 1998) uses the osmotic concentration
of the fruit flesh computed by SUGAR to simulate the
trig-gering of water influx to the fruit, which induces fruit
expansion driven by fruit turgor pressure.
This linked model simulated the complex behaviour of
fruit growth and quality traits in response to environmental
fluctuations (radiation, temperature, air-fruit vapour
pres-sure deficit and soil water deficit) or modified fruit load
(Lescourret & Ge´nard, 2005). These responses were not
accounted for by any of the three PBSMs taken separately,
but resulted from feedback regulation, leading to
compen-sation, adaptation and delayed responses (Ge´nard et al.,
2009). In the future, the implementation of the fruit cell
division (Bertin et al., 2003b) and endoreduplication
(Bertin et al., 2007) models into the integrated peach fruit
model should allow cell population models to be linked
with models describing fruit expansion and the
accumula-tion of chemical compounds (Ge´nard et al., 2007). This
will pave the way to modelling spatial heterogeneity of fruit
composition at the cell level.
An integrated model simulating grain yield (Jamieson &
Semenov, 2000) and protein concentration (Martre et al.,
2006) and composition (Martre et al., 2003) for wheat has
also been developed. The sunflower model described earlier
(Pereyra-Irujo & Aguirreza´bal, 2007) also simulates several
important quality traits besides seed yield (i.e. oil
concentra-tion and composiconcentra-tion and tocopherol concentraconcentra-tion of
seed). The development of such integrated models should
allow fruit, grain and seed end-use value to be assessed more
accurately and facilitate the study of interactions between
the physiological processes determining these quality traits
(Aguirreza´bal et al., 2009).
2. Modelling fruit, grain and seed variability at the
organ, plant and crop scales
The distribution of the size and composition of individual
fruit, grain or seed at harvest is an important factor as
grow-ers may be penalized for fruit, grain or seed that does not
meet specified standards. In the field, variability in size and
composition can emerge at several scales (Loomis et al.,
1979): at the plant level as a result of local heterogeneity in
soil properties or environmental factors; among individual
fruits, grains or seeds within a plant as a result of
physio-logical factors (e.g. distance to carbon sources or ontogenic
differences) or heterogeneity of environmental factors within
the canopy. Within fruit, grain or seed, heterogeneity is also
an issue in both physiological and quality (e.g. textural
characteristics) terms.
For most species, a large part of intraplant variability in the
size and composition of fruit, grain or seed is the result of the
timing of development of reproductive organs (Batchelor
et al., 1996; Cheng et al., 2007). This could be accounted
for by modelling the development of individual fruits, grains
or seeds (or of cohorts of organs of similar physiological age).
For indeterminate fruit species, several stochastic models
have been developed to predict the distribution of the time of
fruit set (Gary et al., 1995; Pearson et al., 1996; Lescourret
et al., 1999). For grain legumes, the development and
growth of pod cohorts were modelled using a deterministic
approach, and it was possible to simulate the changing
seed-size distribution throughout the
seed-filling period
(Batchelor et al., 1996). A similar approach was used to
model tomato fruit development and carbon accumulation
for individual inflorescences (Gary et al., 1995).
Intraplant heterogeneity in the size and composition of
fruit, grain or seed can also emerge from differences in the
microclimate (mainly temperature and the quality and
quan-tity of light) within the canopy as a result of plant architecture.
Using a three-dimensional model of radiative transfer and leaf
gas exchange (Sinoquet et al., 2001) to quantify daily carbon
assimilation of all fruit-bearing shoots of a 6-yr-old peach tree,
Walcroft et al. (2004) showed that local variations in carbon
supply are the major driver of the observed heterogeneity in
fruit size within and among fruit-bearing shoots.
Functional-structural models are being developed for peach tree (Allen
et al., 2005; Lopez et al., 2008), wheat (Evers et al., 2007,
2010; Bertheloot et al., 2008), oilseed rape (Groer et al.,
2007), barley (Wernecke et al., 2007), A. thaliana (Christophe
et al., 2008), and, more recently, kiwifruit (Actinidia deliciosa
A. Chev.) vine (Cieslak et al., 2011). The essence of
func-tional-structural models lies in their capacity to simulate
interactions between plant structure ⁄ morphogenesis and
environmental variables by describing physiological processes
at the organ level (Vos et al., 2010). As they are further
devel-oped and calibrated to include more physiological processes
(Bertheloot et al., 2008; Evers et al., 2010), and coupled with
the fruit, grain and seed models reviewed here,
functional-structural models should provide useful heuristic tools to
analyse differences in the size and composition of fruit, grain
and seed at the organ level as a function of their position
in the canopy and in response to management, genetic and
environmental factors (Allen et al., 2005).
In most fruit, grain and seed storage tissues, there are clear
spatial gradients in mitotic activity, amount of
endoredupli-cation, cell size and storage activity (Lending & Larkins,
1989; Ugalde & Jenner, 1990; Borisjuk et al., 2003). Such
gradients have important consequences, in particular, on
the textural and mechanical properties of fruits, grains and
seeds (Dexter et al., 1989; Vincent, 1991; Greffeuille et al.,
2007). Currently, PBSMs do not deal with heterogeneity
within a tissue. This might be accomplished by linking cell
division and endoreduplication models describing the
behaviour of cell populations with PBSMs describing fruit
expansion and the accumulation of chemical compounds.
The recent development of a three-dimensional physical
model of the spatiotemporal distribution of temperature
(Saudreau et al., 2007, 2009) and O
2and CO
2partial
pres-sure (Ho et al., 2011) within fleshy fruits is a major step
forward, which will allow simulation of temperature-driven
physiological processes at the cell level. Three-dimensional
models at the organ level make it possible to analyse the
effect of daily fluctuations in temperature, which is
particu-larly relevant in the context of global climate change.
3. Modelling genetic variability and use of
characterized genetic materials to test new
hypotheses
Several PBSMs are now able to predict important quality
traits as a function of the environment or management
practices. However, today few genotypic parameters (i.e.
allelic variants) can be advantageously introduced into such
PBSMs (Bertin et al., 2010). This is largely because of the
lack of genetic information on the traits and processes
included in the models, but also because most PBSMs still
lack the necessary degree of functionality. PBSMs need an
enlarged capacity to simulate the complexity of plant and
organ functioning. A stimulating challenge for modellers is
to develop algorithms able to reproduce the wide range of
real plant responses to environmental and genetic variations
with parameters based on clear genetic information.
Incorporation of genetic and genomic information on gene
action and interaction into PBSMs will help modellers
rethink and strengthen the physiological assumptions and
equations of their models and reduce uncertainty related to
differences in cultivar responses to environmental variation.
For that, the physiological basis of the trait actions and
the pleiotropic physiological connections and feedbacks
between traits should be recognized (Hammer et al., 1996).
As discussed by Boote et al. (2003), this requires close
col-laboration between geneticists, physiologists and modellers.
Modellers should, as far as possible, use
well-character-ized genetic materials. Over the last decade, near-isogenic
lines, mutants, transgenics and mapping populations have
been developed by geneticists for several traits related to the
size and composition of fruit, grain or seed. Such material
gives modellers the opportunity to evaluate the hypotheses
introduced in their model and to highlight interactions
between processes and feedback regulation (Tardieu, 2003;
Chenu et al., 2007; Luquet et al., 2007). For example, the
different mutants available for enzymes catalysing starch
biosynthesis will be invaluable in developing and evaluating
a PBSM of starch biosynthesis, which would be expected to
reproduce the pleiotropic effects usually arising from single
mutations in the starch biosynthesis pathways. Mapping
populations for which collocations have been found
between starch biosynthetic enzymes and amylose and
amy-lopectin content and composition (The´venot et al., 2005;
Konik-Rose et al., 2007) would also be useful for evaluating
such a model. Similarly, mutant lines and transgenic plants
for structural or regulatory genes of fatty acid desaturation
have been isolated and characterized for all major oilseed
species (Drexler et al., 2003), and major QTLs for high
oleic acid content collocating with the two major fatty acid
desaturases have been found (Pe´rez-Vich et al., 2002;
Hobbs et al., 2004; Hu et al., 2006). Such materials will be
particularly useful in evaluating a biochemical model of
fatty acid accumulation and desaturation and in analysing
the genetic determinism of its parameters.
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