Journal of Experimental Botany, Vol. 49, No. 321, pp. 721–730, April 1998
Diurnal nitrate uptake in young tomato (Lycopersicon
esculentum Mill.) plants: test of a feedback-based model
Raúl Cárdenas-Navarro, Stéphane Adamowicz1and Paul Robin
Ecophysiologie et Horticulture, INRA, domaine St Paul, site AGROPARC, F-84914 Avignon Cedex 9, France
Received 25 May 1997; Accepted 14 November 1997
Abstract
A simple model is proposed to describe diurnal net
nitrate uptake rate patterns observed experimentally
on young plants grown under constant non-limiting
nutrition. It rests on two hypotheses: net uptake rate
is under negative feedback control by internal plant
nitrate content, and nitrogen metabolism occurs only
during the light period. The model parameters were
determined from the results of three independent
experiments performed under non-disturbing conditions in a growth room at constant air and solution
temperatures. Net hourly nitrate uptake rate was
measured through a diurnal cycle and after an
extended 28 h period of darkness. It increased continuously during the light period and decreased during
the dark period. Under prolonged darkness, net uptake
declined to an asymptotic positive uptake rate of about
10−5 mol h−1 g−1 total plant dry weight. The measured
hourly nitrate uptake rate values were consistent with
independent determinations of long-term nitrate and
total N accumulations in the plant. Realistic simulations of experimental data are achieved with the proposed model. Furthermore, the maintenance of a
positive net uptake rate, measured in non-growing
plants subjected to prolonged darkness, is explained
in the model by the continuous increase of plant water
content. The importance of the diurnal variations of
plant water content for nitrate uptake rate is emphasized and gives consistency to the homeostasis hypothesis of the model. The diurnal changes in nitrate
uptake predicted by the model are strongly dependent
on the assumption made for diurnal changes in nitrate
assimilation. While the purely photosynthetic assumption is convenient, a more realistic metabolism submodel is needed.
Key words: Light/dark cycles, day, night, water content,
nitrogen, hydroponic.
Introduction
During plant growth, nitrate uptake is mainly determined
by dry mass production in relation to ontogeny and
environmental parameters (Imsande and Touraine, 1994).
However, at an hourly time scale, under constant nutrition, uptake rate undergoes continuous variations
(Clement et al., 1978; Triboi-Blondel, 1979; Pearson et al.,
1981; Le Bot and Kirkby, 1992; Delhon et al., 1995a;
Andriolo et al., 1996), with peak values during day time,
and lowest values during the night. This effect, clearly
related to light interception, is based on still unclear
mechanisms. On a large time scale, nitrate uptake correlates with transpiration, but it has been shown that in the
diurnal cycle they are independent ( Triboi-Blondel, 1979;
Le Bot and Kirkby, 1992; Delhon et al., 1995b; Andriolo
et al., 1996). As nitrate uptake also correlates with CO
2
assimilation (Clement et al., 1978), an indirect control by
photosynthesis has been suggested ( Wild et al., 1987).
The flow of carbon compounds from the shoots might
regulate nitrate uptake, an ATP-dependent process,
through root respiration (Glass, 1989). Indeed, diurnal
root respiration seems closely related to nitrate uptake
rate (Hansen, 1980). However, this hypothesis is still
under discussion, as uptake regulation is expected to
1 To whom correspondence should be addressed. Fax: +33 4 90 31 60 28. E-mail: [email protected]
Abbreviations and units: wn, net nitrate uptake rate (mol plant−1 h−1); Qn, net nitrate uptake rate g−1 whole plant dry weight (mol g−1 h−1); wr,
nitrate reduction flux (mol plant−1 h−1); a, parameter (mol g−1 h−1); b, parameter (m3 g−1 h−1); W, whole plant dry weight (g plant−1); V, plant water
(m3 plant−1); v, water content g−1 dry weight (m3 g−1); ni, nitrate concentration in the whole plant, expressed relative to plant water (mol m−3); nt,
total nitrogen content in the whole plant (mol g−1 dry weight); nr, reduced nitrogen content in the whole plant (mol g−1 dry weight); a and b,
allometry parameters linking reduced nitrogen concentration to whole plant dry weight.
© Oxford University Press 1998
722
Cárdenas-Navarro et al.
occur through more specific mechanisms (Glass, 1989;
Imsande and Touraine, 1994).
As nitrate assimilation is mainly a photosynthetic process in non-woody plants, other hypotheses are based on
a control of nitrate uptake either by some assimilation
products, or by plant nitrate content itself. Exogenous
supply of amino acids or malate, a nitrate assimilation
by-product (Ben-Zioni et al., 1971; Touraine et al., 1988),
depress and stimulate nitrate uptake, respectively (Lee
et al., 1992; Muller and Touraine, 1992; Touraine et al.,
1992). However, during the diurnal cycle, or following
nutritional treatments, reports of correlation between root
amino acid content and nitrate uptake are conflicting
(Delhon et al., 1995a, b; Lainé et al., 1995), and malate
production is not specific to nitrogen metabolism.
Although such an hypothesis cannot be rejected, its use
in the form of a predictive model would rely on parameters that are, at present, unavailable.
A simple and more general hypothesis to explain regulation of ion uptake is based on negative feedback by the
internal ion content, as proposed for potassium (Siddiqi
and Glass, 1982–1986), chloride (Cram, 1983) and nitrate
(Scaife, 1989; Buysse et al., 1996). These models rely on
negative correlation observed between uptake rate and
plant internal ion concentration. The present paper aims
to check, during a diurnal cycle under constant nonlimiting nutrition, the existence of such a negative correlation between net nitrate uptake rate and internal nitrate
concentration in young tomato plants. Empirically determined parameters are used in a predictive model devised
to simulate plant nitrate content and uptake. Numerical
simulations are compared to experimental values.
Sensitivity of the model to growth parameters and plant
water content is emphasized.
proportional to the plant’s dry weight production:
wr=
d(nr×W )
dW
dnr
=nr×
+W×
dt
dt
dt
(2)
During growth, plant total and reduced nitrogen contents
decrease progressively. They are related to whole plant
dry mass according to allometric relationships (Lemaire
and Salette, 1984; Greenwood et al., 1990; Justes et al.,
1994):
nr=a×W−b
(3)
dW
ndr
=−abW−b−1×
dt
dt
(4)
Incorporating the above values in equation (2), the
reduction flux can be expressed as:
wr=a[1−b]×W−b
dW
dt
(5)
Variation in whole plant nitrate content is the difference
between net uptake rate and assimilation flux:
d(V×ni)
=wn−wr
dt
(6)
dV
dni
d(V×ni)
=ni
+V
dt
dt
dt
(7)
with
Since V=n×W, the upper relation can be written in
terms of whole plant dry mass (W) and water content
per unit dry weight (v):
C
D
dv
dni
d(V×ni)
dW
+v×W
=ni W
+v
dt
dt
dt
dt
(8)
From (6) and (8), it follows:
The model
C
ni W
Net nitrate uptake rate has been shown to be negatively
and linearly correlated with shoot nitrate content (Lainé
et al., 1995). In the proposed model, the plant is not
compartmented. Net uptake rate (wn) under constant
nutrition is assumed to be proportional to the whole
plant’s dry weight (W ) and negatively related to its
internal nitrate concentration (ni ):
wn=W×(a−b×ni)
(1)
For tomato plants under high nitrate nutrition, 90% of
the nitrate reduction flux (wr) occurs in the shoots
(Andrews, 1986) where it is thought to be closely coupled
to photosynthesis (Pilbeam and Kirkby, 1990). In this
model, wr is formalized as a pure photosynthetic process,
not limited by internal nitrate concentration (ni ), and
D
dv
dni
dW
+v×W
+v
=wn−wr
dt
dt
dt
(9)
Replacing wn and wr by their values in (1) and (5):
C
ni W
D
dv
dni
dW
+v×W
+v
dt
dt
dt
=W×(a−b×ni)−a[1−b]×W−b
dW
dt
(10)
The upper equation describes variations of internal nitrate
content and can be written:
C
D
dW
dni
1
(a−b×ni)−a(1−b)×W−b
=
dt
n
W×dt
−ni
C
D
dv
dW
+
n×dt
W×dt
(11)
Model of diurnal nitrate uptake 723
This differential comprises two main terms. The first
brackets enclose the balance between net uptake rate and
assimilation flux, the second brackets enclose a dilution
term composed of dry matter and water content relative
accumulation rates. Numerical solving of this equation
describes internal nitrate concentration with time. Net
uptake rate of whole plant dry weight g−1 can then be
computed according to this concentration and equation
(1):
Qn=
wn
=a−b×ni
W
(12)
Materials and methods
Experimental set-up
The nutrient film technique set-up (NFT ), placed inside a
growth room, consists of 14 horizontal PVC tubes (internal
diameter: 3.2 cm) wrapped in insulating sheaths. In each tube,
four evenly spaced (26 cm) sets of three holes (diameter: 1.2 cm)
are pierced. In each hole, a small support consisting of a PVC
tube ( length: 4 cm; diameter: 1.1 cm) tapped at the lower end
by a disc of wide-mesh permeable fabric (agryl P17 plus,
Sodoca) is inserted.
Two feeding set-ups, each comprising a tank of nutrient
solution, a centrifugal pump, distribution and recovery tubing
networks, and temperature control, are available. Each allows
the continuous injection of a nutrient solution (0.3 m3) at one
end of each culture tube (36×10−3 m3 h−1), and recycling to
the tank by gravity.
Plant material and growth conditions
Tomato seeds (Lycopersicon esculentum Mill., cv. Rondello,
Ruiter-Seeds) were directly sown in the NFT set-up, one seed
per support, without any substrate. Ten days later, thinning
was carried out to leave only one seedling per group of three
holes, so that only four evenly spaced plantlets were left per
culture tube. The plants to be retained were selected according
to the length of the first true leaf (about 1 cm).
From sowing onwards, the growth room was maintained
under continuous darkness for 3 d. After that time, a 12 h
photoperiod was applied. Photosynthetically active radiation
(PAR) was progressively increased by switching on an increasing
proportion of the fluorescent lamps: 1/4 on day 4, 2/4 on days
5 and 6, 3/4 on day 7 and 4/4 from day 8 to the end of the
culture. Maximum PAR, measured by a silicon sensor (Li-Cor
Li-190) at growth tubes level, was about 400 mmol m−2 s−1.
Hygrometry and air temperature were set to 85% and 25 °C,
respectively, from days 1 to 8, 75% and 20 °C later on.
The nutrient solution (3.0 mol m−3 NO−) was made-up with
3
deionized water and the following pure salts, in mol m−3:
KH PO , 1.0; K SO , 1.0; Ca(NO ) , 1.5; CaSO , 2.0; MgSO ,
2 4
2 4
3 2
4
4
1.5; EDTA-Fe, 43×10−3. Other trace elements following
Kanieltra formula 6-Fe (Hydro azote), were added at 0.1×10−3
m3 m−3. The nitrate-free solution was made up with the same
salts, but Ca(NO ) was omitted, while CaSO concentration
3 2
4
was increased to 3.5 mol m−3. The pH of both solutions was
4.9 and electroconductivity was 1.2 mS. Temperature of both
solutions was regulated at air temperature (20 °C from day 9).
Experiments
Three independent experiments were carried out. In the first,
plant dry weight and total and reduced nitrogen content with
time under constant nutrition were measured. At six sampling
dates (from day 12 to 28), four plants were randomly harvested.
Fresh and dry weights, total and nitrate nitrogen contents were
measured.
In the two following experiments, measurements were carried
out on day 19 when plant characteristics were the following:
plastochron index, 4.4 (base 2 cm); dry weight organ ratios (%
of whole plant), roots 12, stems and petioles 23, leaf laminae 65.
The second experiment aimed to study the relationship
between net nitrate uptake rate and plant nitrate concentration.
Measurements were made every 2 h during a 12 h light/28 h
dark period. To avoid any transplant shock, a procedure
allowing net nitrate uptake rate measurements, without any
plant handling, was devised. Without noticeably interrupting
the flow, a randomly chosen culture tube was disconnected
from the nutrient solution and connected to the nitrate-free
solution for 2 min, the solution flowing off the roots being lost,
not recycled. At the same time, plant supports were also rinsed
manually with nitrate-free solution using a laboratory washing
bottle. At the end of this period, nitrate was not detectable in
the N-free solution coming out of the culture tube. The flow of
solution was then interrupted for 30 s, during which time the
tube was drained, and re-established to an independent
experimental set-up comprising a 3 l glass vial containing about
400 g of a precisely weighed fresh nutrient solution (20 °C,
3.0 mol m−3 NO−), a micro gear pump (Micropump 81511)
3
set at a 36×10−3 m3 h−1 flow rate, and a heat exchanger
connected to a regulated water-bath to maintain the recycled
nutrient solution temperature at 20 °C. The uptake period lasted
1 h, after which pumping was switched from the nutrient
solution to the nitrate-free solution for 2 min in order to flush
all nitrate ions out of the system (pump, growing tubes etc.)
into the glass vial containing the solution, whose final weight
and nitrate concentration were measured. Net nitrate uptake
was computed from initial and final weights and nitrate
concentrations of the nutrient solution. Within 10 min after the
end of the rinsing period, all plants from the culture tube were
harvested and separated into roots, stems with petioles, and
leaf blades, which were put into sealed glass vials for fresh
weight measurements. Dry weight and nitrate content were also
measured.
The third experiment was devised to investigate nitrate and
water accumulations in non-growing plants either supplied with
nitrate or not. Plant nitrate content was monitored during 48 h
darkness at the end of day 19. After 24 h of darkness, one
group of plants was supplied with the nitrate-free solution
instead of the 3.0 mol m−3 NO− solution. Periodically, four
3
plants per treatment were randomly sampled, and their fresh
and dry weights and nitrate content were measured.
Analysis
Fresh weight of roots was obtained after spinning them dry for
2 min in a centrifuge (2 800 g). Fresh and dry weights (48 h at
105 °C ) of plant parts were measured on an analytical balance
(Mettler AE 260, sensitivity 0.1 mg). Water content was
computed as the difference between fresh and dry weights,
divided by dry weight. Plant nitrate was determined on water
extracts of the dried material, in an autoanalyser by colorimetry
of nitrite after reduction by hydrazine sulphate. Total nitrogen
content was determined according to the Dumas method (Carlo
Erba Nitrogen analyser ANA 1500). Reduced nitrogen was
computed as the difference between total and nitrate nitrogen.
724
Cárdenas-Navarro et al.
For uptake measurements, initial and final weights of solution
were measured (Sartorius MC1, model LC 6200–0F2, range
6200 g, sensitivity 0.01 g) and nitrate concentration in the fresh
and final solutions was determined according to an UV method
( Vercambre and Adamowicz, 1995).
Statistical analysis and graphs were carried out using SYSTAT
software (v 5.2.1 for the Macintosh, SPSS Inc.) and numerical
simulations using Extend software (v 3.2 for the Macintosh,
Imagine That, Inc.).
Results
Experiment 1
Plant dry weight, monitored from days 12 to 28 during
the first experiment ( Fig. 1), underwent exponential
increase, with a relative growth rate of 0.3 d−1:
W=0.00119×e0.300×d
On day 19, at which measurements were carried out in
experiments 2 and 3, predicted mean plant weight
increased from 0.356 to 0.480 g plant−1. On an hourly
basis, considering that the increase of biomass occurs
only during the 12 h photoperiod, the calculated relative
growth rate was:
Fig. 2. Relationship between whole plant nitrogen content and dry
weight (W) in experiment 1. Experimental conditions as in Fig. 1. At
each harvest, four randomly sampled plants were pooled and analysed
for total nitrogen nt (open symbols, dashed line) and nitrate nitrogen.
Reduced nitrogen nr (closed symbols, solid line) was computed as the
difference between these values. Lines are fitted according to allometry.
dW
=0.025(h−1)
W×dt
bols, dashed line), following an allometric relationship
similar to equation (3):
Plant reduced nitrogen content fitted equation (3) with
R2=0.98 ( Fig. 2, closed symbols, solid line). Values of
parameters a and b were 3.17×10−3 and 0.070, respectively. On day 19, predicted mean plant reduced nitrogen
content (nr) was 3.33×10−3 mol g−1. Total plant nitrogen
content decreased also during growth (Fig. 2, open sym-
nt=3.67×10−3×W−0.074 R2=0.97
Fig. 1. Whole plant dry weight (W ) versus time in experiment 1, from
days 12 to 28 after sowing. Growth conditions were: 12/12 light/dark
photoperiod, air and solution temperature 20 °C, relative humidity 75%,
3×10−3 mol m−3 NO− in the nutrient solution. Results are means of
3
four randomly sampled plants and vertical bars indicate SE.
(13)
Experiment 2
During the diurnal cycle on day 19, nitrate uptake rate
per unit of whole plant dry weight (Qn) showed large
variations ( Fig. 3A). It increased from 32×10−6
mol g−1 h−1, between 1 and 2 h after the beginning of
photoperiod, to 52×10−6 mol g−1 h−1 at the end of this
period. During the night, it decreased steeply to about
23×10−6 mol g−1 h−1 after 12 h, and then slowly to
12×10−6 mol g−1 h−1 after 28 h of night. Similarly, measured plant nitrate concentration (ni ) underwent a 30%
variation during the diurnal cycle (Fig. 3B). It decreased
from 49 mol m−3 2 h after the beginning of photoperiod
to 41 mol m−3 at the end of this period, increased steeply
to 63 mol m−3 after 12 h of night and then slowly to
70 mol m−3 after 28 h of darkness. As the diurnal changes
of nitrate uptake rate and internal concentration were
concomitant, they were negatively and linearly related
( Fig. 4; R2=0.83) as expected from equation (12). Values
of parameters a and b were 109×10−6 mol g−1 h−1, and
1.41×10−6 m3 g−1 h−1, respectively.
Marked differences in nitrate concentration were
observed among plant parts (Fig. 5). In leaf blades
( Fig. 5, circles), it was the lowest and exhibited a marked
diurnal pattern similar to the whole plant’s ( Fig. 3B). In
stems and petioles ( Fig. 5, squares), nitrate concentration
Model of diurnal nitrate uptake 725
Fig. 4. Relationship between net nitrate uptake rate (Qn) and plant
nitrate concentration (ni ) in 19-d-old plants (experiment 2).
Experimental conditions as in Fig. 3. Open symbols: plants sampled
during the light period; closed symbols: plants sampled during the dark
period. Solid line, computed linear regression.
Fig. 3. Diurnal course of net uptake rate (Qn, A) and plant nitrate
concentration (ni, B) of 19-d-old plants, during light and prolonged
darkness in experiment 2. Plants were grown under the conditions
stated in experiment 1 until day 18 (12 h photoperiod ). On day 19,
plants were submitted to a 12/12/16 light/dark/extended dark period.
Net uptake rate was measured on four pooled plants during 1 h with
constant air and solution temperature at 20 °C, at 13 sampling times.
Immediately after uptake measurement, plants were sampled, their
water and nitrate contents measured, and their nitrate concentration
computed from these values. Simulations of Qn (A) according to
equation (12) and ni (B) according to equation (11) with the following
parameter values: a=109×10−6 mol g−1 h−1; b=1.41×10−6
m3 g−1 h−1; a=3.17x10−3; b=0.07; dW/Wdt=0.021 h−1 ( light period).
Simulations were carried out either with a variable water content (solid
lines, dv/dt=±218×10−9 m3 g−1 h−1) as observed (see Fig. 6), or with
a constant water content (dashed lines, dn/dt=0).
was the highest and its diurnal pattern less pronounced
than in leaf blades, while in roots (Fig. 5, triangles) it
showed intermediate and more stable values. The best
correlations between uptake rate and nitrate concentration were observed for leaf blades (R2=0.85), while they
were lower, but significant (P<1%), for stems and petioles
(R2=0.54) and for roots (R2=0.57).
Plant water content (Fig. 6) underwent marked vari-
Fig. 5. Diurnal course of nitrate concentration in different parts of
19-d-old plants, during light and extended dark period in experiment 2.
Experimental conditions as in Fig. 3. Plants were separated in leaf
blades (#), stems and petioles (%) and roots (6).
ation (20%) during the 24 h diurnal cycle, with a decrease
during the light period followed by an increase during
the night period. Under the growth room climatic conditions, the water content was best fitted by two successive
straight lines of equal slope (dv/dt=218×10−9
m3 g−1 h−1) with opposite sign (Fig. 6) so that water
content was equal at the beginning of the 12 h light period
and after a 12 h dark period. Including the single data
point measured after 28 h darkness did not change signi-
726
Cárdenas-Navarro et al.
Fig. 6. Diurnal course of plant water content (v) of 19-d-old plants,
during light and extended dark period in experiment 2. Experimental
conditions as in Fig. 3. Water content (v) was computed as the ratio
between whole plant water volume and dry weight (W). Solid
line, computed piecewise linear regression by forcing intercept at
12 h: (t≤12 h) (11.4×10−6–218×10−9t)+(t>12 h)(6.36×10−6+218×
10−9t); R2=0.96.
ficantly the regression parameters. Thus, in prolonged
night, the water content appeared to increase at the same
rate, by 67% in 28 h ( Fig. 6). While these linear fits were
purely circumstantial and should not be taken as water
content models, they were conveniently used for the
purpose of simulation.
Experiment 3
At the end of day 19, nitrate and water accumulations in
plants were monitored over a 48 h dark period (Fig. 7).
Under constant nutrition (3.0 mol m−3 NO−), nitrate
3
accumulation was described by two successive linear
relationships (Fig. 7A, open symbols, solid lines) with an
intercept after 22 h of darkness and slopes of 16.8×10−6
and 6.9×10−6 mol g−1 h−1. When plants were supplied
with a nitrate-free solution between 24 and 48 h of
darkness, nitrate content increased slowly but significantly
at a 2.1×10−6 mol g−1 h−1 rate ( Fig. 7A, closed symbols,
dashed line). Water accumulation under nitrate nutrition
was also described by two successive linear relationships
( Fig. 7B, open symbols, solid lines) with an intercept after
25 h of darkness and slopes of 132×10−9 and 40×10−9
m3 g−1 h−1. Water accumulation rate was not affected
when plants were fed with a nitrate-free solution after
24 h darkness ( Fig. 7B, closed symbols, dashed line).
Simulations
Diurnal course of nitrate concentration (ni ) and uptake
rate (Qn) were simulated according to equations (11) and
(12), using the parameter values estimated in experiments
Fig. 7. Time-course of plant nitrate content (A) and water content
(v, B) of 19-d-old plants, during an extended 48 h dark period
(experiment 3). Growth conditions as in experiments 1 and 2
(temperature 20 °C, relative humidity 75%). Plants were either supplied
with 3.0 mol m−3 nitrate throughout the experiment (open symbols,
solid line), or with a nitrate-free solution from 24–48 h of darkness
(closed symbols, dashed line). Both solutions were set at 20 °C, pH 4.9
and the same overall ionic concentration. Periodically, four plants were
randomly sampled in each treatment for water (v) and nitrate content
determinations. All parameters of lines were computed by piecewise
regression: v (m3 g−1)=(t<24.6) (132×10−9t+9.58×10−6)+(t≥24.6)
[(solution 3 mol m−3) (40×10−9t+11.8×10−6)+(solution 0 mol m−3)
(46×10−9t+11.7×10−6)]; R2=0.98. After 24.6 h, slopes for the two
treatments were not significantly different. NO− (mol g−1)=
3
(t<24.7) (16.8×10−6t+544×10−6)+(t≥24.7) [(solution 3 mol m−3)
(6.9×10−6t+790×10−6)+(solution 0 mol m−3) (2.1×10−6t+907×
10−6)]; R2=0.98. Vertical bars indicate SE.
1 and 2. Simulations led to steeper changes in nitrate
concentration and uptake rate than observed during the
light period, while reasonable fits were obtained during
the night (not shown). By varying the values of each
parameter, it appeared that only the relative growth rate
affected the simulations during the day period while
having a slight influence during darkness. Thus, the best
fits between observed data and simulations during both
Model of diurnal nitrate uptake 727
day, night and prolonged darkness (Fig. 3A, B, solid
lines) were obtained by reducing the relative growth rate
from 0.025 to 0.021 h−1, all other parameters being
maintained at their experimental values.
Conversely, modifying the rate of plant water content
changes influenced the simulations during both day and
night. For a null value, i.e. (dv/dt)=0 in equation (11),
simulations showed steeper uptake rate changes than
observed (Fig. 3A, dashed line) and plant nitrate concentration was underestimated during day and overestimated
during darkness ( Fig. 3B, dashed line). Furthermore, in
prolonged darkness, the simulated nitrate concentration
tended to a higher value (about 78 mol m−3) than measured, and the predicted uptake tended to a null rate
( Fig. 3A, dashed line).
Discussion
Advantages of the experimental device and measurement’s
likelihood
Hydroponics are convenient for ion uptake rate measurements. However, due to sensitivity limits at high nitrate
concentrations (i.e. higher than 1 mol m−3), most published data on net uptake rate were obtained over periods
of 3 h or more (Scaife and Schloemer, 1994; Andriolo
et al., 1996). As plant nitrate concentration and uptake
rate vary significantly during the diurnal cycle, a shorter
period is required to minimize the bias in relationships
between plant nitrate concentration, measured at harvest,
and mean net uptake rate during the preceding period
(equation 12). Furthermore, transfer of plants from a
cultivation medium to the experimental set-up is generally
required. The resulting transplant shock may inhibit net
uptake for several hours (Bloom and Sukrapanna, 1990),
which is attributed to a dramatic enhancement of efflux
(Bouma and De Visser, 1993; Delhon et al., 1995a; Aslam
et al., 1996b). Indeed, the preliminary experiments involving transplantation resulted in very low and unrealistic
uptake rates (not shown). The experimental set-up used
in the present work provides net uptake rate measurements over 1 h periods. Furthermore, any plant manipulation, mechanical, osmotic or thermal shocks are avoided.
The realism of actual uptake rate measurements in
experiment 2 can be evaluated by comparing them with
total nitrogen accumulation during growth in experiment
1. According to equation (13) and to the dry weight
increase on day 19 (0.356–0.480 g plant−1), the N accumulation predicted from experiment 1 is 450×10−6
mol plant−1, corresponding to a mean hourly net uptake
rate of 45×10−6 mol g−1 h−1. This value fits actual
uptake rate measurements during the normal 24 h cycle
in experiment 2, which ranged from 23×10−6 to 52×10−6
mol g−1 h−1.
In experiment 2 after a 28 h dark period, an uptake
rate of 12×10−6 mol g−1 h−1 was measured (Fig. 3A).
The realism of this value can be checked in experiment
3, through plant nitrate accumulation rate after 24 h
darkness ( Fig. 7A). When plants were deprived of nitrate
in the solution, their nitrate content, approximately
1×10−3 mol g−1, increased at a 2.1×10−6 mol g−1 h−1
rate (Fig. 7A, closed symbols), corresponding to a relative
increase rate of about 2×10−3 h−1. Such increase in the
absence of external nitrate can be explained as the result
of dry matter loss through respiration. In young tomato
plants after 24 h darkness, the growth component of
respiration is null (Gary, 1988a) and the maintenance
component can be estimated at 2×10−3 g CO g−1 h−1
2
(Gent and Enoch, 1983). Applying a 0.682 conversion
coefficient to this value (Gary, 1988b), the relative dry
weight loss rate is 1.4×10−3 h−1. As it is close to the
measured increase rate of nitrate content in plants
deprived of external nitrate, it can be concluded that, in
this condition, the apparent nitrate accumulation was due
to dry weight loss through respiration. Thus, the assimilation rate was null or negligible and the difference in
nitrate accumulation rate of plants continuously fed with
nitrate (Fig. 7A, solid line) and deprived of nitrate
( Fig. 7A, dashed line) is an unbiased measure of uptake
rate in prolonged darkness (about 5×10−6 mol g−1 h−1).
Though lower than the uptake rate measured after 24 h
of darkness in experiment 2 (12×10−6 mol g−1 h−1), it
agrees with the maintenance of a positive net nitrate
uptake and with the absence of nitrate metabolism after
24 h of darkness. Furthermore, in another experiment
(not shown), plants were exposed to 15NO− (3.0 mol m−3)
3
for 5 min after 24 h of darkness, and significant amounts
of the tracer were found in all tissues, including leaf
blades.
Model hypothesis
Fundamentally, the present model is based on a homeostatic hypothesis, i.e. a regulation of plant nitrate content
exerted through negative feedback of nitrate on its own
uptake. More simple and specific mechanisms can hardly
be imagined and indeed, negative relationships between
uptake rates and the plant non-metabolized ion content
have been stated for sulphate (Clarkson, 1986), phosphate
(Lefebvre and Glass, 1982), chloride (Cram, 1983), potassium (Siddiqi and Glass, 1987), ammonium ( Wang et al.,
1993) and nitrate (Siddiqi et al., 1990; Delhon et al.,
1995a). However, for ions that undergo metabolism,
including nitrate, assimilation compounds or by-products
might be involved in uptake regulation (Clarkson et al.,
1983; Lee et al., 1992; Muller and Touraine, 1992;
Touraine et al., 1992). Whether uptake is regulated by
the non-metabolized ion or (and ) by the assimilation
products is mostly a matter of opinion, as no experimental
data have proved decisive, and both have the potential
728
Cárdenas-Navarro et al.
to explain the relationship between growth and net ion
uptake. However, feedback by the non-metabolized ion
applies also to the regulation of internal ion content.
Moreover, the only existing predictive models for potassium (Siddiqi and Glass, 1982–1986), chloride (Cram,
1983) and nitrate (Scaife, 1989; Buysse et al., 1996) are
based on this hypothesis.
For the sake of simplicity, the negative relationship
between uptake rate and plant nitrate content was
assumed linear. Experimental data were in accordance
with this assumption ( Fig. 4). However, it was observed
on a restricted range of internal nitrate content (roughly
by a factor of 2) and could be an approximation of a
more complex relationship. For instance, Siddiqi and
Glass (1982) found on a large range of root potassium
content (by a factor of 10), that the negative correlation
between potassium uptake rate and content followed an
exponential relationship.
The necessity to change the relative growth rate in
order to obtain a good fit between simulation and measured data during the day, appears as a weakness.
Nevertheless, as the growth rate was used to estimate
nitrate assimilation (equation 5), this is not necessarily
contradictory to the homeostatic hypothesis. Furthermore, as a significant uptake rate was maintained when
nitrate assimilation had ceased after 24 h darkness (exp. 3,
Fig. 7A), it can be assumed that in this condition, nitrate
uptake was not under control of nitrogen metabolism. As
this model predicts adequately a positive uptake rate in
prolonged darkness, which is only driven by plant water
accumulation, it gives consistency to the homeostatic
hypothesis.
variations of uptake rate and nitrate concentration in the
normal 24 h day cycle, and sustain uptake even when
growth has ceased in prolonged darkness. As faster water
content variations may be expected in the open field or
the greenhouse than under the mild conditions of the
growth room, the importance of this variable should thus
be stressed and predictive models of plant water content
are required.
Interaction between water content and nitrate uptake
Compartmentation
Through concentration, a link between nitrate and water
is included in the model as a simple relation between
solute and solvent. It has also been reported in terms of
osmotic regulation (Blom-Zandstra and Lampe, 1985)
and it was suggested that nitrate uptake is regulated in
accordance with plant osmotic adjustments (Steingröver
et al., 1986). In experiment 3, plant water accumulation
rate (Fig. 7B) was similar for plants fed with (open
symbols) or deprived of (closed symbols) nitrate, showing
that it was not dependent on nitrate uptake or content.
Conversely, this strengthens the role of water content
variations in nitrate uptake dynamics as it is included in
the model.
Predictive models usually overlook the importance of
water content changes on solute concentration. The effect
of diurnal plant water content changes (Fig. 6) on nitrate
uptake rate ( Fig. 3A) and concentration (Fig. 3B) can be
inferred from the comparison of simulations based on
actual (solid lines) and constant water contents (dashed
lines). It shows that changes in plant water content damp
Although plants are compartmented both at the micro
and macroscopic levels, compartmentation was not considered in our model. At first sight, it might be objected
that the low correlation between uptake rate and root
nitrate concentration is contrary to the model’s hypothesis. However, this is not necessarily the case from the
modeller’s viewpoint. As nutrient solution, roots and
shoots are in series (Morgan et al., 1973; Glass and
Siddiqi, 1984; Clarkson, 1986), it can be inferred that
uptake rate depends on the nitrate concentration gradient
between the source (nutrient solution) and the sink
(shoots). In these experiments external nitrate concentration was constant. Thus, it can be expected that in this
condition nitrate concentration changes are limited in
roots, while they are the highest in organs where assimilation takes place. Similar results have been published for
rape (Lainé et al., 1995). Conversely, Breteler and Nissen
(1982) showed that submitting plants to various external
nitrate concentrations during 6 h, induced large changes
in their root content. In this case, the uptake rate was
Nitrate assimilation model
For many non-woody plants exposed to high nitrate
nutrition, it is currently agreed that nitrogen metabolism
is mostly a photosynthetic process occurring in the shoots
(Gojon et al., 1994), as has been shown for tomato plants
(Lorenz, 1976; Pilbeam and Kirkby, 1990). This seems
confirmed in these experiments by the diurnal variation
of nitrate concentration in different plant parts ( Fig. 5).
Leaf blades, and to a lesser extent stems and petioles,
exhibited a marked diurnal pattern while roots show a
near constant concentration. In contrast, plants like
soybean reduce more than 50% of nitrate in their roots,
and this organ exhibits a marked diurnal concentration
pattern, while the content of shoots is nearly constant
(Delhon et al., 1995a). On this basis, it is acceptable to
apply a purely photosynthetic model to nitrate reduction
in tomato plants. This is a simple way to formulate the
reduction flux (equation 5) with easily measurable parameters. Nevertheless, to improve the fit between data and
simulation, it was necessary to modify the value of the
growth rate used to estimate the reduction flux. Thus, the
model turns out to be sensitive to the photosynthetic
assimilation hypothesis, and would justify a more
realistic, but still unavailable, diurnal reduction model.
Model of diurnal nitrate uptake 729
highly and negatively correlated to the root nitrate content. From the physiologist’s viewpoint, uptake takes
place across the root cortical cells’ plasmalemma, and
feedback must be exerted by solutes in the cytoplasm.
Nevertheless, according to Miller and Smith (1996) nitrate
concentration in the cytosol and even in the vacuoles is
much lower than in the whole root tissue. Thus, the whole
root nitrate content does not represent any of the compartments relevant for uptake. This paper does not provide any physiological explanation to this compartmental
behaviour and further research is required on the mechanisms of internal nitrate transport to clarify this problem.
Model enhancements
The formulation of this model is not suitable in the case
of variable nitrate concentration in the solution. Uptake
is a net effect between independent influx and efflux
(Clarkson, 1986; Aslam et al., 1996a). The former is
usually formalized following the mechanistic MichaelisMenten kinetics, either dual or with a linear component
( Kronzucker et al., 1995; Peuke and Kaiser, 1996), the
nutrient solution concentration being the substrate. The
latter is formalized as a passive leak, only dependent on
plant internal concentration (Breteler and Nissen, 1982;
Mackown, 1987; Teyker et al., 1988). Some reports
indicate also a negative relationship between nitrate influx
and internal nitrate concentration (Siddiqi et al., 1990;
Delhon et al., 1995a). Thus, it is probably necessary to
model independently influx and efflux to simulate net
nitrate uptake rate under conditions where both light and
external ion concentration are changing. Furthermore,
since nitrate influx is dependent on ATP supplied by root
respiration, an estimation of this flux determines also the
energy cost of net uptake (Johnson, 1990; Bouma and
De Visser, 1993), a relevant information for modelling
plant C–N interactions.
Conclusion
This model illustrates the possibility of simulating diurnal
net uptake rate patterns on the basis of two simple
hypotheses, with statistically estimated parameters. While
the purely photosynthetic nitrate assimilation sub-model
is disputable and should be improved, the homeostatic
hypothesis for nitrate concentration is supported experimentally by (1) a negative correlation between uptake
rate and internal nitrate concentration and (2) the maintenance of uptake in absence of nitrate reduction. An
important consequence of homeostasis is the resulting
influence of plant water on nitrate content and uptake.
As plant water content was changing fast in the diurnal
cycle, it is considered that its relationship with solute
accumulation should be more extensively studied and
explicitly considered in predictive models.
Acknowledgements
J Fabre is gratefully acknowledged for his help in putting
together the experimental set-up and looking after the crops.
Thanks to J Fabre and J Le Bot for their help during the
uptake measurements. During this research, R CárdenasNavarro received a Mexican CONACYT fellowship.
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