Annals of Botany 114: 1555–1570, 2014
doi:10.1093/aob/mcu203, available online at www.aob.oxfordjournals.org
VIEWPOINT
Breaking conceptual locks in modelling root absorption of nutrients: reopening
the thermodynamic viewpoint of ion transport across the root
Erwan Le Deunff1,2,* and Philippe Malagoli3,4
1
Université de Caen Basse-Normandie, UMR EVA, F-14032 Caen cedex, France, 2INRA, UMR 950,
Écophysiologie Végétale & Agronomie Nutritions NCS, F-14032 Caen cedex, France, 3Université Blaise Pascal-INRA,
24, avenue des Landais, BP 80 006, F-63177 Aubière, France and 4INRA, UMR 547 PIAF,
Bâtiment Biologie Végétale Recherche, BP 80 006, F-63177 Aubière, France
* For correspondence. E-mail: [email protected]
Received: 31 March 2014 Returned for revision: 1 July 2014 Accepted: 29 August 2014
† Background The top-down analysis of nitrate influx isotherms through the Enzyme-Substrate interpretation has
not withstood recent molecular and histochemical analyses of nitrate transporters. Indeed, at least four families of
nitrate transporters operating at both high and/or low external nitrate concentrations, and which are located in
series and/or parallel in the different cellular layers of the mature root, are involved in nitrate uptake. Accordingly,
the top-down analysis of the root catalytic structure for ion transport from the Enzyme-Substrate interpretation of
nitrate influx isotherms is inadequate. Moreover, the use of the Enzyme-Substrate velocity equation as a single reference in agronomic models is not suitable in its formalism to account for variations in N uptake under fluctuating
environmental conditions. Therefore, a conceptual paradigm shift is required to improve the mechanistic modelling
of N uptake in agronomic models.
† Scope An alternative formalism, the Flow-Force theory, was proposed in the 1970s to describe ion isotherms based
upon biophysical ‘flows and forces’ relationships of non-equilibrium thermodynamics. This interpretation describes,
with macroscopic parameters, the patterns of N uptake provided by a biological system such as roots. In contrast to the
Enzyme-Substrate interpretation, this approach does not claim to represent molecular characteristics. Here it is shown
that it is possible to combine the Flow-Force formalism with polynomial responses of nitrate influx rate induced by
climatic and in planta factors in relation to nitrate availability.
† Conclusions Application of the Flow-Force formalism allows nitrate uptake to be modelled in a more realistic
manner, and allows scaling-up in time and space of the regulation of nitrate uptake across the plant growth cycle.
Key words: Ion uptake isotherms, Enzyme-Substrate interpretation, Flow-Force interpretation, nitrate uptake regulation,
N uptake modelling, functional–structural plant model, root development, N uptake efficiency, Brassica napus.
IN T RO DU C T IO N
The cellular uptake of nitrate by plant roots can be studied via two
main approaches. The first (called top-down) consists of following the kinetics of nitrate absorption (defined as response curves
of gross or net nitrate influx to external nitrate concentrations) at
the root level to characterize the absorption process through
adjustment of a theoretical model to the kinetic data (Epstein,
1966, 1972). The second approach (called bottom-up) consists
of identifying the carriers involved in the absorption process
and their location in the root system sub-structures using molecular and histochemical tools and genetic methods (Filleur et al.,
2001; Liu and Tsay, 2003; Orsel et al., 2004; Li et al., 2007).
Although these two approaches have generated significant knowledge about ion transport such as the nitrate uptake process in roots,
two questions still remain:
(1) Is it possible to bridge these two approaches? In other
words, is it possible to calculate utilizable parameters of nutrient absorption from knowledge of the molecular and structural
characteristics of ion transport in the system or, reciprocally,
to deduce the molecular and structural characteristics of the
system from the kinetic data?
(2) Is it relevant to use velocity equations, established with
tracers in controlled laboratory conditions with standardized
young plant canopies over short time periods, to predict ion
absorption (including nitrate) under field conditions throughout the growth cycle when climatic conditions are fluctuating?
To clarify the first question it is necessary to re-open an old
debate about interpretation of ion isotherms measured at the
root level. At the time, the fundamental question was how to
scale-up from ion transport into plant cells to ion transport into
tissue or complex organs such as roots. From the different interpretations used to explain ion isotherms (Baker, 1988), the
‘Enzyme-Substrate’ and ‘Flow-Force’ interpretations warrant
consideration (Epstein, 1966, 1972; Thellier, 1970, 1973).
Although these two interpretations model the same data points
of ion absorption curves, they differ completely in their goals
and implicit assumptions (Supplementary Data Text S1 and S3).
Indeed, the Enzyme-Substrate interpretation infers that transporters function as an enzymatic system whereas the Flow-Force
interpretation (refined and updated from the electrokinetic interpretation of ion transport isotherms; Supplementary Data Text
S2) relies upon biophysical laws established from ions flux
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Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
CO N V E N T I O N A L M O D E L L I N G O F T H E IO N
UP TA K E K IN E T I C DATA I N P L A NT ROOT S
Contrary to the one-way rate of diffusion across a membrane
based on Fick’s equation, which corresponds to linear behaviour
of the solute flow when it is plotted against external concentration of the solute (Stein, 1967; Neame and Richards, 1972a),
the diffusion across a membrane facilitated by a transporter is
non-linear and in most cases exhibits saturation phenomena
(Supplementary Data Text S1). In this case, experimental
points of the influx rate plotted against external solute concentration can be adjusted mathematically with a rectangular hyperbola (Fig. 1). Fitting this theoretical model to experimental data
provides values of the parameters, Vmax and Km, derived from
the Michaelis – Menten velocity equation (Text S1). Modelling
kinetic data with the Michaelis – Menten equation assumes that
transporters within the root epidermal membrane act as purified
enzymes in vitro with excess substrate in precisely defined experimental conditions: pH, pressure and temperature (CornishBowden et al., 2004). Likewise, in the case of carrier-mediated
diffusion across a membrane, a set of simplifying conditions
must be satisfied ( presented in Table 1) so that the equation
can be applied, even though most of the time these are not met
in a complex system such as plant roots (Neame and Richards,
1972a; Schachter, 1972; Hill et al., 1977; Thellier et al., 2009).
Moreover, a rectangular hyperbola of Enzyme-Substrate kinetics
is not always observed in plots of biochemical reactions because
sigmoid shapes are also obtained: these are not always the consequence of an allosteric regulation of an enzyme (Garraham
and Glynn, 1967; Hill et al., 1977; Desimone and Price, 1978;
Vincent and Thellier, 1983; Vincent et al., 1988a, b; CornishBowden et al., 2004). Such differences between the conditions
NO3 influx (mol h–1 g–1 root d. wt)
measurements at the root level without any deduction or
characterization of transport systems acting at the cellular level
(see Text S1 and Text S3). Accordingly, for the plant nutrition
biologist the question is: which is the more suitable interpretation
to model ion uptake? Even though the Enzyme-Substrate interpretation has been chosen preferentially by biologists as the
conceptual framework to study ion transport at the cellular and
molecular levels, the absence of any real debate in the last
40 years has not allowed objective resolution of the issue from
a biophysical viewpoint (Anderson, 1973; Baker, 1988; Tinker
and Nye, 2000a).
In line with the first question, the second question examines
whether microscopic parameters of the Enzyme-Substrate velocity equation (maximum uptake, Vmax and apparent affinity
constant, Km) are more suitable to model N uptake in field conditions rather than the macroscopic parameters (root conductance,
L ′ and ordinate to origin, K ′ ) provided by the Flow-Force interpretation. Indeed, extending a single velocity equation from controlled conditions in the laboratory to plants growing in the field
under varying climatic and soil conditions (soil pH, temperature,
pressure, water and ion availability, soil structure-texture, etc.) is
challenging by applying Enzyme-Substrate parameters (Vmax
and Km). By contrast, the macroscopic parameters (L ′ and K ′ )
derived from the Flow-Force interpretation appear more suitable
to describe and study the changes in thermodynamic parameters
involved in the root catalytic structure for ion transport. However,
to be usable, the Flow-Force formalism must be combined with
polynomial functions that describe the response curve of the ion
uptake rate to environmental and in planta factors ( Le Deunff
and Malagoli, 2014; Malagoli and Le Deunff, 2014). Another
challenge for long-term experiments conducted in field is that
the absorption of the plant (function) cannot be separated from
changes in root architecture (structure). In other words, changes
of time scale under field conditions also need to deal with functional and structural compensation mechanisms in the short and long
term that result from responses to changes in climatic conditions
as well as changes in root age and N status (Warncke and Barber,
1974; Edwards and Barber, 1976; Bhat et al., 1979a; Gao et al.,
1998; Glass, 2003; Robinson, 2005).
These questions and their associated answers are of critical
importance as they directly influence the methods for improving
the use of soil resources by crops and, ultimately, the development of a sustainable agriculture in the context of global
climatic changes. Hence, it is likely that reopening the debate
on the restricted applications of the Enzyme-Substrate interpretation via a new perspective on ion isotherms (using nitrate as an
example) is one of the key factors that will help us to develop new
scientific tools and envisage realistic, applicable and efficient
plant breeding approaches.
180
A
160
Mechanism I
140
120
100
80
60
40
20
0
0
NO3 influx (mol h–1 g–1 root d. wt)
1556
300
250
B
500
750
1000
Mechanism II
250
200
150
100
50
0
0
2000
4000
6000
Nitrate concentration (M)
8000
F I G . 1. Original data of nitrate influx rate in Brassica napus (Faure-Rabasse
et al., 2002). Plantlets were subjected to nitrogen deprivation for 7 d (non-induced
plants) or transferred to a solution of KNO3 at 1 mM over 1 d prior to 15N influx rate
determination (induced plants). Immediately after these pretreatments, the seedling roots were rinsed twice for 1 min in 1 mM CaCO3 solution at 20 8C. They were
then immersed in the 15N-labelled uptake solutions for 5 min containing different
concentrations of nitrate comprising between 0 and 1 mM nitrate (A) and 1 and
7.5 mM nitrate (B). Roots were rinsed twice for 1 min in CaCO3 solution at
4 8C to desorb 15NO3– contained in free space. Note that in the low range of
nitrate concentration, experimental points were fitted with a decimal logarithmic
function.
TA B L E 1. Set of simplifying conditions to satisfy the use of the
Michaelis– Menten velocity equation to describe the kinetics of a
carrier-mediated uptake process in plant cells or plant roots
(Neame and Richards, 1972; Schachter, 1972; Hill et al., 1977).
Hypotheses of validity
Kinetic
characteristics
Carrier
characteristics
Root structure
H1: The uptake reaction is at equilibrium
or H2: The uptake process takes places under
quasi-stationary conditions
H3: The uptake kinetic parameters are constant along
the root
H4: A single carrier is responsible for uptake
or H5: several identical carriers are responsible for
uptake
H6: The location of the carrier(s) in root cellular layers
has no effect on carrier characteristics (affinity etc.)
H7: The stochastic changes in the conformation of the
carrier(s) are very rapid
H8: The carrier(s) are arranged in parallel in the
epidermis root membrane
H9: Diffusion constraints are negligible
that satisfy Enzyme-Substrate kinetics and soil solution conditions raise questions about the applicability of the widely
used Enzyme-Substrate interpretation of ion uptake transporters
(Dainty, 1969b; Thellier, 1973; Tinker and Nye, 2000a).
Enzyme-Substrate approach: the functional viewpoint of root
epidermal cell carriers
For some 40 years, the use of radioactive or stable tracers of the
major ions present in soil such as 86Rb+ or 42K for potassium, 13N
and 15N for nitrate, 35SO24 – for sulphate and 32PO24 – and 33PO24 –
for phosphate has allowed exploration of the behaviour of ion
fluxes across complex biological systems such as plant roots
(Bieleski, 1973; Lee and Drew, 1986; Kochian et al., 1985;
Siddiqi et al., 1989, 1990). When ion influx is plotted against increasing ion concentration, the uptake mechanisms can be
described by a dual or biphasic model (Epstein, 1966, 1972).
By analogy, it is assumed that ion intake behaviour corresponds
to reactions catalysed by two distinct enzymes of Michaelis –
Menten type (Epstein, 1966, 1972). Indeed, in a low range of
external ion concentration (,1 mM), the uptake mechanism
fits a hyperbola corresponding to saturable kinetics known as
mechanism I (Fig. 1A and Supplementary Data Fig. S1) whereas
in the higher concentration range (.1 mM), the root uptake mechanism known as mechanism II is less clearly characterized (Fig. 1B
and Fig. S1, mechanism II). Indeed, the ion uptake rate can fit a
hyperbola corresponding to saturable kinetics or most frequently
it may fit non-saturable linear kinetics (Kochian and Lucas,
1982; Kochian et al., 1985; Peuke and Kaiser, 1996; Glass,
2005; Okamoto et al., 2006). In the case of nitrate, studies
under laboratory conditions in different species such as Brassica
napus, Aradopsis thaliana, Hordeum vulgare and Pinus glauca
have generally shown the existence of a linear and non-saturable
mechanism II (Fig. 2 and Fig. S2) in the range of biologically
relevant concentrations (,10 mM). When plants previously
grown without nitrate for 1 or 2 weeks are supplied with 1 mM
KNO3 for 24 h, the synthesis of new NO3– transporters is
induced. These new kinetics represent the behaviour of
NO3 influx (mol h–1 g–1 root d. wt)
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
100
90
80
70
60
50
40
30
20
10
0
0
2
4
6
Log (concentration
1557
8
10
NO3–)
F I G . 2. Transformation of the ‘Enzyme-Substrate’ formalism to the ‘Flow-Force’
formalism of nitrate uptake kinetics from original data of the nitrate influx rate of
Brassica napus (Faure-Rabasse et al., 2002). Details of the experiment are
presented in Fig. 1.
induced plants (Fig. 1 and Fig. S1). The overall trend of the
kinetics is not changed but the nitrate influx rate (Vmax) is strongly
increased.
By analogy, Epstein (1966, 1972) proposed that the ion flux
across a plant root system follows behaviour similar to a
Michaelis – Menten equation for some enzyme kinetics in vitro
(Text S1). This Enzyme-Substrate approach is typical of a mechanistic interpretation because it strives to characterize ion transport mechanisms (carriers) through operational and biochemical
parameters (Vmax and Km) across the root epidermis (Epstein
and Hagen, 1952; Epstein, 1953, 1972; Epstein et al., 1963).
Therefore, as a first approximation, characterization of the
carrier (top-down analysis) proposed in Enzyme-Substrate
modelling may provide a suitable framework to investigate ion
transporters via mutant analyses. In contrast, it is unlikely that
the velocity equations and parameters of this modelling can be
used in agronomic models as the environmental conditions in
the field are highly variable compared with controlled conditions
in the laboratory.
Associated assumptions of the Enzyme-Substrate interpretation
Aside from a set of simplifying conditions (Table 1) based on
analogy to enzymatic functioning that are largely not verified,
there are also several assumptions about root function that
derive from the Michaelis – Menten interpretation. First, this
interpretation is based on the assumption of a ‘single root membrane’ corresponding to an epidermal cell layer. Accordingly this
leads to a model with two compartments (Clarkson, 1988, 1993)
where all carriers are arranged in parallel on this membrane
(Epstein, 1966, 1972; Crawford and Glass, 1998). Secondly,
the kinetic interpretation implicitly reduced the behaviour of
mechanisms I and II to a single carrier or ‘mechanism’ that can
be defined by microscopic parameters such as Vmax and Km.
However, it is now clear that the combination of both duration
and concentration of nitrate pretreatment enhances nitrate
influx by induction of synthesis of new transporters (Siddiqi
et al., 1989, 1990). Likewise, mutant analyses of nitrate transporters have shown that the influx kinetics represent the sum in activity of different types of carriers (see below, Filleur et al.,
2001; Li et al., 2007). Thirdly, uptake kinetics are established
1558
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
from uniform roots along which Vmax and Km are considered
constant. However, it has been shown that these parameters are
not constant over longer distances between young and old roots
in adult plants (Eshel and Waisel, 1973; Lazof et al., 1992;
Colmer and Bloom 1998; Taylor and Bloom, 1998; Sorgona
et al., 2011). Fourthly, the nature of the nitrate transporters
of the root membrane (number, type and/or coupling) can also
vary in response to temperature, light intensity, root age, and N
and C status (Laı̂né et al., 1994; MacDuff et al., 1997; Lejay
et al., 1999). Therefore, values of microscopic parameters
under short- and long-term experiments can change greatly depending on the experimental conditions. This is the principal
weakness of the Enzyme-Substrate interpretation when it is
used in nitrate modelling because a functional nitrate uptake
model should account for these modifications in time and
space. In other words, there are no nitrate influx kinetics with reference values of Vmax and Km but a large number with variable
microscopic parameters depending on the experimental conditions (Tinker and Nye, 2000a; Britto and Kronzucker, 2006a).
US E O F AN A LTER NAT IV E A PPROACH TO
MO D E L I S OT H E R M S OF IO N A B S O R P T I ON
The Flow-Force approach: the thermodynamic viewpoint of ion
transport along the root radius
In the 1970s, an alternative interpretation called the ‘electrokinetic
model’ of ion absorption by roots (Supplementary Data Text S2),
based on electrochemical potentials and thermodynamics, was
proposed (Thellier, 1970, 1971, 1973, 2012). Like the EnzymeSubstrate interpretation, the electrokinetic approach was first
based on analogy where ion uptake was compared with electrical
behaviour (Supplementary Data Text S1 and S2). Recently, this
first interpretation has been refined and updated from isotherm
studies of silicon ions and was renamed the Flow-Force interpretation (Text S3; Thellier et al., 2009; Thellier, 2012). This interpretation considers the kinetics of ion transport as a particular case of a
Flux/Force relationship of non-equilibrium thermodynamics
(Thellier, 1973, 2012; Thellier et al., 2009). This modelling in
fact deals with the net flux, Jj, with:
Jj = Jjei − Jjie = (influx − efflux)
(1)
instead of the influx. Jjei represents the flux of a substrate Sj from external to internal solution (ei) and Jie
j the flux of a substrate Sj
from internal to external (ie). However, as the efflux is
usually small, in most cases there is little error when net flux and
efflux are confused. When the system is close to equilibrium, the
flux of substrate transport becomes a quasi linear function of the
force driving the transport (which is merely, for an intake
process, the equivalent of Ohm’s law for an electric process).
When all calculations are done (Thellier et al., 2009; Thellier,
2012), this may be written:
Jj (cj e ) = Lj · ln ((cj e )/(8cj e ))
where 8cje is the equilibrium concentration of substrate Sj in the external solution with the roots. Lj is a ‘conductance’ term relating the
flux of substance Sj to the force acting on the intake of substance Sj
as a result of the difference in the chemical potential of Sj between
external and internal medium and ln cj represents the overall contribution of the forces of various origins, other than the concentration of substance Sj in the external medium, which drives the intake
of Sj (for details see Supplementary Data Text S3). When plant
growth can be taken as negligible during the experiment, and if
the plant roots have not been rinsed when the plants were transferred from the growth medium to the experimental medium, then
cj e ≈ 8cj e
(2)
where cje isthe new concentration of external solution and 8cj e isthe
equilibrium concentration of a substrate Sj in the growth medium
with the roots.
Although this formalism was new in the field of ion transport
when it was proposed (Thellier, 1970, 1971, 1973), it had already
been used with success in plant water transport (Dainty, 1963,
1969a; Fiscus and Kramer, 1975). Indeed, contrary to ion transport, specific proteins such as aquaporins were not initially suspected as being involved in water transport (Maurel, 2007).
Hence, an equation derived from irreversible thermodynamics
was applied with success to formalize root water uptake by
plant roots (Steudle, 2000a, b). In spite of the complexity of the
differential localization and regulation activities of plant root
aquaporins, this formalism was helpful to understand water transport in plants. This Flow-Force model is typical of a phenomenological interpretation that aims at finding biophysical parameters
such as the overall conductance L ′ and the thermodynamic parameter K ′ (ordinate at the origin when J[NO3 – ]ext ¼ 0), which is able
to characterize ion uptake at the level of the whole root system
(Fig. 2 and Text S3).
Although parameters derived from this model cannot be linked
directly to molecular components, this conceptual model can validate mutant analyses of ion transporters. Indeed, mutations that
affect the functioning of ion transporters will also change the
root conductance for the ion considered. Here, the conductance
summarizes the integration of individual uptake for each carrier,
which is equivalent to Ohm’s law for an electric process where a
network of resistors in series and parallel can be represented by
a single equivalent resistance. Furthermore, the Flow-Force
model seems more suitable to model ion uptake under fluctuating
environments observed under field conditions and to study the
changes in thermodynamic parameters involved in the root catalytic structure for ion transport. Surprisingly, until recently this interpretation had never been tested in agronomic models although
its biophysical assumptions were more realistic and its linear formulation under biologically relevant ion concentrations was more
suitable for ion uptake modelling throughout the plant growth
cycle (Thellier et al., 2009; Le Deunff and Malagoli, 2014;
Malagoli and Le Deunff, 2014).
Associated assumptions of the Flow-Force model
In essence, the Flow-Force model considers ion uptake
kinetics at the level of the overall root system with no insights
into microscopic complexity (number of carriers, affinity and/
or coupling between carriers). Hence, the Flow-Force model
does not enable deduction of the type of transporters involved
in the nitrate uptake process (Supplementary Data Text S3); it
only describes that ion conductance is due to functioning of a
catalytic device formed by a complex of nitrate transporters
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
(CNT) inserted into different cell layers of mature roots.
Accordingly, quantitative or qualitative changes of nitrate conductance can occur through: (1) addition of new transporters
(quantitative changes), (2) changes in the activity (affinity) of individual transporters, and (3) coupling among several carriers in
the different cell layers and/or energy supply for ion transfers
through H+-ATPase activation (qualitative changes). All these
changes at the root system level can be caused by the crosscombined effects of different environmental [ion concentrations
in soil, soil temperature, soil pH, photosynthetically active radiation (PAR), etc.] and in planta factors (shoot demand, period of
day-night or ontogenetic cycles, root age, etc). This modelling
has wider applications and the significance of the parameters is
easier to determine.
Does recent molecular characterization of nitrate transporters
help us to choose between both interpretations?
Because the main goal of the Enzyme-Substrate model was to
identify enzymes responsible for nitrate uptake, it was tempting
to wait for confirmation of this interpretation from molecular
identification and characterization of nitrate transporters. In the
last two decades, many genes encoding nitrate transporters have
been cloned and mutant analyses have assigned them function
with regard to plant N uptake mechanisms I and/or II in low
and high ranges of nitrate concentrations.
At a low range of nitrate concentrations, it was demonstrated
that the NRT2 gene family was mainly involved in mechanism
I of N uptake in arabidopsis. A. thaliana genome sequencing
made it possible to identify seven members in this family.
However, if there was a strong correlation between NRT2.1 and
NRT2.2 transcript abundance and 15NO3 uptake after nitrate
induction (Lejay et al., 1999; Zhuo et al., 1999; Cerezo et al.,
2001; Filleur et al., 2001), the simple or double mutants
nrt2.1nrt2.2 were unable to abolish nitrate uptake completely
(Filleur et al., 2001; Orsel et al., 2004; Li et al., 2007). It is
likely that the multiple NRT2 homologues or other nitrate carriers
could also be involved in this residual root N uptake (Orsel et al.,
2002; Okamoto et al., 2003). Indeed, other root nitrate transporters such as the chloride channel (CLC) or nitrate excretion
transporter (NAXT) involved in nitrate homeostasis or nitrate
efflux could also be involved (De Angeli et al., 2006; Monachello
et al., 2009; Segonzac et al., 2011). Taken together, these results
demonstrate the inconsistency of some associated assumptions of
the Epstein model and prove that the Km of nitrate isotherms
(Text S1, Figs 1 and S1) is in fact a ‘pseudo-Km’ or Kp because it
is related in a complex way to the kinetic constants of each
carrier involved in root NO3– uptake (Neame and Richards, 1972b).
At a high range of nitrate concentrations, it was demonstrated
that some members of the NRT1 gene family belonging to the
peptide transporter family (PTR, recently renamed NRT1/PTR
family) participated in mechanism II of nitrate uptake in
Arabidopsis (Léran et al., 2013). Thus, NRT1.1 and NRT1.2 transporters were characterized in planta as being involved in mechanism II (Tsay et al., 1993; Huang et al., 1996, 1999; Touraine and
Glass, 1997). Therefore, it was shown that NRT1.1 was NO3– inducible whereas NRT1.2 was constitutively expressed. Because
kinetic studies with 13N and 15N tracers anticipated absence of
an inducible component in mechanism II in barley and oil seed
rape (Siddiqi et al., 1990; Faure-Rabasse et al., 2002), the
1559
inducible nature of the NRT1.1 gene raises questions (Lejay
et al., 1999). In addition, the nrt1-5 mutant lost part of mechanism
–
II only when plants were supplied with NH+
4 + NO3 but not when
–
they were supplied only with NO3 (Touraine and Glass, 1997).
Thus, at the high nitrate concentration range, the nrt1-5 mutant
was unable to abolish the nitrate uptake response. Likewise,
nitrate uptake was partially abolished in the nrt1.2-1 mutant
(Liu et al., 1999; Liu and Tsay, 2003; Krouk et al., 2006).
Unfortunately, no studies with the double mutant, nrt1-5 nrt1.2,
or the triple mutant, nrt2.1nrt1.1nrt1.2, have been performed
and we do not know yet if all the nitrate carrier activities can be
combined and if they are all potentially involved in mechanism
II. The difficulty of identifying transporters involved in mechanism II is also observed for potassium. Indeed, at 10 mM K+, the
double mutant for transporters Athak5 (high-affinity K+ transporter)
and Atakt1 (inward-rectifying K+ channel), which are involved
in mechanisms I and II of K+ transport, respectively, showed
no deficient phenotype. In fact, the candidate genes for K+ absorption at the high range of potassium concentrations has not been
clearly identified and characterized (Britto and Kronzucker,
2008; Aleman et al., 2011).
In summary, recent molecular advances and mutant analyses
of root nitrate transporters clearly demonstrate that a top-down
approach from the Enzyme-Substrate interpretation is no longer
appropriate for modelling the biphasic behaviour of root nitrate
uptake in crop species. At the whole root level, the complex
catalytic structure formed by the involvement of at least four
families of nitrate transporters has complicated the top-down
analyses of the root catalytic device (Neame and Richards,
1972b; Hill et al., 1977; Forde and Clarkson, 1999; Touraine
et al., 2001). Moreover, it should also be kept in mind that in
polyploid crop species the interpretation of N uptake kinetics is
seriously complicated by gene redundancy of the different nitrate
carriers (Orsel et al., 2002; Okamoto et al., 2003). For example
in arabidopsis (old autotetraploid) the strong redundancy of NRT2
genes furthercomplicatesthis Enzyme-Substrate top-down analysis
and the correct determination of the kinetic parameters of mechanism I (Filleur et al., 2001; Orsel et al., 2004; Glass, 2005; Li et al.,
2007). Finally, at the high range of nitrate concentrations, uptake
studies with tracers are confronted with technical problems such
as underestimation of root efflux and xylem translocation rates
(Britto and Kronzucker, 2001a, 2003, 2006b; Szczerba et al.,
2006).
Does recent location of nitrate transporters in the mature root
help us to choose between both interpretations?
It is well recognized that nitrate uptake kinetics from the tip to
the basal part of the roots are not uniform (Eshel and Waisel,
1973; Lazof et al., 1992; Colmer and Bloom, 1998; Taylor and
Bloom, 1998; Sorgona et al., 2011). This nitrate uptake heterogeneity results from a functional heterogeneity of ion transporters located in series and/or parallel in the different cellular
layers of the mature root (Fig. 3). Therefore, the functional
mechanisms involved in tight temporal and spatial coordination,
and which depend on the location and regulation of expression
and coupling between nitrate transporters, have not yet been
elucidated and appear more complex than previously thought
(Britto and Kronzucker, 2001b, 2003).
1560
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
A
Apoplastic pathway
Cellular and symplastic pathway
Casparian band
NO3–
Vacuole
Metaxylem
Protoxylem
Pericycle
parenchyma
NAXT1
Endodermis
Cortex
Epidermis
NRT1.2
NRT2.1 and NRT2.2
Perforation
NRT1.1
CLC a,b
Helical-annular
NRT1.5
reinforcing layer
NRT1.8
B
Xylem
Cytoplasm-symplasm
cx
oc
Vacuole
xc
R
co
vc
R
cv
M
F I G . 3. Location of the different nitrate transporters involved in nitrate transport, nitrate efflux and homeostasis in the mature roots of Arabidopsis. (A) Representation
of the location of nitrate transporters and nitrate movement in a mature root of Arabidopsis. NRT: nitrate transporter, NAXT: nitrate excretion transporter, CLC: chloride
channels (from Guo et al., 2001, 2002; Nazoa et al., 2003; Remans et al., 2006a, b; Girin et al., 2007; Orsel et al., 2007; Chopin et al., 2007; Lin et al., 2008; Li et al.,
2010). (B) Model of ion fluxes in relation to organization of the mature root (from Pitman, 1976). Foc and Fco are fluxes in and out of the epidermis membrane, Fcv and
Fvc are fluxes in and out of the vacuole membrane and Fcx and Fxc are fluxes into and out of the xylem. R and R′ are net fluxes across the cytoplasm and vacuole and M is
the net flux outside the symplast.
Thus, in mature roots of Arabidopsis and rice seedlings, in situ
hybridization and histochemical GUS and GFP activities in
pNRT::GUS and pNRT::GFP transgenic seedlings have revealed
that AtNRT2.1 is predominantly localized in the outer layers:
epidermis, cortex, endodermis and root hairs (Nazoa et al.,
2003; Chopin et al., 2007; Girin et al., 2007; Orsel et al., 2007;
Feng et al., 2011). Intriguingly, BnNRT2.1 expression in
B. napus is strongly correlated with changes in root length
induced by nitrate availability or modulation of ethylene biosynthesis (r ¼ 0.9; P , 0.01), suggesting that its expression
level and activity might adapt to elongation changes of the
exploratory root system that are induced by environmental cues
(Leblanc et al., 2013; Le Ny et al., 2013; Lemaire et al., 2013).
Recent identification and characterization of CLC and NAXT genes
has shown that these transporters are involved in nitrate influx into
the vacuole and root nitrate efflux, respectively (De Angeli et al.,
2006; Monachello et al., 2009; Segonzac et al., 2011). However,
we do not know if CLC and NAXT genes respond to the primary
nitrate effect or if some mutants of these genes can impair nitrate
uptake along the roots. Moreover, AtNRT1.1, AtNRT1.2, AtNRT1.3
and AtNRT1.4 transporters are involved in N uptake at the high
range of nitrate concentrations but nitrate flux measurements
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
and NRT expression have shown that AtNRT1.2, AtNRT1.3 and
AtNRT1.4 play minor roles in nitrate uptake (Okamoto et al.,
2003). Contrary to AtNRT2.1 and AtNRT2.2 expression, AtNRT1.1
is mainly located in the deeper cell layers of the mature root:
endodermis and pericycle. AtNRT1.1 is also expressed in the root
tip of primary and lateral roots in the epidermal cell layer (Guo
et al., 2001; Remans et al., 2006a).
Furthermore, there is little certainty about the transporters and
mechanisms involved in nitrate loading into the xylem and what
type of regulation is implicated in the rate of these transfers
(Delhon et al., 1995; Herdel et al., 2001; Britto and Kronzucker,
2003; Lin et al., 2008). Electrophysiological studies on protoplasts
from parenchyma root cells of the stele in maize and barley have
identified three different xylem (X ) anion channels: X-QUAC
(quickly activating anion conductance), X-SLAC (slowly activating anion conductance) and X-IRAC (inward rectifying anion
channel). Among these, X-QUAC is highly permeable to nitrate
and supports a fundamental role in xylem nitrate loading (Köhler
and Raschke, 2000; Köhler et al., 2002; Gilliham and Tester,
2005). Moreover, it has been shown that X-QUAC gating is regulated by a positive feedback during nitrate loading in the xylem
(Köhler et al., 2002). In addition, recent identification of the
AtNRT1.5 nitrate transporter gene has shown that a mutant of
this gene partially reduced xylem nitrate loading and translocation
to the shoot (Lin et al., 2008; Garnett et al., 2013). However, in
B. napus seedlings, during the large shift in 15NO3– translocation
to the shoot that is induced by increases in external nitrate from
0.05 to 5 mM, expression of the NRT1.5 gene was unchanged,
which suggested that BnNRT1.5 is probably not the most important component of xylem nitrate loading (Le Ny et al., 2013).
Molecular identification of genes encoding channels involved in
anion loading into the xylem will allow their relative importance
to be deciphered, especially in relation to nitrate uptake at the
root epidermis level.
In conclusion, recent molecular advances about the location
of nitrate transporters in the mature root clearly demonstrate
that the implicit assumption of a ‘single root membrane’ in the
Enzyme-Substrate interpretation corresponding to the epidermal
cell layer does not agree with the compartmental location of
nitrate transporters. This result is also clearly demonstrated by
compartmental analysis of tracer exchange (CATE) for 13NO3–
(Britto and Kronzucker, 2001b).
Molecular analyses of nitrate carriers confirm the
four-compartment model of N fluxes and reveal linear behaviour
of root N uptake in plants grown under steady-state conditions
The root locations of nitrate transporters deduced from molecular data confirm the cellular root model of N uptake with
four compartments (external medium, cytosol, vacuole and
xylem) for tracer exchange proposed by Walker and Pitman
(1976) (see comparison between Fig. 3A and B). This model describing the cellular inter- and intra-fluxes of N within the root clearly
suggests that the carrier viewpoint of the Enzyme-Substrate interpretation is an oversimplification, based upon the mechanisms
responsible for the only influx step across the plasma membrane
(Foc) according to the model described by Walker and Pitman
(1976). Indeed, even over short periods of 15NO3– or 13NO3–
exchange measurements (5 min) between the external solution
and the root tissues, a large part of the 15N or 13N taken up in
1561
labelling experiments is found in shoots, suggesting that active
transporters in the stelar tissue of the root are also involved in
regulation of the plasma membrane influx step (Pitman, 1977;
Köhler and Raschke, 2000; Köhler et al., 2002). Moreover, the
calculation of rate constants involved in the exchange of
tracers between the different compartments of the cell tissue
and solution needed longer periods of tracer exposure and
several approximations to resolve the complexity of the fluxes
across the root (Jeschke, 1973; Walker and Pitman, 1976; Britto
and Kronzucker, 2001b). The resulting CATE to estimate the halflives (t0·5) for the 13NO3– pool in the cytosol of barley and rice
roots has revealed that t0·5 values were constant whatever the
external nitrate concentrations applied (in the range 10 mM to
10 mM) (Britto and Kronzucker, 2001b, 2003). Such results
suggest that 13NO3– homeostasis is fine-tuned due to coordinated
fluxes across the tonoplast (Fcv and Fvc) and from the cytosol to
the xylem (Fcx), as well as fluxes into metabolic compartments
such as N assimilation pathways. Regulation mechanisms and
their subsequent interactions still need to be deciphered to
provide a more accurate description of NO3– influx at the plasma
membrane (Fig. 3B). Finally, a linear relationship between
cytosolic nitrate pool sizes and nitrate influx at the root plasma
membrane can be deduced in addition to a hyperbolic function
between the cytosolic pool size and external nitrate concentrations
from 10 mM to 10 mM (Britto and Kronzucker, 2003). These surprising results demonstrate that when plants were grown under
steady-state conditions, nitrate influx across the root is resolved
in a quasi-linear manner. Indeed, the equations of irreversible thermodynamics refer only to net flux, while the emphasis in ion transport studies has been on the influx step (Foc). Therefore, these
results validate the Flux-Force interpretation of ion uptake rate
when conditions are not far from equilibrium (Thellier et al., 2009).
How to interpret changes in the ion uptake rate in both kinetic
interpretations?
Understanding the change in the uptake rate of N, K and P ion
transport remains a fundamental issue for modern agriculture.
Indeed, intuitively it is tempting to assume that this behaviour
is the basis for the success of the green revolution by increasing
the yield potential of modern crops. However, an explanation for
the transition between mechanisms I and II of the EnzymeSubstrate model remains unclear (Figs 1 and S1). In fact, the
biphasic behaviour of ion isotherms has been controversial
since the 1960s and several hypotheses have been proposed to
explain this dual-phase behaviour of ion transport.
At the root level, to explain the dual-phase of ion isotherms it
was proposed that the carriers responsible for mechanisms I and
II were located in parallel on the plasmalemma and tonoplast of
epidermal cells, respectively (Torii and Laties, 1966). However,
a study in barley and corn roots that used mutual interaction
between K+ and Na+ demonstrated that mechanisms I and II
of K+ absorption operate in parallel across the epidermal plasmalemna (Welch and Epstein, 1968). This assumption was also confirmed in non-vacuolated cells of Chlorella pyrenoidosa where
biphasic behaviour during absorption studies with Rb+ was
also observed (Kannan, 1971). Other authors have assumed
that the origin of the duality in ion uptake kinetics was due to
ion uptake at low concentrations occurring at the root epidermis
cell layer, and uptake at high external ion concentrations
1562
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
occurring at the epidermis and cortical cell layers (Edwald et al.,
1973; Göring, 1976; Kochian et al., 1985). Therefore, at the high
range of external ion concentrations, active ion uptake would also
be blurred by interaction with the ion diffusion mechanism in
cortical cells (Edwald et al., 1973; Ayadi et al., 1974;
Bowling, 1976; Göring, 1976). Currently, this concept is even
shared by some advocates of the Enzyme-Substrate interpretation in the case of nitrate (Glass, 2007).
At the molecular level, in the heterologous system of Xenopus
oocytes, a study with AtNRT1.1 mutants showed that the
AtNRT1.1 transporter is involved in mechanism I when it is
phosphorylated and in mechanism II in the absence of phosphorylation (Liu and Tsay, 2003). A study in planta with these
mutants has confirmed these results (Liu and Tsay, 2003).
Recently, it has been established that a phosphorylationcontrolled dimerization switch is involved in the two distinct affinity modes for nitrate uptake of the NRT1.1 transporter (Sun
et al., 2014; Parker and Newstead, 2014). In essence, these
data completely invalidate the Enzyme-Substrate model, which
assumes the existence of two distinct transport systems for
mechanisms I and II. In this regard, recent experiments have
demonstrated that under high external nitrate concentrations,
the regulation of AtNRT2.1 and AtNRT1.1 gene expression is
under control of the calcineurin B-like (CBL)-interacting
protein kinase (CIPK) signalling cascade (Ho et al., 2009; Hu
et al., 2009). Indeed, cipk8 and cipk23 mutants showed a complete flattening in AtNRT1.1 and AtNRT2.1 gene expression
under high external nitrate concentrations. Because CBL1 and
CIPK23 proteins are also involved in regulation of the AKT1 potassium transporters (Xu et al., 2006; Cheong et al., 2007), these
results again question the molecular mechanisms involved in the
transition between the phases of ion transport behaviour. Indeed,
as previously observed for potassium kinetics, mechanism II can
be flattened by calcium and magnesium treatments (Epstein and
Leggett, 1954; Thellier, 1970, 1973; Ayadi et al., 1974). Moreover,
we do not know yet if the CBL-CIPK signalling cascade is also
involved either in activities of the CLC and NAXT transporters
(Ho et al., 2009; Hu et al., 2009) or in the X-QUAC channel
involved in xylem loading of nitrate (Köhler et al., 2002;
Gilliham and Tester, 2005). However, the results with AtNRT1.1
should be taken with caution. Indeed, a re-evaluation in planta
of nitrate influx data from the nrt1.1 arabidopsis mutant showed
that AtNRT1.1 transporters could be mainly involved in mechanism II and had no contribution to mechanism I (Glass & Kotur,
2013). Furthermore, a recent study in B. napus revealed that overexpression of BnNRT1.1 cannot compensate for nitrate uptake
when BnNRT2.1 expression and activity are inhibited by glutamate treatment (Leblanc et al., 2013).
The Flow-Force interpretation simply explains the transition
of the ion uptake rate between low and high range of nutrient concentration by switching from the linear ion uptake rate occurring
near equilibrium to a non-linear behaviour when conditions
move away from equilibrium (Fig. 2). For example, a resistor
obeys Ohm’s law as long as the difference in electrical potential
(dep) across the resistor is not too large. If we gradually increase
dep, the resistor will begin to heat, so its behaviour will change,
and Ohm’s law applies less well. The fact that high ion concentrations induce biochemical modifications such as the CBL-CIPK
signalling cascade is not in contradiction with the adaptation of
roots to changes in equilibrium conditions.
In summary, the top-down approach related to the EnzymeSubstrate interpretation has failed to explain the biphasic behaviour of ion uptake. Indeed, it is still unproven whether interference
between facilitated transport and diffusive processes occurs in
mechanism II. Moreover, recent molecular results do not support
the existence of distinct transporters involved in mechanisms
I and II. Indeed, according to their degree of phosphorylation,
some transporters such as NRT1.1 are involved in both mechanisms. At the molecular level, the participation of the CBL-CIPK
cascade signalling in the regulation of K+ and NO3– transporter
expression and the flattening of mechanism II by calcium treatment deserves more attention.
Is the change in the ion uptake rate under the high range of
concentrations observed in laboratory conditions biologically
relevant under field conditions?
One may wonder if the range of 3–5 orders of magnitude (1 mM
to 100 mM) in external nitrate concentrations used in laboratory
studies is biologically relevant (Siddiqi et al., 1989, 1990;
Kronzucker et al., 1995a, b). Indeed, the concentrations used are
often situated beyond the maximum soil nitrate concentrations
observed under field conditions after N fertilizer applications
(≤7–10 mM) or in natural habitats (≤1 mM; Andrew, 1986;
Wolt, 1994; Miller et al., 2007). This is also true for potassium
where typical K+ concentration in the soil solution varies only
from 1 mM to 6 mM (Reisenauer, 1966; Adams, 1971; Maathuis,
2009). Therefore, from the biphasic behaviour of ion transport
observed in the laboratory it is stated that mechanism I will be
mainly used by plantsto acquire nitrate at low nitrate concentrations
in soil (,0.5 mM) whereas it is anticipated that mechanism II will
be responsible for much of the N uptake at the higher range of
nitrate concentrations (Glass 2003, 2005). However, a recent
study in maize growing under hydroponic conditions at two
nitrate concentrations (0.5 and 2.5 mM) has shown that
ZmNRT2.1 and ZmNRT2.2 transcript levels were much higher
than for other transporters, whatever the external nitrate concentration and throughout the life cycle, suggesting a more important role
for these gene products that is independent of nitrate induction on
their expression (Garnett et al., 2013). Moreover, the low expression level of ZmNRT1.1, involved in mechanisms I and II across
the life cycle, suggested an alternative role for this protein
(Garnett et al., 2013). This assumption is also confirmed by a
study in B. napus where the inhibition of BnNRT2.1 activity by glutamate treatment revealed that over-expression of BnNRT1.1 transcripts cannot compensate for nitrate uptake in the absence of
BnNRT2.1 expression and activity (Leblanc et al., 2013).
Likewise in arabidopsis and B. napus, the expression pattern
of NRT2.1 during the plant growth cycle showed that its
transcript levels in the roots increased during early vegetative
growth, peaked prior to floral emergence and decreased to very
low levels at flowering and during the bolting period (Nazoa
et al., 2003; Beuve et al., 2004). It was assumed that the transcriptional regulation of BnNRT2.1 during ontogenesis was caused by
changes in N and C assimilates circulating between roots and
shoots (Nazoa et al., 2003; Beuve et al., 2004; Malagoli et al.,
2008). This was confirmed by the identification of a 150-bp
cis-acting element of the AtNRT2.1 promoter involved in the
regulation of gene expression in response to changes in the N
and C status of the plant (Girin et al., 2007).
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
Furthermore, it has been shown in long-term experiments with
a flowing solution culture system that estimates of the mean
nitrate influx rate per unit root length unit plotted against external
nitrate concentrations from 10 mM to 10 mM displayed linear
behaviour similar to the Flow-Force formalism (Fig. 4).
A flowing solution culture system ensures that all the plants are
in equilibrium or steady-state flux (Tinker and Nye, 2000a),
which leads to the conclusion that when roots are fed with biologically relevant concentrations of nitrate, the average absorption
rate is quasi linear and does not exhibit biphasic behaviour
(Fig. 4B). Likewise, soil-grown plants showed the same behaviour
regarding relative growth rate, total plant nitrogen concentration
and pattern of nitrate uptake rate pattern (Bhat et al., 1979b).
However, as for Michaelis–Menten kinetics, the Flow-Force thermokinetics are introduced by considering instantaneous speeds.
Therefore, it is essential to check if the laws of thermodynamics
are the same with average speeds over a long period of time
where the properties of ion transport mechanisms may change.
How are laboratory results transposed to the field?
0·025
6d
9d
0·015
0·010
15 d
0·005
21 d
0
0·002 0·004 0·006 0·008 0·010 0·012
NO3– concentration (M)
0·025
6 d, r = 0·98 P < 0·01
9 d, r = 0·98 P < 0·01
15 d, r = 0·99 P < 0·01
21 d, r = 0·94 P < 0·05
B
Nitrate influx
(mol h–1 cm–1 root)
200
180
160
140
120
100
80
60
40
20
0
A
0
5 mM
100 µM
4
8
12
16
20
Temperature (°C)
24
28
500
600
500
0
0·020
0·015
Nitrate influx
(µmol h–1 g–1 root d. wt)
Nitrate influx
(mol h–1 cm–1 root)
A
0·020
points of the nitrate uptake kinetics (Fig. 2), the response
curves can be fitted mathematically to polynomial functions
(Fig. 5). In this type of modelling, parameters of the polynomial
equation characterize the responses of a cellular device (CNT)
that catalyses the root absorption process at 100 mM and 5 mM
(Le Deunff and Malagoli, 2014). The parameters of the polynomial function can be qualified as intensive because they characterize the thermodynamic state of the root cells in the absorption
process that are modified by temperature and PAR (e.g. speed of
reactions, cellular processes coupled to absorption). In the physical sciences, an intensive variable is a quantity that does not
depend on the amount of material present in the system considered. For example, if two carriers function at the same
speed, simultaneous functioning does not cause a doubling of
speed. However, because temperature is an intensive variable,
it modifies the speed of N uptake of the two carriers (Fig. 5). In
contrast, the parallel behaviour of the polynomial curves
observed at 100 mM and 5 mM external nitrate concentrations indicate that the root catalytic structure involved in the root absorption process is more affected by variations of temperature and
PAR rather than changes in external nitrate concentrations. In
other words, for different values of temperature and PAR the
overall trend of the nitrate isotherm is not changed. This explains
Nitrate influx
(µmol h–1 g–1 root d. wt)
It is interesting to study the behaviour of ion absorption curves
in response to changes in environmental factors. Indeed, when
measurements of the nitrate influx rate in response to changes
in PAR and temperature are performed at two external nitrate
concentrations, 100 mM and 5 mM, corresponding to extreme
1563
B
400
300
200
100
0·010
0
0·005
Photosynthetically active radiation (µmol m–2 s–1)
0
0
2
4
6
8
10
Log (NO–3 concentration M)
12
F I G . 4. Evolution of the nitrate influx rate at different times after transplanting of
Brassica napus plants (‘Emerald’). The plants were grown in a continuous flow
culture system at 25 8C and 32 kLux and supplied with constant 10 mM, 50 mM,
100 mM, 1 mM or 10 mM of external nitrate concentrations. (A) Mean nitrate
uptake rate and external nitrate concentrations fitted to a decimal logarithmic
function. (B) Flow-Force interpretation of mean nitrate uptake rate (from Bath
et al., 1979a).
0
100
200
300
400
F I G . 5. Temperature and photosynthetically active radiation effects on the
nitrate influx rate established at 100 mM and 5 mM nitrate treatment in Brassica
napus plants. (A) Changes in the nitrate influx rate as a function of root temperature (from Malagoli et al., 2004). (B) Changes in the nitrate influx rate as a function of photosynthetically active radiation (from Le Deunff and Malagoli, 2014).
Vertical bars indicate s.d. for n ¼ 3 when larger than the symbol. In these
two experiments, 3-week-old plants were acclimated for 1.5 h in a nutrient solution with either 100 mM or 5 mM at the temperature used for the measurements.
Then, influx rate was measured over 5 min at 100 mM and 5 mM with K15NO3
(at.% 15N: 99 %). Vertical arrow indicates that a nitrate influx kinetic can be inferred between all the points of the parallel curves at 100 mM and 5 mM external
nitrate concentrations as presented in tridimensional Fig. 8.
1564
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
the parallel behaviour observed at 100 mM and 5 mM external
nitrate concentrations during changes in temperature and PAR
(Fig. 5). This result is very important because it reveals that macroscopic parameters such as L ′ (conductance) and K ′ (thermodynamic) are conserved through variations of environmental
factors. Accordingly, this observation raises the question: is the
same behaviour observed with endogenous or in planta factors?
Introduction of in planta factor effects in nitrate uptake rate
modelling
Regulation of in planta factors on the nitrate uptake rate during
the growth cycle can be considered at two time scales: day – night
and ontogenetic cycles. Indeed, they result from pleiotropic
effects because they combine: (1) the rate of transpiration and
translocation during the transport of long-distance signalling
molecules between the shoots and roots, (2) variations of light
and temperature, (3) the energetic status in the roots (sugar availability), (4) the hormonal status of the roots and (5) a combination
Nitrate influx
(µmol h–1 g–1 root d. wt)
350
A
300
5 mM
100 µM
250
200
150
100
50
0
0
3
6
9
12
15
18
21
G2
G3
G4
24
Nitrate influx
(µmol h–1 g–1 root d. wt)
Time (h)
200
180
160
140
120
100
80
60
40
20
0
B
D1
D2
E
F
Developmental stage
F I G . 6. Day/night and ontogenetic cycle effects on the nitrate influx rate established at 100 mM and 5 mM nitrate treatment in Brassica napus plants. (A) Daily
changes in the nitrate influx rate (from Malagoli et al., 2004). Vertical bars indicate s.d. for n ¼ 3 when larger than the symbol. (B) Changes in the nitrate influx
rate as a function of developmental stages across the growth cycle (from Beuve
et al., 2004; Le Deunff and Malagoli, 2014). Vertical bars indicate s.e. for n ¼
9 when larger than the symbol. In these two experiments, plants were acclimated
for 1.5 h in a nutrient solution with either 100 mM or 5 mM at the temperature used
for the measurements. Then, the influx rate was measured over 5 min at 100 mM
and 5 mM with K15NO3 (at.% 15N: 99 %). Vertical arrow indicates that a nitrate
influx kinetic can be inferred between all the points of the parallel curves at
100 mM and 5 mM external nitrate concentrations as presented in tridimensional
Fig. 8.
of N or nitrate signalling for growth associated with N status (Le
Bot and Kirkby, 1992; Delhon et al., 1995, 1996; MacDuff et al.,
1997).
During the day – night cycle, the parallelism of polynomial
functions at 100 mM and 5 mM observed with temperature and
PAR is repeatedly observed, yet parallelism is less obvious due
to larger fluctuations (at 6 and 18 h) at higher external nitrate concentrations (Fig. 6A; Malagoli et al., 2004). This suggests that
the root catalytic structure during the day is finely tuned by a
bulk of intensive and extensive variables that operate on nitrate
uptake. Intensive variables such as membrane potentials, energetic coupling or carrier structural modifications ( phosphorylation) might be involved in the regulation mechanisms. But we
cannot exclude that extensive characteristics such as biosynthesis or destruction of nitrate transporters might also be associated (Fig. 6A). Indeed, physiological and molecular studies
have shown that the diurnal pattern of nitrate uptake and
NRT2.1 transcript abundance are correlated with the level of
sugar in the roots (Lejay et al., 1999; Matt et al., 2001; Girin
et al., 2007). Moreover, recent studies have demonstrated that
an as yet unidentified oxidative pentose phosphate-dependent
sugar-sensing pathway governs a mechanism for the transcrip2–
tional regulation of NO3– , NH+
4 and SO4 transporters by photosynthesis (Lejay et al., 2003, 2008; De Jong et al., 2013).
During the ontogenesis cycle, the parallel behaviour of polynomial functions at 100 mM and 5 mM nitrate concentrations indicates that for a given developmental stage, the parameters of the
polynomial function are less modified when plants are under a
steady-state growth rate (Fig. 6B). This suggests that long-term
changes associated with different phases of plant development
lead to stable and homogeneous thermodynamic and energy characteristics (intensive characteristics) of the catalytic root structure
whatever the nitrate availability. As the influx measurements were
made for 5 min and consistently at the same time of day, it is not
surprising that we see parallel behaviour between nitrate uptake
at 100 mM and 5 mM (Fig. 6B; Beuve et al., 2004). This confirms
that intensive characteristics of the root catalytic structure such
as those observed with temperature and PAR treatments are not
modified by the plant developmental stage (Fig. 5).
In summary, the nitrate uptake rate in response to environmental and in planta effects show polynomial response curves with
parallelism behaviour between low and high external nitrate concentrations. Although unconventional, the parallelism observed
at 100 mM and 5 mM external nitrate concentrations clearly demonstrates that thermodynamic characteristics of ion uptake
(changes in membrane potentials, energetic coupling or carrier
structural modifications) are less modified by environmental
and in planta effects. This offers a unique opportunity to use
macroscopic parameters (L ′ and K ′ ) instead of Enzyme-Substrate
microscopic parameters (Vmax and Km) for building a mechanistic
approach in agronomic models (Le Deunff and Malagoli, 2014).
The de-induction of nitrate transporters shows a parallel decline
in nitrate uptake rate and reveals preservation of the
thermodynamic characteristics of ion transport
The above relationships with parallel behaviour in nitrate
influx rates at 100 mM and 5 mM nitrate concentrations are also
observed in induction/de-induction studies of nitrate uptake
in short-term experiments (days to weeks). Thus, 1 week deprived
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
350
A
Nitrate influx
(mol h–1 g–1 root f. wt)
uptake kinetics between 100 mM and 5 mM nitrate are less modified by a continuous decrease in the number transporters.
Furthermore, in nitrate-deprived B. napus plants, the nitrate
pulses 12 h before influx measurement reverse the downregulation of the nitrate influx rate to the same level at 24 and
96 h (Fig. 7A) whereas after 24 h of nitrate deprivation the endogenous pools of root nitrate are near zero (Faure-Rabasse
et al., 2002). This demonstrates again that induction of nitrate
transporters does not modify the thermodynamic characteristics of ion uptake. As suggested by Britto and Kronzucker
(2001b, 2003), a nitrate homeostasis regulation related to the
plant’s growth strategy probably operates via a complex coordination of nitrate flux processes via induction/de-induction
of transporters in the different compartments of the root
(Fig. 3B).
100 M
5 mM
Pulse 100 M
Pulse 100 M
300
250
200
150
100
50
0
0
24
48
72
1565
96
Duration of nitrate deprivation (h)
Nitrate influx
(mol h–1 cm–1 root length)
0·040
B
0·035
Root ageing: a critical parameter to model the N uptake
rate at field level
10 M
50 M
100 M
1 mM
10 mM
0·030
0·025
0·020
0·015
0·010
0·005
0
0
5
10
15
20
25
Days from transplanting
F I G . 7. Down-regulation of the nitrate uptake rate in short- and long-term
experiments in Brassica napus L. ‘Capitol’ (A) and ‘Emerald’ (B). (A)
Short-term down-regulation of the 15NO3– influx rate into B. napus roots
induced by deprivation of nitrate for 0– 96 h. During deprivation, additional
batches of plants were exposed for 30 min to a NO3– pulse 12 h prior to 15NO3
flux measurements at 100 mM and 5 mM. Plants were grown in a flowing solution
culture system (Clement et al., 1974) over 26 d before deprivation. The values are
the means + s.d. of three batches of three plants. Vertical arrow indicates that a
nitrate influx kinetic can be inferred between all the points of the parallel
curves at 100 mM and 5 mM external nitrate concentrations as presented in tridimensional Fig. 8. (B) Long-term down-regulation of the nitrate influx rate
after transplanting. The plants were grown in a continuous flow culture system
at 25 8C and 32 kLux and supplied with constant 10 mM, 50 mM, 100 mM, 1 mM
or 10 mM of external nitrate (from Bath et al., 1979a).
Arabidopsis plantstreated for 0–72 h with 1 mM of nitrate showed a
parallel collapse in the nitrate uptake rate at 100 mM and 5 mM after
an induction phase of 12–18 h (Fig. S3; Okamoto et al., 2003).
Likewise, in B. napus plants growing in recycled solution refilled
daily with NO3– (Clement et al., 1974), nitrate deprivation induced
a down-regulation in the nitrate uptake rate when measured at
100 mM and 5 mM external nitrate concentrations (Fig. 7A).
Nitrate pulsing of 30 min with 100 mM nitrate 12 h prior to
nitrate influx measurements lowered the decline in nitrate influx
without any change in the general trend or rate of the subsequent
decline (Faure-Rabasse et al., 2002). Generally, these parallel
relationships are explained by the destruction of nitrate transporters
(extensive characteristic) as it is well known that nitrate transporter genes such NRT2.1 and NRT1.1 are induced by nitrate
treatments (Lejay et al., 1999). Taken together, these results
again indicate that the thermodynamic characteristics of ion
It has also been widely recognized that root ageing can cause
collapse in the macronutrient uptake rate in spite of the production of young roots by the whole root system during development
in crop and tree species (Clarkson et al., 1968; Warncke and
Barber, 1974; Edwards and Barber, 1976; Bhat et al., 1979a, b;
Gao et al., 1998; Eissenstat and Volder, 2005; Chen and
Brassard, 2013). Indeed, in long-term measurements (days to
months) of nitrate uptake, several authors have observed a decrease in nitrate uptake when the whole root system ages
(Warncke and Barber, 1974; Edwards and Barber, 1976; Bhat
et al., 1979a, b; Gao et al., 1998). For example, the measurements
of N uptake levels over weeks of growth in oilseed rape plants fed
on a wide range of external nitrate concentrations (from 10 mM to
10 mM) showed a continuous decrease in the nitrate uptake rate
with plant age (Fig. 7B; Bhat et al., 1979a). In contrast, with
tree species (Eissenstat and Volder, 2005; Chen and Brassard,
2013), it is important to note that increasing external concentrations of nitrate (10 mM) extend the functioning of the roots and
their subsequent capacity for nitrate uptake (Fig. 7B). This longterm down-regulation of the N uptake rate is probably different
from the short-term effect (see above paragraph). Indeed, it
appears to be associated with the transition between the vegetative and reproductive phases during ontogenesis, which is associated with translocation changes in N and C assimilates to the
roots (Malagoli et al., 2008; Malagoli and Le Deunff, 2014).
Surprisingly, although the effect of root ageing on the nitrate
influx rate is very strong (Fig. 7B) it is hardly ever introduced
into N uptake models (Cushman, 1984; Barber, 1995; Gao
et al., 1998; Le Bot et al., 1998; Tinker and Nye, 2000b;
Bassirirad, 2005).
Conceptual shifts required to update N uptake models
As demonstrated in this review, the Enzyme-Substrate interpretation may fit nitrate isotherms at the single cell level under
a set of specific conditions and assumptions. By contrast, its
application cannot be extended to cell layers and root tissue
because several types of transporters expressed differentially in
time and space along the root radius might contribute to nitrate
influx across cell membranes. Accordingly, matching kinetic
data to molecular characterization of nitrate transporters is
1566
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
difficult when the Enzyme-Substrate interpretation is applied, as
demonstrated by contradictory results reported in the literature.
This leads to the conclusion that a more generic interpretation
of nitrate uptake isotherms with macroscopic parameters is
required. Thus, an alternative approach is mandatory to fit the
collection of contradictory results. The Flow-Force interpretation may provide a useful basis to provide a solid, yet less deductive framework to model nitrate uptake (Thellier et al.,
2009). This thermodynamic approach has the advantage of describing nitrate influx across the cell membranes with macroscopic parameters (L ′ and K ′ ) provided by Nernst– Planck
electrochemical potential with no assumptions about transporters acting in the uptake process. To be fully satisfactory for modelling of N uptake in agronomic models, this biophysical
approach should be extended to take into account changes in
the N uptake rate in response to the effects of environmental
(temperature, PAR, soil pH, etc.) and in planta (day/night
cycle, ontogeny) factors encountered by plants under field conditions.
In this regard, the parallelism observed between the N uptake
response to environmental and in planta effects at low and high
external nitrate concentrations (Figs 6 and 7) and the linear
formalism of the Flow-Force interpretation under biologically
relevant external nitrate concentrations offers the opportunity
to integrate these factor effects. Indeed, cross-combination of
external nitrate concentrations and each of these effects allows
inclusion of changes in time scale from hours to days and days
to months as well as to account for these effects with regard to
changes in the external soil nitrate concentrations encountered
by plants under field conditions (Le Deunff and Malagoli,
2014). Figure 8 provides an example of a cross-combination of
the external nitrate concentration and PAR effects on the nitrate
uptake rate using the following type of equation:
−
Influx (PAR, [NO−
3 ]ext ) = A(PAR) ln [NO3 ]ext + B(PAR). (3)
Nitrate influx
(mmol h–1 g–1 root d. wt)
This type of formalism can be applied to each factor (day/night
cycle, ontogeny and PAR) that was investigated. In this way, an
N uptake mechanistic structure – function model previously built
with the Enzyme-Substrate interpretation in winter oilseed rape
500
has been updated with a Flow-Force interpretation of nitrate
influx isotherms (Thellier et al., 2009). This updated version has
greatly improved the ability to predict the uptake of N taken by
oilseed rape during the whole growth cycle (Le Deunff and
Malagoli, 2014; Malagoli and Le Deunff, 2014).
The next problem in structure – function N uptake models will
be concerned with a more accurate formalism to integrate the
collapse of the nitrate influx rate with root ageing during
ontogenesis. Because N fertilization treatments did not significantly affect root growth and length under field experiments
(Petersen et al., 1995; Gabrielle et al., 1998; Albert, 2008), the
down-regulation phenomenon of the root N influx rate during root
ageing is also a challenge (Gao et al., 1998; Bassirirad, 2005;
Bassirirad et al., 2008). In this regard, this effect has been introduced
satisfactorily into the updated version of the N uptake model
(Malagoli and Le Deunff, 2014) through a modification of the
integrated root system age (IRSA) parameter proposed by Gao
et al. (1998). However, this parameter remains to be improved
further. Indeed, we cannot rule out that the reciprocal dynamic
relationships between root branching and ion uptake rate may
be of major importance for our understanding of the downregulation of N uptake in long-term experiments (Roose and
Fowler, 2004; Biondini, 2008; Lemaire et al., 2013).
Furthermore, it is likely that the collapse of N absorption is associated with the N dilution phenomenon observed in crop species
(Gastal and Lemaire, 2002; Sadras and Lemaire, 2014).
Therefore, it is not certain that the architectural changes to the
root system during the short period of N concentration in plants
tissues before N dilution are able to induce a significant change
in plant performance in response to varying N availability. This
is why the Flow-Force interpretation might be very useful because
it could help determine whether ageing of the root causes quantitative conductance changes (increasing or decreasing the number of
carriers) or qualitative changes (modulation in the efficiency of
ion transport through thermodynamic characteristics, such as
changes in membrane potentials, energetic coupling and
carrier structural modifications).
In conclusion, Flow-Force modelling offers the opportunity of
a complete conceptual shift in modelling ion uptake acrossthe root.
Despite four decades of domination by the Enzyme-Substrate
interpretation of ion uptake in physiological and agronomic models, reopening of the thermodynamic viewpoint developed in the
1970s is necessary if physiologists and agronomists want adopt a
shared and realistic view of ion uptake in plants.
ACK N OW L E DG E M E N T S
400
300
200
100
0
0
100 200 300 400
500
PAR (mmol m–2 s–1)
5 tion
a
4
3 entr
2 nc 0)
1 co 00
0
te ×1
tra (M
Ni
We thank Professor Michel Thellier (Laboratoire AMMIS,
Université de Rouen, France) for his help with the Flow-Force
model, his remarks, criticisms and helpful discussions. We also
thank Dr Laurence Cantrill for his help with the English text and
his helpful comments. This work was financially supported by the
French Ministry of National Education, Research and Technology
(MENRT) and the Regional Council of Basse-Normandie (CRBN).
S U P P L E M E N TARY D ATA
F I G . 8. Three-dimensional plot of the photosynthetically active radiation effect
(PAR) on nitrate influx rate variations obtained by cross-combination of the PAR
effect (see Fig. 5B) and based on the Flow-Force reinterpretation of nitrate uptake
isotherms (from Le Deunff and Malagoli, 2014).
Supplementary data are available online at www.aob.oxford
journals.org and consist of the following. Text S1: details of
the Michaelis – Menten modelling of ion absorption. Text S2:
Le Deunff and Malagoli — Thermodynamic viewpoint of ion uptake across the root
details of the electrokinetic modelling of ion absorption. Text S3:
details of the Flow-Force modelling of ion absorption. Figure
S1: original data for nitrate influx rate in Hordeum vulgare.
Figure S2: transformation of the Enzyme-Substrate formalism
to the Flow-Force formalism of nitrate uptake kinetics from original data for the nitrate influx rate of Hordeum vulgare, Pinus glauca
and Arabidopsis thaliana. Figure S3: short-term down-regulation
of the 13NO2
3 influx rate into arabidopsis roots induced by a 1 mm
KNO3 treatment solution for 0–72 h.
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