Abstract
• Background and Aims It has recently found that lowland rice grown hydroponically is exceptionally efficient in absorbing , raising the possibility that rice and other wetland plants growing in flooded soil may absorb significant amounts of formed by nitrification of in the rhizosphere. This is important because (a) this is otherwise lost through denitrification in the soil bulk; and (b) plant growth and yield are generally improved when plants absorb their nitrogen as a mixture of and compared with growth on either N source on its own. A mathematical model is developed here with which to assess the extent of absorption from the rhizosphere by wetland plants growing in flooded soil, considering the important plant and soil processes operating.
• Methods The model considers rates of O2 transport away from an individual root and simultaneous O2 consumption in microbial and non-microbial processes; transport of towards the root and its consumption in nitrification and uptake at the root surface; and transport of formed from towards the root and its consumption in denitrification and uptake by the root. The sensitivity of the model's predictions to its input parameters is tested over the range of conditions in which wetland plants grow.
• Key Results The model calculations show that substantial quantities of can be produced in the rhizosphere of wetland plants through nitrification and taken up by the roots under field conditions. The rates of uptake can be comparable with those of . The model also shows that rates of denitrification and subsequent loss of N from the soil remain small even where production and uptake are considerable.
• Conclusions Nitrate uptake by wetland plants may be far more important than thought hitherto. This has implications for managing wetland soils and water, as discussed in this paper.
Keywords: Ammonium, flooded soil, modelling, nitrate, nitrification–denitrification, rice, rhizosphere, root aeration, soil aeration, wetland plants
INTRODUCTION
In flooded soils, added to the soil or formed by nitrification of in aerobic zones near roots or at the soil surface tends to be rapidly lost through denitrification in the anoxic soil bulk, and it is therefore generally assumed that wetland plants take up little compared with . However, in experiments using the radiotracer 13N and hydroponically grown seedlings of rice, it was found that a widely grown variety of lowland rice was exceptionally efficient in absorbing and assimilating compared with , and compared with other plant species (Kronzucker et al., 1999, 2000). This suggests a particular adaptation of rice to and raises the possibility that absorption by rice and perhaps other wetland plants is more important than generally thought. Since growth and yield of most plant species are superior under mixed nutrition (Taiz and Zeiger, 2002), this possibility is intriguing and warrants further investigation.
Three lines of evidence from Kronzucker et al. suggest unusually efficient absorption. First, in the Michaelis–Menten relationships fitted to N influx data over an ecologically and agronomically relevant range of N supply, and plants of identical N status, Vmax for steady-state N influx was 40 % greater for than for , and KM was 50 % smaller. Secondly, absorption was inducible and, in plants deprived of for 24 h, the induction of uptake was exceptionally rapid, peaking within 2 h; in comparison, in barley, which is considered a highly efficient user, full induction requires up to 24 h, and in white spruce, which is considered poor at using , full induction takes several days (references in Kronzucker et al., 1995, 1997, 2000). Thirdly, from the subcellular distribution of N absorbed by plants fed either or , estimated from the kinetics of 13N efflux from labelled roots, the proportion of translocated to the shoot was 50 % larger, and that lost through efflux back out of the roots 50 % smaller. When and were provided together at the same total N concentration as in the single N species experiments, absorption and assimilation of were repressed, but those of were stimulated to the extent that net N influx was doubled compared with plants fed solely on . Because very little free is translocated to the shoot in rice (Kronzucker et al., 1998), this indicates that enhances assimilation in some way, possibly through the -specific induction of additional pathways for assimilation (Kronzucker et al., 1999; Britto and Kronzucker, 2004).
The extent of uptake by roots in flooded soil will depend on its rate of formation from near root surfaces, its rate of transport to and absorption by the root, and its rate of transport away from the root and loss through denitrification. The rates of formation and subsequent denitrification will depend on reducing conditions in the soil and sinks for O2 other than nitrification. The sinks include microbial and non-microbial processes.
In this paper, a mathematical model of these processes is developed with which to calculate rates of formation, uptake and loss of over the range of conditions in which wetland plants grow.
THEORY
Consider the movements of O2, and in anoxic flooded soil near a cylindrical root that simultaneously releases O2 and absorbs and . The microbial sinks for O2 include both autotrophic processes, such as oxidation of , S2− and CH4, and heterotrophic processes (Conrad and Frenzel, 2002; Kirk, 2004). The non-microbial sinks include oxidation of inorganic reductants in the soil, such as Fe(II), which may be both mobile and immobile (Howeler and Bouldin, 1971; Reddy et al., 1980; Kirk and Solivas, 1994).
In initially anoxic soil, populations of aerobic microbes will be small, and therefore non-microbial processes consuming O2 will initially tend to dominate. As inorganic reductants close to the roots become exhausted, the rate of non-microbial O2 consumption will decline. Concomitantly, the rate of microbial O2 consumption will increase as aerobic populations develop. Hence the system will be complex and dynamic. We have some understanding of the kinetics of the non-microbial processes (Ahmad and Nye, 1990; Kirk et al., 1990; Kirk and Solivas, 1994), but only a weak understanding of the microbial processes and the complex interactions they involve (Bodelier et al., 2000, 2004; Brune et al., 2000; van Bodegum et al., 2001). Therefore, a very elaborate treatment of the O2-consuming processes, dissecting out the various contributors, is unjustified at this stage of our understanding, and, in our model, we therefore combine microbial and non-microbial processes. Likewise, our understanding of growth rates and activities of -oxidizing microbes in the rhizosphere of wetland plants and interactions with nutrients, toxins and competing substrates is insufficient for a very elaborate treatment, and hence we apply the simplest realistic treatment, with the maximum rate of nitrification as a proportion of the maximum rate of overall O2 consumption.
The following sections give the equations we use to describe the system. The symbols used are defined in Table 1.
Table 1.
Symbol |
Meaning |
Dimensions* |
---|---|---|
a | Root radius | Length |
b | Radius of zone of root influence | Length |
bNH4 | Buffer power for , | VolumeL volume−1 |
DL | Solute diffusion coefficient in water, subscripted A, N or O for , and O2 | Area time−1 |
FmNH4 | Maximum influx of into roots | Mass area−1 time−1 |
FmNO3 | Maximum influx of into roots | Mass area−1 time−1 |
f | Soil diffusion impedance factor | |
IDenit | Inhibition function for denitrification | |
KMDenit | Michaelis constant for denitrification | |
KMNH4 | Michaelis constant for uptake | |
KMNit1 | Michaelis constant for nitrification (re O2) | |
KMNit2 | Michaelis constant for nitrification (re ) | |
KMNO3 | Michaelis constant for uptake | |
KMO | Michaelis constant for O2 consumption | |
LV | Root length density | Length volume−1 |
Concentration of in soil solution | ||
Concentration of in soil solution | ||
[O2]L | Moncentration of O2 in soil solution | |
VmDenit | Maximum rate of denitrification | Mass volume−1 time−1 |
VmNit | Maximum rate of nitrification | Mass volume−1 time−1 |
VmO | Maximum rate of O2 consumption | Mass volume−1 time−1 |
v | Water flux into root | Length time−1 |
λ | Root wall permeability factor | Length time−1 |
θ | Soil water fraction by volume | VolumeL volume−1 |
Subscript L indicates soil solution; no subscript indicates whole soil.
Oxygen
The transport of O2 away from the root and its simultaneous consumption in soil processes is described by the equation
where RO is the rate of consumption in soil processes. The whole-soil concentration of O2 is related to the concentration in solution by [O2] = θ[O2]L. Following the reasoning above, we lump together microbial and non-microbial sinks for O2 and describe net O2 consumption using Michaelis–Menten kinetics:
The boundary conditions for eqn (1) are as follows. The flux of O2 across the root surface, r = a, depends on the rate of delivery of O2 through the root, the external sink for O2 in the soil and the permeability of the root wall separating the soil solution from the root gas spaces. Following Armstrong and Beckett (1987), we define a root wall permeability factor, λ, relating the flux across the root wall to the difference in O2 concentration across it. The flux across the root wall is equal to the flux into the soil at r = a. Hence
where subscripts c and a indicate the root cortical tissue and the soil at the root surface, respectively. Armstrong and Beckett give values of λ derived from experiments with polarographic electrodes (see Parameter Values, below). At the other boundary where the zones of influence of adjacent roots overlap, there is no transfer of O2. Thus
Ammonium
The transport of towards the root and its simultaneous consumption in nitrification is described by the equation
The whole-soil concentration of is related to the concentration in solution by the soil buffer power: . The rate of nitrification will depend on the concentrations of O2 and , and we describe this using dual-substrate Michaelis–Menten kinetics (see McConnaughey and Bouldin, 1985, for reduction, or Arah and Stephen, 1998, for CH4 oxidation):
where VmNit is the rate in the absence of substrate limitation and KMNit1 and KMNit2 are Michaelis constants. The boundary conditions for eqn (5) are as follows. The flux of into the root will depend on the concentration of in solution at the root surface and the root absorption properties. In accordance with conventional practice (Kronzucker et al., 1997, 2000), we describe this with a Michaelis–Menten equation:
The quantities FmNH4 and KMNH4 are not constant during plant growth but vary with the plant's N status and other factors. However, we treat them as constants and test the model's sensitivity to them. At the other boundary, we assume there is no transfer of . Thus
Nitrate
The transport of towards the root and its simultaneous production in nitrification and consumption in denitrification is described by the equation
Because is not adsorbed on the soil solid, its concentration in the whole soil is simply related to the concentration in solution by . The rate of denitrification will depend on and also on the concentration of O2, which is the preferred electron acceptor. Following McConnaughey and Bouldin (1985), we describe this with a modified Michaelis–Menten equation:
where IDenit is a function for inhibition by O2. We take inhibition to be linear up to a threshold concentration equal to the Michaelis constant for O2 consumption (Arah and Vinten, 1995):
As for , we use a Michaelis–Menten equation for the relationship between the flux of into the root and the concentration in solution at the root surface:
At the other boundary, we assume there is no transfer of . Thus
Numerical solutions
We expressed eqns (1)–(14) in finite-difference form using Crank–Nicholson approximations and solved the resulting sets of equations by standard numerical methods (Smith, 1985). With time steps of 0·1 h and distance steps of 0·1 mm, mass balances for all solute were conserved to within 1 % for simulations up to 10 d. Copies of the computer program for the numerical solutions, written in Fortran, are available from the first author.
PARAMETER VALUES
The standard set of parameter values used in the calculations are given in Table 2. Our reasons for choosing these values are as follows.
Table 2.
Parameter |
Value |
Reference |
---|---|---|
a | 0·1 mm | Matsuo and Hoshikawa (1993) |
b | 2 mm | Matsuo and Hoshikawa (1993) |
bNH4 | 50 cm3 cm−3 | Kirk (2004) |
DLA,N,O | 2 × 10−5 cm2 s−1 | Kirk (2004) |
FmNH4 | 5 pmol cm−2 s−1 | Kronzucker et al. (1999) |
FmNO3 | 25 pmol cm−2 s−1 | Kronzucker et al. (1999) |
f | 0·4 | Kirk et al. (2003) |
KMDenit | 1 µm | See text |
KMNH4 | 50 µm | Kronzucker et al. (1999) |
KMNit1 | 1 µm | See text |
KMNit2 | 200 µm | See text |
KMNO3 | 10 µm | Kronzucker et al. (1999) |
KMO | 1 µm | See text |
5 µmol cm−3 | Kirk (2004) | |
[O2]Lc | 0·18 µm | See text |
VmDenit | 2 pmol cm−3 s−1 | See text |
VmNit/VmO | 0·25 | See text |
VmO | 500 pmol cm−3 s−1 | See text |
v | 0 cm s−1 | See text |
λ | 1 × 10−4 cm s−1 | Armstrong and Beckett (1987) |
θ | 0·6 cm3 cm−3 | Kirk (2004) |
Rate of O2 release
The O2 budget of an individual root depends both on the rate of O2 movement and consumption within the root—which varies with position along the root and between main roots and laterals—and on the rate of O2 consumption in the surrounding soil. Measurements of rates of release, therefore, need to allow for differences across the root and its laterals and must be made under O2 sink conditions that are realistic for roots in soil. In practice, it is difficult to satisfy these conditions, and consequently reported rates of release for whole root systems vary by more than two orders of magnitude (Bedford et al., 1991; Begg et al., 1994; Sorrel and Armstrong, 1994).
However, mathematical models of root aeration show that rates of release at the upper end of the measured range can be sustained by rice roots with typical characteristics (Armstrong and Beckett, 1987; Kirk, 2003). Kirk (2003) developed a model of the steady-state diffusion of O2 through a primary rice root and its laterals and the simultaneous consumption of O2 in root respiration and loss to the soil. A sensitivity analysis showed that the basic architecture of rice root systems, i.e. a system of coarse, aerenchymatous, primary roots with gas-impermeable walls conducting O2 to short, fine, gas-permeable laterals, provides the greatest absorbing surface per unit aerated root mass. With this architecture and typical rates of root respiration, rates of O2 loss to the soil from the laterals and primary root tip can be at the upper end measured experimentally, equivalent to a flux of up to 25 pmol cm−2 (root surface) s−1.
Based on this and trial runs with the present model, we use as standard a root wall permeability factor, λ = 10−4 cm s−1 and we specify the O2 concentration in the root cortex {[O2]Lc in eqn (3)} as equal to half that in air [8·75 mol cm−3 (gas space) at s.t.p.].
Rate of O2 consumption
For ten soils with a wide range of organic matter and reducible Fe contents, Howeler and Bouldin (1971, Table 4) found steady-state rates of O2 consumption by reduced soil cores exposed to O2 equivalent to 100–1000 pmol cm−3 s−1 (mean value 500 pmol cm−3 s−1). Roughly 50 % of this was microbial. We therefore take VmO = 500 pmol cm−3 s−1 as our standard value. Heterotrophic aerobes will operate efficiently at sub micromolar O2 concentrations (Conrad and Frenzel, 2002) and we take as standard KMO = 1 µm.
Rate of nitrification
The maximum rate of nitrification is taken as a proportion of the maximum overall rate of microbial O2 consumption. From the stoichiometry of nitrification, 2 mol of O2 are consumed per mol of formed:
Therefore, an upper limit on the rate of nitrification is half the net rate of microbial O2 consumption, i.e. VmNit/VmO = 0·5. We take as standard VmNit/VmO = 0·25. Also we take as standard KMNit1 = KMO = 1 µm and KMNit2 = 200 µm based on typical concentrations of in solution in rice soils.
Rate of denitrification
Experiments in which fertilizer is added to flooded soils under field conditions indicate maximum rates of N2 + N2O loss through denitrification of a few kg of N ha−1 d−1 (e.g. Lindau et al., 1990; Samson et al., 1990). Assuming denitrification to be distributed over a soil depth of 10 cm, this is equivalent to a rate of denitrification per unit soil volume of a few pmol cm−3 s−1. We therefore take as standard VmDenit = 2 pmol cm−3 s−1. Measured concentrations of in flooded soils rarely exceed a few micromolar, unless the soil is fertilized with (Arth and Frenzel, 2000; Liesack et al., 2000), and therefore denitrifier populations must operate at concentrations less than this. We assign as standard KMDenit = 1 µm.
The ratio of nitrous oxide to nitrogen gas formed in denitrification will depend on the relative abundance of and organic substrates and on other factors influencing the rates of the sequential steps in denitrification (Kirk, 2004). Small concentrations of relative to organic substrates, as expected near the roots of wetland plants, will favour complete reduction to N2. Also, the slow escape of any N2O formed in flooded soil will favour its further reduction to N2. Hence, reported denitrification losses from rice fields as N2O are at least two orders of magnitude smaller than losses as N2 (Galbally and Chalk, 1987; Mosier et al., 1989; Buresh et al., 1991; Bronson et al., 1997).
Root and uptake properties
Up to a certain point, plants can regulate the inflow of N across their roots according to their need for N, and the inflow for a given external N concentration therefore depends on the plant's past supply of N. Hence, Wang et al. (1993) found for rice grown for 4 weeks in 2, 100 and 1000 µm solutions, the respective values of Vmax (µmol g−1 h−1) and KM (µM) were: 12·8 and 32·2; 8·2 and 90·2; and 3·4 and 122·1, i.e. Vmax was 6-fold smaller and KM 4-fold larger for 2 µM compared with 1000 µm . For rice grown in 100 µm N solutions, Kronzucker et al. (1999) found that Vmax values were 8·1 and 5·7 µmol g−1 h−1 for - and -fed plants, respectively, and KM values were 26 and 51 µm. Given that external concentrations at the root surface will be far smaller than concentrations, uptake will be ‘upregulated’ to a greater extent than uptake, and we take as standard Fmax = 5 pmol cm−2 s−1 (calculated from Vmax in µmol g−1 h−1 using root density = 1 g cm−3 and a = 0·1 mm) and KM = 50 µm for uptake, and Fmax = 25 pmol cm−2 s−1 and KM = 10 µm for uptake.
Root geometry
The root system of rice plants in flooded soils comprises coarse primary roots, 0·3–1 mm in diameter, supporting a dense system of fine laterals, 50–150 µm in diameter (Matsuo and Hoshikawa, 1993). Total root length densities averaged over the 15–20 cm deep puddled soil layer may be as high as 20–30 cm cm−3. Calculations with the above parameters for root absorption properties and measured concentrations of in soil solutions indicate that almost the whole of this root length is required to account for measured rates of N uptake by rice in flooded soils (Kirk and Solivas, 1997).
The corresponding mean inter-root distance is calculated as follows. With a regular parallel array of roots, if each root is assigned a cylinder of influence such that the whole soil volume is divided equally between roots, the radius, b, of the cylinder is given by
where LV is the root length density. The value b = 3 mm, which is realistic for half the distance between neighbouring primary roots, corresponds to LV = 3·5 cm cm−3; b = 1 mm, which is realistic for half the distance between laterals, corresponds to LV = 31·8 cm cm−3.
MODEL PREDICTIONS
Predicted concentration profiles, fluxes and rates of nitrification–denitrification
Figure 1 shows the concentration profiles of O2, and in the soil calculated with the standard set of parameter values over 10 d of root–soil contact, and Fig. 2 gives the fluxes of O2 and N species across the root over time. Figure 1 shows that only very small concentrations of in the soil solution develop: approx. 1–2 µm within <0·5 mm of the root and 0 µm at >1 mm from the root, i.e. given the radial geometry, all but undetectable averaged over the inter-root distance. Nonetheless, the fluxes of into the root shown in Fig. 2 are substantial. The accumulated uptake of nitrogen over 10 d is 1·61 µmol cm−3 of soil, or 33 % of the initial content of the soil (= 5 µmol cm−3, equivalent to 105 kg of N ha−1 over a 15 cm depth), and the concentration of in solution in the soil bulk concomitantly falls from 100 to 64 µm. Nitrate uptake accounted for 34 % of total N uptake, and nitrification accounted for 14 % of the total O2 consumption in 10 d. The ratio of N denitrified to total N uptake was 0·20 or 6·6 % of the initially in the soil.
To gauge how realistic these results are, we compare the calculated rates of denitrification with published values. Measurements of denitrification in flooded rice fields made by following the emission of 15N2 and 15N2O following addition of N-fertilizer strongly labelled with 15N indicate losses in the range 1–5 % of applied ammoniacal-N over the range of soils and management conditions considered (Buresh and Austin, 1988; Mosier et al., 1989; Reddy et al., 1989; Buresh et al., 1991). Arth et al. (1998) directly measured N2 and N2O emitted by rice plants grown in chambers with an atmosphere of O2 and helium. This gave denitrification losses of the order of 6 % of added urea-N in 10 d and mean N2 + N2O emission rates of approx. 30 nmol (N) cm−2 (soil surface) h−1. The mean emission rate calculated here with the standard parameters is 14 nmol (N) cm−2 (soil surface) h−1 assuming 10 cm soil depth. We conclude that our calculated losses are realistic.
We know of no published direct measurements of rates of uptake by wetland plants in flooded soil under field conditions. Because the is rapidly assimilated, direct measurements of uptake are difficult.
Sensitivity analysis
Figure 3 shows the sensitivity of the calculated total N and uptakes and denitrification to model parameter values over what we consider to be realistic ranges for wetland plants. As discussed above, we have some understanding of total rates of O2 consumption in flooded soils, but a much weaker understanding of the growth rates and activities of nitrifying microbes under different circumstances. We therefore show the sensitivity to different parameters in interaction with a varying nitrification potential as represented by Vmax for nitrification as a proportion of Vmax for total O2 consumption (VmNit/VmO).
Effect of nitrification and denitrification rates
Figure 3A shows the sensitivity to the maximum total rate of O2 consumption (VmO). At a given VmNit/VmO, with increases in VmO the proportion of N uptake as increases and total N uptake increases correspondingly. Also, the ratio of N denitrified to total N uptake decreases. This is because with a greater O2 sink, the spread of the oxygenated zone around the root is smaller and nitrification occurs closer to the root. Therefore, the concentration gradient of towards the root is steeper and a greater proportion of the is taken up. The effect of VmO varies with VmNit/VmO: when VmNit/VmO is large, denitrification losses decrease more rapidly with increases in VmO.
Effect of root uptake properties
As FmNO3 increases and KMNO3 decreases, an increasing proportion of N is taken up as and a decreasing proportion of the formed is denitrified (Fig. 3B). Over the range of FmNO3 and KMNO3 values shown in Fig. 3B, and other parameter values as standard, accounts for 15 to nearly 40 % of N uptake. Denitrification losses increase sharply as root uptake decreases.
Effect of root geometry
Figure 3C shows interactions between root geometry and rates of uptake and denitrification. As root length density (LV) increases, the rates of total N uptake and depletion of soil N increase. Simultaneously, with increasing LV, the inter-root distance decreases and therefore the proportion of the inter-root zone that is oxygenated increases, and so nitrification and uptake increase. Superimposed on this is the effect of root radius. With large inter-root distances, increasing the root radius tends to increase the capture of and decrease denitrification (data not shown). However, with small inter-root distances, denitrification rates are small and the capture of increases as the root radius decreases.
Effect of soil buffer power
Figure 3D shows that uptake increases sharply as bNH4 decreases, but the proportion of uptake as is little influenced. As bNH4 decreases, for a given total concentration of in the soil, the concentration of in solution increases, and hence the uptake of tends to increase. Simultaneously, nitrification tends to increase as in solution increases, and hence the rate of uptake increases. Thus, the sensitivity of N uptake to VmNit/VmO increases as bNH4 decreases. There is a corresponding decrease in denitrification relative to N uptake, because the gradient of near the root is shallower at smaller bNH4, and hence a greater proportion of nitrification occurs close to the root.
Effect of mass flow of the soil solution
Mass flow of solution towards the root in the transpiration stream tends to compress the zones of oxygenation and nitrification and extend the zone of depletion. The above calculations were made with v = 0. The model shows that a rapid flux of water across the root surface (v = 10−5 cm s−1) slightly compresses the profile of but has a negligible effect on the profiles of O2 and and rates of uptake and denitrification (data not shown). Approximate solutions of eqn (5) indicate that the fractional increase in influx resulting from mass flow is about av/(0·5DLAθf) (Kirk and Solivas, 1997), or approx. 2 % for the standard parameter values and v = 10−5 cm s−1. Hence, for practical purposes, the effect of mass flow can be ignored.
CONCLUDING REMARKS
Our calculations show that wetland plants growing in flooded soil can take up a large part of their nitrogen as formed from in the rhizosphere, without excessive losses of N through denitrification. The extent of this will vary greatly between soils and management regimes, being sensitive to reducing conditions in the soil and the sinks for O2 other than nitrification. Water regimes will particularly influence this. It is expected that in future rice will have to be produced with far less water across Asia as water resources are increasingly diverted to non-agricultural uses (IRRI, 2003). Therefore, water-saving irrigation methods, such as maintaining a minimal depth of standing water in the field and intermittently draining water from the field, will be increasingly widespread. This will favour increased formation, and it will be important to manage conditions to maximize the capture of by the crop and minimize denitrification.
We have focused on lowland rice, but it is probable that other wetland plants are similarly efficient in capturing formed in the rhizosphere. This would have implications for the selection of plants for waste-water treatment in artificial wetlands.
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