The study and modelling of plant adaptations to anoxia in submerged soils has a long history (reviewed by Armstrong et al., 1991, 1996). But to date, the relation between root properties for internal aeration and those for efficient nutrient acquisition has not received attention. This is important because the characteristics of roots allowing internal aeration may conflict with those for nutrient acquisition, particularly the need for a large absorbing surface per unit root mass and possibly the need to influence conditions in the rhizosphere. This paper develops a simple model to explore these questions, with emphasis on rice.
The relevant root characteristics are as follows. As a root grows through submerged, anoxic soil, the cortex in the region of the base partially disintegrates forming continuous gas channels between the base and the tip. This both permits gas transport from and to the aerial parts of the plant and lessens the amount of respiring tissue per unit root volume. Altered respiratory processes may further reduce the O2 requirement in particular tissues, and low permeability of the root wall to gases as a result of thickenings and suberization lessens the loss of O2 to the soil. The structure of the root is therefore apparently dominated by the need for internal gas transport. But on the face of it, this structure may conflict with the needs for efficient nutrient absorption. The development of gas-impermeable layers in the root wall seems likely to impair the ability of those parts of the root to absorb nutrients, and the disintegration of the cortex might impair transport from the apoplasm to the main solute transport vessels in the stele, though evidence for this is uncertain (Drew & Saker, 1986; Kronzucker et al., 1998).
A further characteristic of rice roots in submerged soil is the system of short fine laterals (1–2 cm long and 0.1–0.2 mm in diameter) that develop as branches along the primary roots. These are much less aerenchymatous than the primary roots (porosities of 1–2% compared with ≤ 50%) and they do not develop secondary thickenings in their walls to the same extent (Matsuo & Hoshikawa, 1993). They account for a small part of the root mass but the bulk of the external surface, and they are plumbed directly into the main water and solute transport vessels in the stele of the primary root. It therefore seems likely that the laterals are responsible for the bulk of the nutrient absorption by the root system and compensate for any impairment of nutrient absorption by the primary roots as a result of adaptations for internal aeration.
The question arises: what combination of fine laterals and aerenchymatous primary roots provides the greatest absorbing surface per unit of root material? Not having impermeable wall layers and having a large surface area to volume ratio, the laterals will tend to leak O2 more rapidly than the adjacent primary root. A related question is therefore how the O2 budget of the root system is affected by the combination of primary roots and laterals. Armstrong et al. (1990, 1996) modelled O2 release from adventitious and lateral roots of the rhizomatous wetland species Phragmites australis, and found that for the appropriate combination of root types, properties and dimensions, and a large but realistic soil O2 demand, the ratio of O2 consumption in root respiration to that in loss to the soil was 13:1 for adventitious roots but 0.15:1, i.e. reversed, for laterals. Evidence for preferential loss of O2 from laterals in rice includes measurements of Fe oxide coatings on roots placed in deoxygenated agar containing Fe(II) (Trolldenier, 1988); changes in redox potential as roots grew across rows of Pt electrodes in anaerobic soil (Flessa & Fischer, 1992); and the abundance of methane oxidizing bacteria, which are obligate aerobes, along rice lateral roots in anaerobic soil (Gilbert et al., 1998).
Although O2 leakage compromises the root's internal aeration, some leakage is desirable for a number of purposes. These include oxidation of toxic products of anaerobic metabolism in submerged soil such as ferrous iron (van Mensvoort et al., 1985); nitrification of ammonium to nitrate, there being benefits in mixed NH4+–NO3− nutrition (Kronzucker et al., 1999, 2000); and mobilization of sparingly soluble nutrients such as phosphorus (Saleque & Kirk, 1995) and zinc (Kirk & Bajita, 1995) as a result of acidification due to iron oxidation and cation-anion intake imbalance. In some situations rates of nitrogen acquisition by rice in submerged soil are limited by the size and characteristics of the root system (Kirk & Solivas, 1997), so the pay-off between requirements for internal aeration and those for efficient nutrient capture is important. A further point is the extent to which the greenhouse gas methane, which is produced in large quantities in submerged rice soils, may be oxidized in the rhizosphere before it can escape from the soil via the root gas channels. Model calculations indicate that roots allowing greater gas transmission may suppress, rather than enhance, methane emission as a result of greater oxidation in the rhizosphere (Arah & Kirk, 2000).
In this paper a simple model is developed to explore these questions, and the model is used to calculate maximum tolerable rates of O2 release from the root system and compare these with measured rates in different experimental systems.
Table 1 gives the nomenclature used.
|AR||Surface area of root capable of absorption||cm2 primary root−1|
|a||Radius of root, subscripted L for laterals and P for primary||cm|
|DG||Diffusion coefficient of oxygen in air||cm2 s−1|
|Flux of oxygen across root surface||mol cm−2 (root) s−1|
|fG||Impedance factor for diffusion in cortical gas space|
|k||Coefficient for distribution of laterals along primary root||cm|
|LV||Length density of roots, subscripted P for primary roots||cm cm−3 (soil)|
|LVL||Length density of lateral roots||cm cm−3 (lateral root cylinder)|
|N||Number of primary roots per hill of plants|
|[O2]G||Concentration of oxygen in the cortical gas space||mol cm−3 (gas space)|
|Rroot||Rate of oxygen consumption in root respiration||mol cm−3 (root) s−1|
|Rsoil||Rate of oxygen loss to soil||mol cm−3 (root) s−1|
|Q||Rate of oxygen consumption in root respiration||mol g−1 (root) s−1|
|r||Axial distance from base of root; subscripted as in Fig. 2||cm|
|x||Radius of cylinder containing laterals||cm|
|WR||Mass of root||g primary root−1|
|θG||Root porosity||cm3 cm−3 (root)|
|ρ||Density of root tissue||g cm−3 (tissue)|
Structure of the root system
Figure 1 shows the main features of the root system of rice growing in submerged soil. The root system and the biogeochemistry of the soil change rapidly during the initial stages of plant growth and as soil reduction proceeds. But the picture given in the figure is reasonable from about the mid-tillering stage until flowering. The roots in the anoxic soil beneath the floodwater – soil interface, receiving their oxygen solely from the aerial parts of the plant, are considered. The distribution of primary roots beneath a hill of plants is approximately hemi-spherical with the individual roots randomly distributed with respect to the vertical and horizontal directions. Thus if there are N primary roots per hill, the length of primary roots per unit soil volume, LVP, at any distance r from the centre of the hill is:
About each primary root there is a cylinder of laterals, increasing in density with distance from the root base as shown in Fig. 2. The laterals may develop up to sixth-order branches. A simple equation to describe this is:
where LVL is the length density of laterals in the cylinder of soil occupied by them, k is a coefficient, equivalent to the distance at which LVL(r) = 0.25LVLmax, and r0 < r ≤ rlat. If the cylinder has outer radius x and inner radius aP (i.e. the radius of the primary root), and x and aP are constant along the root length, then the total length density of primary and lateral roots at distance r from the centre of the hill is:
Eqn 3 gives reasonable fits to measured profiles of LV with depth under field conditions using the parameter values given below (data not shown).
Structure of an individual primary root and its laterals
The internal structure of a primary root approximates three concentric cylinders corresponding to the central stele, the cortex and the wall layers. The porosity of the cortex, permeability of the root wall and the coverage of the root with laterals vary along the root length, with a much smaller porosity, more-permeable wall and no laterals in the region of the tip.
Where the laterals emerge from the primary root, there are generally cracks in the epidermis a few µm wide and apparently directly connected to the primary root aerenchyma (Butterbach-Bahl et al., 2000). It seems likely these will be important in gas transfer, though there are no direct measurements showing this. Beneficial bacteria can evidently enter the root through such cracks, but pathogenic bacteria are somehow excluded (James et al., 2002). In practice leakage of O2 from the cracks and axial gradients of O2 within laterals will lead to gradients of O2 release along laterals. However, for the intended purpose of the model – which is to explore the effects of root properties required for internal aeration vs those for nutrient absorption – an elaborate treatment of these effects is not necessary; it is sufficient that the loss of O2 increases with the density of laterals. A constant leakage along the length of laterals is therefore assumed.
Figure 2 defines, for the purposes of the model, the distances at which the porosity of the primary root and coverage with laterals change, leading to four zones with properties summarized in Table 2. The porosity of the laterals is assumed to be the same as that of the primary root tip. The corresponding equations for the root mass and total surface area capable of absorbing nutrients in each zone are given in the Appendix. It is assumed that, because of the changes in wall permeability along the root, nutrients are only absorbed by the primary root in the zones beyond the laterals (rlat < r < rmax) and by the laterals. This is also the surface across which O2 leaks.
|Zone||Porosity||Length density of laterals|
|r2 < r < rmax||θG2||0|
|r1 < r ≤ r2||θG1 – α(r − r1)||0|
|rlat < r ≤ r1||θG1||0|
|r0 < r≤rlat||θG1|
Transport and respiration in the roots
Transport of gases through the cortical gas spaces is solely by diffusion. A mass flow of air could occur if the O2 consumed in respiration was not replaced by an equal volume of gaseous CO2, the CO2 being much more soluble. However, Beckett et al. (1988) have shown that convection by this means will always be subordinate to diffusion in nonthroughflow systems and will only ever have a minor effect. Hence diffusion is the principal means of gas transport.
Radial homogeneity in tissue respiration rates is assumed. In practice, there may be radial differences in respiratory demand and gas permeability resulting in radial oxygen gradients, and some plants can tolerate a degree of anoxia in the stele, substantially decreasing the oxygen requirement per unit root volume. Armstrong & Beckett (1987) show how this can be modelled. However, it has not been allowed for here, as to do so would unduly complicate the model.
More important for the present purposes are the axial differences in respiration rates. As well as differences due to changes in tissue mass per unit root volume as the aerenchyma develops, there are differences due to changes in root function along the root. Hence the growing tip and the parts of the root actively absorbing nutrients have greater respiratory demands.
Loss of oxygen to the soil
Oxygen is also consumed in loss to the rhizosphere. It is assumed that the primary root wall is completely impermeable to oxygen in the zone covered with laterals (i.e. r0 < r < rlat). In fact the wall is not completely impermeable in this zone, but as discussed in the previous section, it is sufficient to combine the resulting flux with that from the laterals.
The sink for oxygen in the surrounding soil will vary in a complicated way with soil conditions and time. Oxygen is consumed in the soil in both microbial reactions, mainly fuelled by root-derived carbon, and nonmicrobial reactions, mainly with ferrous iron. The rates of O2 consumption in microbial and nonmicrobial reactions are often similar in different submerged soils under steady-state conditions (Howeler & Bouldin, 1971; Reddy et al., 1980; Kirk & Solivas, 1994). However, in the rhizosphere, microbial O2 consumption will tend to increase with time as root-derived carbon accumulates, whereas nonmicrobial consumption will tend to decrease as ferrous iron and other reductants are depleted. Hence the overall rate may be roughly constant. Differences across the root system will also tend to cancel each other (Kirk & Du, 1997). The declining O2 concentration in the root with distance from the base coincides with a declining root length density. So although the internal concentration of O2 will be greater towards the root base, the flux out of the root will not increase correspondingly because the external concentration will be greater as a result of the greater density of neighbouring roots leaking O2. Given these considerations, the additional complexity involved in allowing for differences in flux across the root system is unjustified and a constant flux from the laterals and the primary root in the zone beyond the laterals is assumed.
Also a steady state is assumed to exist in which the flux of oxygen across the root base equals the net consumption in root respiration and loss to the soil. Hence the concentration profile through the root is constant over time, the concentration varying from atmospheric at the root base to near zero at the apex. This is realistic because the rate of root elongation is small compared with the rate of gas transport. The model calculates the maximum primary root length that can be kept aerated for a given set of root characteristics and external sink conditions.
Equations for transport, respiration and loss
The following equation describes the steady-state diffusion of oxygen through the root and its simultaneous consumption in respiration and loss to the soil:
where Rroot is the rate of consumption in tissue respiration and Rsoil the rate of loss to the soil, both on a per unit root volume basis. Rroot at a particular distance along the root is the sum of the respiration in the primary root and in any laterals emerging from it. Hence, if the rate of respiration per unit root mass is Q,
Likewise Rsoil at a particular distance is the sum of the rates of loss from the primary root and from the laterals. Hence, if is the flux across unit root surface:
It is assumed that Q is independent of [O2]G until it reaches a very low value, below which it is zero (Armstrong et al., 1991).
At the root base[O2]G = [O2]G0r = r0
and at the root apex[O2]G = [O2]Gminr = rmax
where [O2]Gmin is the minimum O2 concentration required for root respiration (≈ 30 nmol cm−3 (gas space)).
Solution of the equations
Eqns 4 to 6 were solved, subject to the boundary conditions, using standard numerical methods (Smith, 1985). Copies of the program for the numerical solution, written in Fortran, are available from the author. Distance steps of 0.01 mm were used; 10-fold smaller distance steps gave the same results, indicating that the solution is stable.
Standard values of parameters and coefficients
The dimensions of the root system are taken from Matsuo & Hoshikawa (1993) and personal observations: aP = 0.5 mm, aL = 0.075 mm, x = 1.5 cm, LVLmax = 15 cm cm−3, k = 12.5 cm and ρ = 1 g cm−3. For the dimensions of a primary root: r0 = 2, rmax − r1 = 3 and rmax –r2 = 1 cm; astele = 0.25 and acortex = 0.47 mm, i.e. if 70% of the cortex is occupied by gas space, θG1 = 0.44 and θG2 = 0.095 cm3 cm−3 (root). The maximum θG in rice cultivars averaged over the primary root is about 0.5.
For the gas transport properties of the root: DG = 2.07 × 10−1 cm−2 s−1 at s.t.p. and fG = 1 (Armstrong, 1979). For the rate of root respiration: Q = 6.5 × 10−6 mmol g−1 (root) s−1 at the root tip (and in the laterals) and 40% of this at r0 ≤ r < r2, falling linearly from the tip to r2 (from Luxmoore et al., 1970; Armstrong et al., 1991).
For the flux of O2 across root surfaces: = 5 pmol cm−2 (root) s−1. For soil-grown rice plants Begg et al. (1994) obtained fluxes of 1–12 pmol cm−2 (root) s−1, calculated from rates of Fe2+ oxidation near planar layers of rice roots in anaerobic soil, and Kirk & Bajita (1995) obtained 1–2 pmol cm−2 (root) s−1 with the same experimental system but a soil with a smaller ferrous iron content. These calculations underestimate the total O2 flux because they do not allow for O2 consumed by rhizosphere microbes. Kirk & Du (1997) obtained values of 1–4 pmol cm−2 (root) s−1 for rice plants grown in sand perfused with deoxygenated nutrient solution, and Bedford et al. (1991) obtained slightly smaller fluxes in a similar system but without sand. These measurements also underestimate fluxes for soil-grown plants because the external sink for O2 is smaller. But measurements in which an infinite external sink for O2 is provided (Sorrell & Armstrong, 1994) overestimate fluxes for soil-grown plants. In practice the external sink will depend on O2 consumption in both microbial and nonmicrobial processes, depending on such factors as the soil organic matter content, the reducible iron content, and the rate of water percolation through the soil. The standard flux is a realistic mean for different rice soils.
The concentration of O2 in the gas space at the root base, [O2]G0, is that in air at s.t.p., 8.75 mol cm−3 (gas space).