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Published online 13 September 2006
Published in J Environ Qual 35:1903-1913 (2006)
DOI: 10.2134/jeq2005.0422
© 2006 American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America
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TECHNICAL REPORTS

Plant and Environment Interactions

Theoretical Comparison of How Soil Processes Affect Uptake of Metals by Diffusive Gradients in Thinfilms and Plants

N. J. Lehto*, W. Davison, H. Zhang and W. Tych

Environmental Science Department, Lancaster University, Bailrigg, Lancaster, LA1 4YQ

* Corresponding author (w.davison{at}lancaster.ac.uk)

Received for publication November 5, 2005.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 REFERENCES
 
The theoretical basis for using measurements of metal uptake by the technique of diffusive gradients in thinfilms (DGT) to mimic processes in soils that affect uptake of metals by plants is examined. The uptake of metals by plants and DGT were compared conceptually and quantitatively by using the classic Barber model of plant uptake and the DIFS (DGT-induced fluxes in soils) model of uptake by DGT. For most metals and plants considered, uptake fluxes were similar to those induced by DGT using the most common gel layer thicknesses of 0.2 to 2mm. Consequently DGT perturbs the chemical equilibrium of metals in the soil solution and between soil solution and solid phase, to a similar extent to plants, and therefore induces a similar balance in supply by diffusion and by release from the solid phase. DIFS was used to show that desorption kinetics, which are not considered by the plant uptake model, are likely important for uptake when the capacity of the soil solid phase is large. Model calculations showed that mass flow into a plant root would only contribute appreciably to the total flux of metal under circumstances when the solid phase reservoir of metal was very low. Generally, however, DGT is likely to emulate supply processes from the soil that govern uptake of metal by plants. Exceptions are likely to be found in poorly buffered soils (typically sandy and/or low pH), and at very high concentrations of metals in soil solution, such that the soil solution concentration at the plant root interface is higher than the Michaelis-Menten constant (Km).

Abbreviations: DGT, diffusive gradients in thinfilms • DIFS, DGT-induced fluxes in soils • Kd, solid-solution phase partitioning coefficient • Tc, time needed for the partitioning components of Kd to reach 63% of their equilibrium values, assuming the solution concentration is initially zero • Km, Michaelis-Menten constant • Imax, maximum flux of ions into a root • CE, effective concentration


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
REFERENCES
 
THE UPTAKE by plants of trace metals, such as zinc, cadmium, and nickel is generally thought to occur via ‘active transport’ of the free ion through saturable, high affinity transporters that allow the accumulation of metals against their electrochemical gradients (Whiting et al., 2003; Zhao et al., 2002). If metal uptake is slow, depletion at the root surface is negligible and the metal concentration can be expected to be proportional to the free ion activity in solution. In this situation the free ion activity model applies (Sauvé et al., 1996). However, if metal is removed rapidly from the soil by the plant, the concentration of metal in the solution immediately adjacent to the root surface can become depleted. This can induce resupply of metal from dissociation of metal complexes in the solution and release of metal from the soil particles in contact with the confined zone where depletion in solution occurs. In this case the supply to the plant will be determined by the concentration of total labile metal in solution, its diffusional transport through the soil solution, the concentration of labile metal available from the solid phase, and the kinetics of release from solid phase to solution. Here labile metal is defined as metal that can rapidly exchange within the timescale that can modify the diffusional supply of metal to a plant. Complexes that dissociate rapidly (labile) are able to contribute metal for uptake. They usually have relatively small stability constants (e.g., logK < 8 for Cd and Zn). If dissociation is slow, as for some very strong complexes, particularly of characteristically kinetically limited metals such as Ni, the complex will not contribute any metal to uptake. The potential supply of metal from the solid phase has been implicitly acknowledged by the many schemes that have been devised for assessing available metal by simple chemical treatment (e.g., with a simple salt or complexing agent). Note that although contributions of the metal taken up come from complexes in solution and the solid phase, it may still only be the free ion that undergoes membrane transport. However, when the dynamics of supply from other components is significant, the amount of metal taken up is no longer proportional to the free ion activity.

Recently the new technique of DGT (Davison and Zhang, 1994) has been used to assess the available metal. Like a plant root, DGT removes metal from solution and induces resupply from the solid phase. The analogy of the free ion reacting with the binding phase can still be retained. It is the rapid rate of this binding that induces localized depletion of metal and supply from complexes in solution and the solid phase. Diffusive gradients in thinfilms has been used to determine an effective concentration (CE), that expresses the equivalent soil solution concentration experienced by the DGT device as it is supplied from both solid phase and solution (Zhang et al., 2001). Initial studies where plants have been grown in pots have shown good correlations between metal concentrations in herbage and the metal measured by DGT in the same soil (Zhang et al., 2001; Davison et al., 2000; Zhang et al., 2004; Nowack et al., 2004). By attempting to understand why the DGT measurements of CE correlate well with plant uptake, we should increase our understanding of the physicochemical aspects of plant-soil interactions. This work examines the underlying theoretical basis by using accepted mathematical models that describe the dynamics of metal uptake by plants or DGT. It compares the formulation and outputs of the models to identify the common and distinctive processes.

Plant uptake models that focus on the supply of solutes from soils are well established (Barber, 1995; Tinker and Nye, 2000). Although they were originally developed for nutrients, they have been used to provide a quantitative appreciation of the effect of the plant on metal concentrations in adjacent soil (Whiting et al., 2003; Mullins and Sommers, 1986; Adhikari and Rattan, 2000; Schnepf, 2002). The models have been validated for a limited set of plants and metals (mainly Zn) by comparing measured and predicted concentrations in plants after fixed growth periods (Barber, 1995). Plant uptake models have evolved from simple diffusion and mass-flow based models (Bouldin, 1961; Barber and Cushman, 1981; Olsen et al., 1962) to more complex models that incorporate quantifiable processes in the rhizosphere (Barber and Cushman, 1981; Kirk et al., 1999). This modeling has been especially useful in highlighting gaps in knowledge about rhizosphere processes, including supply of ions from the solid phase in response to depletion in soil solution. For some elements in particular solid phase compartments, the exchange has been found to be very rapid (e.g., magnesium and calcium in kaolinite) (Sparks, 1995). However, the rate of supply of Ni in response to its local depletion in the solution within a soil has been shown to be limited by its release from the solid phase (Ernstberger et al., 2005).

Diffusive gradients in thinfilms physically mimics the removal of metals by a plant by having a layer of chelating resin behind a diffusive layer (usually a gel faced with a filter membrane) that is in contact with the soil solution. This chemically and physically well-defined system introduces a sink for ions in the soil, which results in a concentration gradient in the soil solution adjacent to the device and a consequent supply of ions from the solid phase into the locally depleted solution. A numerical model known as DIFS has been developed by Harper et al. (1998) to simulate the response of a homogeneous soil in contact with the DGT device. This model can be used to interpret DGT measurements to provide information on soil parameters, such as the partitioning coefficients (Kd) for a labile metal between solid and solution phases and the rates of this exchange (Ernstberger et al., 2002).

A quantitative comparison of the two models using published data on plant uptake kinetics allows the identification of conditions where DGT measurements are likely to correlate well with plant uptake of trace metals and where this relationship is likely to break down. A key issue is whether fluxes induced by DGT and plants are similar. Only then do plants and DGT perturb the soil in the same way and therefore induce a similar balance in supply by diffusion and from the solid phase. Existing PC-executable versions of DIFS and the Barber uptake model (NST 3.0: Claassen and Steingrobe, 2000) are used to facilitate this comparison.

The Models
The equations for the two models are shown in Table 1. To provide familiarity, the symbols are those that have usually been used. The positioning of the parameters in the list shows the comparable terms in the two models. The concentration in the solution phase, C, is expressed per cm3 while in the solid phase, Cs, it is per g.


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  		Table 1. The governing equations for the DIFS and the generic plant model (Sources: Harper et al., 2000; Barber, 1995).

 
DGT-Induced Fluxes in Soils and Sediments (DIFS)
The basic concepts of the DIFS model are shown in Fig. 1a . DIFS couples removal and diffusive transport within the DGT device with diffusive transport and exchange between solid phase and solution in the adjacent soil. Transport of ions to the DGT device occurs solely via molecular diffusion in the soil solution. The equations for this model are shown in Table 1. In formulating them several assumptions were made.
  1. Transport of solute to the resin occurs only via diffusion in solution described by Fick's Law in one dimension, appropriate for transport into a planar device.
  2. Reaction within the soil is represented kinetically as a first order exchange between two labile pools: a mobile (dissolved) and an immobile (sorbed) one.
  3. The resin layer has an infinite capacity to remove ions instantaneously from the solution phase.


Figure 1
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  		Fig. 1. Components of the dynamic model of a DGT soil system, (a) DIFS and (b) dynamic plant-soil system.

 
The Generic Plant Uptake Model
Traditional plant uptake models consider diffusion and mass flow as the mechanisms by which ions are supplied to the plant. Supply from the solid phase is incorporated within the concept of buffer power, which has been described in two different ways: (i) the relative change in the concentration of ions in the solid phase exchange pool (Cs) and in the soil solution (C) ({partial}Cs/{partial}C) (Rengel, 1993), or (ii) the ratio of the total number of diffusible ions (CT) per unit volume of soil to the concentration of the ion in soil solution (C) (Cushman, 1984). The latter interpretation is considered to have a larger range of applications (Rengel, 1993). The buffer power concept implies that there is instant exchange between solid and solution phases that is not limited within the time frame of the diffusional transport by the rates of sorption or desorption.

The equations for a generic plant uptake model (Fig. 1b) as described by Barber (1995) are shown in Table 1. When used with the appropriate boundary conditions the equations can be used to calculate how the radial distribution of concentration from the root surface evolves with time, enabling calculation of the flux at the root surface (Barber, 1995). Several assumptions were made in the development of the equations for uptake of nutrient (Barber, 1995).

  1. The soil is homogeneous and isotropic.
  2. Soil moisture is maintained constant at or just below field capacity.
  3. Solute uptake occurs only from solutes in solution at the root interface.
  4. Neither root exudates nor microbial activity influences solute fluxes.
  5. Solutes move to the root surface via mass flow and diffusion.
  6. The relationship between net influx and concentration can be described by Michaelis-Menten kinetics.
  7. Roots are assumed to be smooth cylinders with no root hairs/mycorrhizae.
  8. The effective diffusion coefficient and buffer power are assumed to be independent of concentration.

Conceptual Comparison of DIFS and the Plant Uptake Model
The two models have many similarities: diffusion from the solution phase adjacent to the root/DGT supplies the ions to the interface and interaction between the solid and solution phases is accounted for. The flux into the root/DGT is dependent on the interfacial concentration, which in turn depends on the soil conditions and the rate at which ions diffuse to the root/DGT. The differences between the two models are listed below.

  1. The parameters used appear to be different.
  2. DIFS works in one dimension with Cartesian coordinates; the plant model is designed to work in radial coordinates.
  3. Flux into the root/DGT device is controlled by Michaelis-Menten kinetics, whereas it is determined by Fick's Law for DGT.
  4. There is a transpiration stream to a plant, but as the DGT device has no ingress of water, the DIFS model does not have an advection term.
  5. The exchange between the solid and solution phase is instant in the plant model, whereas in DIFS it is regulated by the sorption and desorption rate constants. Consequently the ratio of concentrations in the solution phase to those in the solid phase remains constant in the plant model, whereas in DIFS it changes locally.

The main reason for the apparently different set of parameters used by the two models is that they originate from two relatively independent schools of thought: sediment geochemistry and soil chemistry/biology. The key parameters can be inter-converted using simple formulae (Table 2).


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  		Table 2. Converting between key parameters used in DIFS and the Plant Model

 
The different geometries of the DGT device (planar) and a plant root (radial) represent a clear difference between the two models. However, these differences may not affect the ability of DGT to mimic plant uptake for two reasons. (i) Depletion occurs adjacent to the surface in both cases. It is this depletion in the soil and the ensuing reaction it induces, which is important, whether or not it is configured radially. (ii) Where plant roots are packed closely together they can collectively approach a planar case. This is the principle of the rhizobox approach, which has produced some of the rare data on solute distributions adjacent to roots (Wenzel et al., 2001). To aid comparison, for the modeling undertaken here, the root radius has been set at a value where there is little difference between radial and planar models. This applies when the width of the depletion zone is smaller than the root radius. In practice, the extent to which modifying the root radius changes the flux of a particular metal into the root depends on the rate of uptake of that metal by the plant. If diffusion is limiting, a decrease in root radius results in larger uptake, due to flux increasing with decreasing radius. If there is no diffusion limitation, uptake is controlled by the plant (Michaelis-Menten parameters) and root radius has no effect. In the case of the nonaccumulator, Thlaspi arvense, increasing the root radius from 0.01 cm to 1 cm results in an approximately 10% decrease in the flux of Zn into the root over a 24 h period. The amount of Zn taken up by unit root area of hyperaccumulator T. caerulescens decreases by 25% when the root radius is similarly modified. These calculated differences apply irrespective of the concentration of Zn, provided its interfacial concentration is substantially less than Km.

The flux to the plant is controlled by Michaelis-Menten kinetics, which limit the flux to a maximum value (Imax) and determine the rate at which the maximum flux is reached (Km). The flux into the root is linear with respect to the metal concentration adjacent to the root, as long as that concentration is significantly below the Km value (Fig. 2 ). These Michaelis-Menten parameters are specific to plant species, genotype, age, soil temperature, and the nutritional status of the plant (Jungk and Claassen, 1989; Teo et al., 1992), and may also be dependent on the technique with which they have been measured (Rengel, 1993). The flux into the DGT device is also directly proportional to the metal concentration in the soil solution adjacent to the DGT device, (Table 1) but there is no maximum flux.


Figure 2
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  		Fig. 2. Total zinc uptake by DGT ({Delta}g = 0.293 cm and 0.1 cm) compared to Thlaspi arvense and Thlaspi caerulescens, when a high rate of water ingress (10–5 cm s–1) into the root is present, at different initial soil solution concentrations (mol cm–3).

 
The rate of ion movement to the root by mass flow depends on the rate of water uptake, which in turn is affected by plant species, climate, and the soil's moisture content (Barber, 1995). Diffusive gradient thinfilm and the associated DIFS model can only be expected to serve as a surrogate for plant uptake for situations when the relative proportion of metal supplied via mass flow to the total metal uptake by the plant is low. The situations where this is likely to arise are explored quantitatively in the next section.

Consideration of the kinetics of desorption from the solid phase can be important. A change in the amount of labile metal available from the solid phase is likely to have two major effects.

  1. The rate at which the metal is supplied to the solution from the solid phase pool will be modified.
  2. If there are several solid phase pools of metal with different rates of metal release, depletion of the concentration of the fast desorbing pool will increase the relative importance of the slower desorbing pools.

The importance of the kinetics of interchange between solid phase and solution when modeling plant uptake depends on the metal considered and the nature of the solid phase. If a metal desorbs very quickly (Tc < 1s) (Honeyman and Santschi, 1988), its supply from solid phase to solution can be regarded as instantaneous. Conversely, if the metal desorbs very slowly (Tc in excess of hours), its supply from solid phase will not be important compared to the supply from diffusion. It is only for intermediate rates of supply that changes in the rate of release from the solid phase appreciably affect the overall flux. This implies that the kinetics of processes associated with aging, which are usually measured on timescales of days and weeks, are unimportant when considering dynamic uptake models. When assessing the uptake of metals that have intermediate rates of desorption, the use of rate constants to quantify the process becomes imperative. Ernstberger et al. (2002) showed that the rate of resupply from the solid phase can have a controlling influence on DGT-measured concentrations for some metals and soils. Similar effects are likely during uptake of metals by some plants, as the mechanisms of ion supply to DGT are also common to ion supply to plants.

Quantitative Comparison of the Two Models
Comparable DGT and Plant Uptake Fluxes
The flux to the DGT resin is regulated by the diffusive layer characteristics and thickness, whereas Michaelis-Menten kinetics regulate the flux to the plant. By ensuring that the other parameters in each model have the same values, it is possible to estimate a diffusion layer thickness that is equivalent to uptake of a specific metal by a given plant (as described by the Michaelis-Menten coefficients Imax and Km). The necessary Michaelis-Menten constants are difficult to measure accurately. They are usually based on simple uptake solutions, and because experimental conditions have a considerable influence on the kinetics of ion uptake Imax and Km values reported by different authors are not strictly comparable (Zhao et al., 2002). However, by using parameters measured for plants that would be expected to have greatly different affinities for metal uptake, e.g. hyperaccumulator and nonaccumulator species, this approach allows assessment in broad terms of a range of the physical characteristics of a DGT device that are likely to emulate uptake of a given metal by plant species. Use of the DIFS model for DGT devices with values of gel layer thickness appropriate to a particular plant then allows investigation of the influence of solid phase reservoir size and the kinetics of (de)sorption on metal uptake by different plants.

Figure 3 shows how the mass of Zn predicted by DIFS to be accumulated by 1 cm2 of DGT resin in 24 h depends on the thickness of the diffusion layer. The soil used for this simulation had the properties reported by Ernstberger et al. (2002): particle concentration (i.e., mass of particles in unit volume of pore water), Pc, 2 g cm–3; porosity, {phi}s, 0.570; soil solid phase density, 2.65 g cm–3; partitioning coefficient, Kd, 150 cm3 g–1; a uniform soil solution concentration of Zn of 1 x 10–10 mol cm–3. The response time, Tc, was set at a low value of 0.1 s to emulate the case of virtually instantaneous supply from solid phase to solution in the plant model. When the thickness of the gel layer is modified, the mass of Zn accumulated changes. If there was no depletion of the soil solution adjacent to the device, the mass accumulated would be inversely proportional to the diffusive layer thickness. In practice this proportionality is moderated because thin diffusive layers allow a larger removal flux, which causes more marked depletion of metal in the soil solution, lowering the concentration gradient from the maximum value.


Figure 3
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  		Fig. 3. Dependence of mass per unit area accumulated by DGT in 24 h on diffusion layer thickness. Diffusion layer thicknesses are shown that correspond to the flux deduced from Michaelis-Menten parameters for Zn accumulated by: Thlaspi arvense (shown by the dotted line) and Thlaspi caerulescens (shown by the solid line) (Lasat et al., 1996).

 
The mass taken up in a 24 h period by a plant root of area 1 cm2 (root radius of 1 cm to emulate the planar case) can be calculated using the Barber model if the Michaelis-Menten parameters are known. Values of Imax (1.11 x 10–13 mol cm–2 s–1) and Km (6 x 10–9 mol cm–3) for Zn uptake by Thlaspi arvense (a nonaccumulator plant) seedlings (Lasat et al., 1996) were used with the same soil parameters used for DIFS (converted to suit the plant model using the relationships described in Table 2) to calculate a flux to the roots of 1.28 x 10–10 mol cm–2 d–1. According to Fig. 3, a DGT device with a diffusive layer thickness of 0.29 cm would accumulate the same amount of Zn per unit area. For this situation the concentration of Zn in the pore water adjacent to the device is depleted during the 24 h. The depletion is ≥5% of the initial value within 0.08 cm of the surface (Fig. 4 ). The small Tc ensures there is no kinetic limitation, so the depletion of metal in the pore water simply reflects the depletion of metal in the solid phase.


Figure 4
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  		Fig. 4. The change in solution phase Zn concentrations with distance from the DGT device after a 24 h deployment for devices with diffusion layer thicknesses that mimic uptake by T. arvense and T. caerulescens (initial equilibrium concentration of 0.1 nmol cm–3).

 
A similar simulation was performed for the uptake of Zn by the hyperaccumulator Thlaspi caerulescens in the same soil for the same period of time, with the published Michaelis-Menten parameters of Imax: 5 x 10–13 mol cm–2 s–1 and Km: 8 x 10–9 mol cm–3 (Lasat et al., 1996). The resulting uptake flux of 3.03 x 10–10 mol cm–2 d–1 was higher than for Thlaspi arvense, corresponding to a thinner diffusive layer of 0.1 cm (Fig. 3). The depletion of zinc in the pore water is shown in Fig. 4. Again due to the low value of Tc, the concentrations in the pore water simply reflect zinc depletion of the solid phase. There is much greater depletion adjacent to the device for the hyperaccumulator (depletion is ≥5% of the initial value within 0.1 cm of the surface) (Fig. 4). In both cases negligible water influx into the root was assumed, to closely emulate the DGT device. To minimize any effect that competition between roots may have, the mean distance between roots was simulated as being at least twice the thickness of the depletion zone of Zn in pore water. Repeating the calculations using a soil with markedly different properties did not affect the estimate of an equivalent diffusion layer thickness for each plant. This is consistent with the effect of soil properties on transport being similarly taken into account by the Barber model used to estimate the flux to the plant and DIFS used to convert a flux to a diffusive layer thickness.

Similar calculations to the above were performed for plants where Michaelis-Menten coefficients for cadmium, zinc, and nickel have been previously determined (Table 3). The standard DGT devices that are most commonly used have had diffusive layer thicknesses of 0.05 or 0.09 cm, but thicknesses ranging from 0.01 to 0.24 cm have been used (Davison and Zhang, 1994; Scally et al., 2003). These thicknesses embrace most of the values in Table 3 that have been calculated to simulate Zn, Cd, and Ni uptake. Clearly, then the DGT device induces metal fluxes that are similar to those that apply during plant uptake. In both cases, therefore, there will be a similar depletion in the soil adjacent to the plant or root and therefore similar control by diffusion or solid phase to solution transfer. It is therefore reasonable to expect that the soil response measured by DGT may be related to the effect of the soil on plant uptake, especially in the cases where the concentration adjacent to the surface is significantly below the Km value. Where the concentration is above that of Km, there is likely to be some overestimation of the total uptake by the DGT device.


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  		Table 3. Values of Michaelis-Menten uptake parameters for various plants and the corresponding DGT gel layer thicknesses. Where published, the numbers in the brackets are the ages of the plants (given in days). The initial soil solution concentration of metal was simulated as being 0.01 nmol cm–3 for Cd and 0.1 nmol cm–3 for Zn and Ni. In cases where the published Imax parameter has been given as units/root-weight/time it is assumed that 1 g of root fresh weight equates to 150 cm2 root surface area (Barber, 1995).

 
Puschenreiter et al. (2005) used a root surface area: root fresh weight ratio of 106 cm2 g–1 to calculate the Michaelis-Menten parameters for Thlaspi goesingense. If this ratio is applied to the parameters provided by Lasat et al. (1996) and Zhao et al. (2002) (where the plants used are of the same Thlaspi genera) the consequent increase in uptake ranges from 32% in the case of Zn uptake by T. arvense (equivalent to a 0.07 cm decrease in {Delta}g) to 8% for Cd uptake by T. caerulescens (equivalent to a 0.025 cm decrease in {Delta}g).

Kinetic Effects
The above calculations were performed using a very fast soil response time (Tc = 0.1s) to simulate the assumed instantaneous exchange between the solid and solution phases described in the Barber model. DIFS allows the soil response times to be varied to reflect the different rates of metal release from solid to solution that can exist in soils, as demonstrated by Ernstberger et al. (2002). The effect of the response time on the accumulated mass depends on the size of the solid phase reservoir. Figure 5 shows that for a small solid phase reservoir (Kd = 10) the soil response time has little effect on the total uptake by the DGT device. In this case the solid phase reservoir is rapidly depleted due to its small size and it is this, rather than the response time, Tc, that is the primary control of mass uptake. Figure 6 illustrates more clearly how depletion of metal in the solution is influenced by depletion of the solid phase metal. When the solid phase reservoir size is large (Kd = 1000), there is little depletion of metal in the solid phase (Fig. 6). The kinetics of release, as reflected in the response time, Tc, then exert a more direct control on the concentration in solution adjacent to the device. For a small Tc the rapid supply from the solid phase ensures that the metal in solution is well buffered, with little diminution at the device interface (Fig. 6) and a large mass taken up by the DGT device (Fig. 5). For a large Tc the kinetics of metal release are the major limit on the supply of metal. This causes a decline in the concentration in soil solution at the device interface (Fig. 6a) and consequently a markedly lower mass taken up by the DGT device (Fig. 5). Although the fast supply to solution for low Tc depletes the solid phase very close to the device, the depletion is still small as a fraction of the very large solid phase reservoir. When the solid phase reservoir is small (Kd = 10), it is substantially depleted even for long response times and the concentration in solution simply reflects this depletion. Clearly both Tc and Kd can be important in determining the flux to DGT and by implication a plant. Consequently a good correlation between plant and DGT uptake is likely to hold even when the concentration in soil solution exceeds Km because the interfacial concentration may still be lower than Km due to limitations by the combined effects of Tc and Kd.


Figure 5
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  		Fig. 5. Modeled effect of changing the soil response time on the amount of Zn accumulated by DGT in a 24 h deployment time (diffusion layer thickness of 0.1 cm).

 

Figure 6
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  		Fig. 6. Effect of solid phase reservoir size, as expressed by Kd, and soil response time, Tc, on concentration of (a) metal in solution and (b) metal in solid phase with distance in the soil. The simulation is for a 24 h deployment time where the diffusion layer is 0.04 cm thick.

 
Until now there was little justification for including the kinetics of supply in plant uptake models because the necessary kinetic data were unavailable. However, the capability of DGT to provide information on both the labile pool size (through Kd) and the kinetics of supply (through Tc) measured on an appropriate time scale may change this situation and allow use of more sophisticated models that include this aspect of soil dynamics. This more comprehensive approach will be especially important when modeling plant uptake in soils with large solid phase reservoirs (clayey soils) and fairly long response times of the metal in the solid phase (Ni) (Ernstberger et al., 2005).

Effect of Mass Flow
There is no ingress of water into a DGT device as there is for plant roots. For conditions under which the rate of transpiration is high, mass flow increases the supply of metal to the root interface. However, as modeled by the Michaelis-Menten boundary condition, the rate of metal uptake into the root is determined solely by the concentration of metal at the root interface (Table 1). As the concentration of the metal increases at the root interface due to advection of pore water to the root, there is a consequent increase in uptake, provided this is allowed by the root membrane. Thus according to the Barber model mass flow contributes indirectly to metal uptake. The model was used to investigate the contribution of advection to the total Zn uptake for Thlaspi caerulescens. The soil and Michaelis-Menten parameters of root uptake were those used before to compare uptake by DGT and plants. The metal uptake of T. caerulescens was calculated for a 24 h period at a water flow rate of 10–5 cm s–1, which is higher than most observed values (Barber, 1995). The NST 3.0-modeled plant uptake of Zn in 24 h was plotted next to the DIFS-modeled Zn uptake by DGT (corresponding gel layer thickness of 0.1 cm from Table 3) over a range of soil solution concentrations (Fig. 2). If transport into the root is limiting (e.g., at high solution concentrations), changing the water flow has no effect on the flux. If transport is limiting, changing the water flow will affect the uptake flux to a certain extent. The results show that there is no more than a 9% difference between the total uptake of the modeled DGT device and the hyperaccumulator until the initial soil solution concentration approaches 8 x 10–9 mol cm–3 (Km, the Michaelis-Menten constant). Close to the Km concentration the similarity breaks down as the uptake kinetics cease to be first order. The effect of advection on root uptake of metal is also influenced by the root radius. In the above case, the root radius was set at 1 cm. Decreasing the root radius increases the diffusive flux and so decreases the importance of advection as a supply mechanism. Simulations at more realistic root radii (0.015 cm) found that increasing the advection from 10–7 to 10–5 cm s–1 resulted in only a 5% increase in the mass uptake over a 24 h period.

The size of the solid phase reservoir (buffer power) has an effect on the relative importance of advection. When the solid phase reservoir is very small (Buffer power = 1), increasing the rate of advection from 10–7 to 10–5 cm s–1 increases the total mass uptake by up to 20%. Conversely when the solid phase reservoir size is large the importance of water flow diminishes and becomes negligible. This has an important implication when assessing the reliability of DGT as a plant surrogate. In situations where the metal is poorly buffered by the soil, advection may make a significant contribution to the metal uptake. Therefore, in a poorly buffered soil system, if there is a high rate of transpiration by the plant, DGT is likely to be limited in its ability to mimic the metal supply process to the plant. The plant will take up more metal than its DGT counterpart.

Increasing the simulation time from 1 to 20 d increases the significance of the water flow, but the majority of the metal taken up by the plants is still supplied by diffusion. This effect can be appreciated by simple logic: as deployment times increase, the depletion distance from the root will increase, limiting the diffusive/solid phase supply, so that mass flow becomes increasingly important in supplying metal to the root.

Implications for Using DGT to Mimic Plants
Both the Barber and DIFS models regulate the transfer of metal from soil to the plant or device by considering supply from diffusion in solution and release from the solid phase. The main differences between the two models are the mechanistic means for metal removal from the soil, absence of mass flow from the DIFS model, and the lack of kinetics of exchange between the solid and solution phase from the plant model. Under certain conditions these differences produce different estimations of uptake between the two models.

By using Michaelis-Menten parameters in the plant uptake model it is possible to compare fluxes to a plant with those to a DGT device. However, data on Michaelis-Menten parameters are sparse and may not be representative of natural conditions. Consequently such an approach is best regarded as an aid to conceptually understanding the conditions under which the DGT device is likely to mimic reasonably well the uptake of metals by plants. The broad range of Michaelis-Menten parameters considered is expected to be reasonably representative of trace metal uptake. They show that the gel layer thicknesses used in DGT determine maximum metal uptake fluxes that are comparable to those observed for some of the plants considered here.

Modeling metal uptake shows that mass flow does not contribute significantly to the uptake in cases where there is a large reservoir in the solid phase. This is due to the lack of solid phase depletion and the consequent abundance of metal available for uptake adjacent to the root. However, when there is poor buffering and long deployment times, the advective supply of undepleted pore water from beyond the depletion zone will supply a greater proportion of metal to the plant. The DGT would consequently be expected to perform well as a plant surrogate in soils where the solid phase has a large capacity to store metal (such as soils rich in clay minerals). The DGT is more likely to underestimate metal uptake by plants in soils that are poorly buffered (such as soils with a high sand content and/or a low pH). Kinetics of exchange, which are metal and soil specific, are also likely to play a part in determining the importance of mass flow to plant uptake. A slow response (high Tc) to depletion is likely to increase the importance of mass flow of metal to the root.

Diffusive gradients in thinfilm measurements are likely to overestimate plant uptake in cases where the Km values for metal uptake by the root are lower or similar to the soil solution concentrations at the soil-root/soil-DGT interface. The degree of error in these cases is likely to increase with the difference between Km and the interfacial concentration. In cases where there is significant depletion at the soil-root/soil-DGT interface, the concentrations may drop to a level where the uptake becomes first order again. However, this is hard to assess without constructing a model that considers both plant uptake kinetics and soil solution reaction kinetics in the way DIFS does.

Active biological effects on plant uptake cannot be disregarded when considering whether DGT is likely to function well as a mimic for plant uptake. Neither of the models consider the effect that plant exudation or microbial activity may have on the amount of metal available to the plant and the dynamic aspects of these processes. Consequently the simple approach used here cannot quantify how much these possible influences will affect the ability of DGT to act as surrogate for plant uptake. The simulations relating the uptake of Zn to a plant with the amount accumulated by a DGT device were done using plants that are thought to be little influenced by microbial activity. However, for plants such as Oryza sativa and Zea mays L. (McLaughlin, 2002) such effects can be considerable. Recently Puschenreiter et al. (2005) used a Rhizobox to provide high resolution measurements of Ni concentrations in solution and in a labile phase in the rhizosphere immediately adjacent to Thlaspi goesingense roots. They found that the Barber plant model was unable to simulate the experimental measurements. This was attributed to ligand-promoted mineral dissolution resulting from organic acid exudation by the plant roots. The possible role of these biologically controlled processes should be considered when attempting to predict how well a DGT device will mimic the plant.

This work expands on and helps to explain the existing evidence that under some conditions DGT performs better than other measuring techniques in assessing bioavailability to plants. Under conditions where the capacity of the solid phase reservoir of available metal and the kinetics of supply from the soil limit uptake, the controls on uptake to DGT and a plant are very similar. Moreover the kinetic constraints that determine whether metals will be contributed from complexes in solution are similar for DGT and plants. No other single measurement technique takes all these factors into account.


   ACKNOWLEDGMENTS
 
This research has been jointly funded by the Natural Environment Research Council and the Macaulay Institute in Aberdeen.


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