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Plant, Cell and Environment (2012) 35, 1558–1566

doi: 10.1111/j.1365-3040.2012.02509.x

First observation of diffusion-limited plant root phosphorus uptake from nutrient solution pce_2509

1558..1566

JAKOB SANTNER1,2, ERIK SMOLDERS2, WALTER W. WENZEL1 & FIEN DEGRYSE2,* 1

Rhizosphere Ecology and Biogeochemistry Group, Department of Forest and Soil Sciences, Institute of Soil Science, University of Natural Resources and Life Sciences Vienna, Konrad-Lorenz Strasse 24, 3430 Tulln, Austria and 2Laboratory for Soil and Water Management, Katholieke Universiteit Leuven, Kasteelpark Arenberg 20, 3001 Heverlee, Belgium

ABSTRACT Diffusion towards the root surface has recently been shown to control the uptake of metal ions from solutions. The uptake flux of phosphorus (P) from solutions often approaches the maximal diffusion flux at low external concentrations, suggesting diffusion-controlled uptake also for P. Potential diffusion limitation in P uptake from nutrient solutions was investigated by measuring P uptake of Brassica napus from solutions using P-loaded Al2O3 nanoparticles as mobile P buffer. At constant, low free phosphate concentration, plant P uptake increased up to eightfold and that of passive, diffusion-based samplers up to 40-fold. This study represents the first experimental evidence of diffusion-limited P uptake by plant roots from nutrient solution. The Michaelis constant of the free phosphate ion obtained in unbuffered solutions (Km = 10.4 mmol L-1) was 20-fold larger than in the buffered system (Km ~0.5 mmol L-1), indicating that Kms determined in unbuffered solutions do not represent the transporter affinity. Increases in the P uptake efficiency of plants by increasing the carrier affinity are therefore unlikely, while increased root surface area or exudation of P-solubilizing compounds are more likely to enhance P uptake. Furthermore, our results highlight the important role natural nanoparticles may have in plant P nutrition. Key-words: Al2O3 nanoparticles; diffusion limitation; diffusive gradients in thin films; Michaelis constant; Michaelis– Menten kinetics.

INTRODUCTION The uptake of most plant nutrients is mediated by membrane proteins, which transport the nutrient ions into the cell against an electrochemical gradient. Because of the mechanistic similarity of the membrane transport to enzyme-substrate reactions and as uptake curves are generally well described with the Michaelis–Menten equation, Correspondence: J. Santner. Fax: +43 1 47654 1186; e-mail: [email protected] *Present address: School of Food, Agriculture and Wine, University of Adelaide, PMB1, Glen Osmond, SA 5064, Australia. 1558

the Michaelis–Menten model has been adopted for the description of plant root nutrient uptake (Epstein & Hagen 1952; Epstein 1953):

Fupt =

FmaxCs K m + Cs

(1)

Fupt is the actual ion uptake flux, Cs the ion concentration at the root surface, Fmax the maximal ion uptake flux and Km is the Michaelis constant, which corresponds to the concentration at which Fupt equals 1/2 Fmax. The free nutrient ions (e.g. K+, NO3-, H2PO4-, SO42-, M2+ for cationic metallic micronutrients), and not complexes that might also be present in the exterior solution, are generally considered to be the species that are readily taken up by plant roots (Marschner 2002). An exception is the direct uptake of intact Fe-phytosiderophore complexes by grasses (Ma & Nomoto 1996). However, departures from the free ion models for nutrient uptake of plants have repeatedly been reported for trace metals. Bell, Chaney & Angle (1991) observed increased uptake of Cu, Fe, Mn and Zn by barley (Hordeum vulgare L.) in ligand-buffered nutrient solutions compared with ligand-free solutions at constant free (ion) metal activity. Enhanced uptake of Cd in the presences of increasing chloride concentrations has been reported in resin buffered nutrient solution at constant free metal activity (Smolders & McLaughlin 1996), indicating that Cd-chloro complexes contribute to the uptake. Degryse, Smolders & Merckx (2006a) explored the hypothesis that labile metal complexes enhance metal uptake from solution by enhancing the diffusive transport of the free metal over an unstirred water layer adjacent to roots. In the vicinity of (bio)surfaces, a boundary layer forms where fluid convection approaches zero and, hence, no convectional solute transport towards the surface occurs. The effect of unstirred water layers [diffusive boundary layers (DBL)] on solute transport has been recognised several decades ago (Dainty 1963; Wilson, Sallee & Dietschy 1971). At low solute concentrations, the ion transport across membranes is limited by the diffusive flux of solute towards the membrane in case of high affinity uptake.Although mass flow towards the root caused by the transpiration stream is an additional solute transport mechanism to the root surface, its contribution to uptake at solute concentrations in the low micromolar © 2012 Blackwell Publishing Ltd

First observation of diffusion-limited P uptake range to uptake is estimated to be very low, often below 0.1% (cf. Tinker & Nye 2000). Degryse, Smolders & Merckx (2006a) showed that Cd uptake by spinach (Spinacia oleracea L.) and by wheat (Triticum aestivum L.) increased as the concentration or the dissociation rate of the complex increased at constant low Cd2+ activity.The observed uptake flux was in good agreement with predicted uptake assuming diffusion limitations (Degryse et al. 2006a; Degryse, Smolders & Parker 2006b). The authors concluded that the enhancement of metal uptake by plant roots in ligandbuffered systems is most likely due to alleviation of the diffusion limitation in presence of complexes rather than due to direct uptake of intact complexes. Labile complexes dissociate within the diffusion layer where the free ion is depleted and thus enhance the uptake, even if the intact complex is not taken up. The same conclusions were drawn for Zn and Cu uptake by spinach and tomato (Solanum lycopersicum L.; Degryse, Smolders & Parker 2006c) and Zn uptake by wheat (Wang et al. 2009). As for trace metals, the uptake of phosphorus (P) by plants is an active process that is mediated by specific transport proteins. The H2PO4- ion is the P species that is readily taken up by plant roots (Smith 2002). In soils, several studies have demonstrated depletion of P around the roots, indicating that uptake is limited by the diffusive transport of P to the root (Bhat & Nye 1973). Uptake curves determined in nutrient solutions are usually assumed to indicate the affinity of the plant roots for P. This assumption implies that the uptake is limited by internalization and not by the transport to the roots. However, the high root absorbing power for P (ratio of uptake flux to free ion concentration in solution; Nye & Tinker 1969) suggests that diffusion-limited plant uptake is likely for P even in nutrient solutions. The aim of this study was to investigate if P uptake by plants in nutrient solutions is limited by the diffusive transport of phosphate to the plant roots. Nanoparticulate Al2O3 loaded with P was used as a mobile buffer for increasing the potential diffusion flux. Implications for the description of root ion uptake by the Michaelis–Menten model, for estimating plant ion uptake from soil and for the role of natural nanoparticles in plant P nutrition, are discussed.

MATERIALS AND METHODS Buffering P in aqueous solutions Al2O3 powder with a nominal particle size of ⱕ 10 nm was obtained from American Elements (Los Angeles, CA, USA). Dynamic light scattering (ALV-NIBS High Performance Particle Sizer, ALV-GmbH, Langen, Germany) was applied to measure the hydrodynamic diameter of the particles in aqueous solution. Light scattering was measured at 173° to the incident He/Ne laser beam (632.8 nm; 3 mW power). The autocorrelation functions were analysed with the Contin algorithm to derive intensity-weighed particle size distributions. The average diameter of the smaller particle population found was 40.3 nm whereas a bigger particle population was on average 477 nm in diameter.

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For the experiments, only the smaller size fraction was used, as smaller particles diffuse faster and are therefore expected to have more effect on the diffusive flux. A suspension containing only the small particle size fraction was prepared by centrifuging a suspension of the Al2O3 particles at ~1600 g for 5 min. The Al concentration in the supernatant was determined by ICP-OES (Perkin-Elmer 3300DV, Wellesley, MA, USA). This way, a suspension of Al2O3 nanoparticles with an average diameter of 40.3 nm at a concentration of 2.46 g Al2O3 L-1 was prepared. For determining the adsorption of P onto the Al2O3 nanoparticles, a solution containing 54.8 mg L-1 nanoparticles and 2 mmol L-1 Ca(NO3)2 as background electrolyte was prepared from this nanoparticle suspension. P (as KH2PO4) was added to this solution to achieve P concentrations of 0.1, 10, 30 and 100 mmol L-1. The solution pH was buffered at pH 6 using 2 mmol L-1 2-(N-morpholino)ethanesulfonic acid (MES). The solutions were radiolabelled with 32P (~50– 320 kBq L-1). Five millilitre subsamples of these solutions were pipetted into dialysis membranes with a cut-off of 3.5 kDa. The closed membrane bags were put into tubes containing 15 mL of 2 mmol L-1 Ca(NO3)2 and 2 mmol L-1 MES solutions at pH 6. After 30 h, the outer solutions were sampled and the 32P activity was measured with a Packard Tri-Carb 1600CA liquid scintillation counter (Packard Instruments, Meriden, CT, USA).

Plant cultivation Brassica napus cv. Caracas seeds were germinated between moist tissue paper sheets. Six-day-old seedlings were transplanted to a nutrient solution [nutrient concentrations in mmol L-1: 2 Ca(NO3)2, 1.2 KNO3, 0.5 MgSO4, 0.1 KH2PO4; in mmol L-1: 25 NaCl, 15 H3BO3, 10 FeNaEDTA, 5 MnSO4, 1 ZnCl2, 0.5 CuSO4, 0.07 (NH4)6Mo7O24]. The solution pH was buffered at pH 6 using 2 mmol L-1 MES. The pH was checked daily and was adjusted to 6.0 ⫾ 0.1 when necessary using HCl. After 4 d, the nutrient solution was replaced by a solution containing no phosphate for P starvation of the plantlets prior to the P uptake experiments. Except for the P concentration, the composition of the nutrient solution remained unchanged. After 24 h of P starvation, the plants were used for P uptake experiments. The experiments were done in a phytotron at a 14/10 h day/night cycle with day/ night temperature of 20/16 °C and a photon flux density of 450 mmol m-2 s-1.

P uptake of B. napus The Michaelis–Menten parameters of B. napus cv. Caracas were determined in a preliminary uptake experiment.Three seedlings were exposed to 0.9 L stagnant, unbuffered nutrient solution (nutrient concentrations as given above) at P concentrations of 0.08, 0.84, 10.9, 103, 255, 506 and 1003 mmol L-1 for 24 h. The nutrient solutions were radiolabelled with 32P at a specific activity of 7 Bq nmol-1. Analysis of plant P uptake was done as described for the main experiment.

© 2012 Blackwell Publishing Ltd, Plant, Cell and Environment, 35, 1558–1566

(0) (0)

Data on B. napus is the average of three replicates; diffusive gradients in thin films (DGT) measurements are the average of two replicates. SD represents the standard deviation of the mean. One of two DGT samples for the B2 treatment was lost, therefore no SD is given. a ratio of total to free P concentration. b a = absorbing power, that is, ratio of uptake flux to free P concentration in solution.

(0.2) (0.1)

(0.02) (0.11)

0.86 0.48 2.7 7.8 16.1 (0.02) (0.2)

0.86 1.0 5.8 17 35 (1.5) (3.8) (6.2) (1.7) (5.5) 8.4 47.6 69.4 72.9 72.3 (1.5) (8) (13) (4) (12) 8.4 101 149 157 156 1 47 306 3311 19767 0.01 0.97 6.57 71.4 427 0 0.01 0.07 0.71 4.27

0.01 0.02 0.02 0.02 0.02

P uptake flux pmol cm-2 s-1 ab 10-4 cm s-1

DGT Brassica napus

P uptake flux pmol cm-2 s-1 Buffer powera Total P concentration mmol L-1 Free P concentration mmol L-1

UB B1 B2 B3 B4

(2)

Tr

M At

Nanoparticle concentration g Al2O3 L-1

Fupt =

Table 1. P buffering treatments (Tr) and overview on experimental data (standard deviation in brackets)

In the main experiment, the P uptake by oilseed rape was determined in buffered solutions with constant free P concentrations of 0.02 mmol L-1, but with increasing total P concentrations. These solutions were prepared using increasing concentrations of Al2O3 nanoparticles (up to 4.3 g L-1) as P buffer (Table 1). P and Al2O3 suspension were mixed at a constant ratio but at increasing total amounts so that all buffered solutions contained 0.1 mmol P per g of Al2O3 (or 0.19 mmol P per g of Al). The unbuffered control solution had a P concentration of 0.01 mmol L-1. The solutions were labelled with 32P as tracer, at a specific activity of 7 Bq nmol-1. Apart from the P-loaded nanoparticles, the composition of the nutrient solutions was the same as during the plant cultivation. The B. napus plantlets were exposed to 0.9 L experimental solutions for 6.75, 24 and 48 h, respectively. The nutrient solutions were aerated during the uptake experiment. For the 24 h uptake period, all five buffering treatments were used, whereas uptake for the two other uptake periods (6.75 and 48 h) was only determined for the unbuffered treatment and the buffered B2 and B3 treatments. Two B. napus plants were used for the unbuffered treatments to reduce the extent of P depletion in the solutions. Three plants were exposed to the buffered solutions where P depletion was expected to be small. At the beginning and at the end of the experiment, the free and the total P concentration in the experimental solutions were measured. To determine the free P concentration, subsamples of the nanoparticle suspensions were centrifuged at 38000 g for 60 min and 32P activity was measured. To determine the total P concentration, the experimental solutions were digested by hot aqua regia digestion. Subsequently, both 32P activity and stable P concentrations were determined. At the end of the exposure, the roots of the plantlets were rinsed with distilled water for about 1 min to wash off adhering Al2O3 nanoparticles as much as possible. The plants were divided in roots and shoots by cutting off the root at the stem base with scissors. The P of shoots and roots was extracted by immersing the plant parts in 10 mL of 5 mol L-1 HNO3 for 24 h. In preliminary experiments, this procedure extracted ~86% of the total plant P. The 32P activity in extracts was determined and corrected for the extraction efficiency. The plant P uptake was calculated based on the specific activity of P in the solution. The plant extracts were also analysed for their Al concentrations to determine the amount of Al2O3 nanoparticles that still adhered to the roots after rinsing and to monitor shoot Al contents. The amount of P associated with Al2O3 adhering to the roots was calculated based on the P loading of the nanoparticles (0.19 mmol per g of Al), and was subtracted from the total amount of P measured in the root extracts. This procedure was used to avoid a bias of the root P contents by adhesion of P-containing Al2O3 nanoparticles. The plant P uptake flux Fupt was calculated as

aDGTb 10-4 cm s-1

1560 J. Santner et al.


First observation of diffusion-limited P uptake where M is the mass of P taken up, A is the root surface area and t is the time of P uptake. A specific root surface area of 200 cm2 (g RFW)-1 (Degryse et al. 2009) was adopted for calculating the root surface area of the experimental plants. In the unbuffered control treatments, considerable depletion of the P concentration in the nutrient solution occurred during plant uptake for the longer uptake periods.The plant uptake flux Fupt was corrected for P depletion in these solutions using Eqns 3 and 4, which were derived based on exponential depletion of the nutrient solution (first-order uptake rate).

fdepl = 1 −

cor Fupt =

cend cini

Fupt ⎛ 1 ⎞ ⋅ ln ⎜ ⎝ 1 − fdepl ⎟⎠ fdepl

(3)

(4)

where fdepl is the P depletion coefficient, and cini and cend are the initial and final P concentrations in the unbuffered solutions. The correction was small (14%) for the first sampling time (6.75 h) but substantial (44%) for the last sampling time. As the duration of the experiment was up to 2 d, there was considerable growth of the plants during the P uptake period. To correct for this, we used an exponential growth model, which was in agreement with the experimental observations:

At = A0 e RGR t

(5)

where A0 and At are the initial root surface area and the root surface area at time t, respectively, and RGR is the relative growth rate. A value of 0.47 d-1 for RGR was obtained by fitting Eqn 5 to the root weights measured at the end of the 6.75, 24 and 48 h P uptake periods. The mass of P taken up by a growing root from time zero to time t can be expressed as t

M = ∫ Fupt At dt

(6)

0

The combination of Eqns 5 and 6 allows the calculation of the growth-corrected P uptake flux, Fplant:

Fplant =

M RGR At − A0

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P uptake of DGT samplers Diffusive gradients in thin films (DGT) is a dynamic speciation technique that measures diffusive fluxes of solutes into DGT samplers (Zhang & Davison 1995). This technique measures the diffusion flux of P from solutions through a diffusion layer (a gel) towards a P-binding ferrihydrite layer that acts as a zero-sink for PO4 ions. DGT gels are permeable for nanoparticles with diameters of up to 260 nm (Van Der Veeken, Pinheiro & Van Leeuwen 2008), so the nanoparticles used here (40 nm diameter) can diffuse towards the binding layer. The same authors showed that this technique can measure increased diffusive fluxes caused by labile, nanoparticle-bound ion species. After the plant experiment, DGT samplers containing ferrihydrite resin gels (Santner et al. 2010) were exposed to the experimental solutions while stirring the solution. The control solution was freshly prepared because of the P depletion in this treatment. After a deployment time of 24 h, both the binding and the diffusion gel were eluted in 10 mL of 0.25 mol L-1 H2SO4, and the activity of 32P in the eluates was determined. This allowed calculating the total P in the gel and the P flux, based on the specific activity of P in the solution. The Al concentration in the eluates was determined by ICP-OES.

RESULTS AND DISCUSSION P buffering in nutrient solutions Sorption of P onto the Al2O3 nanoparticles was almost linear between 0.1 to 10 mmol P L-1. A solid-solution partitioning coefficient, Kd, of 4600 L g-1 was determined for this concentration range. This Kd was used for calculating the free P concentrations in the buffered nutrient solutions in subsequent experiments. Ultracentrifugation and ultrafiltration were used to confirm the free phosphate concentrations in solution. The experimental solutions had a free P concentration of 0.01 [unbuffered (UB)] or 0.02 [buffered (B)] mmol L-1, and a total P concentration (including P sorbed on the nanoparticles) of 0.01 (UB), 1.0 (B1), 6.6 (B2), 71 (B3) and 427 (B4, most strongly buffered solution) mmol L-1. Slow desorption of P from the nanoparticles or slow diffusion of the nanoparticles might prevent the nanoparticles from enhancing the diffusion flux. The DGT technique was used to assess the suitability of the nanoparticles for enhancing the diffusion flux. We normalized the DGTmeasured flux for the free orthophosphate concentration in solution:

(7)

This correction had negligible effect at the shortest sampling time, but amounted to 55% at the last sampling time. The corrections for bulk depletion (Eqn 4) and plant growth (Eqn 7) did not affect the overall trends or conclusions, but resulted in more precise values. These corrections were small at the shortest uptake time (6.75 h).

α DGT =

FDGT [Pfree ]

(8)

In an unbuffered stirred solution, aDGT should correspond to D/Dg according to Fick’s laws, where D is the diffusion coefficient (~9 ¥ 10-6 cm2 s-1 at 25 °C) and Dg the thickness of the diffusive layer in the DGT device (0.076 cm). The observed value for aDGT


1562 J. Santner et al. (0.86 ⫾ 0.02 ¥ 10-4 cm s-1) in the unbuffered solution was in good agreement with the theoretical value (0.80 ¥ 10-4 cm s-1). In the buffered solutions, aDGT will be larger than in the unbuffered solution if the nanoparticles contribute to the flux. An increase in aDGT was indeed observed with increasing degree of buffering (Table 1). This indicates that the P-loaded nanoparticles enhanced the P uptake by diffusing into the DGT sampler, where the free P concentration is decreased compared with the bulk solution, inducing the release of P from the nanoparticulate species. Measurement of Al in the binding gels, by ICP-OES analysis of the gel eluates, confirmed that the nanoparticles could penetrate the gel. The excess P measured in the buffered systems compared with the unbuffered system could not be explained by the P sorbed on Al present in the gel, indicating that there was a continuous P supply from the nanoparticles that were diffusing into the gel and releasing P. The Al2O3 nanoparticles are therefore suitable for buffering the P concentration in nutrient solutions. If plant uptake of P is indeed limited by diffusion of free P to the plant roots in nutrient solution, it is to be expected that buffering with these particles will also increase the plant uptake.

(a)

(b)

Effect of buffering by nanoparticles on plant P uptake The P uptake of the experimental plants in the unbuffered as well as in the buffered treatments increased linearly with time (Fig. 1). Aluminium was measured in acid extracts of the experimental plants in the unbuffered and buffered solutions, which indicated that, despite the washing step, Al2O3 particles were adhering to the roots (Fig. 1b,c). The amount of Al2O3 nanoparticles adhering to the roots increased less than 19% between 6.75 and 48 h. The total amount of P measured in the root samples was corrected for P associated with Al2O3 nanoparticles adhering to the roots. This correction was large (up to 17%) at the first sampling occasion (6.75 h), but much smaller (up to 5%) at the last sampling occasion (48 h). The Al concentration in the shoots after 48 h of seedling exposure to the nutrient solutions were on average 2.4 mg kg-1 (UB) and 5.8 mg kg-1 (B2). The potential error introduced by this slight increase in shoot Al concentration on the total P uptake was 100 mmol L-1 P (Borstlap 1981) and resulted in a better fit than Eqn 1. Figure 2 illustrates these data and shows the difference with P uptake fluxes in aerated solution, either unbuffered or with P-buffered nutrient solutions. The uptake flux in the unbuffered treatment with aerated solution is slightly higher than that in the unbuffered treatment of the unstirred solution, suggesting that the aeration decreases d, thereby increasing the uptake flux. Assuming that Fmax is unaffected by P buffering and solution agitation, a Km of ~4 mmol L-1 is derived for the unbuffered solution with aeration (UB, Table 2), that is, a 2.5-fold smaller Km than in the preliminary experiment with stagnant solutions.A Km of ~0.5 mmol L-1 was estimated for the buffered treatments B2–B4. These results illustrate that the Km highly depends on physical factors (degree of agitation, degree of buffering). The results for the buffered solution indicate that the true Km is at most 0.5 mmol L-1. However, as it is possible that uptake was still limited by diffusion in the buffered solutions, the true Km may be well below this value.


1564 J. Santner et al. Table 2. Literature values of phosphate uptake kinetics for algae and plants Fmax pmol cm-2 s-1

10.7 3.8 0.64 1.5 2.5 6.2 3.7 3.4 3.4 3.4

Km mmol L-1

0.016 0.044 5.4 10.5 5.3 22.0 5.3 10.4 4.0 0.5

aa 10-4 cm s-1

682 85.2 1.2 1.4 4.7 2.8 6.9 3.3 8.4 72.3

db mm

Species

Reference

Algae Synechococcus leopoliensis Various Plants Glycine max cv. Williams-79 Euphorbia pulcherrima Tagetes patula Zea mays Solanum lycopersicum cv. Knox Brassica napus cv. Caracas B. napus cv. Caracas B. napus cv. Caracas

1.3 10.6 750 630 191 322 130 273 107 12

Mierle 1985b Smith & Kalff 1982 Silberbush & Barber 1983 Khandan-Mirkohi & Schenk 2009 Khandan-Mirkohi & Schenk 2009 Bhadoria et al. 2004 Fontes, Barber & Wilcox 1986 This study, preliminary experiment This study, unbufferedc This study, bufferedc

a

a (=Fmax/Km): root absorbing power, corresponding to the slope of the uptake curve at low concentrations. d: effective diffusion layer thickness, estimated assuming diffusion-limited uptake d = D/a (with D = 9 ¥ 10-6 cm2 s-1). c Km values were derived from the experimentally determined a, assuming Fmax was the same as in the preliminary experiment with same plants grown under similar conditions. b

Estimated diffusive boundary layer thickness In case of strongly diffusion-limited uptake, the slope of the uptake curve, a, in an unbuffered solution equals D/d, where d is the thickness of the diffusive boundary layer, in which the free ion is depleted compared with the bulk solution. The effective DBL thickness can therefore be estimated as:

D δ= α

(11)

where D is the diffusion coefficient. Since D of H2PO4- is ~9 ¥ 10-6 cm2 s-1 at 25 °C, the observed root absorbing power in the unbuffered treatment of 8.37 ¥ 10-4 cm s-1 suggests a diffusion boundary layer thickness of ~100 mm. The root absorbing power (which corresponds to Fmax/ Km, the slope of the uptake curve at low concentrations) for P uptake by plants is usually in the range of 10-4 to 10-3 cm s-1 (Table 2). Assuming that P uptake in nutrient solutions is in general transport limited, this indicates DBL thicknesses of 100 to 1000 mm. Diffusive boundary layer thicknesses in the range of 100 mm for agitated (stirred or aerated) solutions and of 500–1000 mm for stagnant solutions have been reported (Warnken, Zhang & Davison 2006) for DGT samplers. For Cd uptake by spinach, Degryse et al. (2009) estimated effective DBL thicknesses of 500 mm for a stagnant solution and of 150 mm for a stirred solution. Thus, the estimated DBL thicknesses are in agreement with expected values in case P uptake is limited by diffusion. The variation in the literature data is most likely caused by differences in the experimental approaches used, in root geometry (thickness) and in the transporter density on the root surface. In addition, the thickness of the diffusive boundary layer also depends on the size and the geometry of the object that takes up solute. Microorganisms such as unicellular algae can induce a larger diffusion flux towards their surface,

because of their smaller size. For small, spherical microorganisms with radius r, the maximal (zero-sink) diffusive flux (on a surface base) corresponds to (Mierle 1985a):

Fupt =

Dc r

(12)

Thus, the DBL thickness of small spherical organisms corresponds to the radius of the organism. It is therefore expected that if P uptake is diffusion-limited, absorbing powers for P uptake by unicellular algae (r in mm range) would be about two orders of magnitude larger than those for plants (d in order of a few 100 mm). Indeed, P absorbing powers for algae in the order of 0.01–0.1 cm s-1, corresponding to Km values in the low nanomolar range, have been observed (Table 2). Even though algae can sustain larger diffusion fluxes, indications have been found that the uptake of phosphate by algae is also diffusion-limited (Smith & Kalff 1982; Mierle 1985b). Algae and vascular plants are very different in structure and physiology. Nevertheless, the literature data for algae show that P membrane transporters with Michaelis constants in the low nanomolar range exist. As the maximal diffusive flux that can be sustained by cylindrical roots is hampering the determination of the true Michaelis constant, the possibility of true Km values for plant root P transporters being much lower than the values usually reported in literature should be considered. Diffusion has been recognized a major factor controlling the mass transport of solutes towards cell membranes and other solid surfaces in several other branches of science. In mammal physiology, diffusion limitations have, for example, been demonstrated for the passive absorption of bile acid and fatty acids by intestinal cells (Wilson et al. 1971), for the uptake of oxygen and other dissolved gases by red blood cells (Holland et al. 1985; Chakraborty, Balakotaiah &


First observation of diffusion-limited P uptake Bidani 2004), and for the uptake of drugs by hepatocytes in rat (Ichikawa et al. 1992). In aquatic sciences, the transportlimiting role of the diffusive boundary layers is not only known for phosphate uptake by algae (Smith & Kalff 1982; Mierle 1985b) but also for algal uptake of other elements, for example, silver (Fortin & Campbell 2000). Furthermore, Kamin & Wilson (1980) demonstrated the importance of diffusion limitations to enzymes immobilized on surfaces in enzyme-electrode applications.

Implications for P uptake predictions Plant P uptake from soil can be predicted with a BarberCushman model, which combines the Michaelis–Menten equation with a transport equation. Using the Michaelis– Menten parameters determined in unbuffered solutions (Table 2), the uptake is usually predicted to be transport limited in soils with low buffering capacity and/or low moisture content (e.g. Silberbush & Barber 1983; Kelly, Barber & Edwards 1992). However, in well-buffered soils, predictions using a Km determined in unbuffered solution may indicate that uptake is not limited by diffusive transport of the free ion to the root surface, but is limited by internalization, in which case no or only little depletion of P at the root surface can be expected. Given that true Km values are at least an order of magnitude smaller than those determined in unbuffered nutrient solution, the P uptake is likely diffusion-limited in more conditions than predicted with apparent Km values. In the case of diffusion limitation, the cell membrane effectively acts as a zero-sink, i.e. all the phosphate arriving at the membrane is taken up. As a consequence, a simple zero-sink condition could be used for the estimation of phosphate uptake by plant roots from soil in the low concentration range (c < apparent Km). As uptake is under transport and not under internalization control, there is no need to have an exact value for the true Km to predict the P uptake. In models where Michaelis–Menten kinetics are used, it is recommended to use a low value for Km (e.g. the one estimated here in buffered solutions: Km ~0.5 mmol L-1) rather than a value determined in unbuffered solutions.

Broader implications Nutrient uptake kinetics and transporter affinity have been suggested as traits that could be optimized in order to enhance the P efficiency of agricultural crops (Vance, UhdeStone & Allan 2003; Gahoonia & Nielsen 2004). Based on our findings, we question if improving the P affinity of the uptake system will enhance phosphate uptake from soil. Rae et al. (2004) did not find changes in the P uptake of transgenic barley (Hordeum vulgarum L.) that overexpressed high affinity P transporters. The increase in P uptake by rice (Oryza sativa) overexpressing high-affinity P transporters (Park et al. 2007) appears contradictory in this context. Potentially, the fraction of the root surface active in

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phosphate uptake was increased in the transgenic plants. Given the evidence that uptake of P in soil is transport limited, strategies to increase crop phosphate efficiency that focus on increasing the active root surface area or enhancing P solubilization are most promising strategies for increasing crop P uptake efficiency (Lynch 2007). The contribution of P bound to the Al2O3 nanoparticles to the P uptake of our experimental plants points out the importance of nanoparticle-bound P for plant P nutrition.A fraction of P is associated with Al and Fe nanoparticles (colloids) in many soils, especially in highly oxidized soils, where it may account for up to 96% of water-extractable P (Sinaj et al. 1998; Turner, Kay & Westermann 2004). Nanoparticles as a source of plant available P are often not considered in plant nutrition. This study shows that nanoparticle-bound P can increase plant P uptake at Al2O3 concentrations as low as 0.01 g L-1. Studies with natural inorganic colloids should be carried out to underpin this hypothesis.

ACKNOWLEDGMENTS We thank Dr. Daniel Leitner for his help on this manuscript. J.S. was funded by the Vienna Science and Technology Fund (WWTF, Project MA07-008). F.D. was supported by a postdoctoral fellowship from the Fund for Scientific Research – Flanders (FWO).

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