Diffusion Limitations in Root Uptake of Cadmium and Zinc, But Not Nickel, and Resulting Bias in the Michaelis Constant

It has long been recognized that diffusive boundary layers affect the determination of active transport parameters, but this has been largely overlooked in plant physiological research. We studied the short-term uptake of cadmium (Cd), zinc (Zn), and nickel (Ni) by spinach (Spinacia oleracea) and tomato (Lycopersicon esculentum) in solutions with or without metal complexes. At same free ion concentration, the presence of complexes, which enhance the diffusion flux, increased the uptake of Cd and Zn, whereas Ni uptake was unaffected. Competition effects of protons on Cd and Zn uptake were observed only at a very large degree of buffering, while competition of magnesium ions on Ni uptake was observed even in unbuffered solutions. These results strongly suggest that uptake of Cd and Zn is limited by diffusion of the free ion to the roots, except at very high degree of solution buffering, whereas Ni uptake is generally internalization limited. All results could be well described by a model that combined a diffusion equation with a competitive Michaelis-Menten equation. Direct uptake of the complex was estimated to be a major contribution only at millimolar concentrations of the complex or at very large ratios of complex to free ion concentration. The true K_m for uptake of Cd²⁺ and Zn²⁺ was estimated at <5 nm, three orders of magnitude smaller than the K_m measured in unbuffered solutions. Published Michaelis constants for plant uptake of Cd and Zn likely strongly overestimate physiological ones and should not be interpreted as an indicator of transporter affinity.Internalization of metals by biota is traditionally described by Michaelis-Menten kinetics (Wilkinson and Buffle, 2004). The K_m corresponds to the concentration in solution at which the uptake is one-half of the maximal uptake, F_max. The Michaelis-Menten equation relates the uptake flux, F, to the free ion concentration at the site of uptake, M]_s:If diffusion of a metal across a diffusive boundary layer adjacent to the roots is the rate-limiting step for uptake, the concentration at the site of uptake will be lower than that in the bulk solution. As a result, diffusion limitations result in an overestimate of the K_m, if the concentration at the root surface is assumed to be the same as in the bulk solution, as is usually done. This bias in K_m has been discussed in detail by Winne (1973) and has, for instance, been demonstrated experimentally for uptake of Glc in rabbit jejunum (Thomson and Dietschy, 1980) and for uptake of several sugars, amino acids, and bile acids in rat ileum (Wilson and Dietschy, 1974).Models used to predict ion availability and toxicity of metals by plants usually rely on the assumption that uptake is controlled by the free metal ion activity and the activity of competing ions in the bulk solution. For instance, the biotic ligand model (BLM), originally developed to predict metal toxicity to aquatic organisms, assumes that toxicity of an ion is mitigated by the presence of competing ions that bind on the biotic ligand (Paquin et al., 2002). Hough et al. (2005) used a free ion activity model taking into account proton competition effects to predict cadmium (Cd) uptake by soil-grown ryegrass (Lolium perenne). The uptake was reasonably well predicted; however, as the authors pointed out, it was not clear whether the derived constants truly represented physiological affinity constants or were just fitting parameters in a rate-limited uptake process. In case of strong diffusion limitation, ion competition effects on the internalization are expected to have negligible effect on the uptake, as the uptake is controlled by diffusion and not by internalization (Campbell et al., 2002; Degryse and Smolders, 2012).In previous studies, we found strong evidence that uptake of Cd and zinc (Zn) is limited by the diffusive transport of the free metal ion to the root at low free ion concentration. At constant free ion concentration, the uptake of Cd and Zn increased in presence of metal complexes and the contribution of the complex increased with increasing dissociation rate of the complex (Degryse et al., 2006a, 2006c). In unbuffered solutions, i.e. solutions without metal complexes, stirring increased Cd uptake by plants (Degryse and Smolders, 2012). For nickel (Ni), however, contribution of complexes was small or undetectable, and stirring did not increase the uptake (Degryse and Smolders, 2012). Given this evidence that Cd and Zn uptake by plants is limited by diffusion, it is likely that published K_m values for uptake of Cd²⁺ and Zn²⁺ by plants overestimate true physiological values. This bias in the K_m when a diffusive boundary layer is present has been largely ignored in plant-physiological research. Indeed, in numerous studies the K_m value has been interpreted as a characteristic of the carrier-mediated transport process, while in many cases it may reflect mass transfer properties. In addition, these diffusion limitations may mask ion competition effects in the uptake.The aim of this article was (1) to present evidence that K_m values determined for Cd²⁺ and Zn²⁺ uptake by plants in general reflect transport limitations rather than transporter affinity; (2) to derive true K_m values by determining the K_m under conditions where the uptake is not transport limited; (3) to identify the consequence of diffusion limitations on competition effects; and (4) to describe uptake of Cd, Zn, and Ni by plants in a single comprehensive model that combines competitive Michaelis-Menten kinetics with a diffusion equation.

Theoretical Framework

In the following, we qualitatively discuss the bias in the K_m because of diffusion limitations, based on Figure 1. Equations are given in the “Materials and Methods” section. Figure 1A presents a case where the potential internalization flux by the plant at low concentrations is much larger than the maximal rate at which the free ion can be supplied through diffusive transport of the ion to the root surface. In this case, the actual uptake flux by the plant will approach the maximal diffusive flux, and the free ion concentration at the root surface is much smaller than that in the bulk solution. The apparent K_m (K_m*; determined as the concentration where the uptake flux is one-half of the maximal uptake) is much larger than the true K_m value. In Figure 1B, the potential internalization flux at low concentration is of the same order of magnitude as the maximal diffusion flux. In this case, the concentration at the root surface is slightly smaller than that in the bulk solution, and there is only a slight bias in the K_m value.Open in a separate windowFigure 1.Conceptual diagram of the internalization flux (Michaelis-Menten curve; full line), maximal diffusive supply from solution to root (dashed line), and actual uptake flux (dotted line) as a function of free ion concentration for two theoretical cases. Left and right sections show the same curves, on log (left) or linear (right) scale. In A, the potential internalization flux is much larger than the maximal diffusive supply at low concentrations, i.e. the uptake is strongly limited by the transport of the free ion to the root. The plant acts as a near-zero sink, and the actual plant uptake equals the maximal diffusive flux. The K_m* is much larger than the true K_m, and the experimental permeability P (slope of the actual uptake curve) is much smaller than the membrane permeability P_m (slope of the internalization curve). In B, the maximal diffusive flux is larger than the potential internalization flux. The uptake is not limited by diffusive transport, and the K_m* and true K_m are almost equal.Given the evidence that uptake of Cd and Zn by plants is diffusion limited, even in stirred nutrient solutions, we hypothesize that reported K_m values of Cd²⁺ and Zn²⁺ are biased, and that the physiological K_m values are much smaller. To test this hypothesis, we measured the uptake of Cd, Zn, and Ni in solution, in absence or in presence of labile hydrophilic metal complexes. If diffusion limitations prevail, the complexes dissociate within the diffusion layer and thus enhance the diffusion flux and therefore the metal uptake. By adding labile complexes in large amounts, it should be possible to abolish the diffusion barrier completely, in which case the physiological K_m can be determined.In addition, the effect of competitive ions on uptake was tested. The presence of competitive ions decreases the internalization flux. However, if uptake is rate limited by the diffusive transport to the uptake site and not by internalization, competition effects should theoretically not affect the uptake flux.