Metal Speciation Dynamics and Bioavailability: Zn(II) and Cd(II

Ac cording to this concept, the kinetic flux is proportional to the volume ... Equation 6 is physically meaningful only if μ is smaller than the diff...
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Environ. Sci. Technol. 2002, 36, 2164-2170

Metal Speciation Dynamics and Bioavailability: Zn(II) and Cd(II) Uptake by Mussel (Mytilus edulis) and Carp (Cyprinus carpio) S T E F A N J A N S E N , * ,† R O N N Y B L U S T , ‡ A N D HERMAN P. VAN LEEUWEN† Laboratory of Physical Chemistry and Colloid Science, Wageningen University, Dreijenplein 6, 6703 HB Wageningen, The Netherlands, and Laboratory for Ecophysiology, Biochemistry and Toxicology, University of Antwerp, Groenenborgerlaan 7, 2020 Antwerp, Belgium

In the analysis of metal biouptake from complexing environments, both chemical speciation and biological uptake characteristics have to be taken into account. The commonly used free ion activity model is based on equilibrium speciation and implies that diffusion of the bioactive free metal toward the organism is not rate-limiting. In the presence of complexes, however, sufficiently labile species might contribute to the biouptake via preceding dissociation. Coupling of the ensuing diffusional mass transfer flux of metal with the biouptake flux of free metal, the supposedly bioactive species, shows under which conditions labile metal complexes can contribute to the uptake. The goal of the present paper is to apply this type of analysis to experimental data on metal uptake by mussel (Mytilus edulis) and carp (Cyprinus carpio) in complexing environments. These biosystems have fairly wellcharacterized uptake parameters, but the uptake fluxes cannot be fully explained by considering equilibrium speciation only. For Zn(II) uptake by mussel, evidence was found for diffusional limitation at low concentrations, whereas for Cd(II) uptake by carp, diffusion is not limiting at all. The analysis provides an example of how a more comprehensive treatment of complex systems can be applied to real experimental data.

Introduction For the biouptake of metals from complexing environments, both chemical speciation and biological internalization characteristics are of importance. Here, we will consider both the diffusional mass transfer from the bulk of the medium toward the actual biological uptake sites and the actual biological uptake flux. Under different chemical conditions, both of these types of fluxes can vary, leading to varying effective metal uptake rates. Common approaches such as the free ion activity model (FIAM) (1) and the biotic ligand model (BLM) (2) assume that the diffusional flux is not ratelimiting. This leads to an equilibrium approach, in which the uptake is correlated to the free metal ion activity in the bulk medium. * Corresponding author phone: +31-317-482582; fax: +31-317483777; e-mail: [email protected]. † Wageningen University. ‡ University of Antwerp. 2164

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The neglection of transport in the medium as an element of the overall metal uptake process has some important consequences. First of all, FIAM fails to describe the possible contributions from labile complexes. If transport of free ions to the uptake sites gives rise to a concentration gradient, a driving force for the net dissociation of sufficiently labile complexes is present. This would effectively lead to the uptake of metal originating from labile complexes, which is not taken into account by the FIAM. It is well-known that a variety of labile complexes can be present in aquatic environments (3). Second, describing metal toxicity as solely determined by adsorption equilibria, as is done in the BLM model, completely neglects the nonequilibrium aspects of the processes involved. However, uptake, accumulation, and effects of metals in living organisms are involved with more than the mere covering of a collection of binding sites. Equilibrium distributions are not generally achieved; more common is some steady state in which fluxes are constant but not zero. Between metal uptake and eventual effects there are several steps, such as the distribution over different tissues, and this requires a kinetic biocompartmental modeling approach. Besides these theoretical shortcomings, experimental data exist which do not correspond with the FIAM approach (4-10). A more comprehensive approach to the biouptake of metals from complexing solutions has been presented recently (11). A Michaelis-Menten type of uptake flux is coupled to the diffusional transport of metal from the solution to the uptake sites, taking into account the possible contributions by labile complexes. The treatment has been extended to microoorganisms (e.g., bacteria (12)). Unfortunately, the approach has not been rigorously applied to many experimental data yet; only a few papers on this subject have been published (9, 13, 14). In the present paper, we analyze the fluxes for some extensive sets of data on the uptake of metals by carp and mussel in complexing environments. We specifically selected data that are difficult to describe by the FIAM and tested whether the kinetic model can explain the observations more adequately. We also define further conditions under which the dynamic model might give an improved description of the resulting uptake fluxes.

Theory The Best equation for the steady-state biouptake flux (15, 16) couples interfacial Michaelis-Menten (MM) kinetics with a limiting rate of mass transfer toward the biosurface. For a bioactive metal ion M and a planar biosurface, the two steps can be represented by (i) the MM equation for the uptake flux Ju

Ju ) Ju*

(

cM0

)

KM + cM0

(1)

where Ju* is the limiting uptake flux, cM0 is the volume concentration at the surface, and KM is the affinity constant of M; and (ii) the convective diffusion equation for the transport flux of M in the medium

Jdif )

DM (c * - cM0) δM M

(2)

with DM the diffusion coefficient of M, cM* the bulk concentration, and δ the steady-state diffusion layer thick10.1021/es010219t CCC: $22.00

 2002 American Chemical Society Published on Web 03/20/2002

ness. The limiting diffusional flux for the case of cM0 ) 0 (i.e., DMcM*/δM) is commonly denoted as Jdif*. The combination of eqs 1 and 2 yields the Best equation, which we write in a two-parameter form for the dimensionless flux J/Ju* (11, 15, 16)

Q ) J/Ju* )

{ [

(1 + a + b) 4b 1- 12b (1 + a + b)2

]} 1/2

(3)

where J is the overall flux, a is the normalized bioaffinity parameter (a ) KM/cM*), and b is the limiting flux ratio (b ) Ju*/Jdif*). Well-known limits of eq 3 include, for example, the case of a . 1, corresponding with a relatively weak affinity of the organism toward M. Then, if a . b, Q approaches 1/a (J ) Ju*cM*/KM; i.e., the biological transport is flux-limiting). If a , b, Q approaches 1/b (J ) Jdif*; i.e., mass transport in the medium is rate-limiting). If the medium contains the metal in its free bioactive form (M) as well as in a complex bioinactive form (ML), the question is to what extent and under which conditions the complex species ML may contribute to the biouptake process via dissociation into free M. In this respect, a crucial parameter is the kinetic flux Jkin, which represents the maximum flux of free M that can be generated by dissociation of ML. An expression for Jkin can be obtained by considering the rate of dissociation Rd and the mean lifetime τM of the free metal formed. These two quantities are defined by

Rd ) kdcML

(4)

where kd is the rate constant for dissociation of ML into M and L and cML is the concentration of ML, and

τM ) 1/kacL

(5)

where ka is the rate constant for reassociation of M with L and cL is the ligand concentration. Note that τM equals cM/Ra, the ratio between the free metal concentration and the complex formation rate Ra ()kacLcM). The mean distance ∆M, travelled by the diffusing free M, is proportional to (DMτM)1/2. This is used in the so-called reaction layer approach to kinetically controlled processes at interfaces (17-19). According to this concept, the kinetic flux is proportional to the volume dissociation rate Rd (eq 4) and the mean distance ∆M that free metal ions travel during their lifetime τM (1/kacL)

Jkin ) kdcMLDM1/2/(kacL)1/2

(6)

in which the factor (DM/kacL)1/2 is often denoted as µ and termed the reaction layer thickness. Equation 6 is physically meaningful only if µ is smaller than the diffusion layer thickness δ, which is coupled to the characteristic time δ 2/D for the complex system (see ref 20 for a detailed analysis). Thus, for an interfacial consumption process involving M, the dynamic behavior of ML is governed by (δ 2/D)/τM, whereas for equilibration between M and ML in the bulk medium, the full period of time of the uptake experiment (τexp) is the relevant parameter. Because (δ 2/D) and τexp usually differ by several orders of magnitude, a metal-ligand (ML) complex can be inert in the biouptake process while maintaining equilibrium in the bulk medium. A complex species ML is said to be labile if the magnitude of the kinetic flux Jkin is so much larger than its diffusional limiting flux Jdif*(ML) that kinetic limitations vanish and pure diffusion results. Thus, the ratio Jkin/Jdif*(ML) constitutes the basic lability criterium parameter which, for large excess of ligand, reduces to generally accepted simple expressions (21).

FIGURE 1. (a) Sketch of the limiting diffusional flux from the free metal ion only (Jdif*(M) (s) and the uptake flux (Ju) as a function of the free metal ion concentration. Two cases are compared: (1) KM ) 10-6 mol m-3 (high affinity) (- -); (2) KM ) 10-4 mol m-3 (low affinity) (‚‚‚). For both uptake systems, a limiting uptake flux Ju* of 10-9 mol m-2 s-1 is taken. The diffusional flux is determined by D/δ, for which, like in the experimental conditions of this paper, a value of 10-4 m s-1 is used. (b) Same as in (a) as a log-log plot. In case of lability, the supply of M toward the biosurface, is given by the coupled diffusion of M and ML

Jdif ) (D h /δ h )(cT* - cT0)

(7)

where D h is the mean diffusion coefficient of M and ML; δ h is the corresponding mean diffusion layer thickness, operative in the case of coupled diffusion of M and ML; and cT ) cM + cML (22). For a biosurface that takes up free M only, the presence of labile species ML is relevant if the diffusional flux of free metal, Jdif(M) (see eq 2), is not much larger than the uptake flux Ju. Under such conditions, the labile complexes restore equilibrium by dissociating inside the diffusion layer and, thus, compensate for the depletion of M. The Best equation remains valid (11) but with the transport parameter b, defined by the total concentration of species participating in the h cT*/δ h ). It has to be transport of M to the surface: b ) Ju*/(D noted that the difference between labile and inert complexes becomes relevant only if the uptake of the free metal by itself would lead to significant depletion of M in the diffusion layer. This distinction can be made at the level of the Best equation and not of the FIAM because the latter only applies to cases where the unsupported diffusion of the bioactive species M is fast compared to the biouptake process. Figure 1 illustrates this by comparing the various fluxes and their dependence on the free metal ion concentration cM*. For relatively low values of KM, that is, for relatively high affinities, the linear regime of the Ju/cM* plot (supposedly of MM nature) appears at such low cM* that Ju intersects with the diffusional flux of free metal only, Jdif*(M). In this situation, the presence of labile complexes is most relevant because these may increase the diffusional flux to (D h /δ h )cT*, which is VOL. 36, NO. 10, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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by a factor of cT*/cM* higher than Jdif*(M). This simply means that, at any cM* lower than the cM at which the limiting diffusional flux equals the potential uptake rate, the free metal is not capable of satisfying the uptake demand of the organism by itself. Lowering cM* to very low values does not change this situation because both Jdif*(M) and the uptake flux decrease proportionally with decreasing cM*. Needless to say, this reasoning is restricted to systems that obey an MM type of dependence of Ju on cM* over the entire range of cM* considered. In logarithmic form (Figure 1b), the behavior of the different fluxes is even more transparent. The region of low cM* is characterized by parallelism of Ju and Jdif*(M), both with unit slope. The separation between the two is a measure of the applicability of FIAM; application of FIAM is justified only if Ju , Jdif*(M). The separation is actually given by the ratio (Ju*/KM)/(DM/δM), which is just identical to b/a, the crucial bioavailability parameter from the Best equation (see refs 23 and 11 for details). For Ju > Jdif*(M) in the absence of complexes or in the presence of inert complexes, metal uptake by the organism at low concentrations cannot be described by Michaelis-Menten uptake anymore, because diffusion is limiting. In this case, uptake will not follow a pure MichaelisMenten behavior but a dependence of the flux on the metal concentration as derived from the Best equation.

Case Studies To apply the flux-based approach to real data, two sets of data were selected. One set deals with Zn(II) uptake by mussel (Mytilus edulis) (24) and the other with Cd(II) uptake by carp (Cyprinus carpio). The latter set consists of data previously published (25) and new data. Several factors make these data very appropriate for the analysis. They provide detailed uptake characteristics, which in combination with the known effective surface area can easily be converted to fluxes (in mol m-2 s-1). Furthermore, both sets comprise complexation by ligands with different metal-binding and lability characteristics. Finally, both datasets contain data which cannot be explained by a singular Michaelis-Menten/FIAM approach. The ligands involved are EDTA, NTA, glycine (Gly), and citrate (Cit). Their Zn(II) and Cd(II) complexes vary widely in stability and lability. Therefore, first the lability of these complexes in the systems of interest will be discussed. Experimental details, results, and disscussion are presented in the individual case-study sections. Labilities of the Complex Systems. For the ligands considered here, the glycine and citrate complexes are not too strong and labile, whereas the NTA and EDTA complexes are fairly strong and inert (Table 1). As a consequence, the systematic reduction of the free Zn2+ or Cd2+ concentrations at a given total metal concentration requires a substantial excess of Gly or Cit, whereas in the case of NTA or EDTA the total metal and total ligand concentrations are necessarily close to each other. Let us consider, for example, the case of a Cd(II)/EDTA solution with a total [Cd(II)] of 10-7 M and a free [Cd(II)] of 10-9 M. The conditional stability constant Kcond for the CdEDTA2-complex requires that, for a [CdEDTA2-] of 0.99 × 10-7 M, [HEDTA3- + EDTA4-] ∼ 10-12 M. The mean lifetime of a free Cd2+, τCd, in this Cd(II)/EDTA solution can be found from [Cd2+]/Ra (see eq 5). If we take into account that the deprotonation of HEDTA3- is fast as compared to the metal complexation reaction of EDTA4-, meaning that the ligand concentration cL effectively equals [HEDTA3-] + [EDTA4-], and taking ka ) 109 s-1 (26), we obtain a τCd on the order of 103 s. As outlined here, the effective timescale for the uptake process (τpr) is determined by δ2/D. The actual hydrodynamic conditions for the uptake experiments are rather involved (13), but for the present purposes, it suffices to have an 2166

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TABLE 1. Labilities of Cd(II) and Zn(II) Complexes as Deduced from the Comparison of the Kinetic Flux Jkin (eq 6) with the Maximum Diffusion Flux of the Complex Jdif* ()DMLcML*/δML; cf. eq 2)a metal ion and condition

cL kd ligand log Kcond (mol dm-3) (s-1)

Cd freshwater Gly Cit NTA EDTA Zn seawater Gly Cit NTA EDTA

4 5 10 14 4 5 10 14

10-2 10-3 10-8 10-12 10-1 10-2 10-7 10-11

105 104 10-1 10-5 105 104 10-1 10-5

Jkin/Jdif* b

labile/ inert

10 3.2 10-2 10-4 3.2 1 3.2 × 10-3 3.2 × 10-5

labile labile inert inert labile labile inert inert

a D -9 m2 s-1; pH ) 8; k ) 109 mol-1 dm3 s-1; δ ≈ δ ML ≈ DM ) 10 a M ML ≈ 10 µm. Lability parameters for Cd are calculated for freshwater conditions, cT* ) 10-7M and cM* ) 10-9 M. Lability parameters for Zn are calculated for seawater conditions, cT* ) 10-6 M and cM* ) 10-9 M. Kcond is the conditional stability constant at pH ) 8 and I ≈ 0.1 M. cL is the sum of the free and protonated forms of the added ligand (see text for explanation). b Jkin is the kinetic flux calculated for the case of an equilibrium speciation with [M]/[M]T ≈ 0.01 for both Cd and Zn. For the corresponding ligand concentrations, see text.

effective value of the convective diffusion layer thickness δ. For the uptake process via the gill of the carp and mussel, δ is, at most, half of the distance between the lamellae (i.e., about 10-20 µm) and probably even less (27, 28). Thus, with a D of the order of 10-9 m2 s-1 (21), we come to a τpr of the order of 10-1 s. When this value is compared to the lifetime of free Cd2+ (103 s), it is clear that the Cd-EDTA complexation equilibrium is not dynamic on the relevant timescale of the uptake process. The comparison of the kinetic flux Jkin with the diffusional flux of CdEDTA2- yields the same clear-cut picture: substituting kd ) 10-5 s-1 (obtained from Kcond and ka) and a [CdEDTA2-] of 10-7 M into eq 6, we get a Jkin on the order of 10-12 mol m-2 s-1, whereas Jdif(CdEDTA2-) is on the order of 10-8 mol m-2 s-1. The conclusion reads again that the CdEDTA2- complex is strongly inert with respect to the biouptake process. It is useful to further note that the kinetic flux of the strong complex CdEDTA2- is also much smaller than the diffusional flux of free Cd2+ only, which is on the order of 10-10 mol m-2 s-1. An overview of the computed labilities of the various complexes is given in Table 1. Case 1: Zn Uptake by Mussel (Mytilus edulis). In chemically defined seawater (salinity 35 ‰), mussels were exposed to a very broad range of free zinc ion activities, ranging from micromolar to below nanomolar level. This concentration range was obtained by varying the concentration and type of ligand at a constant total Zn(II) concentration of 5 µM. Equilibrium was assured by a sufficiently long equilibration time (24 h). Zn(II) uptake in the shell, gill, and hemolymph was separately followed over time for 24 h. From these data, uptake rates at different metal activities were calculated. For further details, see ref 24. Here, we will only discuss uptake in the gill, for which no processes such as digestion take place and uptake can be regarded as directly related to the undisturbed medium properties. The uptake data for gill are shown in Figure 2a. Most of the data can be described by Michaelis-Menten uptake of the free Zn ion, for which the characteristics are shown in Table 2. In the original paper also, data on the uptake in the presence of histidine was presented. However, this case shows a clearly different result. Analysis of the experimental data strongly suggests that this is due to the direct uptake of the complex species ZnHis+ (24). Because of this feature, the histidine complexes are left out of the present analysis. In passing, we note that the case of uptake via two parallel pathways involving two different species requires a careful consideration of the role of the ligand and the differences

TABLE 2. Characteristics of Zn(II) Uptake by Mussel (24) and Cd(II) Uptake by Carp (25) [M] range organism

metal

carp mussel

Cd Zn

gill surface area (m2/g wet mass)

min (µmol dm-3)

0.001 0.0003

0.01 0.00001

max (µmol dm-3) 0.94 6

Ju* (nmol g-1 h-1)

KM (µmol dm-3)

Ju*/KM (L g-1 h-1)

D/δ (L g-1 h-1)

0.37 4.5

0.34 0.07

1.1 × 10-3 6.4 × 10-2

3.6 × 10-1 1.1 × 10-1

FIGURE 3. Uptake rate of Zn by mussel measured and modeled in ref 24, plus the modeled limiting diffusional flux of free metal (loglog): (() citrate, (2) NTA, (×) EDTA, (O) glycine; (s) modeled uptake, (‚‚‚) modeled diffusional flux.

FIGURE 2. Uptake rate of Zn by mussel measured and modeled in ref 24, plus the modeled limiting diffusional flux of free metal: (a) uptake data on linear scale, complete concentration range; (b) linear scale, low concentration range; (() citrate, (2) NTA, (×) EDTA, (O) glycine; (s) modeled uptake, (‚‚‚) modeled diffusional flux. between the diffusion coefficients of the two bioactive species (29). For all of the other ligands, the data suggest that no direct uptake of the complexes takes place. Magnification of the low-concentration range (Figure 2b) shows that, at the lower free zinc ion activities, the measured uptake rate is generally much higher than that predicted by the singular Michaelis-Menten relation, as determined from the highconcentration range. To utilize the data for flux analysis, the uptake in amounts of metal per unit of wet mass was converted to uptake in amounts per unit of gill surface area. The wet mass is converted into gill area using the literature data for mussel, which gives a value for the gill area of 3 × 10-4 m2 (g of wet mass)-1 for a mussel wet mass of 5 g, assuming a gill/total wet mass ratio of 0.1 (30). The recalculated Michaelis-Menten parameters can be found in Table 2. Also, the mass transport coefficient (D/δ) was calculated (Table 2). The product of this factor and the free metal concentration gives the maximum diffusional flux Jdif, M for free metal ion only, which is also shown in Figure 2. As explained before, if the modeled Michaelis-Menten uptake Ju, model is larger than this diffusional flux, diffusion of free metal ion only cannot satisfy the biouptake; thus, contributions by labile complexes can become important. From Figure 2, parts a and b, we can see that, at low concentrations, the diffusional flux and the uptake flux are indeed very close, so possible contribution by labile

species comes into play. In this range, uptake characteristics should be described with a modified Best equation instead of with a Michaelis-Menten equation (11). Some of the actual uptake data points in this region are higher than both the modeled uptake rate and the diffusional flux of free Zn, which cannot be explained by the modeled MM uptake or by any other uptake function of the free metal ion. A more detailed comparison of the modeled and measured fluxes can be made by plotting the same data in a log-log plot, as presented in Figure 3. The calculated diffusional flux is very close to the modeled MM flux, meaning that the ratio between the Best equation parameters a and b (denoted as the bioavailability number before (23)) is close to unity. However, at low concentrations, the measured uptake fluxes are clearly higher than both the modeled Michaelis-Menten flux and the diffusional flux. The set of experimental data shows a few points in the subnanomolar [Zn2+] range which do not follow the general trends and which, anyway, are extremely inaccurate because of an extremely small excess of ligand over metal. In the following discussion, we shall therefore ignore these data points. As for the labile Zn-Gly complexes, the trend of Ju with decreasing Zn2+ is gradual and consistent. The data strongly suggest that the model of a single Michaelis-Menten equation is not applicable down to the 10-8 M range. It would be very interesting to collect some further data on glycine in the nanomolar range to see how the trend develops. The Zn-NTA data do not seem to be very reliable: the value for Ju at 5 nM free Zn2+ is at the level more common in the 10-7 M range. The trend for the EDTA complexes is gradual and fairly coherent. In the nanomolar range, the uptake rates come to the limit of the diffusion of free Zn2+, as should be the case for these inert complexes (cf. Table 1). The overall conclusion for the Zn/mussel system seems to read that labile complexes contribute to the biouptake process in the range of free Zn2+ concentrations below 10-7 M. Case 2: Uptake of Cadmium by Carp (Cyprinus carpio). Relatively many data are available for metal uptake by fish. There are many examples of experimental data that give rather rough information (e.g., see refs 31-34), whereas only a few detailed and well-defined uptake studies exist (e.g., see refs 35 and 36). A discussion of the role of labile complexes VOL. 36, NO. 10, 2002 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Uptake rate of Cd by carp measured and modeled at [Ca2+] ) 2mM: (- -) one-site Michaelis-Menten uptake (Ju* ) 0.30 nmol g-1 h-1; KM ) 0.58 µM); (‚‚‚) two-site Michaelis-Menten uptake (Ju,1* ) 0.012 nmol g-1 h-1; KM,1 ) 0.014 µM; Ju,2* ) 0.36 nmol g-1 h-1; KM,2 ) 0.029 µM). in Co(II) uptake by carp indicated that the complex species do not significantly contribute to the metal transport toward the biosurface (13). Here, we will analyze data on the uptake of cadmium by carp, partly published before (25) and partly new. In the experiments by Van Ginneken et al., the fish were acclimatized in and exposed to moderately hard freshwater. Metal uptake was measured after exposure for 3 h. During this period, the accumulated amount increased linearly with time, so the uptake rates were constant. First, Cd uptake was characterized in the absence of complexing agents. Then, to verify that under the same conditions no metals could be taken up from inert complexes, uptake in the presence of EDTA was measured. Finally, uptake was measured in the presence of varying amounts of different ligands. The same complexing agents were used as for mussel (24). The data in the presence of histidine are left out of the this analysis to minimize the chance of uptake of whole complexes, as was observed for mussel. Because the objective of these experiments was to study both Cd and Zn uptake, carp were simultaneously exposed to Cd and Zn. The experimental conditions of the newly measured data are similar except for a couple of small differences. Fish were acclimatized and exposed in OECD freshwater (37), which contains a higher [Ca2+] than the water used by Van Ginneken et al. (2 instead of 0.44 mM). This can have an effect on the uptake, because Ca and Cd are known to compete for a number of important uptake channels (34). Second, acclimation at different Ca concentrations will lead to different numbers of uptake sites. For these reasons, the exact uptake fluxes are not the same, but the general trends are highly comparable. The newly measured data span a very broad concentration range. This gives valuable information about details of the uptake characteristics. At Cd concentrations below 0.3 µM, uptake was measured in the presence of 1 µM EDTA; at higher Cd concentrations, no organic ligands were present. The Michaelis-Menten parameters as determined by Van Ginneken et al. can be found in Table 2. A one-site MichaelisMenten curve fits the data well. The same relation between metal uptake and free metal ion activity was found in the presence of EDTA, indicating that indeed these inert complexes are not taken up. Figure 4 shows the uptake curve for the data at 2 mM Ca2+. Overall, this curve is somewhat lower than for 0.44 mM Ca2+, which can be explained by the increased competition from the calcium ions. As is quite clear from the picture, these data fit in extremely well with a two-site MichaelisMenten equation, accounting for a low-affinity site that dominates at higher concentrations and a high-affinity site 2168

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FIGURE 5. Difference between the measured and modeled Cd uptake by carp in complexing environments in ref 25: (() citrate, (2) NTA, (×) EDTA, (O) glycine.

FIGURE 6. Comparison between the modeled Michaelis-Menten uptake flux (without Zn competition) and the limiting diffusional flux of free Cd for carp (log-log) for the experimental conditions reported in ref 25: (s) modeled uptake, (‚‚‚) modeled diffusional flux. that dominates at low concentrations. The presence of a highaffinity uptake site enlarges the possibility of contribution by labile complexes at low metal concentration; from Figure 1b it is clear that the uptake flux comes closest to the diffusional flux at low concentration where uptake via the high-affinity uptake sites is dominating. In the experiments by Van Ginneken where the uptake is studied in complexing conditions, competition between Zn and Cd has to be taken into account. This competition has been modeled by a modified Michaelis-Menten equation with competitive inhibition (25). In Figure 5 the difference between the measured and the predicted metal uptake rates are shown. At high metal concentrations, the uptake can be described by the Michaelis-Menten equation, but at low concentration, many measured data are much higher than predicted. Equilibrium calculations (25) have shown that this is not due to changes in Ca2+. The biggest deviations are found in case of citrate and glycine. To see whether contribution by labile complexes might give an explanation for the observed discrepancy in the Michaelis-Menten uptake curve, we performed the same analysis as done for Zn uptake by the mussel. The required gill surface area was obtained from (38), which gives the surface area including the secondary lamellae. The resulting diffusional flux can be found in Table 2 and Figure 6. For the uptake flux, the Michaelis-Menten parameter without competition by Zn is taken. In the presence of Zn, the curve would be slightly lower. The results are totally different from those for mussel. As can be seen most clearly in Figure 6, the limiting diffusional flux of free metal is much larger than the uptake fluxes over the whole concentration range. The relevant bioavailability parameter a/b(1 + K′) (11, 23) is much larger than unity, so the uptake rate is flux-limiting. Also, in other complexing

environments, this uptake system will not need the contribution by labile complexes. The observed inapplicability of Michaelis-Menten predictions is therefore not related to mass-transfer limitations and contributions by labile species. Metal complexes might be taken up as such, although no direct proof for this has been found. Also, multiple uptake sites, which are proven to play a role in this system, cannot explain the deviation, because even the flux of the highaffinity uptake sites lies far beneath the diffusional flux. For labile systems to come into play, much higher affinity uptake systems would be required. Down to the nanomolar range, the free Cd2+ is sufficient to satisfy the demands of the organism, and the system obeys FIAM. The flux analysis as presented previously is relatively simple and gives fruitful insights. The analyses in this paper illustrate that deviations from FIAM are to be expected for combinations of relatively high uptake rates, low free metal concentrations, and significant concentrations of labile complexes. The dynamic approach provides a way to verify whether some basic assumptions of FIAM are justified. Application to more data would be interesting, especially if due attention has been paid to the relevant speciation parameters, including lability, and if the possibility of multiple uptake routes has been envisaged. The hydrodynamics and chemistry of the gill water are known to be complex and variable (39, 40). For the gill hydrodynamics, we have used a simple description which is expected to work well in case the uptake of metal at the gill surface can be assumed to be uniform over the whole gill surface area; only then it is justified to use the literature data for the complete gill surface area as the relevant active surface area. The latter, however, is likely to be smaller, due to the fact that specialized cells are required for metal ion uptake (41). This might not only have an influence on the estimated effective surface area but also on the geometrical setting of the model; instead of diffusion toward a plane, it might give rise to radial diffusion, which not only affects the masstransfer expressions but also reduces the labilities of complexes (12). A more detailed analysis would therefore require a mapping of the active uptake sites on the biosurface and a characterization of the chemical conditions at these sites.

Nomenclature δ

diffusion layer thickness (m)

δM

diffusion layer thickness for free metal (m)

δ h

mean diffusion layer thickness (m)

µ

reaction layer thickness (m)

τpr

effective timescale of uptake process (s)

τM

mean lifetime of free metal (s)

a

()KM/cM*) conditional bioaffinity parameter

b

()Ju*/Jm*) limiting flux ratio

c i*

concentration of species i in the bulk medium (mol dm-3)

ci0

concentration of species i at the biosurface (mol dm-3)

Di

diffusion coefficient of species i (m2 s-1)

D h

mean diffusion coefficient (m2 s-1)

Jdif

metal-transport flux due to diffusion (mol m-2 s-1)

Jkin

metal-transport flux due to dissociation of ML (mol m-2 s-1)

Ju

biouptake flux (mol m-2 s-1)

Jdif*

limiting metal-transport flux due to diffusion (mol m-2 s-1)

Ju*

limiting biouptake flux (mol m-2 s-1)

K

()cML/cMcL) stability constant (mol-1 dm3)

K′

()KcL, t) stability constant times total ligand concentration

ka

association rate constant (mol-1 dm3 s-1)

kd

dissociation rate constant (s-1)

KM

bioaffinity parameter (mol dm-3)

L

ligand

M

free metal

ML

metal-ligand complex

Q

()J/Ju*) normalized flux

Rd

rate of dissociation (mol dm-3 s-1)

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Received for review August 20, 2001. Revised manuscript received February 6, 2002. Accepted February 14, 2002. ES010219T