Which aqueous species control the rates of trace metal uptake by aquatic biota? Observations and predictions of non-equilibrium effects

the Science of the Total Environment An lnlrrnllonrl Journal rar Sclentllle Research Inlo the Envlmnment and 111Rdallanihlp wlth Man

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The Science of the Total Environment 219 (1998) 95-115

Which aqueous species control the rates of trace metal uptake by aquatic biota? Observations and predictions of non-equilibrium effects R.J.M. Hudson" Department of Natural Resources and Environmental Sciences, University of Illinois, W-503 Tuner Hall, 1102 S.Goodwin Aue., Urbana,IL 61801, USA

Abstract

Over the past 2 decades, great progress has been made in understanding the relationship of metal speciation and biotic metal uptake in aquatic systems. Most work in this area has adopted the 'free ion model' (FIM) to express the dependence of metal uptake rates on medium chemistry. Coupled with recent advances in analytical chemistry, this approach has led to successful predictions of metal uptake by aquatic organisms in natural systems. There are some cases that have proved difficult to reconcile with the FIM and one case in which the central assumption of the FIM, that pre-equilibrium exists between metals in solution and bound to cell surface transporter sites, has been proved incorrect. In order to take these exceptions into account, this paper explores the implications of reaction kinetics and diffusion for the uptake of metals. In particular, it shows how the apparent aqueous metal species controlling the rates of metal uptake will depend on whether any of these two rate-limiting factors become important. Guidelines are suggested for predicting when they may be important factors. 0 1998 Elsevier Science B.V. All rights reserved. Keywords: Metal speciation; Biotic metal uptake; Aquatic systems

1. Introduction

Knowing which aqueous species control the rates of trace metal uptake by aquatic biota is essential for modeling their fate and effects in aquatic systems. Metal speciation has been shown to govern important biotic uptake processes including the acquisition of essential metals and the regulation of growth in phytoplankton (Sunda and Huntsman, 1998), the entry of toxic metals into

* e-mail: [email protected]

aquatic food chains (Watras et al., 1998), and the toxic effects of metals on higher organisms, such as fish (Playle, 1998). When 'uptake' is understood more broadly as any direct interaction with an aquatic organism, many significant biologically-mediated transformations of metals, such as redox and methylation reactions, also fall into the category of uptake processes. The speciation of trace metals, or distribution among possible redox states, aqueous complexes, and particulate forms, varies both temporally and between aquatic systems (see Sunda and Huntsman, 1998) and methods of measuring and model-

0048-9697/98/$ - see front matter 0 1998 Elsevier Science B.V. All rights reserved. PZZ S 0 0 4 8 - 9 6 9 7 ( 9 8 ) 0 0 2 30 - 7

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R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

ing the chemical speciation of metals are fast becoming accurate and reliable. Consequently, it is now feasible to use laboratory-established relationships between uptake rates or velocities ( V ) and the concentrations of one or more rate-controlling metal species [Mi]: V = u(Organism, Environment, [Mi])

(1)

to model metal uptake rates in the environment (Sunda and Huntsman, 1995) based on in situ measurements of metal speciation (Coale and Bruland, 1988). Buoyed by this success, it is the fervent hope of modelers that experimental scientists will continue to develop the mechanistic knowledge needed to describe uptake rates V as a function of metal speciation. To achieve this goal, there are three interrelated questions that must be addressed. The first is ‘what is the mechanism of uptake employed in the process of interest’? The second is ‘how do essential and non-essential or toxic metals interact in this process’? These interactions may occur outside the organism, as metals compete for transport, or inside, as they compete for binding sites that regulate metal transport systems (Sunda and Huntsman, 1998). The third is raised in the title of this paper. Note that it differs from the closely related question of ‘which aqueous chemical species are bioauailable’? Although it is widely believed that the ‘free ion model’ (FIM) has adequately explained the relationship between speciation and uptake, it is the purpose of this paper to highlight those insights that are available only by complementing the equilibrium concepts of the ‘free ion model’ (FIM) with kinetic concepts. Although the concepts employed are generally applicable, the focus here will be on phytoplankton. We will see that the kinetics of solute diffusion and metal coordination reactions are both relevant to explaining exceptions (apparent or otherwise) to the FIM in phytoplankton. These exceptions lead to dependencies of metal uptake rates on the bulk concentrations of inorganic metal complexes, for the cases of kinetically controlled iron uptake and diffusion limitation of zinc uptake, and surprisingly even on Cu(1I)EDTA concentrations in cases where reduction is likely

occurring at the cell surface. It is the author’s hope that the following theoretical analysis of these and other observations, which is intended to complement the paper of Sunda and Huntsman (1998) will contribute to the progress being made both by researchers working to further our understanding of metal bioavailability and by modelers seeking to synthesize and apply this knowledge. 2. The equilibrium paradigm Over the past 2 decades, chemical equilibrium principles as embodied in the ‘free ion model’ have risen to a prominent place in the scientific literature on the biotic uptake of trace metals. In applying the FIM, one assumes that: (1) the aqueous complexation reactions of cationic metals (&IZf) and ligands ( L )in solution are essentially at equilibrium; (2) the binding reaction of metal is close to ions with cell surface sites (Xtransporter) equilibrium; and (3) any transmembrane transport occurs slowly relative to the surface complexation/dissociation reaction:

--

Complexation

MZ++L

ML

Binding

M z ++ Xtransporter

Mxtransporter

Transport

M X t r ansporter

Mcell

Under these assumptions, the binding reaction of is termed a pre-equilibrium (or pseudoequilibrium) step, from which it follows that for the FIM metal uptake velocities should be expressible as a single saturable function of the concentration ([M”’]) of the ‘free metal ion’ (the aqua metal cation with only water molecules as coordinating ligands) irrespective of the strength or concentration of the dissolved ligands (Morel, 1983): (3) where V, is the saturated uptake velocity and KM is the affinity of the transport system for the free metal ion. Thus, it may be properly said that

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

the free metal ion concentration (or activity) ‘controls’ the rate of metal uptake as well as any associated biological effects. In one important if somewhat uncommon class of exceptions, either neutral, lipophilic metal complexes (MLO) or metals chelated by ligands exuded by biota specifically for the purpose of metal acquisition (MLexuded) are directly taken up:

--

Binding

M Z f +L

Uptake

Binding

M z f + Lexuded

+

MLo +Mcell L MLexuded

Uptake Mcell

+ Lexuded (4)

For these mechanisms, the rates of metal uptake are functions of the concentration of the transported complex rather than the free metal ion. Whether mechanism (2) or (4) applies, the basic assumption of the FIM remains: that a rapid pre-equilibrium exists between metal species in solution and those bound to ligands ( L ) and that facilitate uptake. Given this sites (XtranSpOrtel) conceptual foundation, it is not surprising that most studies of metal uptake focus on the equilibrium solution speciation of the metal and the stability of its complexes with transport ligands or sites. This image of biotic metal uptake, seen through the digitally-enhanced lenses of computer equilibrium models, will be referred to in the remainder of this paper as the ‘equilibrium paradigm’. The equilibrium paradigm has undeniable power and utility. It has been successfully applied to the analysis of a wide variety of experimental and field data (Sunda and Huntsman, 1992; Hare and Tessier, 1996) and provides a common basis for integrating and/or comparing biological and chemical studies by means of the free ion concentration scale (Allen and Hansen, 1996). Several reviews of the subject have been published in recent years (Sunda, 1991; Tessier et al., 1994; Campbell, 1995). As observed by Campbell (1995) in an exhaustive review of the experimental literature on trace metal bioavailability, documented exceptions to the free ion model are ‘relatively

97

few in number’. The strongest experimental evidence for the FIM is the close correlation of metal uptake rates and [M”’] in media containing synthetic organic chelators of different binding strengths. Aside from the above ‘exceptions that prove the rule’, the only truly unexplained cases cited by Campbell (1995) involved weak organic chelators or natural dissolved organic matter that reduced metal uptake less than expected from their effects on free metal ion concentrations. Campbell (1995) also found no inorganic complexation effects that were not explainable by additional pertinent equilibria. Several studies examining the variations in metal effects with pH are consistent with the FIM, as long as competition with H f at the metal-binding sites is accounted for. However, because experimental studies of metal uptake are most often conducted in media of constant inorganic ion composition, the FIM has not been widely tested with respect to environmentally relevant variations in inorganic metal complexation. Throughout the genesis and evolution of the equilibrium paradigm, there has been an awareness that non-equilibrium conditions could change the apparent rate-controlling species for metal uptake. Jackson and Morgan (1978) were the first to explore the implications of chemical kinetics for metal uptake by aquatic organisms, examining theoretically both the possibility that diffusionlimited uptake of a metal could be enhanced by the dissociation of labile metal complexes in an organism’s diffusive boundary layer and that the reaction kinetics of the different metal complexes with the transporter rather than coordination equilibria controlled the uptake rates of metals. Both of these scenarios would result in an dependence of uptake on kinetically-labile species rather than the free metal ion (Whitfield and Turner, 1979). In other work reviewed in Hering and Morel (19901, it was shown that disequilibrium of coordination reactions in solution affected the toxic effects of copper, but by itself disequilibrium in the solution phase (or diffusive boundary layer) is not inconsistent with the FIM for the metal transport process itself. It was not until the demonstration that pre-equilibrium in the metal-binding reaction did not hold for Fe

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R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

(Hudson and Morel, 1990) that theoreticians of metal uptake began to seriously reexamine the equilibrium paradigm and the assumption of ‘the universal importance of free metal ion activities in determining the uptake of all cationic metals,. .’ (Morel, 1983). This paper continues the exploration of the implications of reaction and diffusion kinetics for the dependence of trace metal uptake by aquatic organisms on chemical speciation begun in the works of Morel et al. (1991) and Hudson and Morel (1993). 3. Definitions of biotic metal uptake

The relative importance of equilibrium and kinetic factors varies greatly depending on how ‘uptake’ is defined. In the simplest form of ‘uptake’, metals are adsorbed onto sites in cell walls and cell membranes without being transported into the cytoplasm. Adsorptive uptake can be substantial for metals that have a high affinity for surfaces, such as aluminum, iron(III), lead, copper, and mercury(I1) (Xue et al., 1988). Adsorption onto the surfaces of phyto- and bacterioplankton can be an important mechanism for scavenging metals from surface waters (Michaels and Flegal, 19901, but because cell surface-associated metals are much less efficiently transferred to grazers than intracellular metals, this process does not generally affect organisms at higher trophic levels (Reinfelder and Fisher, 1991; Reinfelder et al., 1998). The process is also important since the adsorption of toxic metals on cell membranes (usually at high concentrations) can cause acute toxicity in aquatic biota, e.g. through the direct impairment of membrane function or catalysis of membrane-degrading reactions (Playle, 1998). Since adsorptive uptake generally attains equilibrium within minutes to hours, it should conform exactly to the equilibrium paradigm except in rare cases where a cell surface has both such a high affinity and capacity to bind a metal relative to its rate of uptake that the sites do not reach equilibrium within the renewal time of the cell wall or division time of the organism. In a second type of uptake, metals still interact

only with the cell surface but undergo a chemical reaction other than adsorption onto the surface (Price and Morel, 1990). The best known examples are metal redox reactions. Both enzymatic and non-enzymatic reduction of Fe and Cu has been observed at cell surfaces (Jones et al., 1987). Such cell surface transformations of metals can themselves become limited by diffusion. We will not consider this class of processes further except to the extent that surface redox reactions are in some cases the initial step in the uptake of metal complexes, as observed in yeast (Hassett and Kosman, 1995). The processes by which aquatic microorganisms take up metals from their environment into the cell cytoplasm constitute the focus of this paper. With the exception of metals incorporated in cell-surface metalloenzymes, it is metals in the cytoplasm that are either required for or interfere with cellular metabolism and are also transported most efficiently up aquatic food chains (Reinfelder and Fisher, 1991). This distinction between surface-bound and intracellular metals is often neglected in studies of uptake by aquatic biota, partly because it can be difficult to make experimentally and because often much less metal is associated with the surface than is found intracellularly during steady-state growth. (Iron in media supersaturated with respect to iron hydroxide and lead are some of the best-known exceptions). In the studies considered here, surface-adsorbed metals have either been chemically removed or found to be much smaller than the amounts inside the cell. 4. Mechanisms of intracellular transport

Intracellular uptake of cationic metals occurs via several different mechanisms (Fig. 1). For our analysis, the most relevant distinction between these mechanisms is the nature of the interactions between the metals and the ligands responsible for their transport across the plasma membrane. We next briefly review these interactions for three important mechanisms: transporterfacilitated uptake, extracellular chelator-mediated uptake, and passive absorption of lipophilic com-

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115 Transporter

99

hydration. For alkaline earth and transition metals, however, specific binding to a transport site is generally a requisite step in transport (Eide, 1997). While little is known at the molecular level about the metal transporters of most aquatic organisms, several widespread observations give compelling testimony to their role in essential metal uptake (see also Sunda and Huntsman, 1998). The first is the saturability of short-term metal uptake rates, particularly for nutrient metals. Both saturability and competitive inhibition of uptake by non-essential metals require that there be specific transporters involved (Stein, 1990). Since ion transport by channels that do not bind the ions saturate at very high concentrations, e.g. 1 M for monovalent cations (Stein, 19901, it is virtually certain that trace metal transporters, which typically saturate transport at concentrations < 1 pM, must directly bind these metals in order to transport them. Surface binding and subsequent transmembrane transport of Fe has been directly demonstrated in two marine phytoplankton (Hudson and Morel, 1990).

-

Fig. 1. Mechanisms of intracellular transport of trace metals into aquatic biota (see text).

plexes. (A fourth mechanism of uptake, endocytosis, has not yet been found to be important in aquatic systems.) 4.1. Transporters

Biotic uptake of metal ions is most commonly facilitated by transmembrane pumps, channels, and carriers, generically termed ‘transporters’ (Stein, 1990). Pumps and channels are integral membrane proteins with several hydrophobic, membrane-spanning segments that facilitate (often actively) ion transport. Carriers are lipidsoluble molecules that bind a metal on one face of the membrane, diffuse across and transfer the metal to the solution on the opposite face. The nature of the metal-transporter interaction differs significantly between transporters. Some monovalent cations like Naf and Kf can be conducted through transmembrane channels by diffusion without ever truly ‘binding’ to specific sites in the channel or losing their waters of

4.2. Extracellular chelators In a second form of facilitated uptake, aquatic prokaryotes release very high-affinity Fe chelators, or siderophores, into the environment when they become iron-stressed (Wilhelm and Trick, 1994). Generally the complex is transported by membrane receptors back into the cytoplasm where the iron is removed and incorporated into biomolecules. Since uptake of Fe-siderophore complexes is facilitated, its uptake is a saturable function of the complex concentration. A great deal is known about the chemistry and molecular biology of siderophores, although fascinating questions remain about their function in largescale aquatic systems. It can be shown that an individual microbe of bacterial size cannot recover the Fe-complex of a siderophore that it releases in aquatic systems, but must cooperate along with other members of its population that exude the same chelator in order to build up adequate concentrations of the transportable Fesiderophore complex (Hudson and Bruland, submitted). The net effect is to alter the Fe chemistry

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R.J.M. Hudson /The Science of the Total Environment 219 (1998)95-115

of their environment on large physical scales (Rue and Bruland, 19971, since small scale patches would be diluted too quickly. The interactions of siderophore exudation and uptake with metal supply potentially make for very dynamic systems that are challenging to model. Extracellular chelators also influence Cu except that the converse effect, inhibition of Cu uptake, is achieved by cyanobacterial Synnechococcus species that exude strong copper chelators (Moffett et al., 1997). 4.3. Passive absorption

Although most metal species are extremely hydrophilic, a few metal complexes are soluble enough in lipids that they are able to rapidly diffuse through membranes at appreciable rates. This passive absorption of neutral, non-polar complexes of ionic metals is the same mechanism by which hydrophobic organic compounds are taken up. Passive metal absorption is best known for the neutral chloride, and to a lesser extent hydroxide, complexes of Hg2+ and CH,Hg+ ions (Bienvenue et al., 1984). Recent studies have demonstrated that lipophilic, organic chelates of several divalent metal ions can also diffuse through cellular membranes, thereby short-circuiting cellular barriers to toxic metal uptake (Phinney and Bruland, 1997). At present, there is no evidence that lipophilic chelates either from natural or anthropogenic sources occur widely in nature. Thus, while the demonstrated relevance of this mechanism may be restricted to a few metals, it may play a very important role in their environmental chemistry.

Then, following intracellular transport, the metal must exchange the ligand(s) of the transported complex for intracellular ligands, such as the active sites of enzymes, regulatory proteins, and storage/sequestration sites. The rates of reactions in which one ligand substitutes for another bound to a metal ion: ML,

+ L,-

ML,

+L,

(5)

depend strongly on the mechanism(s) favored under the conditions of interest. Ligand exchange reactions can occur via a spectrum of pathways that range from the strictly associative (or adjunctive) pathway, in which both ligands are bound to the central metal ion in the intermediate (transition) state:

to the strictly dissociative (or disjunctive) pathway, in which the initial complex must completely dissociate before the second ligand binds the metal:

(Burgess, 1988; Morel and Hering, 1993). Between the two ends of the spectrum, lies an interchange pathway in which the incoming ligand first forms a largely-electrostatic, outer-sphere complex:

5. Coordination kinetics: mechanisms and rates

Transport via any of these mechanisms requires that the metal ion undergo a series of ligand exchange reactions. In aerobic waters, metals are primarily bound to water itself; inorganic anions such as hydroxide, chloride, and carbonate; humic/fulvic acids; and strong organic chelators of both anthropogenic and biotic origin. To be taken up, a metal ion must first exchange one of the extracellular coordinating ligands for a site or ligand(s) that forms a transportable complex.

with the substitution for the outgoing ligand occurring in a step that may be either associative or dissociative in character. For a given ligand exchange reaction, parallel mechanisms can occur with the various species of the incoming ligand, such as the free ligand and its complexes with hydrogen or secondary metal ions, generally exhibiting different kinetics. Consequently, complex dependencies of ligand exchange reactions on medium composition and on catalytic effects of

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

other ions can occur (Wilkins, 1991; Morel and Hering, 1993). If we consider ligand exchange in the context of a metal transporter and the many metal species present in aquatic systems, we can quickly see that numerous parallel pathways for the uptake of a single metal exist. As an hypothetical example, consider the possible reactions between a metal cation MZf that has significant hydroxy-, chloro- and organic complexes and a transporter site: k&+ 3

Mz++ Xtransporter I M x t r a n s p o r t e r k++ 3 kLOH,X

'

MOHz- + Xtransporter

Mxtransporter

+ OH-

k,OH,X

'

+ X t r a n s p o r t e r I mtransporter k,CI

+ C1-

,x

k$ yo~g,"~C.x morganic

+ +

+ Xtransporter

Mxtransporter

k~yo.g,"lc.X

+ Yorganic kin

M X t r ansporter +Mcell

of the different reaction pathways in (9). This basis is the existence of a common interchange (usually of dissociative character) mechanism for the coordination of many aqua metal cations:

In the first step of this Eigen-Wilkins mechanism, an ion pair or outer sphere complex forms bringing the ligand into close enough proximity to replace a water molecule as it escapes from the metal ion's inner coordination sphere. The second step, interchange of the ligand and inner sphere water molecule, is limited by the intrinsic rate of water exchange at the metal ion kM-H,O leading to the approximation kinterchange kM- H , O . Furthermore, because coordination by the first binding site of a polydentate ligand also hastens the loss of subsequent inner sphere water molecules, the overall coordination kinetics of polydentate ligands are also frequently limited by water-loss kinetics. Exceptions to the EigenWilkins mechanism are discussed by Burgess (1988) and Wilkins (1991). Dramatic differences in k,- H,O arise between metal ions (Fig. 2), with values ranging from 2 X s-l for Cr3+ to 4 x lo1' s-l for CH3Hg+. is related to its charge Each metal ion's kMPHzO to radius ratio as well as factors specific to its electronic structure - crystal field effects and Jahn-Teller distortion. Since the outer-sphere stability constant KO, can be calculated from simple electrostatic considerations (Morel and Hering, 19931, it is possible to predict the forward rate constant of many coordination reactions with reasonable accuracy using:

-

kLCI,X

MC1'-

101

(9)

Note that formation reactions of the aqueous complexes are implicit in (9). Needless to say, modeling such a kinetic scheme would be cumbersome and require parameters not generally available from physiological metal uptake studies. However, it is enlightening to realize that many different metal species do bind to the transporter sites and that a rather complex interaction of speciation and medium chemistry could govern rates if none of the binding reactions are rapid enough to create a pre-equilibrium state. Although the values of many rate constants that are important for metal uptake in the environment have not been measured, there is an empirical basis for predicting the rates of aqua metal ion (and some simple complex) coordination reactions that will help us estimate the rates

Similar analyses of the kinetics of water exchange and coordination reactions for monodentate inorganic complexes have also been made (Margerum et al., 1978; Burgess, 1988). It has

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

102 12

0

10 h

r

0

v)

- 8 c c

m c

0

2

6

0

4

s

iii

A

z) rm :: w

z 3 L

8

0

co2+ Fez+

0

0

0

.

PbZ+

cu2+ Hg2+

Ca2+ Cd2+

0 CYk

K+

Mn2+ Zn2+

0

Ni

a 0

A

@

V 0

0

0

2

Fea 0

O

Ata -2

-4

2? -6

A

0 0

Cr 3+

-8

Metal Fig. 2. Water exchange kinetics of metal aqua ions and inorganic complexes. Values for aqua ions are from Wilkins (1991) except for Pb2+ (Margerum et al., 19781, and CH3Hgf (Erni and Geier, 1979). Values for hydroxy- and chloro-complexes are from Margerum et al. (1978), Burgess (1978), and Monzyk and Crumbliss (1982) and include some estimated from reaction kinetics.

been shown that both water exchange and coordination reactions are in several important cases markedly accelerated by the hydrolysis of polyvalent metal cations, presumably by decreasing the tenacity with which the metal ion binds the re-

maining inner sphere water molecules (Fig. 2; Table 1). Particularly strong effects are observed for Fe(III), with both water exchange and complexation kinetics increasing by factors > lo5 between the free ferric ion and the Fe(OH)l and

Table 1 Rate constants for iron(II1) coordination reactions Fe species

~F~-H*o

Ligand

(S-l) Specific rate constants Fe3+ FeOH”

1.2 x lo5

H3dfboa

0.1

Monzyk and Cmmbliss (1982)

H3dfbo

2 x lo2

Monzyk and Crumbliss (1982)

H3dfbo

0.11

Tufano and Raymond (1982)

Apparent rate constantsb

Fe(II1)’

k + Fe(III)‘,L lo7 (est.)

dfb’

2 x lo6

Hudson et al. (1992)

X’transporter P. carterae T. wessfogii

1.3 X lo6 0.9 X lo6

Hudson and Morel (1990)

adfb is deferri-ferrioxamine B, a microbial siderophore. Measured in synthetic seawater at pH 8. Fe(II1)’ primarily comprises Fe(0H)l and Fe(0H);

b

Reference

k+F+‘

1.6 X 10’

Fe(OH)EDTA2-

Fe(II1)’

Rate constant (M-l s-’)

at pH 8.

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

Fe(OH); species. Interestingly, monomethyl mercury, which binds only one ligand or water molecule, does not follow this trend (Margerum et al., 1978). Complexation by chloride can also accelerate the rates of ligand exchange and addition reactions (Fig. 2). Carbonate ion complexes of Cu2+ and Pb2+ are assumed to be labile based on their lower stability constants than for strong organic chelators. Consequently, complexation by the principal inorganic ligands of aerobic surface waters should either accelerate, or at least not dramatically decrease, the rates of the metal complexation provided the incoming ligand forms a complex that is thermodynamically favored over the outgoing inorganic ligand. Of course, coordination reactions are also influenced by the speciation of the ligand. Since ligands by definition have some Lewis base character, a significant fraction of the ligands not bound to metal ions are often protonated. Protonated monodentate ligands are often nearly inert, while partially protonated polydentate ligands can be quite labile (Margerum et al., 1978). In addition, ligands already bound to another metal react much more slowly than free ligands (Hering and Morel, 1990). Competitive binding of H + and Ca2+ has been shown to be a factor for metal uptake by aquatic organisms (Campbell and Stokes, 1985; Playle, 1998) and certainly is expected to influence metal coordination kinetics. In summary, the Eigen-Wilkins mechanism gives a good basis for predicting the rates at which aqua and simple inorganic metal ions undergo further complexation (ligand exchange) reactions. This in turn allows dissociation rate constants to be estimated based on detailed balancing (Morel and Hering, 1993). The exchange kinetics of strongly-chelated metals are, however, difficult to predict, beyond the generalization that they react much more slowly than aqua or monodentate ligand complexes. For example, at a pH > 7, EDTA-bound Fe(II1) reacts with desferal at > 107-fold slower rates than Fe(II1)-hydroxide species (Table 1). Thus, we will proceed by assuming that highly-stable natural organic complexes are also, for the most part, kinetically inert.

103

6. Equilibrium vs. kinetic control of transportermediated uptake

The preceding discussion of coordination kinetics suggests that every metal species in solution must react at a finite rate with cellular metal transporter sites. For example, a small fraction of Ni2+ as NiCl' in seawater could significantly speed its coordination kinetics due to the greater lability of its coordinated waters (Fig. 2). Extending this to other metals, the binding of labile inorganic complexes such as with hydroxide, chloride, and carbonate may serve as the predominate pathway of metal binding. While this does conflict with simplistic misinterpretations of the FIM's equilibrium reactions (2) as a single-pathway mechanism, the FIM is actually consistent with the multiple reactions in as long as at least one reaction is sufficiently rapid compared to internalization that pre-equilibrium of the metal-transporter reaction is attained (Morel and Hering, 1993). In order to make the kinetic scheme manageable and in recognition of the fact that the individual rate constants are not precisely known, the use of the aggregated inorganic metal complexes, termed M' according to the conventions of electrochemists (Coale and Bruland, 1988), and apparent (conditional) rate constants has been suggested (Hudson and Morel, 1990):

are the apparent or In (121, k&,,x and effective complexation and dissociation rate constants with respect to all the inorganic metal species and are specific to the conditions of the experiment or system (see below). By invoking the steady-state approximation for the intermediate MXtransporter concentration, a kinetically-based Michaelis-Menten type expression can be derived: (13)

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R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

(16)

where the maximum uptake rate and the transporter affinity

are defined in terms of the kinetic parameters in, the surface area of the cell Ace]],and the areal density of transporter sites ( X , ) . Experimentally-determined uptake kinetic curves can be expressed equally well in terms of free ion concentrations or inorganic metal concentrations. However, since the kinetic expression is the more general case, it is appropriate to define the apparent affinity KM for the free ion in terms of K L :

where the coefficients aM, and a M Z +are the speciation fractions of the subscripted species, i.e. a M , = [ M i ] / [ M T ]Whether . KM or K L remains more constant over a range of medium compositions depends on how the speciation of the metal is varied and the relative rates of the reactions in (12). The equilibrium stability constant of the metal binding site KMx is related to the kinetic parameters and metal speciation by: Equilibrium control

Two scenarios for the relative rates of the coordination and internalization reactions are depicted in Fig. 3. The first, which corresponds to the FIM, is referred to here as 'equilibrium control' (equivalent to 'thermodynamic control' in Morel and Hering (1993)) of transport. Under equilibrium control the rates of formation and species are essendissociation of the MXtransporter tially equal and much greater than the intracellular uptake (internalization) rate. In the second, termed 'kinetic control', the formation and internalization rates are nearly equal and much larger than the dissociation rate. Examination of Eq. (15) shows that 'equilibrium control' will hold with KM= K M x if k,,,,% kin,while if k;(,,<< kin the apparent affinity of the transporter is controlled by kinetics rather than the stability constant of the transporter site. Since the metal ion's water exchange kinetics exert primary control on the rate constant for MXtransporter formation, the nature of the transporter primarily influences the rate constants for dissociation and internalization. From the limit on complexation kinetics imposed by the Eigen-Wilkins mechanism, Hudson and Morel (1993) developed theoretical constraints on seKinetic control

Fig. 3. Two limiting cases for control of metal binding to transporters. (A) Equilibrium control (pre-equilibrium defines MX concentration) as assumed in the free ion model. (B) Kinetic control (steady-state defines MX concentration). The width of the arrows for the formation and dissociation reaction of the MX complex and of the internalization step indicate the relative magnitude of the rates. The reactions between solution species are generally very rapid compared to transport (arrow widths not to scale).

R.J.M. Hudson /The Science of the Total Environment 219 (1998)95-115

lected properties of transporter systems, such as the minimum number of sites and internalization rate constants, based on their function of satisfying cellular metal requirements at given levels of metals available in the organism's environment. It was also argued, with some benefit of hindsight, that kinetically-controlled transport is advantageous to the organism since it would minimize the number of transport sites required to meet the organism's nutritional requirements at any given environmental concentration of metals. Minimization of sites is a consideration due to limitations on available space in the plasmamembrane for the large numbers of transporters required when an essential metal's availability is low and/or has coordination kinetics that are moderate to slow (Hudson and Morel, 1993). A significant problem inherent in pursuing this analysis of metal transport kinetics that it is generally not known whether transport is under equilibrium or kinetic control. Of course, the same problem applies to attempts to infer chemical meaning from the apparent transport parameters derived using the free ion model. There has, however, been one study in which the kinetic control of uptake was demonstrated in two ironstressed marine phytoplankton (Hudson and Morel, 1990). In pulse-chase experiments, transmembrane transport of radiolabeled Fe bound to the cell surface was observed to take 5-20 min, an exceptionally long turnover time for a facilitated transporter. Lack of inhibition by high concentrations of unlabeled Fe or chelators added to the medium proved that the Fe was coordinated by a site directly involved in the transport process. Most importantly, the mere fact that uptake from the cell surface was observable during the chase phase of the experiments, when labeled iron was absent from the solution, demonstrated that the Fe bound to the site was not at equilibrium with Fe species in solution. Uptake was therefore kinetically-controlled. (Note that no surface uptake was observed for Fe-replete cells either due to equilibrium control or the cells having down-regulated the number of transport sites to unmeasurable levels.) From these and other kinetic studies, all the parameters in Eq. (14) could be deduced for Fe uptake. Interestingly, k&,,,,r,x (0.9-1.3 X

105

10-6 M-1 s - l ) was much greater than had previously been observed for the water loss kinetics of the Fe3+ and FeOH2+ species (Table 1). It was, however, within a factor of two of the conditional rate constant for Fe complexation by the microbial siderophore desferal measured in seawater at the same pH. This agreement, coupled with the theoretical argument that organisms under iron stress would find it necessary to maximize the coordination kinetics of their transport systems, suggested that the kinetics of Fe binding to the transport systems of these phytoplankton was near rates limited by water exchange kinetics for the Fe(OH)l and Fe(0H); species that dominate under the conditions in the experimental medium (Hudson and Morel, 1990). 7. Selectivity of transporters depend on equilibrium versus kinetic control

The above arguments raise the question of why all transport systems should not be kineticallycontrolled, which would conveniently allow us to predict the uptake rates of nearly all metals from water loss kinetics alone. One answer is that equilibrium control may be necessary to enhance the selectivity of the transporter (Hudson and Morel, 1993). It is widely found that metal transporters cannot take up one metal ion completely to the exclusion of other similar metals (Sunda and Huntsman, 1998). An elegant example is the Mn transport system of the coastal diatom Thalassiosira pseudonana (Sunda and Huntsman, 1996). This transporter has saturated uptake rates (Vmax)for Mn2+,Zn2+ and Cd2+ are equal and affinity constants KMn,KZn,and Kcd that increase in the order 107.1,107.5, M-l. Despite its higher affinity for Zn and Cd, the transporter is effective in acquiring Mn as long as the relative concentrations are appropriate, as they generally are in surface seawater. While it is not known whether kinetics or equilibrium controls the metal-binding reactions, we can devise a simple model for this transporter by applying Eq. (13) to all three metals using the same value of kin (since the Vmax,and implicitly kin and ( X T ) , are equal) and setting k i t , , = kMPHzO for each metal (Kos is near unity in

106

R.J.M. Hudson /The Science of the Total Environment 219 (1998)95-115

seawater as long as the transporter site is not highly charged). First, equivalent affinity constants with respect to M' - Khn = lo7.', K& = 107.3,and K& = 106.6M-' - were derived using (15) and literature values for inorganic complexation fractions (Byrne et al., 1988). Next the kinetically-controlled model was defined by setting kin to 2.6 s-l in order to fit the observed KL, and predict values for other metals (Fig. 4). The predicted values were reasonably close to the observations for Zn (and would be closer if ZnOH2+ exhibits increased water loss rates as with other metals), but 50-fold too high for Cd. Next, the equilibrium-controlled model was defined by setting k,,,, to 2.6 s-l and assuming that the metal-binding site has equilibrium stability constants for the other metals that are proportional to the ratio of their salicylate stability constants to that of Mn. (Salicylate was selected because it is soft enough to not bind Ca very strongly but not so soft as to bind Cu excessively. Other model ligands give similar results.) The internalization rate constant kin was set to 0.003 s-l in order to obtain equilibrium control for all metals simultaneously. Under equilibrium control, the transporter would be relatively more selective against Cd2+ but much less selective against Cu2+ (Fig. 4). A mixed-control scenario was devised by decreasing kin from the kinetically-controlled value to 2.1 s-' but weakening the ligand by increasing k i , for all metals proportionately. Due to its low stability constant, Cd2+ was the first metal whose uptake became equilibrium controlled. A good fit to the observed K,, was obtained in this way (Fig. 4). Although the mixed-control scenario model describes the observations for T. pseudonunu reasonably well and predicts a plausible affinity for Cu, one cannot preclude the possibility that the actual transporter's binding site has equilibrium affinities that account for the observations. However, equilibrium stability constants for Cd are typically only higher than those of Zn for soft ligands (Morel and Hering, 1993),which also tend to bind Cu strongly. Thus, the Mn transporter may be forced to trade off selectivity against Cd for selectivity against Cu. Taken together with the above-mentioned ad-

12

1

Equilibriui

11

--I0

z

y' 0)

2

Kinetic /

9

Aixed

/ /

8

7 6 Mn

Zn

Cd

cu

Fig. 4. Modeled transport system affinities KM for divalent metal cations under equilibrium, kinetic and mixed control (see text). The relative values of the K M x are given by each metal's salicylate stability constant (Morel and Hering, 1993) and were calculated using the expression: KMx/KM.salicylate KMnX/KMn.salicylate. Values of kin and KMnXwere varied as described in the text. Inorganic side reaction coefficients (a&. = [ M " + ] / [ M ' ] )are given in the footnotes of Table 3. Observed K M values for T. pseudonana are for uptake via Mn transporter (Sunda and Huntsman, 1996).

vantages of kinetically-controlled transport, this example illustrates how equilibria and kinetics might both be important factors in determining transport selectivity. As discussed by Hudson and Morel (19931, the case for an organism maintaining kinetic control is most compelling for essential metals with slow water exchange kinetics that are also present at low concentrations. For a given transport system, the degree of kinetic or equilibrium control of uptake for unintended metals depends on both their kinetics (fast kinetics favor equilibrium) and their affinity for the site (weak binding favors equilibrium). 8. Inorganic complexation favors equilibrium control

Beyond its relevance for the selectivity of transport systems, the issue of kinetic vs. equilibrium control has implications for the dependence of uptake rates on the inorganic speciation of metals. Under equilibrium control, increased inorganic complexation will uniformly decrease the rate of metal uptake, while with kinetic control it could have effects that range from slightly posi-

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

tive or negative to very large positive effects, as observed for Fe(II1). To explore this further, we return to the kinetic scheme of Eq. (9). The full expression for the apparent transporter affinity constant K L can be derived from the rate constants of all of the reactions:

by assuming that the concentration of the MXtransporter species is at steady-state and that simple, stoichiometry-dependent rate expressions apply for all of the reactions (no catalysis, etc.). The very detailed experiments needed to establish this relationship are uniformly lacking, but it is useful to consider it more closely. Consider a transporter for a metal M"'. Above, we argued that (weak) inorganic complexation does not greatly decrease and may dramatically increase the rates at which a metal binds to metal transporters. However, the dissociation rates, as defined in the denominator of (17) must increase as well due to the increase in inorganic ligand concentrations. In fact, since the conditional equilibrium constant for the transporter (k&r,x/k;,,x) is inversely related to the extent of inorganic complexation while k&r,x increases proportionately (or at least does not decrease much), it follows that k;,,x must increase at a faster rate than kL,,x and at some point a kinetically-controlled transport system should become equilibrium-controlled. Of course, extensive inorganic complexation does not guarantee equilibrium control, as was found for the Fe(II1) system where [Fe3+]is only one ten-billionth of [Fe(IIIYI, but it should favor it. This effect of inorganic complexation, for example through an estuary, can be illustrated by reconsidering our model for Cd uptake via the Mn transport system. Using the transporter

107

parameters derived above, it is possible to describe the variations in Cd uptake parameters as a function of salinity and the associated changes in inorganic complexation, KO,, and activity coefficients (Fig. 5). The apparent affinity for Cd2+ varies slightly less than the activity coefficient effect of lO-'.'-fold lower at S = 35. The ninefold increase in ked,Xis due to the effects of chloride complexation, but is somewhat less than the 30fold variation in the ratio [Cd2+]/[Cd' 1 through the estuary. Thus, the mixed-control model for the Mn transporter predicts that Cd uptake should be equilibrium-controlled at the mouth and between kinetic and equilibrium control at the inlet (k, = 2kZd,x). These results, while speculative, suggest that complex dependencies of apparent transport system parameters on environmental conditions may be expected especially for metals with wide-ranging inorganic complexation fractions. 9. Diffusion limitation can influence apparent controlling species

We have seen that non-equilibrium conditions in the transmembrane transport process can cause metal uptake to deviate from the free ion model. Another rate-controlled process, diffusion from the bulk medium to the cell surface, can complicate the apparent controlling species in a similar manner (Jackson and Morgan, 1978). Because the diffusive flux through the cellular boundary layer, which is proportional to bulk-to-surface concentration differences, must equal the transmembrane flux, metal uptake necessarily depletes the concentrations of transported species at the surface as well as throughout the cell's boundary layer. If other metal complexes that are kinetically inert with respect to the transporter are able to dissociate to form transportable species, the diffusion limitation is effectively lifted. At the maximum degree of chemical enhancement, which occurs when equilibrium between chemically labile species M,abileand rate controlling species M iis maintained within the boundary layer, the rate of metal uptake is apparently controlled by the concentrations of chemically labile species. In order to investigate this effect further, it is

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R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

s-

High V, 0.005 -

9

Low,,v

3

(3 0.000

0

5

10

15 20 Salinity

25

30

35

0

I

I

I

I

I

I

5

10

15

20

25

30

35

Salinity

Fig. 5 . Effect of salinity variations through an estuary on Cd transport. (A) Mixed-control model (Fig. 4) parameters as a function of salinity. (B) Overall conductance for Cd2+ transport calculated assuming V,,, at maximal and l / l O t h maximal values reported by Sunda and Huntsman (1996). The model for Cd uptake was formulated using (17). k& were estimated as a function of salinity for Cd2+,CdCl', CdCl,, and CdCl; from (11) by assuming all species had kinterchange values of s-' (water loss rate for Cd2+ and estimated value for CdC1, in Fig. 2) and KO, calculated as in Morel and Hering (1993) for a charge of - 1on X . k,dc,t,, were = KCdX/KCdCI, with equilibrium constants corrected for ionic strength using the Davies calculated from using k~dc,L,,/ k; dc,L,, equation. aCd,calculated using stability constants for the above species from Morel and Hering (1993). At a salinity of 35, it was assumed that [Cl-] = 0.53 M and I = 0.7 with values at other salinities being directly proportional. Diffusive conductance as in Table 3.

helpful to find a means of expressing the capacity of various organisms to transport metals and the capacity of diffusion to supply them on a common scale. To do this, we normalize the metal uptake velocities V by the surface area of the organism exposed to the aquatic environment to obtain uptake fluxes (.Ti)and use the linear, unsaturated region of the uptake kinetics equations. The resulting proportionality constant between the uptake flux and the bulk concentration of the ratecontrolling species [ Mi] is termed the 'conductance' for solute uptake Gi due to mechanism i: (18)

The overall conductance is related to the conductance of the cellular transport system gi and of the diffusive boundary layer g , of the organism:

Table 2 includes flux equations, rate-controlling species, and definitions of the conductances for diffusion (g,), for transporter-mediated up-

take ( g M z +and g M r ) ,and for passive absorption of lipophilic metal species such as ML" (gMLo). Note that for facilitated transport, g M z +and g M , are constant only in the undersaturated range of the transporter's uptake curve, which is where diffusion limitation exerts the greatest relative effect. When the transport system conductance gi is comparable or greater than the diffusive conductance g,, the uptake process can exert an effect on metal concentrations in the organism's boundary layer. If non-transported species are sufficiently abundant and labile, they will begin to supply additional metal for uptake. The maximum, diffusion-limited uptake rate is attained when surface concentrations of both the transported and labile species are depleted to zero (which is of course unattainable). When uptake is near diffusion-limited rates, the uptake flux will be proportional to the bulk concentration of labile species [ MIabile1:

(20) which generally includes inorganic and perhaps

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

109

Table 2 Mathematical definitions of transport conductances Mechanism

Transport equationa

Equilibrium-controlled transporter

v = g M z + [ M ' + ]surface

Kinetically-controlled transporter

v=gM"M'lsurface

Definition of conductancea

cell

Ace11

a Cellular uptake rates depend on cell surface concentrations and can be related to bulk concentrations using overall conductances (Eqs. 18,19). Conductances given here are for under-saturated conditions in facilitated transport systems.

weak organic complexes. When uptake rates are far below diffusion-limited values, the approximation Gi =gi may be employed in (18). Whether diffusion limitation of metal uptake occurs in aquatic organisms has been examined in relatively few cases. In the marine phytoplankton literature, it has been shown that diffusion constrains the uptake of the essential metals Fe and Zn in some species when their transport systems are up-regulated in response to metal depletion (Table 3). Diffusion limitation of Mn was not observed in the same species even under fully up-regulated conditions, presumably because interactions with competing metals makes it infeasible (Hudson and Morel, 1993). Note that the maximal uptake of Zn by the Mn transport system of T. pseudonana has a 2.5-fold higher conductance and fraction of the diffusion-limited rate than Mn itself does. This results from the fact that it has a higher affinity constant but the same maximum uptake rate (Sunda and Huntsman, 1998). For the same reason, Cd uptake via the equal to 0.4, has a Mn transporter, with gCdZ+:gD 10-fold higher conductance than Mn does. However, due to the large ratio of labile Cd-chloro complexes to Cd2+ ions, a smaller fraction (0.001 vs. 0.003) of the diffusion-limited flux of Cd is taken up. This chemically-enhanced uptake should be strongly dependent on salinity, as shown in Fig. 5. For equilibrium control of Cd-transport at low V,,,, the K,, varies only due to activity corrections and the overall conductances for Cd2+

vary only slightly between the equilibrium and mixed-control models. At high V,,,, the effects of diffusion accentuate the differences. If we extend this logic to other metals with even higher affinities for co-transport, it suggests that co-transported metals could also attain diffusion-limited rates even if the intended metal does not. For example, note that the uptake velocity for Cu2+ by the same Mn transporter predicted according to the model developed above would have gcu2+= 0.06 cm s-l and could transport Cu2+ at 10% of the diffusion-limited rate (equilibrium-controlled uptake would yield 50-fold greater values of gcu2+).In fact, Cu uptake by this organism in the high concentration range ([Cu2+]= 10-ll.l M), which may have been high enough to discourage induction of the highaffinity Cu transporter (see below), occurred at 9% of the diffusion-limited rate (Sunda and Huntsman, 1995). A similar analysis of Sunda and Huntsman's (1995) data on Cu2+ uptake provides an interesting insight that was originally not noticed. The diffusion calculations indicate that Cu uptake rates exceeds the maximum supply of inorganic copper species to the surface of three phytoplankton by large factors (13-30). These high uptake rates could only be sustained if either the phytoplankton reduced Cu(1I)EDTA to Cu(1) at their surfaces, as has been observed in phytoplankton (Jones et al., 1987) and in yeast (Hassett and Kosman, 19951, or some minor but very labile

R.J.M. Hudson /The Science of the Total Environment219 (1998)95-115

110

Table 3 Metal uptake conductances and diffusion limitation in marine phytoplankton Metal

Organism

Metal transport conductance Type

gi (cm s - l )

Diffusive conductance gD (cm s - l )

Ratio observed: diffusionlimited fluxe

Fe3+=

T. weissflogii T. oceanica

SM, gM'

0.004 0.001

0.016 0.026

0.2 0.038

Zn2

T. pseudonana T. oceanica E. huleyii (BT6) E. huleyii (A13231

SMZ+

0.018 0.044 0.027 0.025

0.030 0.019 0.033 0.028

0.28 0.61 0.35 0.37

T. pseudonana T. oceanica E. huxleyii T. weissflogii

gMz+

17 7.5 9.6 0.007

0.029 0.021 0.037 0.010

31' 17f 13' 0.034

T. pseudonana T.pseudonana

gMz+

0.0012

0.029

0.003

gMz+

0.012

0.029

0.001

SMZ+

0.0030

0.029

0.007

+

cu2

+

Mn2 Cd2 (via Mn-transporter) Zn2 (via Mn-transporter) +

+

+

gMz+ SMZ+

gMz+

gMz+ gMz+

gMz+

T.pseudonana

aT. weissflogii: Hudson and Morel (1990); T. oceanica: Sunda and Huntsman (1992). bSunda and Huntsman (1992). [Zn2']/[Zn'] = 0.66. 'Sunda and Huntsman (1995), Cu uptake data from rates measured at pCu values of 15.12, 14.42, 14.79, 12.04, respectively. [Cu2+]/[Cu'] = 0.05. dSunda and Huntsman (1996). [Mn2+]/[Mn'] = 0.74, [Cd2'l/[Cd'l = 0.029. eCalculated assuming all inorganic species (M'), but not EDTA complexes, are labile,. Denotes apparent uptake flux greater than diffusion-limited value.

Cu-EDTA species existed (Calculations below indicate that dissociation is too slow). Interestingly, the one organism that did not exceed the diffusion limit, T. weissflogzi, was also shown to not reduce Cu(II)EDTA (Jones et al., 1987). This utilization of Cu(1I)EDTA seems ironic since it is often viewed as the classical system used to establish the free ion model. 10. Chemical enhancement can be predicted from complexation kinetics

Finally, it is necessary to define which species are labile for the purpose of chemically-enhancing diffusion via dissociation. First, species that react at significant rates with the transporter should be included in Mlabileand uptake rates calculated from Eq. (181, whether the transporter

is under equilibrium- or kinetic-control. However, it still may be necessary to identify additional complexes M L that react slowly with the transporter but dissociate significantly within the boundary layer to form species that react rapidly M~: G,,L

ML,Mi+L &,,L

A general answer to this question in multispecies systems requires numerical simulation of the reactions in the cell boundary layer. However, we can establish some guidelines through the use of the reacto-diffusive length scale (Wolf-Gladrow and Riebesell, 1997):

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

which reflects the distance at which the mean diffusion time equals the mean reaction time. From numerical simulations (Fig. 6), it is apparent that two conditions must be met for dissociation enhancement to be significant. First, the species M imust itself be taken up at a significant fraction of the diffusion-limited flux (otherwise there is no enhanced dissociation). Second, enhancement starts to occur when rk equals the boundary layer thickness and reaches nearly maximal levels needed to apply Eq. (18) when rk is approx. 0.03 times the boundary layer thickness. (Note that for a spherical aquatic organism, the equivalent boundary layer thickness equals the cell radius rcell; Wolf-Gladrow and Riebesell, 1997). It also goes without saying that dissociation enhancement will not be significant unless the concentration of the M L complex is present in

0.000001 0.00001

0.0001

0.001

111

the bulk solution at a significant fraction of the concentration of the transportable species Mi. Note that Eq. (22) depends on: (1) the lability of the metal ion; and (2) the concentration and speciation of the ligand (since HL and metal-L complexes will decrease k&,,, below the waterloss defined value). The strength of the complex is not relevant, except as it influences whether the complex is present in sufficient concentrations to enhance the uptake of Mi. From Eq. (22) and the previous information on coordination kinetics, it is possible to show (Fig. 7) that there is a simple inverse relationship between the thickness of the diffusive boundary layer at the organismal surface of interest and the concentration of free ligand in reaction at which chemical enhancement begins. For example, note that the BartschatCabaniss-Morel model for fulvic acids (see Morel and Hering, 1993) predicts that a lake with 10 mg 1-l dissolved organic carbon would have approx. 10 p M of fully deprotonated, weak (malonate-

0.01

0.1

1

10

100

Reactodiffusive length (cm) Fig. 6. Chemical enhancement of metal uptake by dissociation of a complex according to reaction. Fluxes are relative to diffusion-limited uptake of M , with no chemical enhancement. Assumptions include [M,abi,e]/[Mi] = 10, boundary layer thickness of 0.001 cm, D = lo5 cm2 s-l and g M r values of (from top line to bottom line) 0.1, 0.01, and 0.001 cm s-’.

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

112 -

1

k

the experiments, the reacto-diffusive length rk for the principal coordination reaction in seawater (CaEDTA2- Cur= =CuEDTA2- Ca2+) is 100 pm, as compared to 2 p m for the radius of the phytoplankton, based on rate constants measured in synthetic seawater (Hering and Morel, 1988). This implies that CuEDTA could not have been dissociating significantly within the boundary layer. Since it is unlikely that a significant rate of direct reaction of CuEDTA with the transport site would have gone unnoticed for so long, it could be that dissociation of a minor species such as CaEDTACu in diffusionlimited systems could be causing the effect or more likely, that CuEDTA is reduced allowing rapid dissociation of Cu(1)EDTA with subsequent uptake of Cu(1) (see above).

k+M,L

0

-

Chemicalenhancement

-2 C

.o Es 4-

-4

8 C 0

2 m

-6

c1)

3

.-8

-0

.-c b

3-10

-12

I

-14 I -5

\ I

I

I

-4

-3

-2

+

-

+

11. Summary and conclusions

-1

log Boundary Layer Thickness (cm) Fig. 7. Critical concentrations of ligands such that dissociation-enhancement of metal uptake is possible. At the critical concentration, r, equals boundary layer thickness. Each line on the figure corresponds to a rate constant for the complex formation reaction of a transportable metal species Mi with the free ligand. If the free ligand concentration lies above the line, the ML complex will be able to enhance diffusion-limited uptake of ML.

type) Cu-binding sites at pH 8.1 as well as 5 pM of stronger sites, which are fully protonated. If Cu2+ reacts with the weak sites at rates close to k,, - H,O (lo9 M- '1, then a reacto-diffusive length scale of < 0.3 p m results. This would allow weak Cu-fulvic complexes to be available to most organisms provided they are taking up Cu2+ at diffusion-limited rates and may account for some of the exceptions to the FIM reviewed by Campbell (1995). As observed above, Cu uptake in certain marine phytoplankton exceeded the calculated diffusion-limited rate for its inorganic complexes and aqua ion and appear to have utilized the Cu(1I)EDTA complex. Under the conditions of

In addressing the question of which species control the rates of metal uptake by aquatic biota, we have seen that the question must be answered both at the cell surface and in bulk solution (Table 4). At the cell surface, disequilibrium in the metal-transporter reaction can lead to a dependence on the concentration of labile metal species. Under such conditions, complex dependencies on inorganic speciation could arise. The second type of disequilibrium would arise if uptake rates at the cell surface approach diffusion limitation, in which case dissociation of labile complexes can chemically enhance the diffusion process. In these cases, the uptake rate would become dependent on the bulk concentration of species that are sufficiently labile to dissociate within the diffusive boundary layer of the organism of interest. From our present limited Table 4 Dependence of apparent rate-controlling species on non-equilibrium effectsa Equilibrium control Kinetic control Diffusion not limiting [M"] Diffusion limiting [Mlabile 1

[M'I [Mlabilel

aApparent rate-controlling species refers to the controlling bulk species concentration.

R.J.M. Hudson / T h e Science of the Total Environment 219 (1998) 95-115

113

INCREASING LIKELIHOOD OF KINETIC CONTROL

SLOW

SLOW

METAL AVAILABILITY IM’I OR [Ma]

METAL COORDINATION KINETICS

METAL COORDINATION KINETICS

METAL AFFINITY FOR TRANSPORTER

Fig. 8. Principal factors determining the likelihood that metal transport is under kinetic control. This depiction should be taken as qualitative.

knowledge of environmental coordination kinetics, it seems reasonable to suggest that these labile species can include complexes with weak inorganic ligands (OH-, Cl-, C o t - ) as well as sufficiently abundant organic ligands (note that weak binding is not necessary). To generalize from these observations, we need to ask in what kinds of systems and with what metals might they become important factors? Whether equilibrium or kinetic control is more likely to describe the state of the metal-transporter coordination reactions depends on the nature of the metals involved and the organism’s environment (Fig. 8). Theoretical arguments have been presented suggesting that kinetic control is most likely for the uptake of essential metals with

slow kinetics adapted to conditions of low metal availability (Hudson and Morel, 1993). Although kinetic control has only been demonstrated for Fe, the question simply has not been addressed enough to know how widespread the phenomenon is. For co-transported, non-essential metals, kinetic control is caused by slow dissociation from the transporter, which requires that the metal have some combination of high affinity for the transport sites and/or sufficiently slow coordination kinetics. Hence, Cu uptake is more likely to be kinetically-controlled than Cd since their kinetics differ only slightly while Cu usually binds much more strongly. The second type of kinetic influence is felt when transport becomes diffusion-limited and a

INCREASING LIKELIHOOD OF DIFFUSION LIMITATION

’

HIGH

FAST

METALS HIGH

METAL AVAILABILITY [MI OR [Ma]

METAL COORDINATION KINETICS

METAL AFFINITY FOR TRANSPORTER

ESSENTIAL METAL AVAILABILITY [ M I OR [Ma]

Fig. 9. Principal factors determining the likelihood that metal transport is diffusion-limited. Note that diffusion limitation of both essential and non-essential (co-transported) metals depends on the degree to which the transporter for the essential metal is up-regulated due to low availability. This depiction should be taken as qualitative.

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R.J.M. Hudson / T h e Science of the Total Environment 219 (1998)95-115

metal’s uptake becomes controlled by the concentrations of complexes that are labile enough to dissociate within the organism’s diffusive boundary layer rather than by the concentration of the species that governs the cellular uptake mechanism. Diffusion limitation of Fe, Zn, and Cu uptake has been observed in marine phytoplankton, and in principle should occur for any essential metal when its concentrations are low and competing metals are not high relative to the selectivity of the transporter (Fig. 9). Due to limitations imposed by available plasmamembrane space, slow kinetics can prevent the attainment of diffusion limitation (Hudson and Morel, 1993). For non-essential metals, the primary factor is the availability of the essential metal whose transporter is responsible for its uptake. In organisms where this transporter is up-regulated in response to nutrient stress, the potential for diffusion-limited uptake of non-essential metals also exists if they have a sufficiently high affinity for the nutrient transporter. The direct relevance of non-equilibrium effects depends on the solution chemistry of the metal and the aquatic system being considered as well. Non-equilibrium effects are much more pronounced where abundant labile species lead to marked differences in rate expressions as a function of solution composition, such as in estuaries or in a range of freshwater systems. When speciation does not change, as in the ocean for metals dominated by chloride complexation, the kinetic/equilibrium control issue is moot, while diffusion limitation demonstrably remains a factor. For iron, variations in speciation with dynamic pH changes may prove important. There is a broader relevance to understanding these non-equilibrium effects beyond predicting the speciation dependence of the uptake rates for a metal. For one, by improving our understanding of the kinetics of facilitated transport processes we may be able to improve our ability to predict the uptake rates of interacting metals, as was attempted here for the example of the Mn-Cd co-transport. Finally, through understanding the interplay of kinetic and equilibrium factors, we may also come to a fuller appreciation of the chemical factors that shape the ways in which

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