Environ. Sci. Technol. 2009, 43, 7170–7174
Chemodynamics and Bioavailability in Natural Waters JACQUES BUFFLE Analytical and Biophysical Environmental Chemistry, University of Geneva KEVIN J. WILKINSON Department of Chemistry, University of Montreal HERMAN P. VAN LEEUWEN* Laboratory of Physical Chemistry and Colloid Science, Wageningen University (The Netherlands)
Bioavailability of various aquatic compounds is significantly dependent on the fundamentals of physical chemistry.
Until the 1980s, it was largely assumed that chemical reactions in environmental systems were at equilibrium. Over the past 30 years, however, chemical kinetics have been shown to limit the rates of a large number of natural processes (1). For example, slow physicochemical reactions are now known to play key roles in weathering processes (e.g., dissolution, nucleation), water treatment (e.g., coagulation/ flocculation), environmental degradation of organics, colloidal fate (e.g., aggregation), chemical fluxes at oxic-anoxic boundaries, etc. In that context, the notion of “chemodynamics” will be used in the broad sense to describe any process that involves the coupling of reactant transport to the chemical reaction(s). Mathematically, the 7170
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modeling of nonequilibrium systems is quite demanding. It generally involves the interpretation of rates and kinetics in terms of relevant chemical species, rather than their mere equilibrium distribution (speciation). Indeed, a large number of codes are available for equilibrium modeling, whereas the development of codes for chemodynamic computations is still in its infancy. The goal of this paper is to show that chemodynamics are essential for understanding and modeling the bioavailability of vital and detrimental compounds, either at the scale of single organisms, or for communities of organisms, such as those found in biofilms.
Chemodynamics and Biouptake in the Water Column The basic elements of chemodynamics that are involved with the bioaccumulation of chemicals are provided in Figure 1. In the simplest case of the bioaccumulation of chemically inert or poorly reactive compounds X (e.g., NO3-, NH4+, PCBs, etc.; note that “chemically poorly reactive” is not necessarily synonymous with “biologically poorly reactive”), steady-state fluxes can be interpreted by comparing the rate of diffusive transport to the rate of transfer through the biological membrane. Processes that are external to the organism play a role if the assimilated compound is significantly depleted, thus creating a concentration gradient in a layer of solution adjacent to the biointerface. The thickness of the corresponding diffusion layer, δ, is usually fixed by natural convection, e.g., flow. By comparing experimental and computed biouptake rates to calculated maximal diffusive supply fluxes under different flow conditions (2, 3), several authors have identified conditions where the mass transport of compounds limits their biological uptake by aquatic organisms. For example, Pasciak and Gavis (4) determined that the experimentally measured nutrient uptake fluxes were very similar to calculated maximal diffusive fluxes. They also showed that fluid shear could increase NO3- uptake by a diatom with a radius of roughly 20 µm (5), thus providing evidence for mass transport limitation. Similar arguments have been made for diffusion limitation of bioaccumulation of PO43-, CO2, and dissolved organics for a number of organisms (6, 7, reviewed in (8)). A high susceptibility to mass transport limitation is generally observed for rapidly accumulating compounds such as nutrients and hydrophobic organic contaminants (9). Figure 1 also provides an example for the chemodynamics of a reactive compound, i.e., the simple case of a hydrated trace metal ion, M [short for M(H2O)6z+], that forms a single 1:1 complex ML with a ligand, L. It is assumed that only M reacts with transporter sites. Several other cellular processes, including excretion and formation of mixed ligand surface complexes, will not be considered. Still, this basic system is useful to discuss the relative importance of chemical and physical factors with respect to biological ones. It generally demonstrates that biouptake not only depends on rates of diffusion and membrane transfer, but also on rates of dissociation/formation of the metal complex ML. Key parameters for this chemical “source” of bioactive free metal 10.1021/es9013695
2009 American Chemical Society
Published on Web 09/29/2009
FIGURE 1. Scheme of the main dynamic processes and their parameters governing the biouptake of trace compounds by an aquatic (micro)organism. X represents a chemically poorly reactive compound, e.g., a nutrient, organic compound, while M represents a complexing compound, e.g., a trace metal that forms complexes ML. Many organic contaminants and nutrients also exist as (colloidal) complexes, including those with humic substances. Biological parameters: kint, kint ′ ) internalization rate constant (10-3 to 100 s-1); r0 ) radius of the (micro)organism (10-6 to 10-5 m); {R}, {R′} ) surface concentration of transport sites (10-9 to 10-6 mol m-2); KS, K S′ ) stability constant of surface complex (104 to 107 m3 mol-1). Chemical source parameters: ka ) association rate constant of ML (102 to 108 m3 mol-1 s-1); kd ) dissociation rate constant of ML ) ka/KML; KML ) stability constant of ML. Physical diffusion parameters: DM ) diffusion coefficient of M (5-10 × 10-10 m2 s-1); ε ) DML/DM (10-3 - 1 including colloidal complexes); cλ ) reaction layer thickness (Box 1); δ ) diffusion layer thickness (10-5 to 10-4 m depending on convection). Ranges of parameter values taken from (8, 10, 11). are the rate constants, kd and ka, for dissociation and association respectively, and the corresponding equilibrium constant, KML, equal to ka/kd. When the biological internalization of M can be described by first-order kinetics, the uptake flux, J, is proportional to the concentration of free metal ion at the biointerface. On the other hand, if mass transport becomes limiting, the concentration of M will be lower at the biointerface than in the bulk medium. Dissociation of ML, providing additional free metal, will then tend to restore the equilibrium M H ML. In this case, both physical transport (diffusion) and a chemical source (dissociation of ML generating M), have to be included in the analysis of the overall biouptake flux. Box 1 gives an overview of the individual fluxes for the three types of processes described in the scheme of Figure 1. Since the thickness δ of the diffusion layer typically is on the order of tens of micrometers, a distinction should be made between macroscopic and microscopic organisms (with sizes typically g100 µm and e10 µm, respectively). For macroscopic organisms, convection in the medium can play an important role in biouptake by controlling the magnitude of δ. Indeed, swimming and sedimentation have been postulated to alleviate diffusive transport limitation for larger organisms (13). In contrast, δ is always larger than the radius r0 for microorganisms, even under conditions of strong convection. As a consequence, with microorganisms, the overall uptake flux will practically not be influenced by convection, unless slow dissociation on spatial scales beyond r0 is significant. Several limiting cases can be distinguished: Case 1: Biological factors control biouptake. If in the scheme of Figure 1 the physical and chemical dynamics are much faster than the biological membrane transfer step, the overall flux J will be governed by the biological internalization parameters Ks and kint. In such a case the depletion of M in the medium is insignificant. For relatively low metal ion concentrations, the transporter-bound metal concentration, {MR}, is linearly proportional to the free metal ion concen-
1. Limiting fluxes in bioaccumulation (12) Biological membrane transfer flux, JB
JB ) kintKS{R}[M]
(1)
which is the flux of M through the plasma membrane as limited by membrane transporters and first-order kinetics. Physical diffusion flux, JD
JD ) DM(1 + εK[L])[M]
r0 + δ r0δ
(2)
which is the metal flux through the diffusion layer (δ in Figure 1) for a labile system (see Box 2). Chemical source flux, JC
JC ) kd[ML]cλ ) (DMka[L])1/2[M]
(3)
which is the flux of M through the reaction layer (cλ, Figure 1) as limited by dissociation of ML for cλ < r0, δ and negligible flux of free metal from bulk (εKML . 1). J ) amount of substance transported per unit area and unit time (mol m-2 s-1); {R} ) surface concentration of transporter sites (mol m-2); [L] ) concentration of free ligand (mol m-3); c λ ) reaction layer thickness, defined as the average diffusion distance of free M in the complex medium, i.e., c λ ) λtanh (δ/λ) with λ ) D¯ M/(ka[L] + kd/ε); ε ) DML/DM. tration [M] in the bulk medium. As a consequence, the biouptake flux is then also linearly dependent on [M] and this relationship is the fundamental basis of the free ion activity model (FIAM) and the biotic ligand model (BLM). The well-known Michaelis-Menten equation is a generalized VOL. 43, NO. 19, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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2. Lability of Metal Complexes The lability of a complex expresses the ratio between its chemical dissociation rate and its rate of diffusive transport toward an interface. Thus, whether lability relates to an organism or an analytical technique, it is always dependent upon the effective diffusion time scale. This implies, for instance, that microelectrodes and macroelectrodes will not necessarily give the same analytical signal, just as the flux of bioavailable metal for unicellular algae will not be equivalent to that for fish (see discussion on micro- and macroorganisms in the main text). Lability considerations come into play in particular when chemical or physical processes are limiting. In that case, it is important to determine whether metal complexes are fully labile (JC . JD) or only semilabile (JC ≈ JD). This is usually done on the basis of the lability index L which is given by the ratio JC/JD as derived from eqs 2 and 3 in Box 1 (16):
L ) r0/cλεKML[L]
(4)
For L . 1, metal complexes are fully labile, i.e., their association/dissociation kinetics is so fast that they effectively maintain equilibrium with the free metal ion over the diffusion layer. In contrast, complexes are nonlabile for L , 1 (i.e., chemical kinetics are slow compared to mass transport), and semilabile for L ≈ 1. form of this linear relationship, in the sense that it accounts for saturation of the transporter sites R and ensuing loss of the linear dependence of the biouptake flux J on [M]. Case 2: Diffusion of labile complexes controls biouptake. The conversion between ML and M can be so fast that the complex is fully labile under the conditions of transport toward a biointerface as outlined in Figure 1 (see Box 2 for details on the concept of lability). If, with such a labile complex in the medium, the biological internalization rate is very fast, the biouptake process will completely deplete M and its complexes at the biointerface. The flux, JD, is then determined by the coupled diffusion of M and ML over the complete diffusion layer (Figure 1) and is usually described in terms j and the sum of the of the average diffusion coefficient, D, concentrations of the free metal ion and the labile complex, ([M] + [ML]). It should be noted, however, that Dj generally varies with the ratio [ML]/[M]. In most natural waters, different types of ligand are usually present in the medium. The uptake flux is then determined by the coupled diffusive flux of all labile metal species, so long as biological internalization remains fast compared to the rate of diffusive supply of metal. Case 3: Chemical kinetics controls biouptake. The biouptake flux will be limited by finite rates of dissociation/ association of the metal complex ML if both the membrane transfer step and the transport in the diffusion layer are faster than the chemical dissociation in the reaction layer (Figure 1). Under conditions of a reaction layer thickness that is smaller than the organism’s radius (cλ , r0) and negligible diffusive flux of free M (DML[ML] . DM[M]), the overall uptake flux is approximately proportional to the bulk concentration of the dissociating complex. For a given KML[L], under given speciation conditions, and equilibrium in the bulk medium, the biouptake flux can be indirectly related to the free [M] as well (cf. eq 3 in Box 1). However, in contrast to case 1, a significant metal concentration gradient is created between the bulk solution and the surface of the organism, albeit not as large as in case 2: thus the flux for case 3 is larger than in case 1. In natural waters, the values of ka for metal/fulvic 7172
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FIGURE 2. Predicted ranges of limiting fluxes J, normalized with respect to the bulk concentration of free M (rectangles), and measured normalized fluxes for different microorganisms (a to e) in the size range from 1 to 10 µm (shaded circles). The numbers in parentheses refer to the cases discussed in the text. Experimental values for [M] were taken from data given in each of the original references (see (8) for sources): a: Pb, C. kesslerii; b: Mn, T. pseudonana; c: Ag, C. reinhardtii; d: Zn, T. pseudonana; e: Cd, E. huxleyi. complexes and the effective values of ka for colloidal metal complexes may be very low (10). This implies that when a significant fraction of the metal is bound to these natural ligands, the chemical dissociation of their metal complexes may limit the biological uptake flux. Case 4: Diffusion of free metal controls biouptake. In many laboratory experiments, but rarely in the natural environment, the medium contains only the free ion and totally inert complexes (JC f 0). If diffusive processes in the medium are limiting, the uptake of metal by microorganisms (r0 , δ) is then simply determined by the diffusion of the free metal ion. The vast majority of natural waters, however, contain a large number of complexes with varying degrees of lability, ranging from labile to inert. The consequence is that in aquatic media the contributions of fully labile complexes (case 2) or slowly dissociating complexes (case 3) to the uptake flux may be more important than the contribution of the free metal ions. Typical ranges of biological, chemical, and physical limiting fluxes are presented in Figure 2. Since the individual processes actually proceed in series (cf. Figure 1), the ratelimiting process is that represented by the smallest flux. Examples of measured fluxes clearly show that, in contrast to equilibrium-based toxicity models (e.g., FIAM, BLM), uptake fluxes may be controlled by chemical and diffusional supply from the medium. For natural systems containing numerous complexes of varying lability, the simple calculations above must be replaced by sophisticated algorithms (e.g., FLUXY, MHEDYN models (14)). Figure 2 shows that biouptake fluxes cover a very wide range of values and that biology controls uptake rates at the lower end of the flux scale. In natural systems, microorganisms often optimize uptake capacities by maximizing biological internalization rates via an increase in the membrane transfer rates (kint), an increased affinity of the transport site for the metal ion (KS), and/or an increased density of these sites ({R}). With the larger uptake capacities, the organism runs the risk of sooner facing limitations imposed by either chemical kinetics and/or diffusive transport of labile complexes. The impact of various natural ligands on biouptake fluxes has been studied in detail for a number of metals (see, e.g., ref 15 for an overview). Complex dissociation/formation rate constants (ka, kd) can be estimated theoretically and a number of them have been measured (11), but more data are badly needed, especially for natural complexes (10). Due to chemical heterogeneity and geometrical factors, the effective formation rate constant, ka, of a metal complex can be substantially lower than expected. For example, for large multisite colloidal ligands the diffusion of M into the colloidal
3. Donnan potentials
FIGURE 3. Schematic representation of a bacterial biofilm in contact with an aqueous medium containing a poorly reactive compound, X, and a complexing compound, M (cf. Figure 1). Both df and δ are highly variable depending upon the health of the biofilm and the convection of the bulk medium (among other factors). For example, δ is typically 50-200 µm, while the biofilm thickness can vary from a few micrometers to several centimeters. The biofilm depicted was imaged by confocal microscopy and shows both live (green) and dead (red) bacterial cells embedded in an exopolymeric matrix. entity drastically reduces the overall association/dissociation rates. Effects of competition for a ligand between different types of metal is also known to significantly slow down the association kinetics of the incoming metal. In spite of its known importance, this effect still awaits due investigation.
Applications of Chemodynamics to Uptake By Biofilms As an example of an environmentally relevant subsystem where chemodynamics are important, we choose the case of the biofilm, which essentially is a heterogeneous mixture of exopolymers, microorganisms, and cellular debris in water (Figure 3). Biofilms are morphologically diverse, heterogeneous, and dynamic, especially with respect to the distribution of cells, which are typically found at an average density of ∼1014 dm-3. The cells are supported by a matrix that includes polysaccharides and peptidoglycans (17) with acidic groups. These may deprotonate to give the biofilm a pHdependent negative electric charge, which generates an electric potential difference with respect to the medium. The spatial distribution of the potential is not uniform throughout the biofilm, but in some cases it can be represented by an average Donnan potential (see Box 3 for details). A biofilm may also include void volumes and channels with flowing solution. An image of a typical biofilm and a scheme of the chemical and physical steps involved in biouptake from the medium is given in Figure 3. For nutrient and pollutant species to reach an organism inside the biofilm, they must diffuse through the gel matrix, in which convection is strongly reduced as compared to that in aqueous solution. The fate of the incoming species includes three components: (i) diffusion into the biofilm, (ii) binding by sites on the biofilm supporting matrix, and (iii) uptake by the organisms in the film. As compared to planktonic cells (section 2), diffusive transport is retarded by steric hindrance (in the biofilm “bulk”) and electrostatic interactions with charged components of the biofilm. The electrostatic effects are generally 2-fold. In the low ionic strength regime (nonuniform field), these effects may significantly decrease the diffusion coefficient of cations. Simultaneously, a negative Donnan potential will increase the cation (and decrease the anion) concentrations in the gel with respect to the bulk medium (see Box 3). Although few studies have been performed that examine the result of these effects on
Densities of protolytic groups in biofilms are typically on the order of 10-2 to 10-1 mol dm-3. In contact with freshwater at an ionic strength of a few millimolars, the free exchange of mobile counterions results in a Donnan potential difference ΨD between the biogel and the medium. For a medium with a symmetrical z, z electrolyte at concentration c, the theoretical expression for ΨD in the low charge density limit is (RT/zF)ln[1 + zsCs/2zc], where zs, is the algebraic charge number of the immobile sites in the biofilm and cs is their density (mol dm-3). In the case of freshwaters, the magnitude of ΨD is normally on the order of tens of millivolts (20). Donnan potentials decrease with increasing ionic strength in the medium, hence they are generally insignificant in estuarine and marine systems.
diffusion, overall Ni and Zn transport has been shown to be substantially retarded in biofilms of Escherichia coli and Pseudomonas aeruginosa (18, 19). Since the biouptake process plays the role of a continuous sink for bioaccumulating species, their concentration profiles in biofilms will be nonlinear, even under steady-state conditions. The dense populations of bacteria thus affect the transport conditions of nutrients which in turn impacts the chemodynamics, especially when compared to planktonic cells (section 2). This will lead to more intricate expressions for the diffusive flux, JD, and to nutrient concentrations inside the biofilm which are not constant, but rather involved functions of position and time. As far as complexation of metal ions in the biofilm is concerned, the rate constants for complex formation with binding sites in the biofilm are generally much larger than biological internalization rate constants. Therefore, the most obvious approach to understanding the role of metal uptake is to assume local equilibrium between the free and bound metal. For example, for a 1 mm biofilm that binds 99% of the incoming metal, the time to achieve steady-state conditions is very long, on the order of 99 d2f /D, i.e., 105 s (∼1 d). The typical environmental situation of numerous dissolved complexes further amplifies the complexity of the problem, especially if they also enter the biofilm. Given the complexity and the spatial heterogeneity described above, numerical methods of modeling are invariably required for flux computations. Future work in the field of chemodynamics along the lines indicated above will be fruitful areas for environmental biophysicochemical research in years to come. Biographical statements for these authors are provided in the October 1, 2009 issue of Environmental Science & Technology, which is a Tribute issue to Jacques Buffle. There is both a Perspective on Buffle’s career and the Guest Editor Comment which contains biographies of Wilkinson and van Leeuwen. Please address correspondence about this article to
[email protected].
Acknowledgments The authors are indebted to Prof. Raewyn M. Town (Odense DK) for support in the preparation of the manuscript.
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