Forward Modeling of Metal Complexation by NOM: II. Prediction of

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Forward Modeling of Metal Complexation by NOM: II. Prediction of Binding Site Properties Stephen E. Cabaniss* Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States ABSTRACT: An a priori model of metal complexation by natural organic matter (NOM) has previously been shown to predict experimental data at pH 7.0 and 0.1 M ionic strength (Cabaniss, S. E. Environ. Sci. Technol. 2009). Unlike macroscopic models based only on stoichiometry and thermodynamics, this a priori model also predicts the ligand groups and properties of complexed (occupied) molecules. Ligand molecules with strong binding sites form complexes at low metal concentrations and have average properties (molecular weight, charge, aromaticity) which can differ significantly from the average properties of bulk NOM. Cu(II), Ni(II) and Pb(II) preferentially bind to strong amine-containing sites which are often located on small (MW < 1000), loweraromaticity molecules. Cd(II) and Zn(II) show generally weaker binding, although they also prefer amine-containing sites to pure carboxylates and bind to smaller, less aromatic molecules. Ca(II) shows no real preference for amine over carboxylate ligand groups, preferentially binding to larger and more negatively charged molecules. Al(III) has a unique preference for phenol-containing sites and larger, more aromatic molecules. While some predictions of this model are consistent with a variety of experimental data from the literature, others await validation by molecular-level analysis.

’ INTRODUCTION Macroscopic models of metal complexation by natural organic matter (NOM) have progressed over the last 30 years from simple one and two binding site “fits” to experimental data1,2 to sophisticated representations of binding site heterogeneity and electrostatic interactions which can represent metal binding by isolated NOM over a considerable range of pH, ionic strength and metal to carbon ratios.3,4 As the availability of calibration data has expanded, improved model reliability has permitted their use in regulatory applications and for the prediction of free metal ion toxicity.5,6 Why should further energy be expended developing an alternative modeling approach which treats molecules individually, thus requiring greater computer resources? While macroscopic models predict free metal ion concentrations well in many laboratory experiments,3,4 their usefulness can be limited by the inherent heterogeneity of NOM. For example, some studies with unfractionated NOM have found good agreement between speciation measurements and model predictions, while others have found significant discrepancies.5,7,8 Is it reasonable to assume that metal binding by unfractionated NOM is similar to binding by the humic acid (HA) and fulvic acid (FA) isolates used to calibrate the models? Metal binding by NOM can be changed by photolysis or other degradation reactions.9-11 Is it reasonable to assume that metal complexation changes only in proportion to the dissolved organic carbon (DOC) or UV absorbance? If a portion of NOM is isolated using ultrafiltration or other size-based separation is it plausible to assume that the isolate has the same metal complexation characteristics the whole NOM sample?12,13 An alternative approach to modeling metal-NOM complexation deals explicitly with molecular reactivity, and permits predictions and hypothesis formulation in response to these questions and others. The evolution and composition of NOM r 2010 American Chemical Society

is simulated using a stochastic, agent-based model (ABM) which begins with a small number of specific biochemical precursors and produces a heterogeneous assemblage of thousands of molecules which can be thought of as simulated NOM.14,15 Conditional metal binding constants (K0 ML at pH 7.0 and ionic strength 0.1) are estimated for each of seven metal ions for each molecule in the assemblage using quantitative structure property relationships (QSPRs).16 The resulting set of K0 ML values can be used to predict metal titration curves which are comparable to experiment.17 The ABM-QSPR combination is referred to as an a priori model because it accomplishes this prediction without requiring a “fitting” step in which constants are optimized to conform to metal-NOM binding data. This manuscript moves the ABM-QSPR model beyond prediction of titration data (see Part I, of ref 17) to address questions of binding site structure. Relationships between molecular properties (molecular weight, aromaticity, charge, etc.) and metal complexation constants in simulated NOM are compared with experimental data from the literature for seven metals.

’ THEORY AND CALCULATIONS The agent-based model of NOM dynamics treats each molecule individually, assigning it a specific elemental and functional group composition.14,15 Reaction probabilities for a set of 12 transformations are calculated based on molecular composition and environmental variables- pH, light intensity, temperature, etc. The molecules then react over time using a stochastic Special Issue: Nanoscale Metal-Organic Matter Interaction Received: August 2, 2010 Accepted: November 1, 2010 Revised: October 15, 2010 Published: November 18, 2010 3202

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algorithm and a heterogeneous simulated NOM data set is obtained. Conditional metal complexation constants (K0 ML) for each of seven metal ions (Al(III), Ca(II), Cd(II), Cu(II), Ni(II), Pb(II), Zn(II)) were calculated for each molecule using previously developed QSPRs.16 For a given ligand molecule Li and metal M at pH 7.0 and ionic strength 0.10, ½MLi  ð1Þ K 0 MLi ¼ ½M½Li 0  where [M] is the concentration of the free aquo metal ion, [Li0 ] is the concentration of the ligand molecule not bound to any metal (but may include protonated HxLi) and [MLi] is the concentration of the metal complex. Equilibrium metal concentrations were calculated by extrapolating from individual molecules to the macroscopic level.17 The overall concentration of bound (complexed) metal, Mbnd, in a system of N molecules is given by N X Mbnd ¼ ½MLi  ð2Þ i¼1

and the total metal concentration MTot by MTot ¼ Mbnd þ ½M

ð3Þ

Because the ABM represents NOM as individual molecules instead of averages, it is possible to examine the properties of only those ligand molecules which are complexing a given metal (occupied ligand molecules). Individual molecular properties examined here include the molecular weight (MW), aromaticity (Ar), charge at pH 7 (Z), charge density at pH 7 (Zdens), elemental ratios (e.g., the atomic oxygen to carbon ratio, O:C) and elemental weight percentages, all calculated exactly from the molecular composition data.14 The octanol-water coefficient (Kow), an indicator of hydrophobicity, is also estimated for each molecule.15 Average or aggregate properties of occupied ligand molecules can be calculated as a function of [M] (or MTot or Mbnd) by weighting each ligand molecule by fractional occupancy, focc,i, of that molecule. Thus, the number average molecular weight of occupied ligand molecules, Mn,bnd is given by N X focc, i MWi Mn, bnd ¼ ð4Þ TO i¼1 where focc, i ¼

½MLi  ½MK 0 MLi ¼ LTotal, i 1 þ ½MK 0 MLi

ð5Þ

and total occupancy of all ligand molecules, TO, is given by N X TO ¼ focc, i ð6Þ i¼1

Similarly, the average aromaticity of occupied ligand molecules, Arbnd, is given by N X focc, i Ari ð7Þ Arbnd ¼ TO i¼1 and the average charge of occupied ligand molecules, Zbnd, is given by N X focc, i Zi Zbnd ¼ ð8Þ TO i¼1

The average log K0 ML of the complexes formed at a specific [M], log K0 bnd, is given by N X focc, i log K 0 MLi ð9Þ log K 0 bnd ¼ TO i¼1 The average number of a particular ligand group g (carboxylate, amine, phenol, etc.) attached to a metal M as a function of [M] (LNg) may be calculated by N X focc, i #gi LNg ¼ ð10Þ TO i¼1 where #gi is the number of ligand groups g on the ith molecule which attach to the metal ion. (Note: this is not the same as the total number of ligand groups g in the molecule, since the QSPR in ref 16 assumes a maximum of six ligand groups with not more than two phenol or two amine groups coordinating.) This paper uses NOM data sets from previously published simulations, a ‘soil NOM’ derived from small molecule precursors incubated in a dark, moist, acidic environment, a “water NOM” derived from macromolecular precursors incubated in a sunlit, pH 7 water14 and a third “combined NOM” data set obtained from the first two.17 Titrations of each of the 7 metal ions into a solution of 10 mg C/L at pH 7.0 and I = 0.10 were simulated using each data set. [M] was systematically varied in increments of 0.10 log units and the various properties from eqs 2-10 were calculated for each point using the MetalComplex program (available from the author17).

’ RESULTS In most experimental work, binding measurements are aggregate quantities, for example, total Hþ consumed or total metal ion complexed in a titration. Similarly, properties like carboxylate content, molecular weight and aromaticity are averages over the entire collection of molecules. To relate a specific property like molecular weight or aromaticity to metal complexation thus requires multiple NOM samples with significant differences in that property. This is difficult to accomplish since the range of values for a property like aromaticity or MW may vary more among molecules within a sample than the average value varies among samples of different origin or isolation method. The agent-based representation used here provides an alternative approach to understanding binding mechanism- direct comparison of individual molecular properties and log K0 ML values. For preliminary screening, Table 1 presents a correlation analysis (r2) between log K0 ML and individual molecular properties for all three data sets. Some variables which give strong correlations (no. COOH groups, no. amine groups) have been intentionally excluded from the table because they occur in the predictive QSPRs, and so strong correlations are both expected and observed. These r2 values indicate linear relationships ranging from utterly insignificant (0.5). Since r2 represents the fraction of the variance in log K0 ML which is described by a single, linear variable, it is not reasonable to expect the very high r2 values (>0.9) obtained, for example, from calibration curves. Rather, the values of ∼0.6 obtained between MW and log K0 PbL or log K0 NiL for the “soil NOM” indicate that over half of the variance in these log K0 ML values (which range ∼10 log units) can be explained by molecular size alone. Seen in 3203

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Table 1. Log K0 ML Property Correlations (r2)a property

Al(III) Ca(II) Cd(II) Cu(II) Ni(II) Pb(II) Zn(II) Soil Simulation (N = 1153)

MW

0.503

0.680

0.690

0.498

0.573

0.638

0.529

charge Z

0.574

0.721

0.716

0.615

0.623

0.660

0.641

Z/MW

0.035

0.020

0.008

0.103

0.008

0.006

0.073

aromaticity

0.094

0.066

0.064

0.071

0.057

0.082

0.081

log Kow

0.071

0.103

0.111

0.067

0.079

0.076

0.039

O:C

0.296

0.313

0.292

0.313

0.329

0.358

0.405

H:C

0.425

0.469

0.449

0.431

0.432

0.493

0.511

MW

0.015

0.520

0.084

0.001

0.001

0.035

0.018

charge Z

0.059

0.581

0.049

0.004

0.001

0.024

0.038

Z/MW

0.000

0.082

0.001

0.000

0.001

0.000

0.004

aromaticity

0.053

0.109

0.003

0.102

0.067

0.014

0.041

Log Kow

0.114

0.471

0.216

0.049

0.066

0.144

0.111

% nitrogen

0.214

0.155

0.057

0.318

0.229

0.095

0.135

Water Simulation (N = 4804)

O:C

0.164

0.148

0.053

0.254

0.196

0.084

0.104

H:C

0.042

0.195

0.000

0.073

0.040

0.002

0.007

MW

0.214

0.593

0.290

0.105

0.150

0.257

0.204

charge Z

0.273

0.344

0.099

0.143

0.114

0.125

0.218

Z/MW

0.004

0.000

0.049

0.003

0.009

0.026

0.004

Combined Soil and Water (N = 10,574)

a

aromaticity

0.008

0.053

0.003

0.001

0.000

0.004

0.004

log Kow

0.048

0.051

0.007

0.016

0.011

0.007

0.022

%nitrogen

0.109

0.001

0.144

0.230

0.207

0.147

0.106

O:C

0.045

0.339

0.148

0.020

0.046

0.139

0.079

H:C

0.029

0.164

0.010

0.002

0.003

0.019

0.042

Bold face indicates a negative correlation.

this light, even the smaller r2 values in the range 0.2-0.4 indicate an important relationship: 20-40% of the variance is being explained by a single variable like the atomic O:C ratio or the percent nitrogen (%N). Correlations within each data set differ substantially. In general, correlations of log K0 ML with Z and MW and the inverse correlation with H:C ratio are much stronger in the soil simulation than in the water simulation. The only exception is log K0 CaL, which is strongly correlated with all Z and MW in both simulations. On the other hand, the soil simulation contains no N, so the weaker correlation between %N and Cu(II), Ni(II), and Al(III) in the water simulation is simply absent from the soil simulation. The combined NOM data set has no r2 > 0.5 except for log K0 CaL, although MW and %N have r2 > 0.2 for several metals. While correlation analysis provides a rough guide to influential properties, scatter diagrams of log K0 ML versus property reveal more detail. For example, although r2 between log K0 AlL and molecular H:C ratio in the soil NOM is fairly high (0.425), Figure 1a shows that the actual distribution is almost triangular, with the strongest binding molecules having H:C between 0.59 and 1.00; the overall correlation is due to a large number of molecules with weak binding strength and high H:C (∼1.5) and molecules with moderate binding strength and H:C ∼1.0. (Note: In describing binding strength, “weak” refers to log K0 ML < 5, “moderate” to 5 < log K0 ML < 10, and ‘strong’ to log K0 ML >10, as in Part I of this work.) On the other hand, both log K0 PbL and log

Figure 1. a. Plot of log K0 AlL versus the hydrogen:carbon atomic ratio for molecules in the soil simulation assemblage. b. Plot of log K0 PbL versus aromaticity for molecules in the combined (water þ soil) simulation assemblage c. Plot of log K0 PbL versus aromaticity for molecules in the combined (water þ soil) simulation assemblage.

K0 AlL correlate poorly with aromaticity in the combined simulation (r2 < 0.01), but no highly aromatic molecules (Ar > 0.2) are strong ligands for Pb(II) in this assemblage (Figure 1b), while some of the strongest Al(III) ligand molecules have Ar > 0.2 (Figure 1c). Log K0 AlL has a moderate correlation (r2 = 0.20) with Ar for the strong (log K0 >10) Al(III) ligands, whereas Ar shows no similar correlation (r2 = 0.02) for the strong Pb(II) ligand molecules. Clearly, simple linear relationships between molecular structure and binding strength are not predicted by this model. Combining two molecular properties in a single graph can provide additional insight. For example, the correlation between log K0 ML and MW (and to a lesser extent, O:C) is quite noticeable in the soil simulation but absent from the water simulation (r2 < 0.1 for MW, Table 1). Figure 2a plots the O: C ratio versus the log MW of each molecule in the soil simulation, showing that the moderate K0 PbL ligands are all higher MW with 3204

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Figure 2. Molecular composition plot of O:C ratio versus log molecular weight grouped by Log K0 Pb for the molecules in simulated (a) soil and (b) water NOM.

Figure 3. The weighted average K0 of bound metal complexes (eq 9) for Pb(II), Cd(II), and Ca(II) as a function of -log of total metal (pMTot) for solutions with 10 mg C l-1 of the combined (soil þ water) simulated NOM.

O:C in the range 0.5-1.0, weak-binding molecules having low MW and a wider range of O:C values. On the other hand, the water simulation has similar trends for the weak and moderate ligand molecules but also a large number molecules of smaller size (MW 3 mmol metal per mole C).

Part I of this work showed that the ABM-QSPR, calibrated on small molecules, can predict equilibrium metal speciation surprisingly well.17 This is an interesting intellectual exercise for students of NOM (or humic substances), in that the rules of the ABM are few and relatively simple, and yet the titration curves are similar to those of a “complex” natural mixture. Nonetheless, it would be only an intellectual exercise if simulated titration curves were the sole product, since more extensively tested macroscopic models can often fit the thermodynamic data.3,4 The molecular nature of the ABM-QSPR model allows predictions which extend beyond equilibrium concentrations to the chemical nature of NOM molecules and binding sites. While a thorough validation of this model will require extensive experimental work, a priori predictions concerning ligand groups, and molecular size and aromaticity can be compared with published results and used as a guide for future experiments. Ligand Groups. The acidity of NOM and of humic substances is attributed primarily to carboxylic acid groups, which are responsible for the average negative charge on NOM molecules even at fairly low pH.18-20 It is commonly supposed that these are the most numerous metal-binding groups, as well, although amine, phenol and thiol groups have been suggested as potential contributors to strong binding sites.21-23 Although the ABM-QSPR model does not yet include thiol ligands, carboxylates, phenols, alcohols and amines are included. To some degree, the relative importance of these groups in metal binding may be anticipated by examining the linear QSPR equations, which reflect the trends in the set of ligand groups used in calibration and testing.16 Based on the QSPRs, carboxylates and amines are expected to bind to all of the seven metal ions studied, and all but Ca(II) and Al(III) have a significant preference for amines over carboxylates. At pH 7.0, Al(III) prefers binding to phenols over carboxylates or amines, while Pb(II) binds in the order amines > phenols > carboxylates and Cu(II) in the order amines > phenols ≈ carboxylates; no other metals bind to phenols significantly. The larger ions Pb(II), Ca(II), and Cd(II) also bind to ether groups, and Ni(II) and Pb(II) bind to alcohols. Negative charge density favors binding for all metals except Cu(II) and Zn(II). However, binding by simulated NOM does not simply mimic the QSPR coefficients, but is also constrained by relative number of ligand groups available, which varies with the source and history of the NOM. In the absence of nitrogen (the simulated soil NOM uses precursors containing only C, H and O), log K0 ML correlates strongly with charge and COOH content, while in the 3206

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Environmental Science & Technology simulated water NOM (which uses proteins as a precursors) only log K0 CaL shows a strong correlation with charge or size (Table 1). In the combined data set, all metals except Ca(II) show some correlation between log K0 ML and %N, and all metals except Ca(II) show significant amine participation in binding at low metal loading (2 mmol M per mole C), binding is dominated by carboxylate sites for all metals, since the stronger amine and phenolic sites are filled. In addition, metals are bound to 1000 amu, most of the strong binding molecules have lower MW (300-1000 amu). These correspond to amine-containing molecules derived from the protein precursors in the water simulation, as opposed to the larger, lignin-derived molecules which are N-poor. The other heavy metals behave similarly. Nonetheless, metal loading calculations on the combined data set indicate that most of the metals examined will bind preferentially to larger molecules at very low metal loadings (3 mmol metal/mol C), the average molecular weight of bound molecules increases again, since all the aminecontaining binding sites are filled. For Al(III) and Ca(II), preferential binding to amine-containing ligand molecules is not observed, and the average MW of bound molecules remains relatively high (>1000 amu and >1500 amu, respectively, Figure 5a and b) for all loadings. Thus, the ABM-QSPR predicts that the size-dependence of metal binding should be a function of (a) precursor materials and reaction history, which can influence the distribution of functional groups on different sizes of molecules, and (b) the metal loading. The effect of softer (e.g., amine) ligand groups is predicted to be less important for harder metals like Ca(II) and Al(III) than for softer metals like Pb(II) and Cd(II). Is this consistent with experimental observation? Studies of size-dependent metal binding are consistent with ABM-QSPR predictions, suggesting that the transition metals Cu(II) and Ni(II) are bound by smaller ligand molecules while Al(III) is bound by larger molecules. Gordon and co-workers31 used immobilized metal ion affinity chromatography (IMAC) to isolate NOM from seawater, and found that the stronger Cu(II) binding ligand molecules were in the smallest size fraction (MW < 1000) obtained from subsequent filtration. Strong Cu(II)binding ligand molecules in IMAC isolates from Chesapeake Bay had a narrower MW range than moderate-binding molecules in those isolates, with a peak mass below 500 amu.25 In compost extract analyzed by size-exclusion high pressure liquid chromatography (SE-HPLC) and field flow fractionation (FFF), Cu(II), Ni(II), and Zn(II) were associated with a size fraction below 1000 amu, whereas Al(III) preferentially bound to larger material.32 Similarly, SE-HPLC with ICP-MS detection indicated that Ni(II) in porewaters was principally bound to molecules of MW 300-1000 amu, while Al(III) was present in larger complexes.33 These results support the idea that model prediction that Al(III) binding is favored by larger molecules, while Cu(II), Ni(II), and Zn(II) are relatively more likely to be bound by smaller molecules; however, the operational nature of ultrafiltration separation and the IMAC procedure do not allow firm quantitation of MW or log K0 ML, respectively, and no results were found for Pb(II), Cd(II), or Ca(II). Further research using separation (SE-HPLC, FFF) coupled to MS detection may provide more definitive answers. Aromaticity. The earliest work on metal-NOM binding hypothesized aromatic ligand structures.1,21,34 The observation that metal binding influences fluorescence, due to presumably aromatic structures, supports this hypothesis, and several papers have noted a correlation between metal binding and optical properties (ultraviolet absorbance and fluorescence), which the authors attributed to aromaticity of ligand molecules.35-37 However, 13C NMR measurements of a Cu(II)FA system suggested that most bound copper was associated with oxygenated aliphatic carbon (chapter 7 in ref 38), and UV absorbance does not correlate significantly to metal binding in all cases.36 3207

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Environmental Science & Technology ABM-QSPR model predictions are less equivocal. Of the seven metals examined, none show overall correlations between aromaticity and log K0 ML, and only Al(III) binds preferentially to aromatic sites, a consequence of strong binding to phenolic groups. The metal loading plots for the combined NOM show that Cd(II), Cu(II), Ni(II), Pb(II), and Zn(II) have Arbnd below the bulk Ar value (0.10) for low metal loadings, although all metals have Arbnd near 0.10 at high loading. Given the indirect nature of optical evidence, it is possible to argue that fluorescence quenching or enhancement could arise from a minority of binding sites, and that correlations between absorbance (or fluorescence) and metal binding do not necessarily indicate that metal binding occurs primarily to aromatic molecules. For example, fluorescence quenching by Cu(II) could be due to the presence of a small fraction of aromatic (and fluorescent) ligand molecules that occur together with more numerous aliphatic ligand molecules. While this hypothesis is consistent with evidence to date, conclusive molecular level experimental data is still lacking. Variation among Metals. Al(III). A model “hard” metal ion, Al(III) binds strongly to phenol groups, which produces a number of strong binding sites even in the absence of N- and S- containing precursors. However, the presence of amine groups enhances Al(III) binding less than heavy metal binding. Because of the strong binding to phenols, Al(III) is the only metal studied which preferentially binds to highly aromatic molecules. Ca(II). Another a hard cation, Ca(II) is predicted to have the lowest overall binding constants with N-rich NOM and some of the lowest (comparable to Cd(II)) even with carboxylate dominated binding. Ca(II) binds most strongly to large molecules with significant negative charge. In many environmental systems, high Ca(II) levels may lead to large quantities of organically bound Ca(II) even though the apparent binding constants are low. Cd(II). Cd(II) is a very soft cation, and is weakly bound by lownitrogen NOM (comparable to Ca(II)) but more strongly bound to amine groups. One note of caution- the presence of reduced sulfur groups not included in the current model could greatly increase the number of strong binding sites for Cd(II). Cu(II). Cu(II), a metal of “intermediate” hardness, binds to both amine and phenol groups. In low-nitrogen, high-phenol NOM it should be bound more strongly than other heavy metals and have comparable binding to Al(III). For high amine NOM, Cu(II) binding should be comparable to Ni(II) and Pb(II) and stronger than other metals. Note that binding to phenols does not imply that most of the binding sites will be aromatic. Ni(II). Ni(II) binding is similar to Cu(II) without the binding to phenols. It binds strongly to N-rich NOM, only slightly weaker than Cu(II) and Pb(II); binding to carboxylate dominated NOM is much weaker, comparable to Zn(II). The lack of binding to phenols may explain why Cu(II) quenches NOM fluorescence more strongly than Ni(II). Pb(II). A large, soft ion, Pb(II) binds strongly to amines but also binds phenols, alcohols and even ether groups. Binding strength is comparable to Cu(II), slightly stronger in the N-rich and slightly weaker in the carboxylate dominated NOM, but with a preference for binding to larger molecules. Zn(II). Zn(II) is intermediate in hardness, like Cu(II), and binds preferentially to amine groups over carboxylates. However, Zn(II) forms weaker complexes with NOM than the transition metals Cu(II), Pb(II), and Ni(II).

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Future Work. Ongoing work on this model includes addition of diurnal and seasonal effects on NOM processing in the environment and the development of QSPRs for Hg(II), U(VI) and U(IV) complexation. Two planned improvements are the extension of the metal speciation calculations to other pH and ionic strengths using the oligoelectrolyte model of Bartschat et al.,39 and the addition of sulfur chemistry to the NOM model.

’ AUTHOR INFORMATION Corresponding Author

*Phone: (505) 277-4445; fax: 277-2609; e-mail: [email protected].

’ ACKNOWLEDGMENT The author and this manuscript have benefited from conversations with E.M. Perdue, E. Tipping, D. DiToro, and R. Carbonaro, and from reviewer comments. Financial support was provided by NSF grant DEB-0113570. ’ ABBREVIATIONS AND TERMS ABM agent-based model Ar aromaticity, fraction of carbon which is aromatic bnd bnd subscript to aggregate properties Ar, Mn, Z, etc. indicates property is calculated for molecules bound to a metal at specified [M] FA, HA fulvic acid, humic acid fraction of ith ligand molecules bound to a metal focc,i conditional formation constant for complex MLi from K0 MLi M and L0 I Kow octanol-water partition coefficient molarity of uncomplexed ligand molecule (ith mole[L0 i] cule of N) LTotal, i summed molarity of all forms of the ith molecule average number of ligand groups g (carboxylate, amine, LNg phenol) attached to a metal [M] molarity of uncomplexed metal ion [MLi] molarity of metal complexed with ith ligand molecule summed molarity of all MLi Mbnd MTot summed molarity of all forms of metal, free and complexed MW molecular weight number average molecular weight of a set of molecules Mn N number of molecules in a data set NOM natural organic matter QSPR quantitative structure property relationship Z molecular charge at pH 7 Molecular charge density at pH 7, Z/MW Zdens ’ REFERENCES (1) Gamble, D. S.; Schnitzer, M.; Hoffman, I. Cu2þ-fulvic acid chelation equilibrium in 0.1 m KCl at 25.0 °C. Can. J. Chem. 1970, 48, 3197–3240. (2) Saar, R. A.; Weber, J. H. Lead (II)-Fulvic acid complexes. Conditional stability constants, solubility and implications for Lead (II) mobility. Environ. Sci. Technol. 1980, 14, 877–880. (3) Tipping, E. Cation Binding by Humic Substances; Cambridge University Press: Cambridge, England, 2005, 444 pp. (4) Koopal, L. K.; Saito, T.; Pinheiro, J. P.; van Riemsdijk, W. H. Ion binding to natural organic matter: General considerations and the NICA-Donnan model. Colloids Surf., A 2005, 265, 40–54. (5) Di Toro, D. M.; Allen, H. E.; Bergman, H. L.; Meyer, J. S.; Paquin, P. R.; Santore, R. C. Biotic ligand model of the acute toxicity 3208

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