Influence of Albumin on Sorption Kinetics in Solid-Phase

Aug 21, 2007 - ... T. T. Oosterwijk , Sibylle Rutishauser , Helmut Segner , and John Nichols ..... Miyoung Yoon , Alina Efremenko , Bas J. Blaauboer ,...
0 downloads 0 Views 230KB Size
Download PDF
Anal. Chem. 2007, 79, 6941-6948

Influence of Albumin on Sorption Kinetics in Solid-Phase Microextraction: Consequences for Chemical Analyses and Uptake Processes Nynke I. Kramer,*,† Jan C. H. van Eijkeren,‡ and Joop L. M. Hermens†

Institute for Risk Assessment Sciences (IRAS), Utrecht University, P.O. Box 80177, NL-3508 TD Utrecht, The Netherlands, and National Institute of Public Health and the Environment (RIVM), P.O. Box 1, NL-3720 BA Bilthoven, The Netherlands

Only the freely dissolved concentration of a compound is considered to exert a response in organisms.1,2 This concentration is, therefore, an important entity in toxicological studies and ecological risk assessment.3-5 Several techniques exist to estimate free concentrations of compounds. These include equilibrium

dialysis, ultrafiltration, and centrifugation. Yet these techniques prove labor intensive and time-consuming. Moreover, these techniques are not always compatible with the sample matrix.4 Hence, recent studies have focused on developing such techniques as solid-phase microextraction (SPME) for this purpose. SPME was introduced by Arthur and Pawliszyn6 and is considered to be a simple and effortless technique that simultaneously separates and samples test compounds. SPME fibers consist of a polymer coating around an optical glass fiber. The coating serves as a hydrophobic solid phase that extracts freely dissolved molecules from aqueous solutions. The concentration of analytes in the fiber can subsequently be analyzed with conventional analysis methods, such as gas chromatography or high-performance liquid chromatography (HPLC).7,8 Indeed, a number of studies have successfully used the technique to estimate the extent of binding of compounds to serum protein in aqueous phases.5,9-11 One limitation of using SPME to determine free concentrations in biological matrixes is that binding matrixes such as serum protein should not interact with the SPME fiber. Binding matrixes may interact by adsorbing to the fiber surface, thus possibly blocking the exchange of the analyte across the fiber boundary. It may also lead to an overestimation of the concentration in the fiber coating as the matrix-bound analyte adsorbed to the fiber coating is measured along with the analyte in the fiber coating. This has previously been referred to as fouling.4,8 A related matrix effect causing a stir in recent years is the possible influence of a binding matrix on the uptake kinetics of compounds into the fiber. The literature is inconsistent when it comes to showing such effects. Some studies find an increase in fiber uptake and depletion kinetics in the presence of a binding matrix12-15 wheareas others do not.11,16-18 Understanding the

* Corresponding author. Tel: +31 30 253 5314. Fax: +31 30 253 5077. E-mail: [email protected]. † Utrecht University. ‡ National Institute of Public Health and the Environment (RIVM). (1) Herve, F.; Urien, S.; Albengres, E.; Duche, J.-C.; Tillement, J.-P. Clin. Pharmacokinet. 1994, 26, 44-58. (2) Seydel, J. K.; Schaper, K.-J. Pharmacol. Ther. 1981, 15, 131-182. (3) Kraaij, R.; Mayer, P.; Busser, F. J. M.; van het Bolscher, M.; Seinen, W.; Tolls, J.; Belfroid, A. C. Environ. Sci. Technol. 2003, 37, 268-274. (4) Heringa, M. B.; Hermens, J. L. M. TrAC, Trends Anal. Chem. 2003, 22, 575-587. (5) Vaes, W. H. J.; UrrestarazuRamos, E.; Verhaar, H. J. M.; Seinen, W.; Hermens, J. L. M. Anal. Chem. 1996, 68, 4463-4467.

(6) Arthur, C. L.; Pawliszyn, J. Anal. Chem. 1990, 62, 2145-2148. (7) Lord, H.; Pawliszyn, J. J. Chromatogr., A 2000, 885, 153-193. (8) Ulrich, S. J. Chromatogr., A 2000, 902, 167-194. (9) Yuan, H.; Pawliszyn, J. Anal. Chem. 2001, 73, 4410-4416. (10) Yuan, H.; Ranatunga, R.; Carr, P. W.; Pawliszyn, J. Analyst 1999, 124, 14431448. (11) Heringa, M. B.; Pastor, D.; Algra, J.; Vaes, W. H. J.; Hermens, J. L. M. Anal. Chem. 2002, 74, 5993-5997. (12) Kopinke, F.-D.; Georgi, A.; Mackenzie, K. Acta Hydrochim. Hydrobiol. 2000, 28, 385-399. (13) Ohlenbusch, G.; Kumke, M. U.; Frimmel, F. H. Sci. Total Environ. 2000, 253, 63-74. (14) Oomen, A. G.; Mayer, P.; Tolls, J. Anal. Chem. 2000, 72, 2802-2808.

Because of its simplicity, solid-phase microextraction (SPME) is an increasingly popular technique to use in experiments measuring freely dissolved concentrations of compounds in biological and environmental samples. However, a number of studies have shown that sorption kinetics of compounds in such SPME systems is dependent on the presence of a binding matrix. This affects the interpretability of nonequilibrium SPME data. In this study, this phenomenon was investigated by measuring the rate of depletion of pyrene from a “loaded” poly(dimethylsiloxane) fiber into surrounding cell culture medium containing different concentrations of bovine serum albumin (BSA). The rate of depletion was found to steadily increase with increasing concentrations of BSA. It was postulated that BSA facilitated the transport of pyrene through the medium. This phenomenon was modeled by considering diffusion of BSA-bound pyrene in addition to diffusion of unbound pyrene in the aqueous boundary layer (BL) around the fiber. The model closely fit the experimental data and illustrated that diffusion in the BL was rate limiting because the analyte’s affinity for the fiber was high and the BL thickness significant. The concentration of binding matrix and the analyte’s affinity for the matrix further determined the extent to which BSAfacilitated transport contributed to the kinetics of the system.

10.1021/ac070574n CCC: $37.00 Published on Web 08/21/2007

© 2007 American Chemical Society

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007 6941

underlying mechanisms dictating such effects is particularly important when considering SPME measurements performed under nonequilibrium conditions. Using nonequilibrium SPME measurements may be necessary when testing the partitioning behavior of highly hydrophobic chemicals for which equilibration times are prohibitively long.16,19 When considering measurements in the dynamic stages of SPME, the classical one-compartment, first-order kinetic model with absorption and desorption rate constants as parameters has been applied in the past.11,16,20 However, the disadvantage of this model is that it is not explicitly based on processes like diffusion and partitioning of the analyte. Nor does it take into account the experimental conditions such as medium volume and fiber geometry. This hampers a more fundamental understanding of the experimental data. Louch et al.21 and others therefore developed a mechanistically based model based on Fick’s laws that describes sorption in terms of diffusion through the fiber coating and a boundary layer surrounding the fiber.17,19,22,23 The aim of this study was to elaborate on the aforementioned mechanistic modeling work to predict the processes that determine how the presence of binding matrixes such as serum proteins increases SPME fiber kinetics. Because spiking aqueous solutions with a solvent may lead to precipitation and slow dissolution of a chemical,9,24 SPME fibers were loaded with pyrene and exposed for different amounts of time in cell culture medium containing different concentrations of serum. The fraction of pyrene left in the fiber was measured and used to determine the rate of pyrene depletion from the fiber and the association constant (Ka) of pyrene to bovine serum albumin (BSA), the dominant binding protein in serum.25 The SPME system was then mechanistically modeled and fit to the measured data. Mass-transfer coefficients, diffusion coefficients, and diffusion layer thickness were subsequently estimated. By modeling an extra flux of bound pyrene through the boundary layer around the fiber, possible effects of proteins on sorption kinetics were taken into account. The results of this study can be extrapolated to a broad range of analyses of environmental samples containing binding matrixes.

THEORETICAL BASIS The model describes how pyrene desorbs from a loaded hydrophobic SPME fiber coating into surrounding gently stirred medium containing different concentrations of BSA over time. The model is split up in two parts: equilibrium in the SPME system (15) Heringa, M. B.; Hogevonder, C.; Busser, F.; Hermens, J. L. M. J. Chromatogr., B 2006, 834, 35-41. (16) Urrestarazu Ramos, E.; Meijer, S. N.; Vaes, W. H. J.; Verhaar, H. J. M.; Hermens, J. L. M. Environ. Sci. Technol. 1998, 32, 3430-3435. (17) van Eijkeren, J. C. H.; Heringa, M. B.; Hermens, J. L. M. Analyst 2004, 129, 1137-1142. (18) Holten Lutzhoft, H.-C.; Vaes, W. H. J.; Freidig, A. P.; Halling-Sorensen, B.; Hermens, J. L. M. Environ. Sci. Technol. 2000, 34, 4989-4994. (19) Ai, J. Anal. Chem. 1997, 69, 1230-1236. (20) Vaes, W. H. J.; Hamwijk, C.; UrrestarazuRamos, E.; Verhaar, H. J. M.; Hermens, J. L. M. Anal. Chem. 1996, 68, 4458-4462. (21) Louch, D.; Motlagh, S.; Pawliszyn, J. Anal. Chem. 1992, 64, 1187-1199. (22) Pawliszyn, J. Solid-phase microextraction: Theory and Practice; Wiley-VCH: Toronto, 1997. (23) Ai, J. Anal. Chem. 1998, 70, 4822-4826. (24) Ter Laak, T. L.; Durjava, M.; Struijs, J.; Hermens, J. L. M. Environ. Sci. Technol. 2005, 39, 3736-3742. (25) Peters Jr., T. All About Albumin: Biochemistry, Genetics, and Medical Applications; Academic Press: San Diego, CA, 1996.

6942

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

is described by the equilibrium partitioning theory, and the dynamics of depletion of a compound into surrounding medium is based on diffusion of pyrene in the fiber coating and in the surrounding boundary layer. Measuring Binding Affinity at Equilibrium. Pyrene partitions between three phases: fiber, medium, and albumin. It is assumed that, at equilibrium, the concentrations in each phase are related to each other by their partition coefficient, K, due to chemical potential equilibration.9,22 Thus,

Cmu ) Cf/Kf

(1)

and, when incorporating possible saturation,

Cmb ) CalbCum/(Kd + Cum)

(2)

Calb, Cf, Cmu, and Cmb refer to the concentration of albumin in the medium, the concentration of pyrene in the fiber, unbound and bound to albumin in the medium. Kf, Ka, and Kd (where Ka ) 1/Kd) refer to the fiber-medium partition coefficient and the association and dissociation constants of pyrene to albumin, respectively. Even though the kinetic model in this study incorporates possible saturation, under nonsaturated conditions and accounting for the mass balance of the system, the fraction F of pyrene left in the fiber and the fraction 1 - F in the medium at equilibrium is given by

F)

KfVf KfVf + (1 + CalbKa)Vm 1-F)

(1 + CalbKa)Vm KfVf + (1 + CalbKa)Vm (3)

where Vf and Vm refer to the volume of fiber coating and of medium, respectively. The parameters Kf and Ka can be obtained by fitting the fraction F in eq 3 to experimental data obtained at equilibrium at different values for the albumin concentration Calb. Yuan and Pawliszyn9 and Ter Laak et al.24 gave a detailed account of the derivation of eq 3. Kinetic Fiber Depletion Model. Previous SPME kinetic models modeled the absorption of analytes from medium to SPME fibers.17,19,21,22 The model developed for this study is different in two ways. It models desorption of an analyte from a SPME fiber into medium instead of absorption into the fiber and models the transport of albumin bound pyrene additional to transport of unbound pyrene. Despite these differences, however, the underlying mathematical reasoning remains essentially the same. Figure 1 shows a schematic depiction of the kinetic compartments considered in this model. A detailed description of the model is available as Supporting Information. Our boundary layer model is based on the boundary layer theory developed by Prandtl26 which uses pure fluid mechanical considerations. Following this theory, the boundary layer thickness only depends on the fiber radius, fluid velocity and fluid (26) Prandtl, L. U ¨ ber Flu ¨ ssigkeitsbewegung bei sehr kleiner Reibung. Verhandlungen des III. Internationalen Mathematiker Kongresses, Heidelberg 1904; pp 484491, Teubner, Leizig. See Gesammelte Abhandlungen II, 1905; pp 575584.

Figure 1. Simplified schematic overview of the model set in radial coordinates (r). It is based on Fick’s law, i.e., on diffusion coefficients in the fiber coating, Df, and in a BL (thickness ∆l) of bound, Dbl and unbound Dul pyrene. The ratio bound/unbound is determined by the pyrene-BSA association constant (Ka ) 1/Kd) and the BSA concentration (Calb). The concentration in the fiber (Cf) in time (t) is the model’s input. Increased depletion rates in the presence of serum can be explained by the diffusion of the albumin-pyrene complex in the BL.

viscosity. This approach is customary in SPME literature and is introduced in Pawliszyn22 (chapter 3). However, other boundary layer models, notably those used in electrochemical literature on reactive surfaces, are based on the boundary layer theory developed by Nernst.27 The main difference is that in the ‘Nernst’ approach, unlike in our model, boundary layer thickness depends on the diffusing compounds diffusion coefficient. For a recent comparison see Jenissen et al.28 The model assumes that diffusion of pyrene in the fiber and in the BL surrounding the coating is the rate controlling factor. Transport by diffusion is governed by Fick’s law:

J(r,t) ) -D

∂C(r,t) ∂r

(4)

Here, the diffusive mass flux J (mol dm-2 h-1) at time t and at the radial coordinate r is proportional to the concentration gradient and D is the diffusion coefficient. For the coating this assumption is valid if it can be considered as a normal liquid and if no activation energy is necessary to transfer an analyte between solution and coating.21,29 A distinction between three characteristic times scales in this system can be made: one for depleting the fiber, one for achieving analyte partition equilibrium at the fiber/medium interface, and the third of reaching chemical equilibrium between unbound and albumin-bound pyrene. It is assumed that that both the second and third characteristic times are very short as compared to the characteristic depletion time. As a consequence, it is assumed that at any instant unbound and bound concentrations in medium are in chemical equilibrium (eq 2) and that at any instant at the fibermedium interface the concentration in fiber and the unbound concentration in medium are in equilibrium (eq 1). Furthermore, continuity of fluxes over both the fiber coating-BL interface and BL-bulk medium interface is assumed. (27) Nernst, W. Z. Z. Phys. Chem. 1904, 47, 52-55. (28) Jenissen, H. P.; Sanders, A.; Schnittler, H. J.; Hlady, V. Materialwiss. Werkstofftech. 1999, 30, 850 -861. (29) Mayer, P.; Vaes, W. H. J.; Hermens, J. L. M. Anal. Chem. 2000, 72, 459464.

To accommodate possible facilitated transport of pyrene by albumin, the model explicitly models both bound and unbound pyrene in the BL. Consequently, the flux of analyte within the BL can be described by

(

Jl(r,t) ) - Dul

)

∂Clu(r,t) ∂Clb(r,t) + Dbl ∂r ∂r

(5)

Here, the subscript l refers to the BL and the superscripts u and b to “unbound” and “bound”. The second term at the right-hand side denotes the facilitated transport by the pyrene-albumin complex. The radial coordinate r ranges between Rf < r < Rf + ∆l, where Rf is the coating outer radius and ∆l the BL thickness. The utility of including an additional flux of bound analyte to explain the role of a binding matrix in facilitating the transport of an analyte across a diffusion layer has also been studied in models of metal biouptake from complex environments.30-32 Note that under unsaturated conditions one can express transport in terms of the total pyrene concentration Cl ) Cul + Cbl and an average diffusion coefficient Dl ) (Dul + KaCalbDbl )/(1 + KaCalb) ) (Cul /Cl) Dul + (Cbl /Cl)Dbl . This is illustrated in de Jong et al.33 However, under saturated conditions, such a simplification would lead to a far more complicated general expression for the average diffusion coefficient Dl ) (Dul + (dCbl /dCul )Dbl )(dCul /dCl), which would detract from the more conceivable, simple view of two pyrene species, one unbound and one bound to albumin, with two different diffusion coefficients. The flux of analyte in the fiber coating, f, is described by

Jf(r,t) ) -Df

∂Cf(r,t) ∂r

(6)

The radial coordinate r ranges between Rc < r < Rf, where Rc is (30) van Leeuwen, H. P. Environ. Sci. Technol. 1999, 33, 3743-3748. (31) van Leeuwen, H. P.; Town, R. M.; Buffle, J.; Cleven, R. F. M. J.; Davison, W.; Puy, J.; vanRiemsdijk, W. H.; Sigg, L. Environ. Sci. Technol. 2005, 39, 8545-8556. (32) DelRaso, N. J.; Foy, B. D.; Gearhart, J. M.; Frazier, J. M. Toxicol. Sci. 2003, 72, 19-30. (33) de Jong, H. G.; van Leeuwen, H. P.; Holub, K. J. Electroanal. Chem. 1987, 234, 1-16.

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

6943

the coating inner radius. The model outlined by eqs 4- 6 will be referred to from now on as the BL model. Since the fiber coating thickness and the initial concentration of pyrene in the fiber are known, the model requires the estimation of six parameters: Dbl , Dul , ∆l, Ka, Df, and Kf. These are to be estimated by fitting the model to experimental data. From a numerical point of view, the model calculation times or numerical stability can become prohibitive for some combinations of these parameter values. As a quasi-steady-state diffusion process is assumed in this system, mass-transfer coefficients, ml, where

ml )

Dl Rf ln(1 + ∆l/Rf)

(7)

can be used to simplify the model and quantify matrix effects. Note that when the layer thickness, ∆l, is small with respect to the coating outer radius (not in this study), the expression for the mass-transfer coefficient reduces to the more familiar expression ml ) Dl/∆l. Mass-transfer coefficients refer to the ratio of the diffusivity and the diffusion distance of an analyte. Thus, under this quasi-steady-state assumption, the flux of pyrene through the BL can be rewritten as u b (t) - Cum(t)) + mbl (Ci,m (t) - Cbm(t))) Jl(t) ) -(mul (Ci,m

(8)

Here, the unbound and bound concentration at the fiber-medium u b u u interface, i, are Ci,m ) Ci,f/Kf and Ci,m ) CalbCi,m /(Kd + Ci,m ), respectively, and derived using eqs 1 and 2. This model has more favorable numerical properties and needs the estimation of five parameters: Df, Kf, mul , mbl , and Kd. The model using this quasisteady-state approximation will be referred to as mass-transfer model in this study. MATERIALS AND METHODS Chemicals, Fibers, and Solvents. Pyrene (98%) and sodium chloride (g99.5%) were purchased at Aldrich Chemie BV (Zwijndrecht, The Netherlands). Glass fibers with a core diameter of 110- and a 28.5-µm poly(dimethylsiloxane) (PDMS) coating (volume 12.4 µL/m) were obtained from Poly Micro Industries (Phoenix, AZ). Acetonitrile, methanol, and n-hexane (Labscan, Dublin, Ireland) were of analytical grade (99.9, 99.9, and 95% purity, respectively). Highly pure deionized water was prepared using the Millipore water purification system equipped with an organic-free kit (Millipore Waters, Amsterdam, The Netherlands). The culture medium consisted of Dulbecco’s Modified Eagle Medium (DMEM) with 4500 mg/L glucose, 4 mM L-glutamine, 110 mg/L sodium pyruvate, 100 U/L penicillin, and 100 µg/L streptomycin. Heat-inactivated newborn calf serum (NCS) was used to supplement the medium and contained an estimated 31 mg/mL BSA (as communicated by the supplier). All culture medium ingredients were purchased from Gibco BRL (Breda, The Netherlands). Dosing the SPME System with Pyrene. The solid-phase dosing technique was used as described in Ter Laak et al.24 All PDMS fibers were cut to a length of 2.5 cm and loaded with pyrene by exposing them to a 30-mL sterilized 1:1 methanol-water (v/ v) mixture spiked with 2 mg/L pyrene for 24 h on a “rock ‘n roller” 6944

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

shaker (rocking 5 cycles/min, turning 5 rpm, Snijders Scientific, Tilburg, The Netherlands). Five fibers were immediately analyzed for their pyrene concentration after dosing to determine the initial pyrene concentrations in the fiber. Obtaining SPME Data on Kinetics and Partitioning. The loaded fibers were fully submerged in 5 mL of culture medium supplemented with NCS at 0, 0.47, 1.40, 2.33, 4.67, 11.67, 23.34, 46.68, and 116.70 µM BSA in 5-mL glass vials (Aluglas B.V., Uithoorn, The Netherlands) on a rock ‘n roller. The experiment was carried out in triplicate. Three nonloaded fibers were exposed for 48 h in bare cell culture medium to serve as negative controls. For input into the kinetic model including saturation (eq 2), the fibers exposed to medium with 0, 0.47, 1.40, and 23.34 µM BSA were sampled after 0.1, 0.25, 0.5, 1, 2, 4, 24, and 48 h. For input into eq 3, fibers exposed to 2.33, 4.67, 11.67, 46.68, and 116.70 µM BSA were sampled after 48 h. The experiments were performed at 20 °C in the dark to avoid photodegradation of pyrene. After exposure, each fiber was gently blotted dry with a tissue. They were put into 1.8-mL autosampler vials containing a 250-µL glass insert with 200 µL of acetonitrile for 24 h to extract the pyrene out of the fiber coating. Three subsequent extractions showed an extraction recovery of 99.6 ( 0.1%. The samples were then stored at -20 °C prior to analysis. Analysis of Pyrene Concentrations. Analyses determining pyrene concentrations were performed using HPLC fluorescence. The HPLC system was equipped with a Shimadzu DGU 14A degasser (Den Bosch, The Netherlands), a Varian 9012 pump, a Basic Marathon autosampler (Middelburg, The Netherlands), a Merck Hitachi F-1050 fluorescence spectrophotometer (Maarssen, The Netherlands), and a 100 mm × 3 mm i.d. × 5 µm PAH ChromSpher 5 C18 column (Varian) that was operated at 20 °C. All analyses were performed with a flow rate of 400 µL/min and an injection volume of 20 µL. The excitation and emission wavelengths of pyrene were set at 274/400 nm. The detection limit was ∼0.15 µg/L. The compounds were separated using an elution of 90% methanol and 10% Millipore water. Quantification was done using calibration standards prepared for pyrene (0.15100 µg/L acetonitrile). Chromatographs were analyzed using Chromcard version 1.21 (Milan, Italy). Mass Balance Calculations. To determine the percentage recovery of pyrene, pyrene concentrations in culture medium were determined alongside fiber concentrations. Initial fiber concentrations of pyrene were compared with the sum of concentrations of pyrene in the fiber and in the medium after exposure. Medium concentrations were determined by liquid-liquid extraction, which involved extracting pyrene from the medium with 1 mL of n-hexane (repeated three times).24 To reduce the formation of a foamy mass due to the mixing of hexane with serum protein in medium, 3 mL instead of 1 mL of hexane and an excess of sodium chloride was added to the medium containing serum. After extracting, the hexane was evaporated to ∼0.5 mL using a gentle stream of nitrogen. Subsequently, 2 mL of acetonitrile was added and the mixture was evaporated to ∼1 mL. Given the weight of acetonitrile, the concentration of pyrene in these aliquots of acetonitrile was determined using HPLC. Data Analysis. The quotient of the concentration of pyrene in the fiber after and before exposure was calculated to obtain the fractions of pyrene left in the fiber, F. Partition coefficients

Figure 2. Fraction of pyrene in the fiber over time. The mechanistic model calculations (straight lines) are compared to data (symbols). BSA concentrations from top to bottom are 0 (*), 0.47 (+), 1.40 (o), and 23.34 µM (x), respectively. The right upper panel shows the result for albumin concentration 23.34 µM on a log-log scale.

were determined using eq 3. GraphPad Prism 3.0 (San Diego, CA) was used for plotting data. The mechanistic model was implemented in the versatile ACSL software package (Aegis Software Group, Huntsville, AL) and used to fit the measured depletion data over time. See Supporting Information for details. RESULTS AND DISCUSSION Determination of Partition Coefficients at Equilibrium and Implications. The desorption profile of pyrene from PDMS into medium containing 0, 0.1, 0.3, and 5% NCS is depicted in Figure 2. The profile shows that the SPME system in this study required at most 24 h to reach equilibrium as the fraction of pyrene in the fiber remained stable from this time point onward. Fitting the fraction of pyrene in the fiber at equilibrium at all tested BSA concentrations to eq 3 (i.e., assuming no saturation occurs) yielded a close fit (R2 of 0.99) (Figure 3). The fit estimated a fiber-medium partition coefficient, Kf, of 1.95 × 104 ((0.03 × 104) and a pyrene-albumin association constant, Ka, of 8.58 × 106 ((0.34 × 106) M-1. The assumption of nonsaturation is upheld because at the lowest BSA concentration tested (i.e., 0.47 µM), the difference between fitting the equilibrium data to eq 3 and fitting the kinetics data to the mechanistic model, which includes eq 2, was only 3%. The estimate of the fiber-medium partition coefficient for pyrene, Kf, falls within the literature range of 6.3 × 103-7.2 × 104 for Kf in water and is very close to the Kf value ((1.6-2.5) × 104) determined by Ter Laak et al.24 using exactly the same fibers. This is to be expected as bare medium (DMEM) is a simple buffer solution devoid of major binding elements. Even though a literature value for the association constant, Ka, of pyrene to BSA is scarce, a number of studies validated the use of SPME to determine Ka, which adds weight to the notion that Ka value in this study is plausible.5,8-11 Arguably, however, there may be other minor binding agents in serum than BSA (e.g., glycolipids), despite BSA being the most dominant binding protein.25,34,35 When (34) Gulden, M.; Morchel, S.; Tahan, S.; Seibert, H. Toxicology 2002, 175, 201213. (35) Gulden, M.; Seibert, H. Toxicology 2003, 189, 211-222.

using pure BSA instead of NCS in determining Ka of pyrene to BSA in this experiment, a similar value is obtained as when using NCS (8.35 × 106 ( 1.3 × 106 M-1 instead of 8.58 × 106 M-1). Strictly speaking, however, Ka can be referred to a compounded association constant of pyrene to NCS binding elements. This compounded association constant is most relevant to determining binding of compounds to extracellular matrixes in in vitro systems. Indeed, considering Calb as a relevant scaling concentration, Ka should be considered as a apparent association constant that incorporates the (unknown) mean number of binding sites available in NCS-enriched medium. The association constant for pyrene to serum components suggests that serum binding is significant. A Ka of 8.58 × 106 M-1 indicates that in culture medium containing a typical 5% NCS (estimated 23.34 µM BSA) over 99% of pyrene is bound. Thus, in a typical in vitro assay, very little pyrene is expected to be free in the medium to cause toxicity and differences in serum levels between in vitro toxicity assays may cause large variations in effect concentrations measured. Even with chemicals with lower BSA binding affinities, both Gu¨lden et al.34 and Heringa et al.36 found that median effect concentrations, EC50’s, based on nominal concentrations increase significantly with increasing BSA concentrations in cell culture medium. Mass Balance. Equation 3 assumes a 100% mass balance. It assumes no sorption to phases other than what is described by the model. Antibiotics were added to inhibit biological degradation. Photodegradation was prevented by performing the experiments in the dark. Glass binding was measured to be lower than 2%. Evaporation to headspace was calculated to be lower than 0.05% using the air-water partition coefficient at 20 °C.24,37 Recovery varied from 66 to 100%, where extracting pyrene from medium containing serum was more cumbersome (66-87%) than medium containing no serum (98-101%). The lowery recovery of samples (36) Heringa, M. B.; Schreurs, R. H. M. M.; Busser, F.; van der Saag, P. T.; van der Burg, B.; Hermens, J. L. M. Environ. Sci. Technol. 2004, 38, 62636270. (37) de Maagd, P. G.-J.; ten Hulscher, D. T. E. M.; van den Heuvel, H.; Opperhuizen, A.; Sijm, D. T. H. M. Environ. Toxicol. Chem. 1998, 17, 251257.

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

6945

Figure 3. Effect of serum content on the fraction of pyrene left in the fiber F at equilibrium. Fitting eq 3 to the data points yielded values for Kf and Ka of 1.95 × 104 ((0.03 × 104) and 8.58 × 106 ((0.34 × 106) M-1, respectively. The R2 of the fit was 0.99.

Figure 4. Plot of individually calculated association constants, Ka, for pyrene to BSA against the BSA concentration.

containing serum is likely due to the poor dissociation of pyrene from the albumin during the extraction phase with hexane.38 Fouling. BSA is not to interact with PDMS to block the flow of pyrene at the fiber-medium interface or provide an additional source of pyrene on the fiber other than freely dissolved pyrene. Although such BSA fouling to PDMS and fiber coating has been considered insignificant in previous studies,15 this study revealed a decline in Ka values with increasing BSA concentration when Ka was calculated for each BSA concentration individually (Figure 4). Figure 4 suggests that the methodology works well for BSA concentrations up to 23.34 µM. Above this concentration, fouling is arguably influencing Ka measurements. If fouling is significant, adsorption of BSA with bound pyrene to the fiber would increase the measured pyrene concentration in the fiber coating, consequently causing the free concentration of pyrene to be overpredicted and Ka to diminish with increasing BSA concentrations. Poon et al.39 found that human serum albumin interacted with the fiber in such a way as to cause problems with reproducibility. Yet, Heringa et al.15 and Oomen et al.14 investigated the occurrence of such fouling by measuring the amount of binding matrix adsorbed to the fiber after exposure using competitive ELISA and the Bradford assay, respectively. In both cases, adsorption of BSA (38) Schirmer, K.; Chan, A. G. J.; Greenberg, B. M.; Dixon, D. G.; Bols, N. C. Toxicol. In Vitro 1997, 11, 107-119. (39) Poon, K.-F.; Lam, P. K. S.; Lam, M. H. W. Chemosphere 1999, 39, 905912.

6946

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

and chime to fiber, respectively, was not enough to cause significant changes in the measured free concentration of octylphenol and PCBs, respectively. The negative results for fouling in both studies is arguably due to the lower affinity for the binding matrix of the tested compounds than used in this study. Further investigation is needed for a greater understanding of when fouling could play a role in SPME systems. Using alternative fiber coatings, constructing a semipermeable membrane around the fiber or using headspace analyses may circumvent possible fouling.7,40-42 Modeling the Influence of BSA on Sorption Kinetics. As is apparent from Figure 2, equilibration times are faster in SPME systems containing serum protein. To model this phenomenon, the mechanistic model developed in this study was fit to the experimental data. To obtain estimates of the model parameters, the log likelihood (LLF) was optimized using ACSL Optimize. First parameters of the model representing the BL with a simple masstransfer coefficient (eq 8) were fitted because of the numerical robustness of this model. As a result, the following parameter values were obtained: Df ) (3.77 ( 3.63) × 10-7 dm2/h, mul ) 1.17 ( 0.20 dm/h, mbl ) (6.27 ( 1.24) × 10-2 dm/h, Kf ) (2.29 ( 0.24) × 104, and Ka ) (1.18 ( 0.13) × 107 M-1 (Kd ) (8.47 ( 1.05) × 10-8 M). The large uncertainty in the value of the coefficient of diffusion in the fiber coating indicates that transport may be limited by diffusion in the BL. If the mass-transfer model is a reasonable approximation to the BL model, then it is to be expected that fitting the values of the diffusion coefficients of bound and unbound pyrene together with the value for the BL thickness will be highly correlated (eq 7). From the literature, the diffusion coefficient of free pyrene in the boundary layer Dul is estimated to be 4.37 × 10-6 cm2/s (1.57 × 10-4 dm2/h).43 Taking this value, the corresponding BL thickness ∆l ) 14.6 µm can be estimated from eq 7 using the value for mul found above. Then, the diffusion coefficient for bound pyrene Dbl ) 8.4 × 10-6 dm/h, corresponding to this BL thickness can be estimated from eq 7 and using the value for mbl found above. Both estimates served the initial estimation of parameter values in a BL model parameter fitting procedure for ∆l and Dbl (values for Kf, Ka kept at the values found above with the mass-transfer model). This way, the BL thickness of ∆l ) 18.5 µm was found and Dbl ) 8.9 × 10-6 dm2/h. When assuming the diffusion coefficient of bound pyrene is the estimated diffusion coefficient of albumin in water, Dbl ) 5.9 × 10-7 cm2/s (2.12 × 10-5 dm2/h),25 values for ∆l and Dul were estimated to be 41.7 µm and 3.65 × 10-4 dm2/h, respectively. Thus, BL thickness ∆l, unbound Dul , and bound pyrene Dbl diffusion coefficients ranged from 18.5 to 41.7 µm, 1.57 × 10-4 to 3.65 × 10-4 dm2/h, and 0.84 × 10-5 to 2.12 × 10-5 dm2/h in this model, respectively. The estimated BL thickness is comparable to the coating thickness of 30 µm and ranges from 20 to 50% of the outer coating radius. The observed effect of BSA on the kinetics strongly suggests that diffusion in the aqueous diffusion layer is the ratelimiting step, consistent with the observed uncertainty in the (40) Zhang, Z.; Poerschmann, J.; Pawliszyn, J. Anal. Commun. 1996, 33, 219221. (41) Zhang, Z.; Pawliszyn, J. Anal. Chem. 1993, 65, 1843-1852. (42) Musteata, F. M.; Pawliszyn, J.; Qian, M. G.; Wu, J.-T.; Miwa, G. T. J. Pharm. Sci. 2006, 95, 1712-1722. (43) Gustafson, K. E.; Dickhut, R. M. J. Chem. Eng. Data 1994, 39, 281-285.

estimated value of the diffusion coefficient in the fiber coating. The increased desorption rate of pyrene from the fiber coating into the surrounding medium is consistent with the hypothesis that BSA facilitates the transport of pyrene. This hypothesis stipulates that there is a BL around the SPME fiber through which an analyte can diffuse. If diffusion through the BL is the ratelimiting step for the entire sorption process, a concentration gradient in the BL is formed. In the presence of a binding matrix in the BL, the free analyte can bind to the matrix. This binding can create a steeper concentration gradient if our assumption on (dis)association of the analyte to the matrix is very much faster than diffusion of the analyte through layer is valid. The steeper concentration gradient enhances the flux of analyte at the fiber coating-medium interface. Facilitated transport by a binding matrix has also been used by Heringa et al.,15 Kopinke et al.,12 and Oomen et al.14 to explain the enhanced kinetics of phenols, PAHs, and PCBs in SPME systems containing BSA, humic acid, and chime, respectively. Heringa et al.,11 Holten Lutzhoft et al.18 and Urrestarazu Ramos et al.16 did not find BSA speeding-up estradiol sorption, humic acid speeding-up quinolones sorption, and humic acid speedingup PCB sorption into SPME fibers, respectively. The mechanistic model developed in this study can help explain why facilitated transport occurred in some studies and not in others as the flux of bound analyte is explicitly modeled. Fitting the model to experimental data in this study revealed that diffusion of pyrene through the boundary layer is the rate-limiting step of the whole desorption process. The factors determining whether diffusion in the BL or in the fiber coating is rate limiting include the diffusion rates of the analyte through the BL and the fiber coating, the thickness of the BL and the fiber coating, and the fiber-medium partition coefficient (eqs 1, 6, and 7), Kf, which is influenced by the compounds hydrophobicity.44,45 Indeed, a limitation by diffusion in the PDMS coating in this study is unlikely since the literature suggests that diffusion in PDMS is generally a factor of five to six lower than in the aqueous phase.22 The coating and BL thicknesses are approximately the same, and the high Kf value more than compensates for the relatively minor magnitude difference in diffusion rates. The prerequisite for facilitated transport is that diffusion in the BL is rate limiting because only then can the extra flux of bound pyrene through this layer contribute to system kinetics (eq 6). In Heringa et al.,11 for example, diffusion was likely to be limiting in the polyacrylate coating of the SPME fiber. Polyacrylate is a more solid polymer than PDMS is, thus lowering the diffusivity of analytes through it.23 Moreover, the partition coefficient of estradiol to the coating was lower than in this study and the system was stirred violently. The stirring regime dictates the BL thickness.21 The thickness, in turn, influences the contribution of facilitated transport to the sorption kinetics.46 Bound analyte can only contribute to the diffusion flux if there is a frequent interconversion between the bound and free state during diffusive transport.16,31 In this study, we assume instanta(44) Flynn, G. L.; Yalkowsky, S. H. J. Pharm. Sci. 1972, 61, 838-852. (45) Gobas, F. A.; Lahittete, J. M.; Garofalo, G.; Shiu, W. Y.; Mackay, D. J. Pharm. Sci. 1988, 77, 265-272. (46) Mayer, P.; Karlson, U.; Christensen, P. S.; Johnsen, A. R.; Trapp, S. Environ. Sci. Technol. 2005, 39, 6123-6129.

Figure 5. Simulation of the FTR through the BL in an SPME system described in this study (i.e., similar volumes of PDMS and medium and similar agitation regime). The FTR is proportional to the ratio of the total flux and the flux of unbound analyte. The simulation is based on eq 9 and assumes the mass transfer of the bound, mbm, and unbound analyte, mum, as equal to 0.0627 and 1.17 dm/h, respectively. It illustrates how both the association constant and concentration of BSA determine the contribution of the bound analyte to the overall flux in the BL.

neous chemical equilibrium between analyte and BSA. Moreover, we assume instantaneous equilibrium at the fiber coating-BL interface. Also assuming that chemical binding is nonsaturated and that the mass-transfer model approximates the BL model well, one can infer from eq 8 that at t ) 0 the flux across the BL is jl ) - (mul + mbl KaCalb)(Cf/Kf). This implies that the fiber depletion rate ratio at t ) 0 of medium containing BSA and not containing BSA is the following facilitated transport ratio (FTR):

FTR )

mul + mbl KaCalb mul

)1+

Dbl Dul

KaCalb

(9)

Thus, the depletion rate is enhanced by a factor that is totally determined by the ratio of diffusivities of the bound and unbound analyte, the association constant of binding, and the BSA concentration. For example, the depletion rate with 5% serum added in the medium is about eight times as fast as the depletion rate with medium void of BSA in this study. For a wide range of environmental chemicals, the ratio of diffusivities can be approximated by the ratio of diffusivities of albumin and of the chemical. Therefore, the FTR will not show a large variation and enhanced contribution of facilitated transport will depend mainly on the sorption coefficient or binding affinity to BSA or to any matrix with large molecular weight and the actual concentration of the matrix (in this case the concentration of albumin, Calb). The hydrophobicity (e.g., Kow) and the type of binding matrix influence Ka.13 The relationship between FTR, association constant, Ka, and matrix concentration is simulated in Figure 5. This figure shows Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

6947

that the flux due to facilitated transport can be much higher than the flux of unbound analyte. As a consequence, equilibration times will be highly affected and shortened by the presence of a binding matrix. Arguably, however, the contribution of the binding matrix on the kinetics of the system will not increase continuously with increasing binding matrix affinity and concentration. At one point, diffusion in the fiber will become rate limiting as the rate of diffusion of pyrene through the BL catches up with that in the fiber. Relevance of Facilitated Transport in Chemical Analyses and Uptake Studies. The possible existence of a matrix effect on the kinetics of an SPME system is important to consider when using SPME in nonequilibrium settings as such an effect may hamper the interpretability of the measured fiber concentrations of the test compound. Applications of nonequilibrium SPME include possibly the use of SPME in acute toxicity assays of hydrophobic chemicals where exposure is usually no more than 24 h, and equilibrium between the system compartments may be much longer than this.47 SPMEs applied to environmental samples are also likely to be affected by a matrix effect as these systems often contain many binding matrixes. They are also highly dynamic, and therefore, measurements in such systems often occur in nonequilibrium situations. The effect is likely to occur and have consequences on a broader scale. Indeed, SPME is considered by some to be a good (47) Hendriks, A. J.; Van Der Linde, A.; Cornelissen, G.; Sijm, D. T. H. M. Environ. Toxicol. Chem. 2001, 20, 1399-1420. (48) Leslie, H. A.; Oosthoek, A. J. P.; Busser, F. J. M.; Kraak, M. H. S.; Hermens, J. L. M. Environ. Toxicol. Chem. 2002, 21, 229-234. (49) Degryse, F.; Smolders, E.; Merckx, R. Environ. Sci. Technol. 2006, 40, 830-836. (50) Degryse, F.; Smolders, E.; Parker, D. R. Plant Soil 2006, 289, 171-185. (51) Jansen, S.; Blust, R.; Van Leeuwen, H. P. Environ. Sci. Technol. 2002, 36, 2164 -2170.

6948

Analytical Chemistry, Vol. 79, No. 18, September 15, 2007

model for understanding the uptake of chemicals by organisms.48 The uptake rate of chemicals into cells or organisms (i.e., the solid phase) may likewise be affected by the presence of a binding matrix in surrounding aqueous solution. If the uptake rate is subsequently directly related to toxicity, binding matrixes may affect toxicity in two ways. First, it reduces the availability of the compound for uptake and may thus reduce accumulation and bioactivity of the compound in the cell or organism.34,36 Second, however, this reduction in bioavailability and related bioactivity may be partly counteracted by the enhanced uptake of the compound into the organism at a given point in time. Indeed, DelRaso et al.32 found that uptake rates in rat hepatocytes exposed to cadmium in the presence of albumin were two times as fast as when albumin was not present. The authors suggested that cytotoxicity to cadmium was dependent on both the reduction of freely dissolved cadmium and the enhanced uptake of free cadmium into cells in the presence of albumin. Degryse et al.49,50 and Jansen et al.51 reported similar findings for cadmium uptake into plants and fish, respectively. ACKNOWLEDGMENT The authors thank Dr. B. J. Blaauboer and Dr. T. L. Ter Laak for their critical comments on this work. This work was financed by A-Cute-Tox (EU LSHD CT 2004-512051). SUPPORTING INFORMATION AVAILABLE Detailed mathematical description of the kinetic model. Numerical model implementation. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review March 22, 2007. Accepted July 13, 2007. AC070574N