Anal. Chem. 2004, 76, 6058-6063
In Vitro Characterization of Microdialysis Sampling of Macromolecules Robert J. Schutte, Shadia A. Oshodi, and W. Monty Reichert*
Department of Biomedical Engineering, Duke University, Durham, North Carolina 27708
Experiments were performed to characterize the in vitro collection of macromolecules using microdialysis. Fluorescently labeled proteins and dextrans ranging from 3000 to 150 000 were sampled using a 10-mm, 100 000 molecular weight cutoff, polyethersulfone microdialysis probe. Published models describing microdialysis mass transport of small molecules were examined to determine their appropriateness for sampling of macromolecules. Collection efficiencies, reported as relative recoveries, for macromolecules from 3000 to 70 000 ranged from 5 to 44%. Collection efficiencies determined for microdialysis sampling of macromolecules follow the functionality of published models, although experimental mass transport resistances are to some extent smaller than predicted. Implications of the current study for in vivo microdialysis sampling of cytokines and growth factors are discussed. Microdialysis is a molecular sampling procedure performed by inserting a cylindrical semipermeable membrane into the medium of interest.1 Microdialysis probes can be inserted with minimal damage into virtually any externally accessible tissue for continuous molecular sampling. As the probe is perfused with buffer, molecules of the external medium diffuse through the membrane into the probe lumen to be collected in the exiting dialysate (Figure 1). The dialysate containing sampled molecules is typically collected in a fraction collector and analyzed externally. The microdialysis sampling of a given analyte is governed by the transport of the molecule from an external medium, through the membrane, and into the perfusing buffer. The efficiency of microdialysis sampling is commonly reported as the relative recovery, the percentage of available analyte collected by the probe. Factors such as membrane physical dimensions, accessible volume, perfusate flow rate, and analyte diffusion coefficient (and thus molecular weight) strongly influence relative recovery.2 A theoretical model developed by Bungay, Morrison, and Dedrick (BMD) uses these parameters to describe mass transport of analytes in microdialysis experiments.3 Commercially available microdialysis probes have molecular weight cutoffs (MWCO) that range from 6000 to 100 000. MWCOs are defined as the molecular weight at which ∼80% of the analytes are prohibited from membrane diffusion.4 However, membrane MWCO is typically determined from equilibrium mass transport, * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Ungerstedt, U. J. Intern. Med. 1991, 230, 365-73. (2) Benveniste, H.; Hansen, A. J. Microdialysis in the Neurosciences, Robinson, T. E., Justice, J. B., Jr., Eds.; Elsevier: New York, 1991; Chapter 4. (3) Bungay, P. M.; Morrison, P. F.; Dedrick, R. L. Life Sci. 1990, 46, 105-19.
6058 Analytical Chemistry, Vol. 76, No. 20, October 15, 2004
which is not an exact representation of the nonequilibrium setting of microdialysis. Microdialysis sampling is most often used to collect pharmaceuticals and neurochemicals with smaller molecular weights than proteins; yet recent studies demonstrate the capacity of microdialysis to collect proteins such as cytokines and growth factors both in vitro and in vivo.5-8 In vivo cytokine sampling via microdialysis could provide a wealth of information such as the local concentration of signaling and mediating molecules involved in inflammation, wound healing, and vascular formation. Although a handful of researchers have used microdialysis to recover large molecular weight molecules, analyte collection efficiencies have varied markedly (Table 1).5-7;9-13 To our knowledge, the current study is the first systematic characterization of the collection of macromolecules by microdialysis. In this study, 100 000 MWCO polyethersulfone (PES) microdialysis probes were employed to collect macromolecules ranging from 3000 to 150 000. Relative recovery data were used to determine the appropriateness of the BMD microdialysis mass transport model for macromolecule sampling. An additional model of general membrane flux was employed for estimating the apparent solute diffusion coefficient in the microdialysis membrane and for calculating mass transport resistances for comparison to the BMD model. Results show that macromolecule collection efficiency fits the general trend of the BMD model, though the model appears to underestimate mass transport resistances. MATERIALS AND METHODS Microdialysis System. Figure 1 shows the experimental configuration for the microdialysis measurements. A 1-mL glass syringe attached to a microsyringe pump (Bioanalytical Systems) was connected to the distal end of a 45-cm-long, 0.12-mm-i.d. fluorinated ethylene polymer (FEP) tubing (CMA/Microdialysis, North Chelmsford, MA). The proximal end of the tubing was (4) CMA Microdialysis. CMA Microdialysis Website, Application Note 2. http:// www.microdialysis.com/PDFfiler/Application_notes/Appnot2.pdf. 2004. (5) Phillips, T. M. Luminescence 2001, 16, 145-52. (6) Sjogren, S.; Svensson, C.; Anderson, C. Br. J. Dermatol. 2002, 146, 37582. (7) Winter, C. D.; Iannotti, F.; Pringle, A. K.; Trikkas, C.; Clough, G. F.; Church, M. K. J. Neurosci. Methods 2002, 119, 45-50. (8) Ao, X.; Sellati, T. J.; Stenken, J. A. Anal. Chem. 2004, 76, 3777. (9) Kalantarinia, K.; Awad, A. S.; Siragy, H. M. Kidney Int. 2003, 64, 1208-13. (10) Trickler, W.; Miller, D. W. J. Pharm. Sci. 2003, 92, 1419-27. (11) Dabrosin, C.; Chen, J. M.; Wang, L.; Thompson, L. U. Cancer Lett. 2002, 185, 31-7. (12) Woodroofe, M. N.; Sarna, G. S.; Wadhwa, M.; Hayes, G. M.; Loughlin, A. J.; Tinker, A.; Cuzner, M. L. J. Neuroimmunol. 1991, 33, 227-36. (13) Yamaguchi, F.; Itano, T.; Mizobuchi, M.; Miyamoto, O.; Janjua, N. A.; Matsui, H.; Tokuda, M.; Ohmoto, T.; Hosokawa, K.; Hatase, O. Brain Res. 1990, 533, 344-7. 10.1021/ac0493626 CCC: $27.50
© 2004 American Chemical Society Published on Web 09/14/2004
Figure 1. Diagram of the microdialysis system. PBS is perfused through the FEP tubing into the microdialysis probe at 1 µL/min. The macromolecule solution is buffered with PBS and continuously stirred. Dialysate from the microdialysis probe outlet is collected in a microcentrifuge tube. The capture depicts an enlarged image of the microdialysis probe where mass transport across the membrane occurs for molecules permeable to the membrane. Table 1. Literature Examples of in Vitro Microdialysis Collection Efficiencies of Macromolecules citation
analyte (MW)
Kalantarinia et al.9
TNF-R (17 000)
73
1
IL-1β (17 300) TNF (53 000) IL-1β (17 000) IL-6 (26 000) NGF (13 600) VEGF (28 000-42 000) IL-6 (26 000) trypsin (24 000) IL-1 (17 000) IL-6 (20 300) IL-6 (17 500) IL-1 (28 000) IGF-1 (7600)
1.9 0.1 27.8 45.2 22.2 4
1
Trickler et Winter et
al.10
al.7
Dabrosin et al.11 Sjogren et al.6 Phillips5 Woodroofe et al.12 Yamaguchi et
al.13
mean rel recovery (%)
flow rate (µL/min)
commentsa 5 mm, 40 000-45 000 MWCO, Filtral 20 (acrylonitrile/sodium methallyl copolymer) 4 mm, 100 000 MWCO, CMA/12 (polyethersulfone)
1
12-15 mm, 3 000 000 MWCO, Asahi Plasmaseparator (polyethylene)
2
4 mm, 100 000 MWCO, CMA/20 (polyethersulfone)
3.0 35 92-98 000
1
10 mm, 100 000 MWCO (polyethylenesulfone)
1
10 mm, 100 000 MWCO, CMA/20 (polyethersulfone)
0.5-1.0b
2
16 mm, 100 000 MWCO, Diaflow Hollow Fiber
2.5
2
4 mm, 100 000 MWCO, Evaflux 4A fiber
a Comments include membrane length, molecular weight cutoff (MWCO), and material. b Relative recovery here is reported as a range rather than a mean value.
connected to the 20-cm-long inlet of a 10-mm PES microdialysis probe (CMA/Microdialysis) with a 100 000 MWCO. Tubing connections were made via CMA tubing adapters. The 20-cm-long probe outlet tubing was inserted into a dialysate collection vial. The macromolecules sampled in this experiment were fluorescently labeled proteins or dextrans ranging in molecular weight from 3000 to 150 000. The microdialysis probe was submerged in a 5-mL Vacutainer vial (Becton Dickinson) filled with a macromolecule solution (0.4 mg/mL) in phosphate-buffered saline (PBS). The solution was continuously rocked on a rotisserie (Labquake). Access to the microdialysis probe inlet and outlet tubing was through perforations in the vacutainer stopper, as described elsewhere.14 In Vitro Microdialysis Sampling Procedure. Microdialysis probes were soaked for at least 1 h in PBS prior to experimentation. The microdialysis system (syringe, probe, tubing) was perfused with PBS for 5 min at a flow rate of 10 µL/min to remove glycerol (from packaging) and air bubbles. Fluorescently labeled dextrans (20 000, 150 000, Sigma-Aldrich; all others, Molecular (14) Shin, B. C.; Wisniewski, N.; Reichert, W. M. J. Biomater. Sci.-Polym. Ed. 2001, 12, 467-77.
Probes) were used as purchased. Proteins (Sigma-Aldrich) were labeled in house with Cy5 bisfunctional reactive dye (Amersham Biosciences, Piscataway, NJ). The free fluorescent dye removal was performed using 3500 and 1000 MWCO dialysis membranes (Fisher, only 3000 dextran). Protein and dextran microdialysis sampling was performed at a perfusate flow rate of 1 µL/min for nine sequential samples, each collected for 20 min. Macromolecule concentrations in the external solution and dialysate were determined by fluorescence spectrometry (SLM Aminco) against calibrated standards. Microdialysis collection efficiency was reported as the relative recovery
relative recovery ) Ed × 100%
(1)
where Ed is the extraction fraction given by
Ed ) (Co - Ci)/(Cs - Ci)
(2)
and Ci, Co, and Cs are the analyte concentrations in the perfusate, dialysate, and the external solution, respectively (Figure 1). Analytical Chemistry, Vol. 76, No. 20, October 15, 2004
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Fluid Convection. To assess fluid convection through the microdialysis probe, dialysate samples were massed to determine the dialysate volume after a separate microdialysis sampling of BSA. Microdialysis sampling was performed at a flow rate of 1 µL/min for seven sequential samples for a total duration of 3 h. Fluid filtration or absorption from the microdialysis probe was calculated using the final dialysate mass, expected dialysate mass (perfusate flow rate × time), and density of water. In Vitro Microdialysis Models. BMD Model. A theoretical microdialysis model describing the relationship between the extraction fraction of the solute (Ed), the dialysate flow rate (Qd), and the resistances to mass transport was previously derived from a series of steady-state mass balances.3
Ed )
(
)
Co - Ci 1 ) 1 - exp Cs - Ci Qd(Rd + Rm + Re)
(3)
Resistances to solute mass transport defined in this model are resistance in the dialysate (Rd), resistance in the membrane (Rm), and resistance in the external environment (Re) (Figure 1). In a well-stirred solution, one obtains3
Rd ) 13(rβ - rR)/70πLrβDd
(4)
Rm ) ln(ro/rβ)/2πLDmφm
(5)
Re ) 0
(6)
where rβ is the internal radius of the microdialysis membrane, rR is the external radius of the cannula, ro is the external radius of the microdialysis membrane, L is the effective length of the microdialysis membrane, Dd is the solute diffusion coefficient in the dialysate, Dm is the solute diffusion coefficient in the membrane, and φm is the solvent-accessible volume fraction of the membrane. The product, Dmφm, is defined as the apparent membrane diffusion coefficient. Cussler Model. To see whether values of Rd and Rm calculated via the BMD model (eqs 4 and 5) fall within an acceptable range, an alternative model was employed for estimating mass transport resistances.15 In Cussler’s model, the mass transport of a solute through a membrane subject to a transverse laminar flow is given by
∆C j) 1/k1 + ∆rm/Dmφm + 1/k3
(7)
By analogy with eq 3, we obtain
mass-transfer resistance ) 1/k3 ∼ Rd
membrane diffusive resistance ) ∆rm/Dmφm ∼ Rm (10) For laminar flow along a flat plate, an approximation for dialysate flow within the microdialysis probe, k3 is given by15
k3 ) 0.646(Dd/L)(Lvo/ν)1/2(ν/Dd)1/3
j) 6060
∆C ∆rm/Dmφm + 1/k3
Analytical Chemistry, Vol. 76, No. 20, October 15, 2004
(8)
(11)
where Dd is the solute diffusion coefficient in the dialysate, L is the length of the dialysis membrane, vo is the dialysate bulk velocity, and ν is the dialysate kinematic viscosity. Determination of Aqueous Diffusion Coefficients (Dd). Jain reported a power law equation relating the aqueous diffusion coefficient at 37 °C to molecular weight for dextran in the range of 10 000-147 000.16 Combining this power law equation with the Stokes-Einstein equation yields the room-temperature diffusion coefficient at 23 °C, the temperature at which microdialysis sampling was performed
Dd.23 °C ) (1.26 × 10-4[MW]-0.478) (296 K/310 K) (µ37 °C/µ23 °C) (12) where Dd is the dextran diffusion coefficient in the dialysate, MW is the dextran molecular weight, and µ is the viscosity of water at the respective temperatures. Unlike a homologous series of dextrans, the diffusion coefficients of the heterogeneous proteins had to be determined experimentally by dynamic light scattering. Proteins were dissolved in PBS at a concentration of 10 mg/mL and analyzed at 23 °C using a DynaPro light scattering instrument (Protein Solutions, Charlottesville, VA) to determine the translational diffusion coefficients. Protein diffusion coefficient was determined from a multimodal set of data indexed by molecular weight. Determination of Apparent Membrane Diffusion Coefficients (DmOm). The apparent membrane diffusion coefficients (Dmφm) for dextrans and proteins were calculated from the definition of mass flux through the membrane
j ) CoVo/St
(13)
where Co is the concentration of analyte in the dialysate, Vo is the dialysate volume, S is the surface area of the membrane, and t is the collection time. Setting eq 13 equal to eq 8 yields
Dmφm ) where j is the solute flux through the membrane, ∆C is the concentration gradient across the membrane, k1 and k3 are masstransfer coefficients in the external solution and dialysate, respectively, ∆rm is the membrane thickness, Dm is the solute diffusion coefficient in the membrane, and φm is the solvent-accessible volume fraction of the membrane. The product Dmφm is the apparent solute diffusion coefficient in the membrane. For a wellmixed external solution, k1 approaches infinity, yielding
(9)
∆rmCoVok3 (∆CStk3) - (CoVo)
(14)
from which it is possible to estimate the apparent membrane diffusion coefficient (Dmφm). RESULTS Relative Recovery of Macromolecules. Fluorescently labeled dextran and protein ranging from 3000 to 150 000 were sampled (15) Cussler, E. L. Diffusion, Mass Transfer in Fluid Systems, 2nd ed.; Cambridge University Press: New York, 2004. (16) Jain, R. K. Cancer Res. 1987, 47, 3039-51.
Table 2. Steady-State Relative Recoveries of Macromolecules
Table 4. In Vitro Mass Transport Resistances Calculated from the BMD Model
analyte
steady-state rel recovery (%)
pI/chargeb
insulin (5700) lysozyme (14 400) SBTIa (20 100) ovalbumin (45 000) BSA (66 200) IgG (150 000)
18.5 ( 0.8 16 ( 2 13.4 ( 0.7 8.6 ( 0.7 8.1 ( 0.8 1.7 ( 0.4
5.2 11.35 4.5 4.4-4.6 4.7-4.9 5.8-7.3
globular globular globular globular globular globular
44 ( 3 14 ( 1 6.6 ( 0.6 7.6 ( 0.4 5(1 1.0 ( 0.7
anionic neutral c neutral anionic c
expandable coil expandable coil highly branched highly branched highly branched highly branched
3000 dextran 10 000 dextran 20 000 dextran 40 000 dextran 70 000 dextran 150 000 dextran
shape
protein
Rd, DLS (s/cm3)
Rm (103 s/cm3)
lysozyme (14 400) trypsin inh. (20 100) ovalbumin (45 000) BSA (66 200 IgG (150 000
6900 ( 300 8200 ( 400 10200 ( 500 12900 ( 600 16000 ( 800
108 ( 6 159 ( 3 373 ( 5 372 ( 6 3120 ( 20
a a
Soybean trypsin inhibitor. b Buffer pH 7.4. c Information not available. Data are shown ( SEM (n ) 3).
dextran
Rd, PL (s/cm3)a
Rm (103 s/cm3)
10 000 20 000 40 000 70 000 150 000
5700 8000 11000 15000 21000
198 ( 5 631 ( 5 451 ( 3 860 ( 10 5360 ( 40
Calculated from DPL (Table 3). Data are shown ( SEM (n ) 3).
Table 3. Aqueous and Apparent Membrane Diffusion Coefficients Determined for Macromolecules protein
DLS (10-7 cm2/s)
Dmφm (10-7 cm2/s)
lysozyme (14 400) trypsin inh. (20 100) ovalbumin (45 000) BSA (66 200) IgG (150 000)
12.2 ( 0.6 10.3 ( 0.5 8.3 ( 0.4 6.5 ( 0.3 5.3 ( 0.3
2.5 ( 0.1 1.74 ( 0.03 0.743 ( 0.009 0.75 ( 0.01 0.0889 ( 0.0005
dextran
DPL (10-7 cm2/s)a
Dmφm (10-7 cm2/s)
10 000 20 000 40 000 70 000 150 000
14.7 10.6 7.59 5.81 4.04
1.40 ( 0.04 0.440 ( 0.004 0.615 ( 0.005 0.323 ( 0.005 0.0518 ( 0.0004
a Calculated from the power law relationship of Jain (eq 12). Data are shown ( SEM (n ) 3).
Figure 2. Comparisons of microdialysis probe mass transport resistances determined by two theoretical models. Mass transport resistances in the dialysate are compared as calculated by the BMD (open square) and Cussler (filled square) models. Similarly, membrane resistances are compared as calculated by the BMD (open circle) and Cussler (filled circle) models. Resistance values are shown for lysozyme (L), trypsin inhibitor (TI), ovalbumin (Ov), bovine serum albumin (BSA), and IgG (IgG). Error bars represent ( SEM (n ) 3).
from buffered solution under identical conditions to examine the relationship between relative recovery and molecular weight. Relative recovery of an analyte was determined using steady-state macromolecule concentrations in the external medium and dialysate (eqs 1 and 2). The time to reach steady state was estimated to be 40 min for all microdialysis measurements. Steady-state relative recoveries reported in Table 2 are the mean values calculated between 40 and 180 min. Steady-state relative recoveries decreased with increasing molecular weights of macromolecules, from 44 to 1.0% for dextrans and 18.5 to 1.7% for proteins. An assessment of fluid convection through the microdialysis probe yielded a mean fluid outflow of 0.0 ( 0.4 µL/min. Macromolecule Diffusion Coefficients. Mass transport resistances calculated via the BMD and Cussler models require knowledge of analyte diffusion coefficients. Aqueous diffusion coefficients were determined by dynamic light scattering for proteins and calculated from a published power law relationship for dextrans (Table 3). For both proteins and dextrans, diffusion coefficients decreased with increasing analyte molecular weight. An apparent membrane diffusion coefficient (Dmφm), calculated from relative recovery data via the Cussler model (eq 14), also decreased with increasing analyte molecular weight.
In Vitro Microdialysis Resistances. The membrane-induced hindrance to diffusion in microdialysis was examined using the resistances to mass transfer and diffusion determined from the BMD model (eqs 4 and 5). Resistances due to the dialysate and the membrane increased with increasing molecular weight of the analyte (Table 4). The membrane resistances of proteins and dextrans smaller than the microdialysis probe MWCO were 1660 times greater than their respective dialysate resistances. In contrast, the membrane resistances of IgG and 150 000 dextran were 190 and 195 times greater than their respective dialysate resistances. Comparison of BMD and Cussler Models. Aqueous protein mass-transfer resistances calculated from the BMD model (eq 4) were compared to mass-transfer resistances calculated from the Cussler model (eq 9). The mass-transfer resistances estimated from the two models differed by less than 1 order of magnitude for the proteins indicated (Figure 2). Membrane diffusive resistances were also compared for proteins using the BMD and Cussler models (eqs 5 and 10). Again, the estimated resistances from the two models differed by less than 1 order of magnitude for each protein (Figure 2). Fit of Macromolecule Recovery to BMD Model. Algebraic rearrangement of the BMD theoretical model (eq 3) yields the Analytical Chemistry, Vol. 76, No. 20, October 15, 2004
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Figure 3. Extraction fraction and mass transport resistance data depicted according to a rearrangement of the BMD model (eq 15). Linear regressions were calculated for both proteins (b) and dextrans (∆). The ideal line was calculated by inputting the experimental flow rate into the linear BMD model. Error bars represent ( SEM (n ) 3).
following log-normal equation for our experimental conditions (Re ) 0)
ln[1 - Ed] )
( )( 1 Qd
-1 Rd + Rm
)
(15)
where 1/Qd is the slope, (-1/Rd + Rm) is the independent variable, and the y-intercept is zero. Figure 3 depicts macromolecule recovery data plotted in the form of eq 15. The dashed lines are linear regression fits (IGOR Pro, Wavemetrics, Lake Oswego, OR) to the dextran and protein data. The ideal fit calculated from the experimental flow rate is shown as the solid line. Figure 3 also contains the values of flow rate and y-intercept determined by linear regression, as well as theoretical values calculated based on the experimental flow rate. The variance in the data presented in Figure 3 is expressed at the 95% confidence limit (as calculated by IGOR Pro). DISCUSSION An important goal of our research is to use microdialysis probes as “mock sensors” to simultaneously (1) examine the impact of wound healing on glucose transport through the probe membrane and (2) sample the host of cytokines and growth factors that populate the surrounding wound healing tissue. It is generally accepted that macrophage-derived cytokines and growth factors are critical molecular mediators of acute inflammation and ultimately whether an implant remains mired in chronic inflammation or progresses through the stages of wound healing to fibrous encapsulation.17 These events have a broad range of impact regarding implant performance, from a negligible effect to rendering the implanted device useless. For example, while stable fibrous encapsulation is a desirable condition for many implants, surrounding an implanted glucose sensor with avascular and densely collagenous encapsulation tissue limits sensor performance by 6062
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restricting diffusional and perfusional access to blood-borne glucose. Although microdialysis has been used to collect proteins in vivo, the reported collection efficiencies vary markedly (Table 1), and it is difficult to determine an acceptable range of macromolecule collection efficiencies for commonly used microdialysis experimental conditions. Before this technique can be used reliably to sample macromolecules in vivo, it must be shown to perform predictably and quantitatively with macromolecules in vitro under favorable conditions, providing an upper limit of collection efficiencies compared to what may be observed in vivo. The current study systematically measured the collection efficiencies of macromolecules in vitro and determined whether these values adhered to published transport models that describe microdialysis sampling.3,15 Fluorescently labeled dextrans and proteins ranging from 3000 to 150 000 were sampled from a wellstirred solution via 100 000 MWCO (10 mm) microdialysis probes perfused with PBS at a flow rate of 1 µL/min. In all cases, diffusion through the probe reached steady state after 40 min. Overall, the steady-state relative recoveries decreased with increasing molecular weight of the macromolecule (Table 2). The lone exception to this trend was 20 000 dextran, which was supplied exclusively from a manufacturer different from the maker of the other dextrans. The choice of a 100 000 MWCO probe made possible the collection of proteins and dextrans with molecular weights typical of cytokines. Of particular interest were the collection efficiencies of proteins from 5700 to 66 200 that ranged from 8.1 to 18.5%, respectively. This relatively narrow range of recoveries differed significantly from the broad spectrum of protein collection efficiencies reported elsewhere (Table 1). Relative recoveries for 150 000 dextran and IgG, both of which exceeded the MWCO of the membrane, were very small but nonzero. The observed decrease in relative recovery with increased analyte molecular weight (Table 2) arose from greater resistance to mass transport as molecular size increased. Mass transport resistances were estimated using a model derived by Bungay et al.3 Modifications to this model have been suggested for in vivo microdialysis sampling,18,19 but it remains acceptable for our in vitro microdialysis sampling from a well-stirred solution. Although the BMD model is frequently applied to quantitative microdialysis,20,21 it has not, to our knowledge, been applied to macromolecules. Calculation of mass transport resistances via the BMD model required accurate determination of aqueous diffusion coefficients (Table 3). Dynamic light scattering revealed aqueous protein diffusion coefficients similar to values in the literature.22 Aqueous dextran diffusion coefficients calculated via a published power law expression (eq 12) were comparable to similarly sized protein diffusion coefficients. Apparent membrane diffusion coefficients were calculated via eq 14. Apparent membrane diffusion coefficients for macromolecules smaller than the 100 000 MWCO were 5-18-fold smaller than their (17) Anderson, J. M. Annu. Rev. Mater. Res. 2001, 31, 81-110. (18) Tong, S.; Yuan, F. J. Pharm. Biomed. Anal. 2002, 28, 269-78. (19) Peters, J. L.; Yang, H.; Michael, A. C. Anal. Chim. Acta 2000, 412, 1-12. (20) Snyder, K. L.; Nathan, C. E.; Yee, A.; Stenken, J. A. Analyst 2001, 126, 1261-8. (21) Tang, A.; Bungay, P. M.; Gonzales, R. A. J. Neurosci. Methods 2003, 126, 1-11. (22) Tanford, C. Physical Chemistry of Macromolecules, 1st ed.; John Wiley and Sons: New York, 1961.
respective aqueous diffusion coefficients, a relationship similar to previous studies.20 Calculated membrane resistances of macromolecules with molecular weights smaller than the membrane MWCO were 16-60-fold larger than their respective dialysate resistances. Macromolecules larger than the microdialysis membrane MWCO had apparent membrane diffusion coefficients that were 58-60-fold smaller than aqueous diffusion coefficients and membrane resistances that were 190-195-fold larger than dialysate resistances. In all cases, analyte collection was limited by passage through the membrane, and this effect was significantly more pronounced for molecules larger than the membrane MWCO. The appropriateness of the BMD model for characterizing microdialysis sampling of macromolecules was examined in two ways. First, the Cussler model (eqs 8-10) was employed to determine whether values of Rd and Rm calculated via the Cussler model and the BMD model (eqs 3-5) were of the same order and were reasonable for macromolecules passing through a porous membrane. Calculations from the Cussler model produced dialysate and membrane resistances within 1 order of magnitude of those calculated by the BMD model (Figure 2). Second, the calculated resistances to mass transport and observed collection efficiencies were fit to a plot of ln(1 - Ed) versus [-1/(Rd + Rm)] (Figure 3; eq 15). Ideally, this treatment would have produced a straight line with a y-intercept of zero and a slope equal to the inverse of flow rate, which in our experiments was 1.0 µL/min (solid line in Figure 2). The dextran regression had a y-intercept of -0.02 ( 0.02 and flow rate from the slope of 2.3 ( 0.6 µL/min. Similarly, the protein regression had a y-intercept of -0.03 ( 0.04 and flow rate from the slope of 4 ( 2 µL/min. The dextran and protein data were both linear and had near-zero y-intercepts, suggesting that the behavior of these macromolecules follows the functionality of the BMD model. However, since the flow rate was fixed experimentally at 1.0 µL/ min, the estimated slopes were less steep than expected, and thus nonideal. Assuming that the relative recovery values are accurate, then the BMD resistance equations underestimated the sum of mass transport resistances (Rd + Rm) for microdialysis sampling of macromolecules. Equations 4 and 5 derived from the BMD model are based on microdialysis probe geometry, the volume fraction accessible to the analyte, and the analyte diffusion coefficient in solution and in the membrane. Since all terms in these resistance expressions, except the diffusion coefficient terms, are fixed by probe geometry, the remaining source of their underestimation is in the aqueous and apparent membrane diffusion coefficients. Aqueous diffusion coefficients for the protein and dextran compare well to literature values.22 Underestimation of mass transport resistances arising from overestimation of the membrane diffusion coefficient could come from several sources. Membrane diffusion coefficients are affected not only by solute diffusion properties but also membrane properties such as pore size, pore distribution, and electrical charge.23 While difficult to quantify separately, these interaction effects also contribute to the calculated membrane diffusion coefficient.
Finally, membrane transport can be influenced by convection. Pressure gradients, including hydrostatic, hydrodynamic, and osmotic, across the microdialysis membrane can cause fluid convection through the membrane. Depending on whether the direction of convection is into (absorption) or out of (filtration) the probe, relative recovery values can increase or decrease. For ideal microdialysis, all pressure gradients across the membrane are zero. For our microdialysis experiment, fluid convection through the membrane was measured as 0.0 ( 0.4 µL/min. Although these data were variable, the net fluid convection is not expected to have a significant effect on the mass transport resistances. By using the Cussler model to determine apparent membrane diffusion coefficients from experimental data, all of the diffusion and convection properties of our microdialysis system are encompassed into one coefficient. Underestimation of mass transport resistances is likely the result of inaccuracies in using the Cussler or BMD models for microdialysis sampling of macromolecules. Despite this inaccuracy, collection efficiencies of macromolecules via microdialysis sampling seem to adhere to a predictable pattern following the functionality of the BMD model.
(23) Sakai, K. J. Membr. Sci. 1994, 96, 91-130.
AC0493626
CONCLUSIONS Determining the level of relative recoveries expected for macromolecules under favorable in vitro conditions was the first step prior to performing quantitative in vivo microdialysis sampling of proteins. In this study, collection efficiencies of 3000-70 000 macromolecules from well-stirred solution ranged from 5 to 44% for a 100 000 MWCO PES probe. Macromolecule sampling, though nonideal, fit the functionality of the BMD model, yielding transport resistances similar in magnitude to values calculated via the Cussler model. While yielding results generally predictable according to established models, the in vitro relative recovery of proteins in the molecular weight range of cytokines did not exceed 20%. For in vivo microdialysis, the tissue surrounding the probe imposes yet an additional mass transport resistance that was not considered in this study. The complex nature of this tissue leads to unpredictable molecular behavior and thus complicates the mass transport characterization. However, the additional tissue resistance imposed by in vivo microdialysis is likely to further depress analyte relative recovery. A possible solution to these low collection efficiencies has been reported by Stenken, who employed antibody-coated microspheres to enhance cytokine mass transport through the microdialysis probe.8 ACKNOWLEDGMENT The authors thank Dr. George Truskey for assistance with mass transport models and Drs. Bruce Klitzman and Kevin Olbrich for helpful microdialysis discussion. This work was supported by the National Institute of Health (DK54932) and a National Science Foundation Graduate Research Fellowship (R.J.S.). Received for review April 30, 2004. Accepted August 4, 2004.
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