Anal. Chem. 1998, 70, 2268-2279
Automated Particle Electrophoresis: Modeling and Control of Adverse Chamber Surface Properties Robert J. Knox,† Norman L. Burns,‡ James M. Van Alstine,*,§,⊥ J. Milton Harris,§ and Geoffrey V. F. Seaman†
Emerald Diagnostics, Eugene, Oregon 97402, Institute for Surface Chemistry, POB 5607, SE 114 86, Stockholm, Sweden, Department of Chemistry, University of Alabama in Huntsville, Huntsville, Alabama 35899, and Department of Chemical Engineering and Technology, Royal Institute of Technology, SE 100 44, Stockholm, Sweden
Electrophoretic analysis of colloidal particles is adversely affected by a host of surface phenomena, including electroosmosis, phase wall wetting, and sample or air bubble adsorption. Neutral, hydrophilic polymer coatings control such phenomena on a variety of surfaces. Poly(ethylene glycol)-poly(ethylene imine) (PEG-PEI) conjugates significantly reduce electroosmosis and positively control adsorption and wetting in the glass sample chambers (5 mm × 3 mm × 1 mm i.d.) employed in a representative commercial electrophoresis apparatus (Coulter DELSA 440). The reduction in electroosmosis (e.g., 80% in 7.5 mM solution at pH 11) was similar to that exhibited by coated 2-mm-i.d. quartz capillaries in a Rank MK I manual apparatus. PEG-PEI coatings significantly reduce electroosmosis over a wide range of pH (2-11) and ionic strength (1-100 mM) and can be stable for weeks under normal laboratory conditions. They greatly enhance ease of operation and accuracy (sample mean electrophoretic mobility ( SD) of the DELSA 440. The latter results from reduced electroosmosis flow profile gradients near the chamber center-axis stationary levels, where particle mobility is typically measured. Such flow profiles may also be affected by chamber wall surface asymmetries. A hydrodynamic description of electroosmotic fluid flow in rectangular chambers was adapted in order to analyze the propagation of errors due to both nonideal focusing and chamber surface asymmetry. The analysis indicated that the accuracy of rectangular chambered devices may be improved by measuring particle mobility at stationary levels different than chamber centeraxes. As a result, some rectangular chambers may confer accuracy advantages over cylindrical chambers. Analytical particle electrophoresis (or microelectrophoresis) typically refers to the electrophoretic characterization of small particles of diameter 0.1 µm up to the size of biological cells (∼1* Address correspondence to Dr. Van Alstine at Royal Institute of Technology. E-mail:
[email protected]. Fax: +46-8-10-52-28. † Emerald Diagnostics. ‡ Institute for Surface Chemistry. § University of Alabama in Huntsville. ⊥ Royal Institute of Technology.
2268 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
15 µm).1 It generally entails measuring the velocity per unit field strength of particles suspended in a fluid medium under the influence of an applied voltage. Such conditions yield significant electroosmosis, an electrically induced fluid flow. Capillaries filled with gels, to enhance separation parameters and reduce electroosmosis, have been used to electrophoretically characterize the surface properties of particles up to 500 nm.2 However, most microelectrophoresis devices measure “free solution” particle velocity, at sample chamber locations (called stationary levels) where the velocity of the suspending medium is assumed to be zero and not contributing to observed particle velocity. Electroosmosis compromises the resolution or accuracy of a variety of free solution electrophoretic methods, including the “capillary electrophoresis” of molecules in micrometer diameter capillaries3-7 and particles in larger sample chambers.1,8,9 It limits accurate mobility measurements to stationary levels and is a major determinant of precision and accuracy. Commercially available analytical particle electrophoresis equipment, such as the manual Rank Mark I and II models, or automated equipment, such as the PenKem System 3000, the Coulter DELSA 440, and the Malvern Zeta Sizer, routinely use sample glass chambers composed of borosilicate glass or silica quartz in configurations where two electrodes are connected by a closed cylindrical or, so as to improve system optics, rectangular chamber. Electroosmosis arises from the influence of the applied electric field on the diffuse double-layer charge in the fluid layer adjacent to the charged chamber surface. The negative charge of borosilicate surface has been reported to arise from both silanol (1) Seaman, G. V. F. In The Red Blood Cell, 2nd ed.; Surgenor, D. M., Ed.; Academic Press: New York, 1975; pp 1135-1229. (2) Pospichal, J.; Tietz, D.; Halpern, D.; Chrambach, A. Electrophoresis 1991, 12, 338-341. (3) Hunter, R. J. Zeta Potential in Colloid Science; Academic Press: New York, 1981; pp 125-178. (4) Grossman, P. D. In Capillary Electrophoresis: Theory and Practice; Grossman, P. D., Colburn, J. C., Eds.; Academic Press: New York, 1992; pp 3-43. (5) Zhao, Z.; Malik, A.; Lee, M. L. Anal. Chem. 1993, 65, 2747-2752. (6) O’Neill, K.; Shao, X.; Zhao, Z.; Malik, A.; Lee, M. L. Anal. Biochem. 1994, 222, 185-189. (7) Gilges, M.; Kleemiss, M. H.; Schomburg, G. Anal. Chem. 1994, 66, 20382046. (8) Nordt, F. J.; Knox, R. J.; Seaman, G. V. F. In Hydrogels for Medical and Related Applications; Andrade, J. D., Ed.; ACS Symposium Series 31; American Chemical Society: Washington, DC, 1976; Chapter 17, pp 225-240. (9) Herren, B. J.; Shafer, S. G.; Van Alstine, J.; Harris, J. M.; Snyder, R. S. J. Colloid Interface Sci. 1987, 115, 46-55. S0003-2700(97)00913-X CCC: $15.00
© 1998 American Chemical Society Published on Web 05/06/1998
and boronol (pKa ≈ 7) groups,10 while that on quartz has been attributed to silanol groups.11,12 Recent information suggests that surface silanols exist in different forms (of pKa ) 3.5-7.5), whose concentration varies with both glass type and history (see refs 13-16). Chamber surface charge is also affected by adsorption of ions, detergents, macromolecules, or small particles from sample media. Nonspecific sample adsorption can significantly alter electroosmosis, block optical pathways, or result in sample-to-sample contamination. It is a noteworthy problem in the automated electrophoretic analysis of a large number of samples. Air or gas bubble adsorption also causes problems, including blockage of optical paths or sample fluid feed lines. Bubble localization at a chamber wall is often exhibited by chambers composed of more hydrophobic materials, such as cast polymer plastics, e.g., poly(methyl methacrylate) or polystyrene. Use of such chambers is appealing due to their cost and the fact that, in aqueous solution, their interfacial free energies and surface charge (both of which promote nonspecific adsorption) are often less than those of glass chambers. They offer cost advantages when processing medical, contaminated, or other toxic samples which call for use of disposable chambers. However, much recent research, particularly that related to the use of such materials in disposable test tubes, culture dishes, and microtiter plates, attests to significant nonspecific adsorption, particularly following surface oxidation.17-20 Some years ago, the authors initiated studies related to the use of neutral hydrophilic polymers to control electroosmosis in analytical particle electrophoresis, including determining criteria for assessing such coatings. This early work indicated that adsorbed alkylated celluloses performed well but tended to desorb.8,9 It led to the patented21 development of covalent, terminally linked polymer coatings,9,13,14 as opposed to in situ polymerized coatings,22 for free solution electrophoresis. Such covalent coatings, epitomized by surface treatments involving poly(ethylene glycol) (PEG), can be applied via a variety of chemical approaches to control electroosmosis and significantly improve both microcapillary electrophoresis4-6 and analytical particle electrophoresis.9,14-16 Much recent work by a number of scientists, including the authors, indicates the ability of PEG and related (10) Hair, M. L.; Altug, I. J. Phys. Chem. 1967, 71, 4260-4263. (11) Xu, B.; Vermeullen, N. P. E. J. Chromatogr. 1988, 445, 1-28. (12) Caravajal, S. G.; Leyden, D. E.; Quinting, G. R.; Maciel, G. E. Anal. Chem. 1988, 60, 1776-1786. (13) Burns, N.; Emoto, K.; Holmberg, K.; Van Alstine, J. M.; Harris, J. M. Biomaterials, in press. (14) Van Alstine, J. M.; Burns, N. L.; Riggs, J. A.; Holmberg, K.; Harris, J. M. Colloids Surf. A 1993, 77, 149-158. (15) Burns, N. L.; Van Alstine, J. M.; Harris, J. M. Langmuir 1995, 11, 27682776. (16) Emoto, K.; Harris, J. M.; Van Alstine, J. M. Anal. Chem. 1996, 68, 37513757. (17) O ¨ sterberg, E.; Bergstro¨m, K.; Holmberg, K.; Riggs, J. A.; Van Alstine, J. M.; Shuman, T. P.; Burns, N. L.; Harris, J. M. Colloids Surf. A 1993, 77, 159-169. (18) O ¨ sterberg, E.; Bergstro¨m, K.; Holmberg, K.; Schuman, T. P.; Riggs, J.; Burns, N. L.; Van Alstine, J. M.; Harris, J. M. J. Biomed. Mater. Res. 1995, 29, 741-747. (19) Malmsten, M.; Lassen, B.; Holmberg, K.; Thomas, V.; Quash, G. J. Colloid Interface Sci. 1996, 177, 70-78. (20) Burns, N. L. J. Colloid Interface Sci. 1996, 183, 249-259. (21) Van Alstine, J. M.; Harris, J. M.; Shafer, S.; Snyder, R. S.; Herren, B. U.S. Patent 4,690,749, 1987. (22) Hjerte´n, S. J. Chromatogr. 1985, 347, 191-198.
neutral polymer coatings to significantly reduce nonspecific protein and particle adsorption at a variety of surfaces, while also “hydrophilizing” glass and cast polymer surfaces so as to improve their wetting characteristics.4-7,17-19,23 However, little, if any, research has been done to quantify the ability of such coatings to improve the performance of automated analytical particle electrophoresis apparatus. PEG and related polymers may be localized at surfaces23-36 via linking to a group which encourages strong adsorption via hydrophobic or ionic interactions.7,17,18,24-28 They may also be covalently grafted by reacting surfaces with functionalized PEGs. Such surfaces can be preactivated by chemical, plasma, or other means.5,6,9,14,15,17,19,20,29,36 Preactivation may include covalent modification of a surface with organosilanes9,15,16 or prior adsorption of a polymer with chemically reactive groups, such as poly(ethylene imine) (PEI).15,17,18,24,27,30 PEG-PEI conjugates can be produced a priori and used as a water-soluble, in situ adsorption coating for various chambers.15,30,31 In addition to this “one-step” coating approach, PEG can be covalently reacted with preadsorbed PEI to form a “two-step” coating. Although one-step and twostep coatings differ in regard to surface structure and stability,15,30,32 they both offer good control over electroosmosis, nonspecific adsorption, and wetting (see above). In the present work, PEG-PEI one- and two-step coatings were found to significantly improve the performance of a representative commercial analytical microelectrophoresis, a dynamic electrophoretic light scattering analyzer (DELSA) 440 (Coulter Instruments) with standard rectangular Spectrosil glass chambers. Various practical evaluation criteria were investigated. The impact of electroosmosis on accurate determination of particle mobility was analyzed in relation to a new hydrodynamic description of rectangular chambers, which allowed analysis of the propagation of errors due to both nonideal focusing and asymmetries in chamber wall surface properties. The analysis indicated that, independent of optical considerations, use of rectangular chambers may enhance accuracy by measuring particle mobility at stationary level locations removed from the chamber center-axes and may be more accurate than use of cylindrical chambers. (23) Harris, J. M., Ed. Poly(ethylene glycol) Chemistry: Biotechnical and Biomedical Applications; Plenum: New York, 1992. (24) Malmsten, M.; Lindman, B.; Holmberg, K.; Brink, C. Langmuir 1991, 7, 2412-2413. (25) Malmsten, M.; Van Alstine, J. M. J. Colloid Interface Sci. 1996, 177, 502512. (26) Malmsten, M.; Lassen, B.; Van Alstine, J. M.; Nilsson, U. R. J. Colloid Interface Sci. 1996, 178, 123-134. (27) Tiberg, F.; Brink, C.; Hellsten, M.; Holmberg, K. Colloid Polym. Sci. 1992, 270, 1188-1193. (28) Mrksich, M.; Whitesides, G. M. Trends Biotechnol. 1995, 13, 228-235. (29) Lin, Y. S.; Hlady, V.; Go ¨lander, C. G. Colloids Surf. B 1994, 3, 49-62. (30) Brink, C.; O ¨ sterberg, E.; Holmberg, K.; Tiberg, F. Colloids Surf. 1992, 66, 149-156. (31) Go ¨lander, C.-G.; Kiss, E. J. Colloid Interface Sci. 1988, 121, 240-245. (32) Claesson, P. M.; Blomberg, E.; Paulson, O.; Malmsten, M. Colloids Surf. A 1996, 112, 131-139. (33) Bergstro¨m, K.; O ¨ sterberg, E.; Holmberg, K.; Hoffman, A. S.; Schuman, T. P.; Kozlowski, A.; Harris, J. M. J. Biomater. Sci. Polym. Ed. 1994, 6, 123132. (34) Zalipsky, S.; Seltzer, R.; Menon-Rudolf, S. Biotechnol. Appl. Biochem. 1992, 15, 100-108. (35) Towns, J. K.; Regnier, F. E. J. Chromatogr. 1990, 616, 69-78. (36) Hommel, H.; Hali, A.; Touhami, A.; Legrand, A. P. Colloids Surf. A 1996, 111, 67-74.
Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
2269
EXPERIMENTAL SECTION All chemicals were ACS grade or better. Solutions were prepared immediately prior to use. High-purity, ion-exchangetreated (Barnsted Ultrapure or E-Pure system, with 0.2-µm filter) purified water was used throughout. Surfactant-free polystyrene latex (PSL) microspheres were obtained from Interfacial Dynamics Corp. Routinely sulfated PSL microspheres, lot 10-86-15.213, of 1.02 µm diameter (charge density ) 0.003 22 mequiv g-1), were used in all quartz capillary studies, since their surface pKa ≈ 1 ensures that their mobilities are constant over a broad range of pH.17,18 Mobility measurements were performed as described above at a microsphere concentration of 5 × 108 particles mL-1. Nominal microsphere mobility was 8.5 ( 0.2 µm‚cm‚V-1‚s-1 in unbuffered, pH 5.8, 7.5 mM NaCl at 25 °C. Suspensions of 0.004% of 1.02-µm PSL 10-86-15.213, or 0.865-µm carboxylate-modified latex (CML) 10-36-23 particles were used in DELSA experiments. Quartz Glass Capillaries. Quartz capillaries of 2.0-mm i.d., 4.0-mm o.d., and 100-mm length (Vitro Dynamics Inc.) were used to minimize extraneous fluid flow and provide the large lengthto-diameter ratio needed for effective electroosmosis measurement.8,9,14,15 They were cleaned prior to coating by sequential exposure to 1% (w/w) NaOH (60 °C, 10 min), 3% (w/w) HCl (60 °C, 10 min), and boiling 30% (v/v) H2O2 for 1 h, before being rinsed repeatedly with distilled water.14,15 Capillaries were used fresh or stored in distilled water at 22 °C and rinsed copiously with water before use. PEI and PEG-PEI Coatings. The present study involved three PEG-PEI coatings, whose preparation and use in cylindrical quartz capillary electrophoresis were described previously.15,17 Polymer-coated DELSA inserts were prepared in the same manner and at the same time as control coated quartz capillaries. PEGPEI conjugation involved fine cut molecular weight fractions of either PEG-epoxide (glycidyl ether)16,18,33 or the more reactive PEG-succinimidyl carbonate14,15 pioneered by Zalipsky et al.34 Functionalized PEGs were obtained from Shearwater Polymers. The PEI was Polymin SN (BASF), a branched poly(ethylene imine) of broad molecular weight (mass average 1 800 000). The three coatings were (I) a “one-step” coating of PEG 3400 with epoxide groups at both ends, prereacted with PEI to form a conjugate, adsorbed from aqueous solution; (II) a “one-step” coating of monomethoxy-PEG 5000-succinimidyl carbonate reacted with PEI to form a conjugate, adsorbed from ethanol; and (III) a “two-step” coating of PEG 8000-disuccinimidyl carbonate, reacted with PEI preadsorbed onto chamber surfaces, and then further stabilized by glutaraldehyde cross-linking. The PEG-PEI onestep conjugates were prepared as described previously15 via reaction of 5% (w/v) PEG-epoxide with 0.5% PEI in 0.05 M sodium carbonate, pH 9.5, at 60 °C for 4 h, or 5% (w/v) PEG-succinimidyl carbonate with 0.5% PEI in anhydrous 2-propanol at 60 °C for 4 h. Coating was effected by exposing clean quartz capillaries or DELSA chambers to the respective reaction solutions for 12 h at 25 °C and then rinsing with ethanol, followed by 0.05 M sodium borate pH 9.5 solution, followed by distilled water. The PEGPEI two-step conjugate15 was formed by exposing (4 h, 22 °C) clean capillaries or DELSA chambers to 3% (w/v) PEI in ethanol, prepared by evaporating a 20% distilled water solution of the polymer under vacuum and diluting with anhydrous ethanol to 3% (w/w). This was followed by extensive rinsing in pH 9.5 borate 2270 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
Figure 1. Schematic representation of a rectangular electrophoresis chamber.
buffer, followed by distilled water. PEI-coated surfaces were reacted (12 h, 25 °C) with succinimidyl carbonate-activated PEG 8000 in anhydrous toluene. The PEG-PEI coating was further stabilized via cross-linking35 with 1% (v/v) glutaraldehyde (Ladd Labs) in 0.05 M sodium borate buffer for 12 h at 25 °C. Approximately 1-2 mg of sodium cyanoborohydride was added per 20 mL of reaction volume to chemically reduce Schiff base imines formed during the cross-linking reactions. Quartz Capillary Electrophoresis Measurements. Microparticle analytical electrophoresis was used as described previously9,14,15 to determine the variation in electroosmosis associated with native and modified capillaries from pH 2 to 11, in 7.5 mM NaCl medium adjusted with 7.5 mM HCl or NaOH. Similar methods were used with media containing 1-100 mM salt. The mean electrophoretic mobility of detergent-free, 1-µm-diameter, sulfated PSL microspheres (see below) was measured in a modified Rank Mark I analytical microelectrophoresis system (Rank Bros., Cambridge, UK) with platinum electrodes and digital multimeters (J. Fluke Co.). Care was taken to reduce the time of exposure of particles to extremes of pH.17 A 2-mm-diameter quartz capillary was mounted horizontally between two poly(methyl methacrylate) blocks containing chambers for electrodes. The electrophoresis chamber was filled with a suspension of PSL beads in 7.5 mM medium, and electrodes were tightly set into the blocks. The chamber was immersed in a water bath (25.0 ( 0.1 °C). A 400× water immersion microscope equipped with three-axis distance micrometers and an ocular graticule was used to visually determine the mobility of PSL particles subject to a 40 V (4 V‚cm-1) dc potential. Particle mobility was determined by averaging 8-10 measurements (with the field reversed between measurements in order to avoid electrode polarization) at 8-16 locations across the capillary diameter (Figure 3a,b). Results were reproducible (e.g., 14, 15, and 16), exhibiting good parabolic correlation (e.g., r2 > 0.98) and error bars similar in size to the symbols shown in the figures.16 This allowed electroosmosis to be taken as half the second-order term coefficient of a leastsquares second-order polynomial curve fit of particle mobility versus position across the capillary.15,16 Automated Electrophoresis Apparatus and Chambers. A Coulter DELSA 440 (dynamic electrophoretic light scattering analyzer) was used throughout.37 It consists of a rectangular capillary electrophoresis system with laser illumination of particles at varied measurement positions in the sample chamber. The velocities of the particles are assessed by the Doppler effect, in which the frequency of light is slightly altered upon being (37) DELSA Application Note 2, Coulter Electronics, Hialeah, FL.
Figure 2. Location of stationary levels and three ( ) sampling * locations in a rectangular electrophoresis chamber of aspect ratio 3. For convenience, the chambers axes are shown in relative depth.
Figure 3. Electroosmosis flow parabolas obtained in 7.5 mM NaCl at 25 °C and pH 2 (4), 6 (2), or 11 (O)with PSL microsphere suspensions in uncoated (a) and PEG-coated (b) quartz capillaries (location in relation to radius), plus uncoated (c) and PEG-coated (d) DELSA 440 Spectrasil chambers (location in relation to Figure 1 x-axis).
scattered from a moving particle. When this light is mixed with an unaltered beam, the resultant light beam oscillates at a frequency proportional to the Doppler shift. The instrument uses Fourier analysis to transform the oscillatory signal from its photodiode light detectors into a profile of scattered light signal intensity versus shift frequency. This profile can be displayed as intensity (scatter intensity) versus frequency shift, electrophoretic mobility, or ζ potential. The instrument monitors the light scattered from moving particles at four angles, approximately 7.5°, 17°, 22.5°, and 34° (uncorrected for the sample refractive index). The signal intensity at the different angles is affected to differing degrees by particle size, a feature which can be used to advantage when sample size and particle surface charge are heterogeneous.
The DELSA 440 glass sample chamber inserts (Starna Cells) were fabricated by heat fusion (O2 flame, approximately 1700 °C) of four pieces of polished, optical grade synthetic fused (Spectrosil) silica.37 The approximate insert dimensions are 21 mm × 13 mm × 5 mm, with the 5-mm edges polished for laser illumination of the sample capillary (Figure 1). In operation, the rectangular sample capillary (5 mm long × 3 mm wide × 1 mm high) is sandwiched between solid silver electrodes with hemispherical sample cavities (1 cm diameter), machined to provide for sample loading. The sample chamber is illuminated by passage of the beams through its 5- × 1-mm faces. Following installation of the insert, the cell height and wall locations were confirmed by the manufacturer’s ADC output method.37 This involves locating the chamber wall on the basis of a minimum detector output observed for one of the reference laser beams as it passes the glass/sample boundary. The measured cell height (1.04 mm, see Figure 4a) was used to calculate the depth gauge settings corresponding to the chamber walls, midpoint, and stationary levels. Automated Electrophoresis Measurements. In keeping with standard laboratory procedure, DELSA chambers were rinsed with E-Pure water and stored dry when not in use. Uncoated DELSA inserts were cleaned by cold soaking in 2% Micro38 (1 h, 25 °C), followed by light scrubbing of the capillary channel with “floss” provided in the instrument service kit. The instrument was operated in constant current mode set at 0.5-0.7 mA for 7.5 and 10 mM, 3.5 mA for 100 mM, and in constant voltage mode for lower ionic strengths, i.e., 10 V at 1 mM and 15 V at ∼0 mM. Measurements were typically collected at the center-axis top stationary level and the bottom stationary level positions (Figure 2) and then alternatively along the center-axis (the x-axis in Figure 1) and in the zones near the top and bottom walls, progressing from the walls toward the center of the chamber. The resulting two-dimensional (position versus flow) parabolas were used to obtain an extrapolated value for flow at the chamber wall for the DELSA inserts (e.g., Figures 3 and 4). In operation, the DELSA chamber was filled with the sample medium, the set of data was collected, and then the chamber was rinsed with 10 or 20 mL of the next medium, and the process was repeated. Measurements were collected at 25 ( 0.5 °C for 30-60 s at each depth setting, where the field was reversed every 3 s with an “on time” of 2.5 s and an “off time” of 0.5 s. One sample analysis yielded a mobility distribution for each of the four scattering angles. The region of the frequency-mobility spectrum containing the mobility profiles is marked for statistical analysis, and the DELSA software computed a mean and standard deviation for the electrophoretic mobility. For particle populations which are monodisperse with regard to their electrophoretic mobilities, the means should be the same for each scatter angle. Unless otherwise noted, a mean was computed from the four means associated with each of four scattering angles and expressed as a mean whose standard deviation represents the standard error of the mean. Center-axis top and bottom stationary level measurements were variously repeated in order to test for the time-dependent changes common to coating layers desorption. Rapid alteration in particle mobilities, due to readsorption of desorbed coating at particle surfaces, was also taken as evidence of coating loss.15 To assess DELSA 440 (38) Manske, P. L.; Stimpfel, T. M.; Gershey, G. L. J. Chem. Educ. 1990, 67, A280-A282.
Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
2271
experiments involving standard test medium and particles were undertaken between studies involving the effects of various pH and ionic strength media on electroosmosis. ELECTROPHORESIS THEORY AND MODELING CONSIDERATIONS Cylindrical and Rectangular Chambers. Application of an electric field to a suspension of charged particles contained in a closed cylindrical chamber with a charged wall results in electrophoresis of the particles and electroosmotic flow of the suspending medium. Experimental measurements of particle velocity results in an observed velocity, V, which is subject to error, as is the resulting calculated electrophoretic mobility, U.1,3,15,20 The observed velocity, V, of a particle in a cylindrical tube is the sum of the electrophoretic velocity of the particle, Vp, and the velocity of the suspending medium, Vsr due to electroosmosis at the measurement location distance, r, from the tube center:
V ) Vp + Vsr
(1)
Dividing all terms in eq 1 by the electrical field strength, x, gives the relationship in terms of electrophoretic mobility:
U ) Up + Usr
(2)
Bangham et al.39 have shown for cylindrical tubes that the observed velocity of the particle is related to its distance, r, from the axis of the tube by the expression
V ) Vp + Vs[2r2/R2 - 1]
Figure 4. Electroosmosis flow parabolas (a) and detail thereof (b) in an uncoated (open symbols) and PEG 8000-PEI coated (solid symbols) DELSA 440 chamber as indicated by PSL microsphere mobility in 100 (squares), 10 (circles), and 1 mM (triangles) NaCl solutions at 25 °C. The abscissa relates to the x-axis in Figure 1.
coating desorption, two analogous studies were performed. First, chamber electroosmosis was monitored for change in relation to time and exposure to various test media. In this, the chamber was first rinsed with a “standard” medium (100 mM NaCl, pH 7), and particle electrophoretic mobility was determined at “top” and “bottom” x-axis stationary levels, as well as at the midpoint of the chamber. Subtraction of the mean mobility of the test particle at the two stationary levels from that observed at the chamber midpoint gives an estimate for -cUeo, where the value of the coefficient, c, depends on the geometry of the sample chamber. For cylindrical chambers, c ) 1, while for rectangular chambers, as in the DELSA 440, c < 1, with values in the study ranging from 0.83 to 0.90, where Ueo was obtained by the extrapolation method using eq 4 (see below). To establish whether electroosmosis changed reversibly upon exposure to various test media, 2272 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
(3)
where Vs is the fluid velocity adjacent to the tube wall (taken to be equivalent to electroosmotic velocity related to electroosmosis, Veo) and R is the radius of the tube. Solution of flow eq 3 shows that, at a distance r ) 0.707R from the tube axis, there is a “stationary level” of no net flow. Noncylindrical chamber geometries have been treated by many authors, including Lane and White,40 Abramson et al.,41 Seaman,1 Doren et al.,42 and, more recently, Burns.20 In general, the applicable considerations are similar to those for cylindrical capillaries. Approximations used to describe the fluid flow parabola in the central chamber axis of the rectangular chamber typically assume an aspect ratio (capillary width to depth) > 20. This allows the assumption that sidewall effects are negligible, so that a second-order polynomial can be used describe the fluid flow parabola. For several decades, this aspect ratio has been a maxim for expectations of the accuracy obtainable from rectangular-chambered devices.1,42 In the present treatment, exact solutions to the hydrodynamic equations describing fluid flow in the rectangular chamber in the general case are considered.20 (39) Bangham, A. D.; Flemans, R.; Heard, D. H.; Seaman, G. V. F. Nature 1958, 182, 642-644. (40) Lane, T. B.; White, P. Philos. Mag. 1937, 23, 824-828. (41) Abramson, H. A.; Moyer, L. S.; Gorin, M. H. Electrophoresis of Proteins and the Chemistry of Cell Surfaces; Reinhold Publishing Corp.: New York, 1942; p 341. (42) Doren, A.; Lemaitre, J.; Rouxhet, P. G. J. Colloid Interface Sci. 1989, 130, 146-156.
Propagation of Errors Due to Electroosmosis. In theory, electrophoretic mobility measurements which are made at the calculated stationary level are not subject to error as a result of fluid flow. However, these levels of “null” flow are infinitesimally small, and, in practice, mobility estimates are erroneous as a result of (a) the finite size of the particles which cannot be contained in an infinitely thin stationary level; (b) focusing errors at the stationary level, i.e., a requirement for appropriate optical corrections to rectify the effects of refraction and aberration, depth of focus, and shape and size of focal field relative to the radius of curvature of the stationary level; (c) heterogeneous distribution of charge on the tube wall (inherent or acquired from sample suspensions) resulting in a shift in location of the stationary level; (d) Brownian motion and sedimentation of the particle; and (e) thermal convection arising from Joule heating and heat transfer out of the chamber. The magnitude of errors in the electrophoretic velocity as a result of fluid flow may be estimated from differentiated forms of equations describing fluid flow in the chamber. The hydrodynamics of fluid flow in rectangular chambers, including chambers with wall surface charge-associated flow asymmetries, can be described by solutions to the Navier-Stokes equation for steady laminar flow, with boundary values defined by the chamber geometry. Burns recently derived equations to describe the hydrodynamics of rectangular chambers for the general case where electroosmosis may vary at upper, lower, and sidewall chamber surfaces.20 In the present study, these equations were modified to analyze propagation of error due to both focusing errors and chamber surface asymmetries. Particle mobility U at a location (x,y) in rectangular electrophoresis chamber in the scheme of Figure 1 may be given by
U(x,y) ) Ueof(x,y) + Up
noted in Figure 2). The magnitude of errors in the electrophoretic velocity as a result of fluid flow may be estimated from the differentiated form of eq 4. By evaluating the propagation of random error at the stationary levels due to electroosmosis and focusing error, we can express the uncertainty in the mobility measurement in terms of the uncertainty in the location of x (σx) and in the location of y (σy) by
σU2 )
K)
π χ)
32a2 π3
∞
∑
n)0
5
∑
(-1)n+1
n)0(2n
+ 1)
(-1)n+1 (2n + 1)3
cosh
cos
[
[
5
tanh
[
(5)
]
(2n + 1)π b 2a
]
(2n + 1)π (y - b) × 2a
] [
2
(8)
y
[(∂x∂f ) s + (∂y∂f ) s ] 2 2 x
2 2 1/2 y
(9)
If the uncertainty in y is the same as the uncertainty in x, then eq 9 may be rewritten:
[(∂x∂f ) + (∂y∂f ) ]
sU ) Ueo
2
2 1/2
(10)
sx
Equation 10 indicates that random error due to focusing errors is directly proportional to electroosmotic fluid mobility at the walls. Thus, a reduction in electroosmosis will result in a corresponding decrease in random error. From eq 10, the relative random error due to electroosmosis at the stationary levels can be given by
(4)
24ab (x2 - a2 - χ) + 1 6K + 16a3b ∞
2
2
x
sU ) Ueo
where
512a4
2
or, in terms of estimated error s and eq 4,
sr )
f(x,y) )
(∂U∂x ) σ + (∂U∂y ) σ
(6)
]
(2n + 1)π (2n + 1)π x sech b (7) 2a 2a
for Ueo, the electroosmotic fluid mobility at the chamber walls, and Up, the intrinsic electrophoretic mobility of the particle.20 For the DELSA 440, the aspect ratio (b/a) is 3. In practice, electrophoretic mobility determinations are taken at “stationary levels”, where f(x,y) ) 0. Figure 2 shows the relative location of these stationary levels for a rectangular chamber with an aspect ratio of 3 in the scheme of Figure 1. In the present study, and as is common with the DELSA 440, measurements were taken at the “top” and “bottom” stationary levels in the vertical plane (center axis) of symmetry, where y/2b ) 0.5 (as
sU ) sxUeo
[(∂x∂f ) + (∂y∂f ) ] 2
2 1/2
(11)
In earlier work, Burns derived equations for the hydrodynamics of the rectangular chamber, where electroosmosis may vary at the upper, lower, and sidewall chamber surfaces.20 This provides an opportunity to address herein the systematic errors associated with an asymmetry in respect to electroosmosis in the chamber. If the electroosmosis at the lower chamber wall is different than at the upper wall or sidewalls, we can represent the electroosmosis at the lower wall as Ueo(1 + A), where Ueo is electroosmosis at the upper wall and sidewalls, and A is the degree of asymmetry. It can be shown20 that the particle mobility in the chamber may then be given by
U(x,y) ) Ueo[f(x,y) + Ag(x,y)] + Up
(12)
where
g(x,y) )
x - χ′ 1 - χ′′ 12ab - 3K′ 2 (x - a2 - χ) + + (13) 3 2a 2 6K + 16a b
K′ ) -
64a2 π3
∞
∑
(-1)n+1
n)0(2n
+ 1)3
tanh
[
(2n + 1)π b 2a
]
Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
(14) 2273
χ′ ) -
2a
∞
∑
(-1)n+1
π n)0 n + 1
cosh
[ [
sin ∞
(-1)n+1
[
] ] [ ] ] [
(n + 1)π (y - b) × a
Table 1. PEG Coating Control of Electroosmosisa
]
(n + 1)π (n + 1)π x sech b (15) a a
(2n + 1)π cosh (y - b) × χ′′ ) πn)0 2n + 1 2a 4
∑
cos
[
]
Since f(x,y) ) 0 at the theoretical stationary level, assuming no asymmetry, the systematic error introduced by asymmetry can be described by
(17)
This equation shows that the systematic error introduced by asymmetries with respect to electroosmosis is directly proportional to both electroosmosis and the degree of asymmetry. A reduction in either correspondingly decreases the systematic error. A relative systematic error can now be defined with respect to the location of the stationary level (x,y) as
∆Ur )
∆U ) g(x,y) UeoA
(18)
The random error (in the case of asymmetries with respect to electroosmosis) comes from the total differential of eq 12, which yields a relative random error analogous to eq 11.
sr )
sU ∂g 2 ∂g ∂f ∂f ) + +A +A sxUeo ∂x ∂x ∂y ∂y
[(
) (
)]
2 1/2
(19)
The practical significance of these results is discussed at the end of the next section. RESULTS AND DISCUSSION The present study was prompted by a desire to use both modern coating technology and hydrodynamic modeling to understand and control surface phenomena which adversely affect the analytical use of automated microelectrophoresis apparatus for biomedical and other tests (see the introduction). The DELSA 440 apparatus was chosen as a representative commercial apparatus whose chamber aspect ratio of 3 (Figure 1) may encourage significant error when particle mobilities are measured in normal fashionsalong the x-axis (Figure 1) at stationary flow level locations corresponding to a y-axis center-line (Figure 2). As a control, quartz capillaries were coated and electrokinetically characterized, since their electrokinetic behavior and its relation to coating performance was previously documented.9,14-18 Coating Control of Electroosmosis. Two major tenets of this study were that (a) electroosmosis has a large influence over the accuracy and precision of the DELSA sample chamber and (b) electroosmosis can be controlled via the use of neutral polymer surface treatments, represented by PEG-PEI coatings. To assess 2274 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
sample medium 7.5 mM NaCl, pH 2 7.5 mM NaCl, pH 6 7.5 mM NaCl, pH 11
(2n + 1)π (2n + 1)π x sech b (16) 2a 2a
∆U ) U - Up ) UeoAg(x,y)
model quartz capillary
DELSA 440 silica insert
Ueo Ueo % % uncoated coatedb ∆ uncoated coatedb ∆ 0.54 3.24 8.20
-0.46 0.14 1.44
na 96 82
0.15 2.33 8.25
-0.20 0.85 1.81
na 64 78
a Electroosmotic mobilities expressed in (µm‚cm‚V-1‚s-1). b PEGPEI coating III of di-SC-PEG 8000 reacted with preadsorbed PEI, followed by glutaraldehyde cross-linking. Similar results were initially seen with coatings II and III (see Experimental Section).
coating effectiveness, standard particle mobilities were determined at various distances from the walls of the sample chamberssacross 2.00-mm-diameter capillaries or along the 1.04-mm DELSA chamber x-axis at the y-axis center line (Figures 1 and 2, see also Experimental Section). This provided flow parabola profiles (Figures 3 and 4) of diameter or x-axis position versus observed particle mobility, i.e., particle plus fluid mobilities. Such parabolic flow profiles occur in the sealed chambers due to wall electroosmosis being compensated by a return flow down the center of the chamber. Only at “stationary levels”, where electroosmotic and compensatory flows cancel (Figure 2), is particle mobility independent of electroosmosis. The resulting parabolas (Figures 3 and 4) were used to calculate the expected mobility at the wall of the chamber, from which the known electrophoretic mobility of the suspended particle sample was subtracted to yield a value for the electroosmotic mobility, i.e., fluid velocity per unit of field strength. This mobility is characteristic of the average chamber surface charge without dependence on chamber geometry. Particle mobilities were measured at predetermined stationary flow levels. The levels correspond to 0.707R in the capillaries (Figure 3a,b) and approximate the vertical lines shown in Figures 3c,d and 4. Stationary level alteration in particle mobility with media pH or ionic strength is related to alteration in particle surface charge and ζ potential.17,18 Table 1 and Figures 3 and 4 present results for the PEG 8000PEI two-step coating (III) stabilized by glutaraldehyde crosslinking (see Experimental Section). The figures illustrate data related to particle mobility versus measured sample position in relation to the 2 mm capillary diameter (Figure 3a,b) or DELSA chamber 1.040-mm x-axis (Figures 3c,d and 4). Similar, though somewhat less dramatic, results were seen for the other PEGPEI coatings described in the Experimental Section (data not shown). All three coatings were initially able to maintain quartz capillary and DELSA chamber electroosmosis at low levels over a broad range of pH (2-11) and ionic strength (1-100 mM). (For examples, see Table 1 and Figures 3 and 4.) Quartz capillary results similar to those shown in Figure 3a,b, were presented and discussed previously.9,14-16 The quartz surface appears to be composed of a heterogeneous mixture of variously interacting silanol groups which give rise to a steady increase in negative surface charge and electroosmosis from pH 2 (where most surface silanol groups are protonated and the surface exhibits little negative character) to pH 11 (where most silanols exist in negatively charged siloxy form). Electroosmosis is very noticeable over the range pH 6-11. Under the same 7.5 mM NaCl
conditions, adsorbing PEI to the surface15 changes electroosmosis to approximately -4.0 µm‚cm‚V-1‚s-1 from pH 2 to 7, whereupon it increases with pH up to +4.0 µm‚cm‚V-1‚s-1 at pH 11. The latter occurs as the positive surface charge, related to PEI amino groups, becomes dominated by the increasing surface concentration of siloxy groups (not shown). Grafting succinimidyl carbonate or epoxide-activated PEG polymers to preadsorbed PEI greatly reduces the alteration of electroosmosis with pH. At low pH, the PEG-PEI coated quartz exhibits a small positive surface charge (related to underlying PEI amines), and at high pH it exhibits a small negative surface charge, with positive electroosmosis, related to underlying siloxy groups.15 Generally similar electroosmosis versus pH behavior was exhibited in the present study by capillaries or DELSA 440 chambers grafted with “two-step glutaraldehyde cross-linked” PEG-PEI coatings and analogous “one-step” adsorbed coatings (data not shown). Figure 3a,b indicates 7.5 mM solution flow parabolas of particle mobility versus capillary position. Electroosmosis is much more pronounced as pH increases, especially from pH 6 to 11; however, the PEG-PEI coating reduces it by approximately 90% over this pH range. Figure 3c,d indicates the ability of a PEG-PEI coating to maintain electroosmosis at relatively low levels in Spectrosil-based DELSA chambers. Uncoated chambers exhibited parabolas similar to those exhibited by control capillaries. PEG-PEI (coating III)-treated DELSA chambers displayed ∼70% reduction in electroosmosis from pH 6 to 11 (Table 1). DELSA chamber results are similar to those for quartz capillaries, although, as might be expected, (a) uncoated chambers displayed slight differences due to material and production history and (b) coatings performed slightly better in the capillaries for which they were previously optimized. Figure 4 indicates the effect of ionic strength (1-100 mM NaCl, pH 7) on the ability of the two-step PEG 8000-PEI coating (III) to control electroosmosis in DELSA chambers. On going from 100 to 1 mM, there is a pronounced increase in electroosmosis, as the charge on the chamber surface becomes less shielded by background electrolyte, i.e., double-layer expansion.2 The ability of the PEG coating to reduce electroosmosis is somewhat compromised, as the double layer expands in relation to polymer layer thickness15,16 (see also ref 25). When altering ionic strength from 100 to 1 mM at pH 7.0, the reduction in electroosmosis went from 70% to 40% with coating I, from 50% to 40% with coating II, and, as shown in Figure 4, from 80% to 60% for coating III. Control of Nonspecific Adsorption and Wetting. Adsorption and wetting phenomena present challenging optical and sample handling problems when adapting apparatus to the rapid assay of numerous samples. Particles or air bubbles that adsorb at the corners of DELSA 440 chambers often defy removal, short of rinsing the chamber with detergent solution or solvents such as acetone. The authors previously demonstrated that PEG coatings that provide significant control over electroosmosis typically exhibit similarly positive effects on nonspecific adsorption and wetting.14,17-19 In the present study, PEG-PEI coatings significantly reduced adsorption of PSL particles to chamber surfaces and enhanced chamber wetting. The latter eased chamber filling and reduced wall localization of bubbles. Research by the authors (see above references) and collaborators such as Holmberg et al.30,33 and Malmsten et al.25,26 have demonstrated
that PEG-PEI coatings reduce protein adsorption at a variety of surfaces. Coating Stability. Electrophoresis chamber coating stability has long been recognized as a major concern.8 Chamber wall charge properties can be dramatically affected by adsorption/ desorption of ions, proteins, polymers, or particles. This may affect chamber wall surface charge symmetry. Coating desorption may also alter apparatus operating parameters and (upon readsorption on standard particles) control particle mobilities.8,9,15 Previous studies, involving monitoring PSL particle mobility and electroosmosis in quartz capillaries, indicated that the two-step, cross-linked PEG 8000-PEI (type III) coating was reasonably stable. PEG 5000-PEI (II) coating was somewhat stable, whereas the PEG 3400 (I) coating appeared relatively unstable, especially at pH 2, where lack of appreciable surface siloxy groups promotes desorption of the underlying PEI.15 To assess coating desorption in the DELSA 440 chamber, electroosmosis was monitored for change in relation to time and exposure to various test media. In addition, standard particle mobilities were monitored for changes related to adsorption of desorbed wall coating17,18 (see Experimental Section). DELSA chamber results again mimicked those reported previously for quartz capillaries. Under the influence of surface shear forces related to experiments involving electrophoresis and electroosmosis, PEG-PEI coatings I and II began to desorb after 1 h of exposure to pH 2 solution. Over 1 h in 7.5 mM solution of pH 2, desorption of coating I caused PSL microsphere mobility (∼5.0 µm‚cm‚V-1‚s-1) to decrease to ∼0 µm‚cm‚V-1‚s-1 at the upper level and -4.6 µm‚cm‚V-1‚s-1 at the lower level. This was interpreted as the result of PEG-PEI preferentially desorbing from the chamber top and bottom walls and adsorbing onto nearby particles, which settled in a top-to-bottom gradient through the stationary levels. Mobility tests for PSL particles in 10 mM NaCl at pH 7, interspersed with short-term (40 s) chamber exposure to 100 mM, pH 2 and 11 media indicated that such exposure did not affect the cross-linked PEG-PEI coating III (Figures 3 and 4). However, over a 2-month period, repeated use and drying between runs slowly resulted in complete loss of the coating. Desirable properties for any coating are highly dependent on individual applications and operating conditions, e.g., chamber cleaning, wet or dry storage, operating temperature, medium or solvent composition, pH, ionic strength, and particles to be tested. Many biological tests are conducted under relatively mild conditions, where adsorbed PEG-PEI coatings, which can be applied in situ and are relatively stable in neutral (as opposed to acidic) solutions, may function adequately, especially if further stabilized via cross-linking. Other applications may call for more resilient covalent coatings. Emoto et al. recently reported monomethoxyPEG-epoxide coatings which can be applied in aqueous solution to quartz surfaces prereacted with aminopropylsilane in toluene and appear to be capable of withstanding 3 weeks at 25 °C in 0.5 M salt at pH 4-11.43 While such coatings are promising for replaceable chambers, their grafting chemistry may be limiting in other applications.16,43 The authors are researching covalent, one-step PEG-silane and other covalent coatings which can be applied in situ to a variety of surfaces under relatively mild, aqueous conditions (manuscript in preparation). (43) Emoto, K.; Harris, J. M.; Van Alstine, J. M. Langmuir, in press.
Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
2275
Table 2. Stationary Level Mobility Error Estimates versus DELSA Laser Beam Widtha 10 µm related mobility 50 µm related mobility (µm • cm • V-1 • s-1) (µm • cm • V-1 • s-1)
Table 3. Mean Standard Deviations in DELSA 440 34.2° Mobility Distributions in Uncoated and PEG-Coated Chambersa mean of SD ( sd (no.) (µm‚cm‚V-1‚s-1)
medium
uncoated
coated
uncoated
coated
medium (Hz)
uncoated
coatedb
distilled H2O 1.0 mM NaCl, pH 7 10.0 mM NaCl, pH 7 100.0 mM NaCl, pH 7 7.5 mM NaCl, pH 2 7.5 mM NaCl, pH 6 7.5 mM NaCl, pH 11
0.27 0.16 0.10 0.05 0.01 0.06 0.21
nd 0.046 0.024 0.016 0.005 0.022 0.046
1.32 0.80 0.49 0.27 0.02 0.30 1.05
nd 0.23 0.12 0.08 0.03 0.11 0.23
1 mM NaCl, pH 7 (500) 10 mM NaCl, pH 7 (500) 100 mM NaCl, pH 7 (250)
0.510 ( 0.038 (6) 0.548 ( 0.058 (4) 0.765 ( 0.067 (4)
0.395 ( 0.073 (4) 0.448 ( 0.014 (2) 0.628 ( 0.052 (4)
a For native and PEG (coating III)-coated DELSA 440 chambers (see text).
Coating Related Improvement in Accuracy. The gain in accuracy and precision related to coating-induced reduction in electroosmosis can be substantial. In evaluating such gain, one must account for two types of focusing errors which commonly arise from electroosmotic contributions to measurements at the stationary level in the DELSA 440. The first represents the “probable” error in establishing the position of the wall and locating the stationary level. For the DELSA 440, the probable locating error is about 10 µm, since the various micrometer gauges used are accurate to about 5 µm. The second error arises from the depth of the region through which particles are illuminated by the laser for measurement, i.e., the width of the laser beam in the DELSA (or focused area in optical units). In the DELSA 440, laser beam width is a matter of optical system adjustment, but the nominal setting is listed as 50 µm. While setting error will produce “random” errors in the mean determined mobility of the sample, the beam width produces “systematic” errors which broadened mobility distributions. Figure 4b details the effect of electroosmosis on the alteration of particle mobility with distance from the stationary level, i.e., the slope of the flow parabolas. Over a wide range of electroosmosis, induced by varying ionic strength from 1 to 100 mM, coating-related reductions in electroosmosis reduce error associated with imprecise “setting” in terms of not determining a particle’s mobility exactly at the stationary level. The PEG coatings should increase setting tolerances and the fraction of sample particles available for accurate mobility measurement. Table 2 presents estimates of the magnitude of errors in observed electrophoretic mobility mobility (sU from eq 10) for the above two types of error, based on representative data for various media at pH 2-11 and 1-100 mM. Assuming the 70% reduction in electroosmosis seen with coating III, the values listed in Table 2 are proportional to Ueo and serve as (a) useful indicators of the relative magnitude of Ueo for the listed media conditions and (b) guides to the probable magnitude of errors under typical experimental conditions. Since the relative error in the mobility of a particle population is sU/Up, the Table 2 entries for the 10-µm setting errors can also be regarded as probable fractional (random setting) errors for the mobility of a particle population of mean mobility 1. The setting errors associated with uncoated chambers is substantial at moderate ionic strengths and neutral to alkaline pH’s. PEG-PEI coating substantially reduces such errors. With regard to systematic errors, three primary determinants of the breadth of the electrophoretic mobility distributions are 2276 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
a
PEG-PEI coating III (see text).
(a) electrophoretic mobility variation within the particle population; (b) Brownian motion altering the electrophoretic velocity of particles, especially those smaller than 1 µm; and (c) optically sampling of a region experiencing both negative and positive (electroosmotic and compensatory) flows. Electroosmosis and Brownian motion decrease the ability of an instrument to resolve real variations in sample electrophoretic mobility. It can be seen from the estimation of sU for a depth of 50 µm (Table 2) that significant broadening of electrophoretic mobility distributions is anticipated for uncoated capillaries at neutral to alkaline pH and low to moderate ionic strengths. Coatings can substantially reduce mobility distribution broadening, particularly at alkaline pH and lower ionic strengths. The significance of such reductions will depend on other factors, such as particle size and heterogeneity in electrophoretic mobility. However it is clear that particle electrophoresis methods requiring precision benefit from control of electroosmosis. Table 3 provides a comparison of averaged standard deviations for DELSA mobility distributions obtained at 34° at the stationary level in the uncoated insert and the coated insert assessed in Table 2. The test particle was polystyrene latex with a diameter of 0.865 µm, which is in the size range where random movement makes significant contributions to the mobility determination. As expected, consistent reductions are observed in the standard deviation of the mobility distributions over a broad range of electroosmosis (1-100 mM NaCl). Chamber Geometry, Electroosmotic Asymmetry, and Measurement Accuracy. For several decades, the hydrodynamic equations related to the location of the stationary levels in cylindrical chambers, or rectangular chambers where the aspect ratio of the capillary width to depth is g20, have been a maxim for expectations of the accuracy obtainable from analytical microelectrophoresis apparatus (for discussion, see ref 20). However the desire to obtain such an aspect ratio is often compromised in the interest of chamber engineering, optics, or manufacture. The DELSA 440 used in the present studies has a b/a aspect ratio of 3 (Figure 1), plus a nominal x-axis chamber depth of 1 mm, resulting in steep electroosmotic flow profiles (Figures 3 and 4) and associated accuracy errors (see above). Similar flow profiles and problems are expected for many automated electrophoretic apparatus. DELSA stationary level mobility data are typically taken as an average of measurements made at the upper and lower stationary levels, discussed above (Figure 2). Throughout this study, uncoated DELSA chambers exhibited 10-15% mobility differences between the upper and lower stationary levels. Use of coatings substantially reduced accuracy errors due to electroosmosis (Tables 1-3), but small differences (4% or less) persisted between
mobilities measured at the two levels. Such differences may be due to chamber wall asymmetry. Asymmetries in electroosmosis related to differences in surface charge character of the walls which help form the DELSA chamber may lead to flow parabolas asymmetries, which do not allow stationary levels to be readily deduced from the stated chamber geometry. Lane and White40 analyzed asymmetries of flow profiles in rectangular sample chambers and found that the profiles typically remained parabolic, although they shifted from the center of the chamber. They ascribed the asymmetries to electroosmosis rather than to convection, which would have produced higher order profiles, or to particle sedimentation, which was insignificant for the sols studied. They noted that substantial errors due to such asymmetry, which they speculated arose from differences in the charge properties of the top and bottom chamber walls, could be significantly reduced by obtaining an average electrophoretic mobility at upper and lower stationary levels. The behavior noted by Lane and White40 matches that observed for the DELSA chamber, with a symmetrical flow parabola shifted in the vertical axis of the insert such that observed mobilities at the upper and lower stationary levels reproducibly differ. The belief that such behavior arises from differences in the charge properties of the top and bottom capillary walls is plausible, since the DELSA insert is fabricated from four pieces of Spectrosil, whose surface properties may vary as a result of slightly different manufacturing histories. Such asymmetry might be related to differences in average surface charge density for the clean surface, or in aging, adsorption, and other timedependent processes. Similar problems may be associated with other rectangular-chambered electrophoresis devices. Enhanced Hydrodynamic ModelingsChamber Geometry, Asymmetry, and Accuracy. To further investigate the impact of chamber geometry and wall charge asymmetry on accuracy, the DELSA chamber was mathematically analyzed in relation to solutions to the Navier-Stokes equation for steady laminar flow, with boundary values defined by the chamber geometry. Burns recently derived equations to describe the hydrodynamics of rectangular chambers for the general case where electroosmosis may vary at upper, lower, and sidewall chamber surfaces.20 These equations were adapted to investigate propagation of error due to both focus setting and chamber surface asymmetries (see above). Figure 2 indicates the location of stationary levels in a rectangular chamber with an aspect ratio of 3. Typical sampling locations are in the vertical plane of symmetry of the chamber (y/2b ) 0.5) and one atypical location (y/2b ) 0.1). Equation 9 indicates that, as shown experimentally, random error due to setting errors is directly proportional to electroosmotic fluid mobility at the walls. Thus, a reduction in electroosmosis is expected to result in a corresponding decrease in random error. Figure 5 shows a plot of this relative random error (eq 11) as a function of the location of the stationary level. The relative random error due to electroosmosis is greatest at the stationary levels in the vertical plane of symmetry of the chamber (y/2b ) 0.5), where particle mobility measurements are commonly made. The relative random error is the least nearer the sidewalls, at y/2b ) 0.1. This suggests consideration be given to measuring particle mobility at the stationary level corresponding to y/2b ) 0.1 (Figure 2).
Figure 5. Relative random error due to electroosmosis as a function of location of stationary level in a symmetric rectangular electrophoresis chamber with an aspect ratio of 3.
Figure 6. Relative systematic error introduced by an asymmetry with respect to electroosmosis as a function of location of the “stationary level” in a rectangular chamber with an aspect ratio of 3. The solid line corresponds stationary levels in the upper chamber (+x direction), and the dashed line corresponds to stationary levels in the lower chamber (-x direction).
As noted above, asymmetries in wall charge properties are translated into asymmetries in flow profiles so that the stationary levels are not located at theoretical positions.40 Figure 6 shows such relative systematic error (eq 18) with respect to the theoretical location of the stationary level in the symmetric rectangular chamber. There is a stationary level position at y/2b ) 0.1 where this type of systematic error is zero. This is the same level where random error is the least in the symmetric chamber. Figure 6 also indicates that systematic error is quite significant at the stationary levels in the vertical plane of symmetry (y/2b ) 0.5), where particle mobility measurements are commonly made. Returning to Lane and White,40 Figure 7 indicates the relative systematic error as a result of averaging at the stationary levels. There is significant systematic error when using the method of averaging in the vertical plane of symmetry (∆Ur ) 0.06). This type of error does not exist for particle mobility measurement at the stationary level located at x/a ) 0.367, y/2b ) 0.1. Equation 17 suggests that, with respect to electroosmosis, the systematic error introduced by asymmetries is directly proportional to both electroosmosis and the degree of asymmetry. Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
2277
Figure 7. Relative systematic error introduced when averaging at stationary levels as a function of location of the level when introduced by an asymmetry with respect to electroosmosis in a rectangular chamber with an aspect ratio of 3. (Corresponds to the sum of the dashed and solid lines of Figure 6.)
Figure 8. Relative random error as a function of the degree of asymmetry at the various stationary levels. Averaging at y/2b ) 0.5 corresponds to the result of averaging the stationary levels in the vertical plane of symmetry.
A reduction in either of these terms due to application of a uniform PEG coating is expected to correspondingly decrease the systematic error. When introducing an asymmetry, the relative random error (eq 19) is not directly proportional to the degree of asymmetry and, thus, must be presented as functions of both the location of the stationary level and the degree of asymmetry. Figure 8 shows relative random error as a function of the degree of asymmetry for several select locations of the stationary level; those in the vertical plane of symmetry and those where the systematic error was determined to be zero in the asymmetric chamber. Included also is the random error associated with averaging in the vertical plane of symmetry. It is clear that random error is the least at the stationary level, where the systematic error was zero (x/a ) 0.367, y/2b ) 0.1). Related Experimental Results. The DELSA apparatus and optical system are not designed to readily accommodate the optical sampling realignment necessary to test theoretical results related to measuring particle mobility nearer the sidewall. Nevertheless, attempts were made to compare DELSA 440 measurements of 2278 Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
standard particle mobilities at the normal vertical stationary level setting and y/2b settings of 0.5 compared to 0.1. No significant detector signal was obtained for the DELSA 34° detector at the latter setting. However, detector signals were obtained for all scattering angles at the complementary location of y/2b ) 0.9 (Figures 5-7). In partial vindication, results (not shown) indicated comparable average mobility determinations. However, the 0.9 setting was associated with larger standard deviation. This appeared to be due to larger variation in the mean mobility determinations associated with different detector angles when sampling at the 0.9 setting. Such differences may relate to unequal volumes of measurement zones sampled at the different angles. Although the results were encouraging, it was apparent that the present DELSA 440 design does not allow a fair evaluation of the enhanced accuracy obtainable by measuring at y/2b ) 0.1 or analogous off-center settings. Other apparatus, such as the device produced by Galai (Ramat Gabriel, Israel) may be more amenable to such studies. General Conclusions and Suggested Studies. Neutral, hydrophilic, nonfouling, polymer coatings exemplified by PEGPEI conjugates are able to control a variety of surface phenomena which adversely affect the practice and accuracy of analytical microelectrophoresis over a wide range of pH and ionic strength. Although coating stability and ease of application need to be enhanced, initial results are promising. Experimental results correspond with theoretical analysis with regard to the above plus the observation that (a) chamber wall electroosmosis asymmetry may be partially reduced via the use of coatings and (b) errors due to such asymmetry can be reduced by averaging mobilities taken at upper and lower stationary levels. Modeling results suggest that, for a chamber of aspect ratio 3, under a variety of operating conditions, a significant source of systematic error relates to measurements at stationary levels affected by chamber asymmetry, such as those denoted by y/2b ) 0.5. In the presence of wall asymmetry, random error is the least at the stationary level where the systematic error is zero (x/a ) 0.367, y/2b ) 0.1). Experimental verification of such findings can only be made using apparatus whose data gathering is not optically or mechanically biased in favor of one setting over another. Appreciation of the enhanced accuracy necessary for many applications of analytical microelectrophoresis may be gained from the Unsaturated Fatty Acid Electrophoretic Mobility Test for Multiple Sclerosis.44-46 This test, which involves determination of the electrophoretic mobility difference between serum-exposed blood cells or particles in the absence and presence of linoleic acid micelles, requires a precision of (0.1 µm‚cm‚V-1‚s-1.46,47 Similar accuracy is required by, or would aid, many other bioanalytical and bioseparation methods related to particle or cell electrophoresis.1,48 This includes an ASTM method involving use (44) Field, E. J.; Joyce, G. Neurol. Res. 1986, 8, 57-60. (45) Seaman, G. V. F.; Swank, R. L.; Tamblyn, C. H. Neurology 1984, 34, 547549. (46) Swank, R. L.; Vaden, I. A.; Leckband, A. J. Clin. Hemorheol. 1991, 11, 281293. (47) Zukoski, C. F., IV; Tamblyn, C. H.; Swank, R. L.; Seaman, G. V. F. In Cell Electrophoresis: Clinical Application and Methodology; Preece, A. W., Sabolovic, D., Eds.; North-Holland Biomedical Press: Amsterdam, 1979; pp 303-312. (48) Bauer, J. J. Chromatogr. 1986, 418, 359-383.
of the DELSA 440 to electrophoretically characterize proteins.49 Use of the coating and modeling techniques described above may improve the analytical performance of a variety of electrophoresis instruments. This encourages future efforts to extend the above coating and modeling research to different chamber materials, polymer coatings, samples, procedures, and instruments. ACKNOWLEDGMENT The authors thank Dr. Anne Shaver for aid with Rank apparatus measurements and Coulter Instruments for encourage(49) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 1992.
ment. This work was supported by grants from the Margaret W. and Herbert Hoover, Jr., Foundation, National Aeronautics and Space Administration, National Science Foundation, Naval Research Laboratory, and Swedish Natural Science Research Council. N.B. acknowledges personal support from The Foundation for Surface Chemistry, Sweden.
Received for review August 20, 1997. Accepted January 22, 1998. AC970913K
Analytical Chemistry, Vol. 70, No. 11, June 1, 1998
2279
