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Influence of Electrostatic Interactions on the Surface Adsorption of a Viral Protein Cage Peter A. Suci,†,⊥ Michael T. Klem,†,‡ Trevor Douglas,*,†,‡ and Mark Young*,†,§ Center for BioInspired Nanomaterials, Department of Chemistry & Biochemistry, Department of Plant Sciences, and Department of Microbiology, Montana State University, Bozeman, Montana 59717 Received January 25, 2005. In Final Form: May 3, 2005 The Cowpea chlorotic mottle virus (CCMV) provides a useful protein-cage architecture that can be used for the size- and shape-constrained chemistry of nanomaterials. The control of surface assembly is necessary for the realization of many applications of these nanoscale reaction vessels. Electrostatic interactions provide a useful (and reversible) method for controlled surface assembly. CCMV absorption behavior was studied on Formvar, bare Si, Formvar-coated Si, and Si modified by aminopropyltriethoxysilane (APS). Transmission electron microscopy (TEM), atomic force microscopy (AFM), and attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) were used to characterize the CCMV surface adsorption. Combined AFM and ATR-FTIR data indicated that the viral coverage on the modified surfaces was ∼84% of the jamming limit predicted by the random sequential adsorption (RSA) model. According to the ATRFTIR results, surface coverage was not increased at higher ionic strengths nor at a pH near the isoelectric point (pI) of the virus. The Langmuir model was used to provide a description of the kinetic absorption behavior.
Introduction Protein cages provide high-symmetry architectures, which have been used as spatially defined templates for the incorporation of ligands,1 peptides,2 nanoparticles,3 and drugs, utilizing both the interior and the exterior interfaces.4 These nanoscale reaction vessels have been also been used to initiate and constrain mineralization, resulting in monodisperse nanoparticles with applications in imaging,5 magnetic storage,6 and catalysis.7,8 Learning to manipulate the surface assembly of protein cages, including surface coverage and in-plane and lamellar order, is the first step in the realization of a new generation of functionalized surfaces. Applications for solid supports that are decorated with novel arrangements of supramolecular assemblies include solid-state nanodevices,9-11 sensors,12 and antifouling surfaces.13 A primary consideration in engineering the surface assembly of protein cages is the type of bond to promote †
Center for BioInspired Nanomaterials. Department of Chemistry & Biochemistry. § Department of Plant Sciences. ⊥ Department of Microbiology. ‡
(1) Wang, Q.; Kaltgrad, E.; Lin, T.; Johnson, J.; Finn, M. Chem. Biol. 2002, 9, 805. (2) Porta, C.; Spall, V.; Loveland, J.; Johnson, J.; Barker, P.; Lomonossoff, G. Virology 1994, 202, 949. (3) Douglas, T.; Young, M. Nature 1998, 393, 152. (4) Flenniken, M. L.; Liepold, L. O.; Crowley, B. E.; Willits, D. A.; Young, M. J.; Douglas, T. Chem. Commun. 2005, 447. (5) Bulte, J. W.; Douglas, T.; Mann, S.; Frankel, R. B.; Moskowitz, B. M.; Brooks, R. A.; Baumgarner, C. D.; Vymazal, J.; Strub, M. P.; Frank, J. A. J. Magn. Reson. Imaging. 1994, 4, 497. (6) Warne, B.; Kasyutich, O. I.; Mayes, E. L.; Wiggins, J. A. L.; Wong, K. K. W. IEEE Trans. Magn. 2000, 36, 3009. (7) Ensign, D.; Young, M.; Douglas, T. Inorg. Chem. 2004, 43, 3441. (8) Kim, I.; Hosein, H.-A.; Strongin, D. R.; Douglas, T. Chem. Mater. 2002, 14, 4874. (9) Dutta, A. K.; Ho, T.; Zhang, L.; Stroeve, P. Chem. Mater. 2000, 12, 1042. (10) Ghannoum, S.; Xin, Y.; Jaber, J.; Halaoui, L. I. Langmuir 2003, 19, 4804. (11) Lee, S.-M.; Jun, Y.-W.; Cho, S.-N.; Cheon, J. J. Am. Chem. Soc. 2002, 124, 11244. (12) Cai, Q.-Y.; Zellers, E. T. Anal. Chem. 2002, 74, 3533. (13) Nie, F.-Q.; Xu, Z.-K.; Huang, X.-J.; Ye, P.; Jian Wu, J. Langmuir 2003, 19, 9889.
between the surface and the protein. Ideally, one would like to be able to cater the nature of this interaction (covalent, electrostatic, hydrogen-bonding, stereospecific, etc.) to fit the application. A number of studies provide a starting point for this type of approach. Two-dimensional arrays of iron oxide-loaded ferritin have been demonstrated.14,15 The adsorption behavior of the tobacco mosaic virus (TMV) was examined for conditions that promoted van der Waals, hydrophilic, or covalent bonding.16 The potential of TMV to serve as a template for the nanopatterning of minerals on surfaces has been demonstrated.17 Cowpea chlorotic mottle virus (CCMV) and cowpea mosaic virus (CPMV) capsids were covalently bound to patterned gold templates using thiol chemistry.18,19 Interestingly, in-plane, self-induced, molecularscale pattern formation was observed when CPMV films were formed under conditions that allowed some mobility.20 Electrostatically bound vesicular stomatitis virus was shown to influence the orientation of underlying liquid crystalline phases.21 The role of electrostatic interactions in determining the adsorption behavior of the ferritin cage has been studied extensively.22 From a nanofabrication perspective, electrostatic interactions offer a set of potentially useful qualities. They are among the strongest bonds and are comparable in strength to covalent bonds.23 Electrostatic interactions (14) Yamashita, I. Thin Solid Films 2001, 393, 12. (15) Nagayama, K. Adv. Biophys. 1997, 34, 3. (16) Knez, M.; Sumser, M. P.; Bittner, A. M.; Wege, C.; Jeske, H.; Hoffmann, D. M. P.; Kuhnke, K.; Kern, K. Langmuir 2004, 20, 441. (17) Dujardin, E.; Peet, C.; Stubbs, G.; Culver, J. N.; Mann, S. Nano Lett. 2003, 3, 413. (18) Klem, M. T.; Willits, D.; Young, M.; Douglas, T. J. Am. Chem. Soc. 2003, 125, 10806. (19) Smith, J. C.; Lee, K.-B.; Wang, Q.; Finn, M. G.; Johnson, J. E.; Mrksich, M.; Mirkin, C. A. Nano Lett. 2003, 3, 883. (20) Fang, J.; Soto, C. M.; Lin, T.; Johnson, J. E.; Ratna, B. Langmuir 2002, 18, 308. (21) Espinoza, L. A.; Kate, T.; Schumann, R.; Luk, Y.-Y.; Israel B. A.; Abbott, N. L. Langmuir 2004, 20, 2375. (22) Johnson, C. A.; Yuan, Y.; Lenhoff, A. M. J. Colloid Interface Sci. 2000, 223, 261. (23) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992; pp 1-450.
10.1021/la050217c CCC: $30.25 © 2005 American Chemical Society Published on Web 08/16/2005
Surface Adsorption of a Viral Protein Cage
can be promoted without catalysts simply by regulating the charge of the cage and the surface; they are relatively long-range, on the order of 50 nm, and this range can be modulated by ionic strength; they can also be disrupted in some cases by altering the pH, which may be an advantage or a disadvantage, depending on the application. The interaction of proteins with surfaces is a potentially complex process that can induce large conformational changes leading, in some cases, to complete unfolding.24 For most applications, it would be optimal if protein cages behaved in a predictable manner in terms of their interaction with surfaces; that is, it would be ideal if they could be treated as simple inert particles (“hard” proteins) that retained their structural integrity upon encountering a surface. CCMV, an icosahedral plant virus that is ∼28 nm in diameter, has become a model system for the development of cage-based nanoengineering applications. Methods for the functionalization of CCMV through chemical means and for site-directed mutagenesis are well-developed.25,26 CCMV capsids have been used as a template for biomineralization.26 In addition, CCMV capsids exhibit reversible pH-dependent gating.3,27 The versatility and robust nature of this protein cage encourage efforts to fabricate surface-associated nanostructures. In this respect, two-dimensional arrays of symmetry-disrupted CCMV have been induced to form through covalent interaction with gold substrates.18 The objective of this study was to characterize CCMV adsorption behavior on charged surfaces to delineate issues involved in the electrostatic control of CCMV surface adsorption. Methods Transmission Electron Microscopy (TEM) Adsorption Protocol and Estimation of Surface Coverage. Formvarcoated grids were exposed to adsorbates sequentially for 1 min by placing a 5-µL drop on the grid and then wicking off the drop with filter paper. Solutions consisted of 1 mg/mL of polylysine (Sigma Corp., St. Louis, MO) in ultrapure water (18 MΩ) and 100 µL/mL of CCMV in buffer (either 10 mM sodium acetate or 10 mM sodium formate). All buffers were made with ultrapure water. Grids were stained with 2% uranyl acetate. CCMV counts were made by analyzing TEM images using Media Cybernetics Image-Pro Plus software (Media Cybernetics, Silver Spring, MD). The total pixel area of the virus-populated regions was determined by first convolving the background graininess using a low-pass filter and then setting a gray threshold value that outlined the populated regions. The number of viruses in each image was obtained as the product of this area and the mean viral density. The mean viral density was determined by counting the viruses in areas of known size that were contained within the viruspopulated regions. Atomic Force Microscopy (AFM) Adsorption Protocol and Estimation of Surface Coverage. Si (100) wafers (Virginia Semiconductor Inc., Fredericksburg, VA) were exposed to 20 µg/ mL of CCMV in 10 mM sodium acetate buffer (pH 4.8) for 50 min at room temperature. The wafers were rinsed by immersing them in 10 mM sodium acetate buffer (pH 4.8) for 3 min and then immersing them in environmental grade water (Fisher Scientific, Pittsburgh, PA) (pH 5.8) for 1 min to remove the salts. During the rinse steps, the wafer was gently displaced to disrupt the boundary layer. The surfaces remained completely wetted after the polylysine-coated and aminopropyltriethoxysilane (APS)modified Si wafers were withdrawn from the CCMV solution. (24) Lyklema, J.; Norde, W. Prog. Colloid Polym. Sci. 1996, 101, 9. (25) Gillitzer, E.; Willits, D.; Young, M.; Douglas, T. Chem. Commun. (Cambridge, U. K.). 2002, 2390. (26) Douglas, T.; Strable; E.; Willits, D.; Aitouchen, A.; Libera, M.; Young, M. Adv. Mater. 2002, 14, 415. (27) Speir, J. A.; Munshi, S.; Wang, G.; Baker, T. S.; Johnson, J. E. Structure 1995, 3, 63.
Langmuir, Vol. 21, No. 19, 2005 8687 Thus, the adlayer was not passed through the air-water interface during the rinse process. After the water rinse, the wafer was held vertically, and the edge was placed in contact with filter paper to drain off the large droplet of water that accumulated at the base. The wafer was subsequently placed horizontally on the filter paper, covered, and allowed to air-dry. After the wafer was placed on the filter paper, a thin layer of water ( B. For x ) 0 (i.e., at the surface) dC/dt was defined by the adsorption process (eq 4). The adsorption at the interface was modeled by an empirical generalized Langmuir process:28
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dθ ) kaC0(θ∞ - θ) - kdθ dt
(3)
dC0 ) kdθ dt
(4)
and
in which θ is the CCMV surface coverage, θ∞ is the surface coverage at a saturation determined empirically, ka and kd are rate constants for adsorption and desorption, respectively, and C0 is the concentration in the bulk phase at the interface (x ) 0) that was determined from eq 1. Commercially available software (AQUASIM, 2.0, Peter Reichert, Computer Systems Sciences Department, EAWAG, Switzerland) was used to simulate data curves and to provide estimates of kd and θ∞ by a leastsquares criterion optimization. Appropriate initial values for C and θ were used in eqs 1 and 3 for fitting data from the second step of the step-binding curves (20 µg/mL bulk CCMV). A number of expressions were used to generate the curves presented in the results section. The relationship between ka and θ that was predicted by the random sequential adsorption (RSA) model has been formulated in terms of a generalized Langmuir expression (in which the kd term vanishes because adsorption is constrained to be irreversible),28
dθ ) kaC0φ(θ) dt
(5)
in which
Figure 1. TEM micrographs of CCMV adsorbed to grid supports: (a) polylysine-coated Formvar, pH 4.8; (b) polylysinecoated Formvar, pH 2.8; (c) uncoated Formvar, pH 4.8; and (d) uncoated Formvar, pH 2.8. Scale bars are 500 nm. Table 1. CCMV Surface Coverage (TEM)
φ(θ) ≈ 1 - 4θ + 3.3079θ2 + 1.4069θ3
(6)
This approximation is considered accurate for θ < 0.35.28 Equation 5 was used to fit the data using AQUASIM to compute the residuals presented in the results. In this case, cσ was substituted for θ, in which σ represents the data, and c and ka were optimized (allowed to float) with C0 set arbitrarily to 1. The modified RSA model that incorporates the influence of lateral double-layer interactions between particles predicts an approximately linear relationship between the surface coverage and the inverse square root of the adsorption time.29 Thus, for this model,
θ(t) ≈ m(t-1/2)
(7)
in which t represents the number of simulation steps, and m is the slope of the curve generated by the model. From this, an expression similar to eq 5 can be obtained:
dθ 1 ) m2 (θ∞ - θ)3 dt 2
( )
(8)
Simulated Langmuir binding curves were generated from ka and kd using
Keq-1 ) Cb[(θ∞/θ) - 1]
(9)
in which Cb is the bulk concentration, and Keq is the equilibrium constant, which is related to ka and kd by
Keq ) ka/kd
(10)
Results The hypothesis that the adsorption behavior of CCMV onto charged surfaces is dominated by electrostatic interactions was examined using TEM, AFM, and ATRFTIR. A simple prediction is that, at a pH above the isoelectric point (pI), the virus should adsorb strongly to positively charged surfaces and absorb only weakly to negatively charged surfaces. The pI of the CCMV prepa(28) Schaaf, P.; Talbot, J. J. Chem. Phys. 1989, 91, 4401. (29) Adamczyk, Z.; Zembala, M.; Siwek B.; Warszynski, P. J. Colloid Interface Sci. 1990, 140, 123.
polylysa (pH 4.8)
polylysa (pH 2.8)
Formvar (pH 4.8)
Formvar (pH 2.8)
mean 1543 (143b) 192 (202) 86 (59) 628 (305) count/ field mean θc 0.231 (0.021) 0.029 (0.030) 0.013 (0.009) 0.094 (0.046) a Formvar coated with polylysine. b Standard deviation (five fields). c Fractional area coverage.
ration used in the adsorption experiments was determined by measuring the ζ potential for a range of pH (see Figure 1, Supporting Information). These data indicated that the pI of the assembled CCMV was approximately 3.8, which is consistent with previous studies.30,31 The adsorption of CCMV onto Formvar and polylysinecoated Formvar was initially studied using TEM (Figure 1, Table 1), which is a technique that is optimal for observing individual virus particles. At a pH above the pI (4.8), the surface coverage of the CCMV was substantially greater on the positively charged polylysine-coated surface (pKa approximately 10) than that on the uncoated Formvar. At a pH below the pI (2.8) this trend was reversed, suggesting that Formvar has a negative surface charge at this pH. The viruses tended to coalesce into relatively densely packed regions on the EM grid supports (Figure 1). The mean viral density in these regions was ∼70% of the maximum possible area surface coverage. CCMV interactions with Si and modified Si surfaces were examined using AFM and ATR-FTIR. It is wellknown that the surface of Si forms an oxide when exposed to air. X-ray photoelectron spectroscopy (XPS) results indicated that this overlayer was silica for the Si (100) wafers because the Si2p band consisted of one component with a maximum at 103 eV. The point of zero charge of silica has been characterized in numerous studies and lies between pH 2 and 4.32 The elemental composition of (30) Bancroft, J. B.; Heibert, E.; Rees, M. W.; Marham, R. Virology, 1968, 34, 224. (31) Rice, R. H.; Horst, J. Virology 1972, 49, 602. (32) Kosmulski, M. J. Colloid Interface Sci. 2002, 253, 77.
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Figure 2. AFM images of CCMV on solid supports (200 nm scale bar; Height data, 30 nm z-range): (a) polylysine-coated Si; (b) APS-modified Si; (c) APS-modified Si after rinsing at pH 2.8 (arrow indicates an adsorbed virus particle); and (d) APSmodified Si. Table 2. CCMV Surface Coverage (AFM) APSb
Sic
rinse (pH 2.8)d
377 (17e)
421 (127)
0f
0g
0.362 (0.016)
0.401 (0.122)
0
0
polylysa mean count/field mean θh a
Si coated with polylysine. b APS-modified Si. c Clean Si. d CCMV adsorbed to APS-modified Si followed by a rinse with buffer (pH 2.8). e Standard deviation. f No particles observed in six fields. g 1 particle observed in six fields. h Fractional area coverage.
the APS-modified Si that was determined by XPS was consistent with the presence of a monolayer of APS (Table 1, Supporting Information). At pH 4.8, Si was expected to present a negatively charged surface to an adjoining aqueous phase, whereas the polylysine-coated and APSmodified Si molecules were expected to be positively charged. Similar to the TEM results, the AFM results for modified Si indicated that the adsorption behavior of CCMV was primarily determined by electrostatic interactions. Selected AFM images are presented in Figure 2. At pH 4.8, the surface coverage of CCMV was much greater on the polylysine-coated and APS-modified Si than it was on clean Si, with the surface coverage being slightly less on the polylysine-coated Si than it was on the APS-modified Si (Table 2). In addition, AFM data indicated that essentially all of the bound CCMV was removed from the APSmodified Si by rinsing the Si at pH 2.8. This result is consistent with the control of adsorption behavior by electrostatic interactions because, on the basis of its pI, CCMV should have a positive surface charge at pH 2.8. Although nearly all virus particles were rinsed from the APS-modified Si at pH 2.8, the rinsed surface exhibited some features that indicated the presence of some surface contamination (compare Figure 2, panels c and d). To monitor the kinetics of CCMV absorption to Si, we used ATR-FTIR, which is a surface sensitive technique. For the Si-water interface, the evanescent field that samples the interfacial region has a penetration depth of 254 nm.33 The evanescent field extends over a relatively large lateral area (6 × 45 mm2) in this interfacial region.
Figure 3. Kinetics of CCMV adsorption and desorption measured by ATR-FTIR. (a,b) Step-binding curves performed serially at 10- (circles), 20 (squares), 50 (triangles) and 100 (spades) µg/mL bulk concentrations for (a) polylysine-coated Si (open symbols) and clean Si (shaded symbols) and for (b) APSmodified Si. (c,d) APS-modified Si: (c) rinsed at pH 4.8, followed by a rinse at pH 2.8 at 22 min and a rinse at pH 4.8 at 32 min; and (d) kinetics of binding onto preconditioned surfaces at 20 µg/mL.
Thus, ATR-FTIR samples a large population of virus particles that have entered the interfacial region. Although there is theoretically some contribution from the bulk protein to the IR signal, this contribution was negligible for the bulk concentrations used in these experiments. The area under the amide II band, which originates from the peptide linkages of the protein, was used to follow the adsorption kinetics.34 The adsorption behavior of CCMV was similar for polylysine-coated and APS-modified Si. Figure 3a,b are step-binding curves (step isotherms) for CCMV adsorption onto polylysine-coated Si (Figure 3a) and APS-modified Si (Figure 3b). To obtain the step-binding curve, the surface was exposed to a series of increasingly concentrated solutions of the adsorbate. The step-binding curve yielded the kinetics of adsorption for dilute bulk solutions and a good estimate of the surface coverage at saturation θ∞ for more concentrated bulk solutions. In Figure 3a, the data curve for clean Si is also presented. The adsorption onto clean Si was below the threshold of detection. Thus, ATRFTIR results were qualitatively similar to the results obtained using TEM and AFM. Note that the absence of any IR signal from the clean Si confirmed that the component of the signal originating from the virus in solution was below the threshold of detection, even at the highest bulk concentration (100 µg/mL). The data indicated that the binding sites became saturated during the exposure to this highest bulk concentration of CCMV for the two positively charged surfaces. Absorbed virus was removed from the modified Si surface by changing the charge of the virus via lowering the buffer pH to 2.8. Figure 3c shows the data curve obtained during a rinse of the surface with buffer at pH 4.8, followed by a rinse with buffer at pH 2.8, and finally another rinse with buffer at pH 4.8. The absence of any substantial decrease in the IR signal during the rinse at pH 4.8 indicated that the desorption rate (kd) was small or negligible. The rapid decrease in the IR signal upon exposure to the buffer at pH 2.8 was consistent with the AFM results indicating that the virus was desorbing from (33) Knutzen, K.; Lyman, D. J. Surface infrared spectroscopy. In Surface and Interfacial Aspects of Biomedical Polymers; Andrade, J. D., Ed.; Surface chemistry and physics; Plenum Press: New York, 1985; Vol. 1, p 197. (34) Suci, P. A.; Geesey, G. G. Langmuir 2001, 17, 2538.
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Table 3. Parameters of ATR-FTIR Data Curves expa polylys (1) polylys (2) meang APS (1) APS (2) meanh meani
ka,10 (µM s-1)b (0.03f)
0.34 0.32 (0.02) 0.33 (0.01) 0.49 (0.03) 0.22 (0.02) 0.36 (0.19) 0.34 (0.11)
θp,10c
ka,20 (µM s-1)d
θp,20e
0.449 (0.019) 0.807 (0.029) 0.628 (0.253) 0.374 (0.008) 0.511 (0.027) 0.443 (0.097) 0.535 (0.189)
0.53 (0.03) 0.30 (0.03) 0.42 (0.16) 0.41 (0.02) 0.30 (0.01) 0.36 (0.08) 0.39 (0.11)
0.882 (0.006) 1.088 (0.014) 0.985 (0.146) 0.917 (0.007) 0.951 (0.008) 0.934 (0.024) 0.959 (0.090)
a Experiment: polylys ) polylysine-coated Si; APS ) APSmodified Si; 1 and 2 refer to the results from two independent experiments. b Rate constant for adsorption (10 µg/mL bulk concentration). c Projected surface coverage at infinite time normalized to saturation coverage (10 µg/mL bulk concentration). d Rate constant for adsorption (20 µg/mL bulk concentration). e Projected surface coverage at infinite time normalized to saturation coverage (20 µg/mL bulk concentration). f Standard deviation in parameter estimated by the fitting routine. g Mean for polylys surfaces. h Mean for APS surfaces. i Mean for both surfaces.
the surface. The data in Figure 3c also indicated that there was a small remnant IR signal left at the end of the rinse period, which was accentuated in the standard buffer at pH 4.8. The AFM results indicated that this signal did not originate from intact virus particles, but was likely due to adsorbed disassembled virus proteins. As shown in Figure 3d, the virus was subsequently reabsorbed back onto this preconditioned Si surface at pH 4.8 (20 µg/mL bulk CCMV concentration). Modeling Kinetics of Adsorption. The kinetics of CCMV absorption to the modified Si surfaces was described by a Langmuir model. Table 3 presents a summary of model parameters describing the adsorption behavior of CCMV onto polylysine-coated Si and APS-modified Si. Data curves were analyzed from two independent ATRFTIR experiments for each positively charged surface. The model yielded the rate of adsorption from the 10 and 20 µg/mL bulk CCMV solutions (ka,10 and ka,20) and the projected surface coverage for an infinite adsorption time (θp). The ka values are presented in standard units (M s-1). Thus, the rate constants are normalized to the bulk concentration. According to the model, when expressed in these units, ka should be the same regardless of the bulk concentration. This hypothesis was tested by grouping the data for the polylysine-coated and APS-modified Si. With this grouping of the data, a comparison of the means for ka,10 and ka,20 indicated that they are not significantly different (p value ) 0.37, paired t-test). To obtain θp, kd was fixed at 1 × 10-5 s-1 (essentially a negligible value) based on the data curves obtained for rinses at pH 4.8 for the four experiments. For presentation, θp values were normalized to θ∞ (the saturation surface coverage), which was obtained from the mean of the amide II areas that were acquired during the exposure to the 100 µg/mL CCMV bulk solution. Figure 4shows fits of the Langmuir model (eqs 1-4) to data curves from virus adsorption onto polylysine-coated and APS-modified Si at 10 and 20 µg/ mL bulk concentrations. The small value of the residuals indicated that the model provided a reasonable description of the kinetics of adsorption. The model indicated that the diffusion though the boundary layer was 99% complete in ∼4 min. Modeling Equilibrium Adsorption Behavior. The simple Langmuir model described the kinetics of the adsorption of CCMV onto the two positively charged surfaces reasonably well. However, the equilibrium constant that was predicted on the basis of the Langmuir model provided a poor predictor of the projected surface coverage at infinite time for the more dilute bulk con-
Figure 4. Model fits of ATR-FTIR kinetic data curves. (a) Polylysine-coated Si: (i) 20 µg/mL bulk; (ii) 10 µg/mL bulk. (b) APS-modified Si: (i) 20 µg/mL bulk CCMV; (ii) 10 µg/mL bulk CCMV. Residuals for each fit are presented directly below the plots.
Figure 5. Binding curve constructed from the mean θp of the four step-binding experiments (closed circles with error bars; see text for details). Solid lines: binding curves predicted on the basis of a kd of either 1 × 10-4 s-1 (lower curve) or 1 × 10-5 s-1 (upper curve).
centration. Figure 5 shows a binding curve in which bulk concentration was plotted versus the projected surface coverage at an infinite adsorption time. For the 10 and 20 µg/mL bulk concentrations, the surface coverage was computed as the mean of θp values given in Table 3 (columns 3 and 5). For the 50 and 100 µg/mL bulk concentrations, the surface coverage was computed as the mean of the plateau values that were attained during adsorption. The data for all four step-binding curves were combined because they all exhibited the same trend. The error bars represent the standard deviations for each of the means. The solid lines are the binding curves that were predicted using eq 9 on the basis of the mean ka for all four data sets (Table 3, columns 2 and 4) for two different rates of desorption (kd), for which the equilibrium (binding) constants (Keq) were determined from eq 10. The curve that comes closer to describing the data set is that for which kd ) 1 × 10-4 s-1, and the more steeply rising curve is for kd ) 1 × 10-5 s-1 (the kd that was used for modeling the kinetic data curves). The discrepancy between the model and the data is obvious. It originates primarily from the low θp for the 10 µg/mL bulk concentration (θp,10). For θp,10 to be substantially less than the saturation level, kd must be significant. However, the direct determination of the kd obtained from the kinetics of the CCMV removal from the surfaces upon rinsing at pH 4.8 indicated that kd was negligible (
