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A New Model of Protein Adsorption Kinetics Derived from Simultaneous Measurement of Mass Loading and Changes in Surface Energy Alison J. Clark,† Andrzej Kotlicki,† Charles A. Haynes,*,‡ and Lorne A. Whitehead*,† Department of Physics and Astronomy, and the Michael Smith Laboratories, UniVersity of British Columbia, VancouVer, BC V6T 1Z1 ReceiVed December 6, 2006. In Final Form: February 5, 2007 We describe a novel technology based on changes in the resonant frequency of an acoustically actuated surface and use it to measure temporal changes in the surface energy γ (N m-1) of an elastomeric polymer membrane due to the adsorption of macromolecules from aqueous solution. The resonant elastomeric surface-tension (REST) sensor permits simultaneous determination of mass loading kinetics and γ(t) for a given adsorption process, thereby providing a multivariable data set from which to build and test models of the kinetics of adsorption at solid-liquid interfaces. The technique is used to measure γ(t) during the adsorption of either sodium dodecyl sulfate (SDS) or hen egg-white lysozyme (HEWL) onto an acrylic polymer membrane. The adsorption of SDS is reversible and is characterized by a decrease in γ over a time period that coincides with that required for the mass loading of the membrane. For the adsorption of HEWL labeled with Alexa Fluor 532 dye, γ continues to change long after the surface concentration of labeled HEWL, measured by using the elastomeric polymer membrane as an optical waveguide, reaches steady state. Gradual but significant changes in γ(t) are observed as long as the concentration of protein in the bulk solution, cb, remains nonzero. HEWL remains adsorbed to the membrane when cb ) 0, but changes in γ(t) are not observed under this condition, indicating that the interaction of bound protein molecules with those free in solution contribute to the prolonged change in the surface energy. This observation has been used to define a new model for the kinetics of globular protein adsorption to a solid-liquid interface that includes a mechanism by which the molecules in the bulk can facilitate the desorption of a sorbate molecule or change the energetic states of adsorbed molecules and, thus, the overall surface energy. The model is shown to capture the unique features of protein adsorption kinetics, including the relatively fast mass loading, the much more gradual change in surface energy that does not cease until the protein is removed from the bulk, the rapid desorption of an incubation-time-dependent fraction of bound protein when the protein is removed from the bulk, and the fixing of the residual surface concentration and surface energy at constant values once the removal of reversibly bound protein and free protein is complete.
Introduction A notable and perplexing characteristic of protein adsorption at solid-liquid interfaces is the history dependence of the process.1,2 Protein macromolecules adsorbed for short time periods will often spontaneously desorb upon dilution of the protein in the bulk liquid.3,4 Longer contact times generally result in a rapid and dramatic slowing of desorption kinetics, with slower evolving processes such as changes in adsorbed protein orientation,5,6 conformation,7-10 and state of aggregation11 known to be contributing factors. Unraveling the history dependence of protein * To whom correspondence should be addressed. E-mail: israels@ chml.ubc.ca (C.A.H.),
[email protected] (L.A.W.). † Department of Physics and Astronomy. ‡ Michael Smith Laboratories. (1) Mura-Galelli, M. J.; Voegel, J. C.; Behr, S.; Bres, E. F.; Schaaf, P. Proc. Nat. Acad. Sci. U.S.A. 1991, 88, 5557-5561. (2) Tie, Y.; Calonder, C.; Van Tassel, P. R. J. Colloid Interface Sci. 2003, 268, 1-11. (3) Wahlgren, M.; Arnebrant, T.; Lundstrom, I. J. Colloid Interface Sci. 1995, 175, 506-514. (4) Buijs, J.; van den Berg, P. A. W.; Linchtenbelt, J. W. T.; Norde, W.; Lyklema, J. J. Colloid Interface Sci. 1996, 178, 594-605. (5) Daly, S. M.; Przybycien, T. M.; Tilton, R. D. Langmuir 2003, 19, 38483857. (6) Lee, C. S.; Belfort, G. Proc. Natl. Acad. Sci. U.S.A. 1989, 86, 8392-8396. (7) Renner, L.; Pompe, T.; Salchert, K.; Werner, C. Langmuir 2005, 21, 45714577. (8) Sethuraman, A.; Vedantham, G.; Imoto, T.; Przybycien, T.; Belfort, G. Proteins: Struct., Funct., Bioinf. 2004, 56, 669-678. (9) Haynes, C. A.; Norde, W. J. Colloid Interface Sci. 1995, 169, 313-328. (10) Haynes, C. A.; Norde, W. Colloids Surf., B 1994, 2, 517-533. (11) Schakenraad, J. M.; Stokroos, I.; Busscher, H. J. Biofouling 1991, 4, 61-70.
adsorption therefore requires an understanding of the various kinetic subprocesses that contribute to it. As the kinetics and energetics of protein adsorption are complex, no single experimental or theoretical strategy has provided or is likely to provide a comprehensive understanding of the process. Instead, the problem must be attacked using a number of complementary tools that together define the overall time course of the adsorption process and the associated rates of change in the energy and structure of the adlayer. A number of high-sensitivity methods are available for measuring the mass-loading kinetics of protein adsorption and desorption at solid-liquid interfaces, including ellipsometry,3 surface plasmon resonance,12 optical waveguide lightmode spectroscopy,13,14 quartz crystal microbalance technology,15,16 fluorescence recovery after photobleaching (FRAP),17,18 and total internal reflection fluorescence (TIRF).19,20 Proven technologies (12) Schuck, P. Annu. ReV. Biophys. Biomol. Struct. 1997, 26, 541-566. (13) Voros, J.; Ramsden, J. J.; Csucs, G.; Szendro, I.; De Paul, S. M.; Textor, M.; Spencer, N. D. Biomaterials 2002, 23, 3699-3710. (14) Brusatori, M. A.; Tie, Y.; Van Tassel, P. R. Langmuir 2003, 19 (12), 5089-5097. (15) Osaki, T.; Renner, L.; Herklotz, M.; Werner, C. J. Phys. Chem. B 2006, 110 (24), 12119-12124. (16) Shen, D. Z.; Huang, M. H.; Chow, L. M.; Yang, M. Sens. Actuators, B 2001, 77 (3), 664-670. (17) Jervis, E. J.; Haynes, C. A.; Kilburn, D. G. J. Biol. Chem. 1997, 272, 24016-24023. (18) Kragel, J.; Wustneck, R.; Husband, F.; Wilde, P. J.; Makievski, A. V.; Grigoriev, D. O.; Li, J. B. Colloids Surf., B 1999, 12, 399-407. (19) Lok, B. K.; Cheng, Y. L.; Robertson, C. R. J. Colloid Interface Sci. 1983, 91, 87-96. (20) Robeson, J. L.; Tilton, R. D. Langmuir 1996, 12, 6104-6113.
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for characterizing conformational changes in adsorbed proteins and the overall structure of the adlayer are also available. They include Raman spectroscopy,21 nuclear magnetic resonance spectroscopy,22,23 fluorescence spectroscopy,24 circular dichroism,25 neutron reflectivity,26 atomic force microscopy,27 and attenuated total reflection Fourier transform infrared spectroscopy.28 Knowledge of the structures of protein adlayers gained from these studies has provided an incomplete but useful molecular context for understanding both the rates at which protein macromolecules adsorb/desorb and the associated process energetics, which can be characterized by calorimetry and by potentiometric titration experiments.29,30 Isothermal titration calorimetry provides a direct measure of the enthalpy of adsorption and of any postadsorption transitions.10,31,32 Differential scanning calorimetry provides excess heat capacity data that may be used to analyze adsorbed protein energies and conformations.9 Together, these calorimetric methods have shown that protein adsorption can proceed athermally or even endothermically, indicating that an increase in system entropy can drive the adsorption process in certain cases, particularly those involving a change in adsorbed protein conformation. These complementary experimental methods, along with recent mesoscopic and molecular simulations of the adsorption process,33-37 have therefore provided a wealth of structural information, including the discovery that, depending on the system, adsorption can lead to no significant change in protein structure,38 to a slow conversion to a more random and disordered peptide structure,21,39 or to a slow conversion of an R-helix structure to a β-sheet structure without a noticeable change in random (and presumably higher entropy) peptide structure.8 The fact that the state of folding of adsorbed proteins can depend both on the system and on the history of the adlayer poses a serious challenge for the theoretical description of the protein adsorption process. An additional piece of knowledge that can improve the understanding of the history dependence of the adlayer is the temporal change in the surface energy γ (N m-1), also known as the surface tension. Measuring γ(t) offers the potential to monitor changes to the structure and energy of the adlayer associated with subprocesses occurring during and following mass loading. The measurement of γ(t) during an adsorption process is technically challenging, but a few methods have been (21) Sane, S. U.; Cramer, S. M.; Przybycien, T. M. J. Chromatogr., A 1999, 849, 149-159. (22) Lundqvist, M.; Sethson, I.; Jonsson, B. H. Langmuir 2004, 20, 1063910647. (23) McNay, J. L. M.; Fernandez, E. J. Biotechnol. Bioeng. 2001, 76, 224232. (24) Santore, M. M.; Wertz, C. F. Langmuir 2005, 21, 10172-10178. (25) Vermeer, A. W. P.; Norde, W. J. Colloid Interface Sci. 2000, 225, 394397. (26) Su, T. J.; Lu, J. R.; Thomas, R. K.; Cui, Z. F.; Penfold, J. J. Phys. Chem. B 1998, 102 (41), 8100-8108. (27) Agnihotri, A.; Siedlecki, C. A. Langmuir 2004, 20, 8846-8852. (28) Clarke, M. L.; Wang, J.; Chen, Z. J. Phys. Chem. B 2005, 109, 2202722035. (29) Brandes, N.; Welzel, P. B.; Werner, C.; Kroh, L. W. J. Colloid Interface Sci. 2006, 299, 56-69. (30) Haynes, C. A.; Sliwinsky, E.; Norde, W. J. Colloid Interface Sci. 1994, 164, 394-409. (31) Kamyshny, A.; Lagerge, S.; Partyka, S.; Relkin, P.; Magdassi, S. Langmuir 2001, 17, 8242-8248. (32) Gill, D. S.; Roush, D. J.; Shick, K. A.; Willson, R. C. J. Chromatogr. A 1995, 715, 81-93. (33) Skepo, M.; Linse, P.; Arnebrant, T. J. Phys. Chem. B 2006, 110, 1214112148. (34) Liu, S. M.; Haynes, C. A. J. Colloid Interface Sci. 2005, 284, 7-13. (35) Agashe, M.; Raut, V.; Stuart, S. J.; Latour, R. A. Langmuir 2005, 21, 1103-1117. (36) Mungikar, A. A.; Forciniti, D. Biomacromolecules 2004, 5, 2147-2159. (37) Makrodimitris, K.; Fernandez, E. J.; Woolf, T. B.; O’Connell, J. P. Mol. Simul. 2005, 31, 623-636. (38) Jones, T. T.; Fernandez, E. J. Biotechnol. Bioeng. 2004, 87, 388-399. (39) Liu, S. M.; Haynes, C. A. J. Colloid Interface Sci. 2005, 282, 283-292.
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proposed. The first, axisymmetric drop shape analysis (ADSA),40,41 is based on filming and digitizing an image of a proteinloaded liquid droplet on a well-defined flat surface to allow the drop shape and contact angle θ to be monitored as a function of time. The energy of the solid-liquid interface can then be obtained from Young’s equation, assuming the energy of the solid-vapor interface to be constant over the course of the experiment. Van der Vegt et al. used ADSA to measure γ(t) for the adsorption of human immunoglobulin G (IgG) onto fluoroethylenepropylene (Teflon).40 They found that γ continued to change long after steady-state surface concentrations were achieved and concluded that the continued variance in surface energy was due to slow conformational changes in the adsorbed protein molecules. While ADSA shows promise, it suffers from several problems that limit the accuracy of the results. First, the droplet typically changes its contact area during the course of the experiment, invalidating certain assumptions made in the calculation of γ. Second, the hydrodynamics of solute mass transport to both interfaces are ill-defined and unaccounted for in the analysis. Finally, due to the finite amount of time it takes to initially form the droplet, t ) 0 is ambiguous and could cause a large error in calculated values of γ. A second method based on Stoney’s equation overcomes many of these limitations by permitting complete immersion of the sorbent surface in the sorbate-loaded liquid phase. It involves measuring the radius of curvature of an atomic force microscopy microfabricated silicon nitride cantilever during the course of an adsorption process.42,43 This method requires functionalizing one side of the cantilever so as to prevent adsorption to that surface. The differential in the change in stress resulting from protein adsorption to the unprotected side then causes the cantilever to bend. By enclosing the cantilever in a flow cell providing well-characterized hydrodynamics, protein molecules can be added to the environment immediately surrounding the cantilever and the change in surface energy can be monitored as a function of time. Unfortunately, producing the functionalized microcantilever is not a trivial process, and only certain materials may be used in its construction. As a result, no applications of this technique have appeared following the initial proof-of-concept paper.43 Our goal was therefore to develop a low-cost, less technically challenging method for measuring γ(t) that can be applied to silicone rubber and other elastomeric polymers commonly used as biomaterials and blood-contacting surfaces in medical procedures.44,45 We previously reported on a new resonant frequency sensor that utilizes an elastomeric polymer as the sorbent and sensor surface in a manner that allows temporal observation of γ(t) and the related variable T(t), the total membrane tension (N m-1), through the change in resonant frequency of the acoustically actuated surface.46 A resonant frequency sensor is a mechanical vibrator whose resonant frequency is sensitive to changes in its environment, such as temperature, pressure, or adsorption to its surfaces. The most widely characterized and commercialized resonant frequency sensors are those based on the piezoelectric material quartz (e.g., (40) Van der Vegt, W.; Van der Mei, H. A.; Busscher, H. J. J. Colloid Interface Sci. 1993, 156 (1), 129-136. (41) Noordmans, J.; Wormeester, H.; Busscher, H. J. Colloids Surf., B 1999, 15 (3-4), 227-233. (42) Butt, H. J. J. Colloid Interface Sci. 1996, 180 (1), 251-260. (43) Moulin, A. M.; O’Shea, S. J.; Badley, R. A.; Doyle, P.; Welland, M. E. Langmuir 1999, 15 (26), 8776-8779. (44) Yoda, R. J. Biomater. Sci., Polym. Ed. 1998, 9, 561-626. (45) Dahiyat, B. I.; Posadas, E. M.; Hirosue, S. React. Polym. 1995, 25, 101109. (46) Clark, A. J.; Whitehead, L. A.; Haynes, C. A.; Kotlicki, A. ReV. Sci. Instrum. 2002, 73, 4339-4346.
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the quartz-crystal microbalance (QCMB)) because of its high stiffness and sharp resonances.47-49 The QCMB and related sensors50,51 operate at a high frequency in the MHz range and are therefore principally sensitive to the addition of mass to their surfaces. In contrast, the resonant frequency elastomeric polymer sensor we describe operates at low frequencies, in the Hz range, and is sensitive to changes in the surface energy.46 In this work, we extend our resonant frequency technology by utilizing the elastomeric polymer membrane as an optical waveguide to monitor the mass loading of the sorbent membrane through fluorescent excitation of tagged or autofluorescing protein molecules in an optical evanescent field. The resulting resonant elastomeric surface-tension (REST) sensor permits simultaneous determination of mass loading kinetics and γ(t) for a given adsorption process, thereby providing a multivariable data set from which to build and test models of the history dependence of macromolecular adsorption at solid-liquid interfaces. In principle, the technology is applicable to a wide range of elastomeric polymer chemistries, including silicone, polyurethane, and acrylic-based rubbers. Here, it is used to monitor the adsorption of fluorescently labeled hen egg-white lysozyme on an acrylic polymer membrane. The ability to independently and simultaneously measure mass loading and tension data is shown to provide insights into the kinetics of protein adsorption that are used to propose and test a new model for the adsorption reaction.
REST Sensor Description and Theory of Operation Components and Instrumentation. Figure 1a shows the basic experimental configuration for the resonant frequency measurement. A thin membrane (25 or 50 µm in thickness) of the elastomeric sorbent material is mounted on an annular support and positioned directly above an acoustic transducer that excites the membrane to resonate within a flow cell having well-defined hydrodynamics. The vibration of the membrane is detected with an optical vibration detection probe consisting of a bundle of optical fibers with an illuminating fiber (I) at the core, surrounded by return fibers (R) as shown in Figure 1b. When this detection probe is positioned at a standoff distance, y, and the vibrating surface has an amplitude of motion, dy, the amount of light reflected back through the return fibers is modulated with the same frequency as that of the vibrating surface. Light collected by the return fibers is sent to a photosensor to produce a representative output voltage signal. A fiber-pigtailed laser (532 nm) terminated with a ceramic ferrule is used to provide efficient light injection into the edge of the membrane (Figure 1c). The output from the fiber has a mode field diameter of 3.3 µm and a Gaussian angular distribution with a 1/e2 half-angle of 7.47°. It provides 0.3 mW of laser power from the end of the fiber with a stability of (5%. The output of the fiber is ∼3 µm in diameter, while the sensor membrane thickness is ∼25 or 50 µm. Precise alignment of the fiber with the edge of the membrane is therefore required. A differential screw between a sensor support leg and the membrane support ring permitted alignment of the fiber to maximize the amount of light introduced into the waveguide. Light emitted by the excited fluorophore was collected by a set of five large-core (9 mm diameter) optical fibers positioned around the tip of the (47) Mermut, O.; Phillips, D. C.; York, R. L.; McCrea, K. R.; Ward, R. S.; Somorjai, G. A. J. Am. Chem. Soc. 2006, 128, 3598-3607. (48) Stine, R.; Pishko, M. V.; Hampton, J. R.; Dameron, A. A.; Weiss, P. S. Langmuir 2005, 21, 11352-11356. (49) Cavic, B. A.; Thompson, M. Analyst 1998, 123 (10), 2191-2196. (50) Cavic, B. A.; Hayward, G. L.; Thompson, M. Analyst 1999, 124 (10), 1405-1420. (51) Ebersole, R. C.; Ward, M. D. J. Am. Chem. Soc. 1988, 110, 8623-8628.
Figure 1. Components and configuration of the elastomeric polymer resonant frequency sensor: (a) flow cell and basic sensor components, (b) side view (left) and end view (right) cross sections of the vibration detection probe, and (c) coupling of the pig-tailed laser to the optical waveguide.
vibration detection probe. The collection fibers were encased in a low refractive index cladding to efficiently transmit radiation along their length. Two filters were used to isolate the signal due to light emitted by the fluorophores. The first, the XF3021 (OG550) filter (Omega Optical Inc.), cut out scattered light from the 532 nm laser. The second, a cyan subtractive filter (F52-536 filter, Edmund Optics Inc.), cut out scattered light from the nearinfrared LED of the vibration detection probe. The filtered light collected from the fiber array was spatially concentrated into the side of the photomultiplier tube using a cone of specular multilayer mirror film (3M radiant mirror film, 3M Corp.). The large end of the concentration cone was installed at the end of the fiber array. The second filter was placed at the small end of the concentration cone. Another large core optical fiber was then used to transmit the fluorescent light from the end of the concentration cone to the opening of the photomultiplier tube. This light-collection assembly and the overall REST sensor were enclosed in a light-tight box and a darkened curtained room, respectively, to prevent background light radiation from leaking into the photomultiplier tube. With the experiment turned off, the signal measured by the photomultiplier tube was then
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comparable to the dark noise current of the photomultiplier tube itself. Control experiments were performed to correct collected fluorescence emission (555 nm) for unwanted contributions from photobleaching and labeled protein in the adjacent bulk solution. The geometry and sample injection system of the REST sensor was designed to permit careful control of the bulk sorbate concentration and fluid hydrodynamics near the sensor surface. Since temperature fluctuations affect the resonant frequency of the sensor, a recirculating temperature control bath of ∼30 L and the appropriate heat transfer surfaces were used to maintain the sensor and fluid delivery chambers at 27 ( 0.1 °C root mean square (rms). Theory of Operation. When proteins or other macromolecules adsorb to the sensor surface, the resonant frequencies fmn of particular vibration modes drop significantly. Since the mass of a protein monolayer (mmonolayer ) 0.0005 to 0.0013 mg) is significantly less than the mass of the membrane (mmembrane ) 6.95 mg) itself, this drop in fmn is not due to changes in the mass of the membrane but rather to a change in the surface energy of the membrane.43 It is therefore necessary to understand how γ depends on fmn. For a thin membrane of elastomeric material freely mounted on an annular holder, the total tension T of the membrane is related to γ through eq 1, where Tinherent is the tension due to added mechanical stresses on the membrane, that is, stretching of the film by thermal, curing, or mounting stresses.
T ) Tinherent + 2γ
(1)
The membrane tension T can be related to fmn through the equation of motion of an ideal membrane,
∂2w(r,φ,t) T∇2w(r,φ,t) + P ) Fh ∂t2
(2)
where w(r,φ,t) is the out-of-plane displacement of the membrane, F is the membrane density (kg m-3), and h is the membrane thickness (m). The interaction of the membrane with the surrounding fluid is accounted for through the pressure P (N m-2). Equation 2 ignores any energy losses due to radiative damping, which is valid since the wavelength of the radiation in the fluid is much greater than the wavelength of the vibrating membrane. Viscous damping is expected to contribute insignificantly to w(r,φ,t) due to the low viscosity of the aqueous solution. As a result, well-defined harmonic modes are generated in the vibrating membranes, with the dominant loss mechanism being mechanical hysteresis in the rubber. Finally, eq 2 assumes that the restoring force due to the membrane stiffness does not contribute to the mechanical behavior of the membrane. Tong et al.52 define the conditions for when this is true, which are satisfied for the membranes used in this study. To relate T to fmn, we first solve eq 2 with P ) 0 to obtain the ideal resonant frequencies of the membrane, fideal mn , when interactions with a surrounding fluid are ignored:
fideal mn )
µmn 2πa
xFhT
(3)
where µmn is the nth root of Jm, the mth-order Bessel function of the first kind, and a is the membrane radius (m). Based on an analysis of the problem by Gottlieb and Aebischer,53,54 Tong et al.52 have solved, for the circularly symmetric modes, the (52) Tong, Q. K.; Maden, M. A.; Jagota, A.; Farris, R. J. J. Am. Ceram. Soc. 1994, 77 (3), 636-647.
radiation mass impedance terms that act on a membrane when immersed in a fluid such as water. We have used their iterative method to solve for the ideal resonant frequencies in vacuum, fideal 0n , given the actual resonant frequencies f0n measured in the experiment by the optical vibration detection probe. The application of eq 3 then yields experimental values for membrane tension. In all of the experiments reported here, the resonant frequency of the second circularly symmetric mode of the membrane was measured and used to compute T. Materials and Methods Reagents. Hen egg-white lysozyme (HEWL) and sodium dodecyl sulfate were purchased from Sigma Chemicals (St. Louis, MO) and used without further purification. Potassium phosphate monobasicsodium hydroxide buffer solution (50 mM, pH 7.00) was prepared with a commercially available buffer solution concentrate (Fisher Scientific; Ottawa, Canada) and deionized, distilled water. Prior to use, the buffer solution was degassed by mixing under a vacuumpump aspirator. 2000MP Acrylic, an optically clear elastomeric membrane, was donated by 3M Inc. The membrane is supplied sandwiched between two sheets of plastic release liner material and is available in two thicknesses, 25 µm (3M 2000MP Acrylic 8141 film; 3M Corp.) and 50 µm (3M 2000MP Acrylic 8142 film; 3M Corp). As alignment of the optical waveguide laser was more difficult with the thinner 3M 8141 membrane, most experiments were performed using the 3M 8142 membrane as the sorbent. All water used in the experiments was distilled and filtered through a Sybron/ Barnstead NANOpure II system. HEWL Labeling. HEWL was labeled with the carboxylic acid, succinimidyl ester dye Alexa Fluor 532 (MW ) 724 amu, λexcitation ) 532 nm, λemission ) 555 nm), which forms a covalent bond with the primary amine groups on proteins through its succinimidyl ester, using the Alexa Fluor 532 nm protein labeling kit of Molecular Probes. A HEWL stock solution (6.15 mg mL-1) was prepared by dissolving 62.3 mg of lysozyme in 10 mL of buffer solution. A portion of this stock solution was diluted 1 in 3 to produce ∼1.5 mL of ∼2 mg mL-1 lysozyme solution for use in the labeling reaction. Since succinimidyl esters react most efficiently at pH 7.5-8.5, 150 µL of 1 M bicarbonate solution was added to raise the pH of the protein solution. The protein solution was then added to the vial of reactive dye and mixed for 1 h at room temperature. Unreacted dye molecules were separated from the reacted dye conjugates by size exclusion chromatography on a prepacked P6 Biogel column. A portion of the labeled-protein eluent was diluted 1 in 20 with buffer solution to measure the degree of labeling by absorbance at 280 nm (HEWL molar extinction coefficient at 280 nm ) 37 600 cm-1 M-1), A280, and 530 nm (Alexa 532 dye molar extinction coefficient at 530 nm ) 81 000 cm-1 M-1), A530. The average degree of labeling was determined to be 0.715 mol dye/mol HEWL. The purified reaction product was diluted 1 in 10 with unlabeled protein to a final HEWL concentration of 1.82 mg mL-1, divided into 10 light-proof 1 mL vials, and then refrigerated for later use.
Results and Discussion Characterization of System Hydrodynamics and Resonant Frequencies. The fluid pumping system permits solution flow across the REST sensor so that sorbate (protein) can be added or removed from the bulk solution in contact with the elastomeric membrane at any time point. The hydrodynamics within the system are well-defined, allowing accurate prediction of the sorbate concentration within the well-mixed sensor chamber as a function of time by solution of the differential mass and momentum conservation equations. This is demonstrated in Figure 2, which compares the concentration in the sensor cell predicted (53) Gottlieb, H. P. W.; Aebischer, H. A. Acustica 1986, 61 (4), 223-230. (54) Gottlieb, H. P. W.; Aebischer, H. A. Acust. Acta Acust. 1998, 84 (4), 779-785.
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Figure 2. Measurement of bulk fluorescence compared with predicted bulk concentration from the fluid mixing model.
Figure 3. Air-loaded resonant spectra for a 3M 2000MP acrylic 8141 membrane (20 °C). Table 1. Characteristic Tensions of the Membranes Used in This Study in Both Their Air-Loaded and Buffer-Loaded States air-loaded tension (N m-1)
water-loaded tension (N m-1)
8141
0.065 ( 0.002 0.073 ( 0.001
0.032 ( 0.002 0.036 ( 0.001
8142
0.076 ( 0.004
0.042 ( 0.002
membrane material
Table 2. Water-Loaded Tensions and Characteristic Frequencies for the First Four Circularly Symmetric Modes of the 3M 2000MP Acrylic 8141 Membrane membrane mode
fwater (Hz)
fideal (Hz)
Twater (N m-1)
(0,1) (0,2) (0,3) (0,4)
1.9 7.6 16.0 26.4
46.2 101.9 163.9 226.8
0.032 ( 0.002 0.030 ( 0.002 0.031 ( 0.002 0.032 ( 0.002
by the fluid mixing model with a scaled measurement of bulk fluid fluorescence. The sensor properties required to interpret adsorption experiments were determined by measuring the resonant frequencies of each acoustically actuated membrane. For example, the airloaded resonant spectra for a 3M 2000MP acrylic 8141 membrane (Figure 3) was used to determine both the resonant frequencies of the first four circularly symmetric modes f0n and the associated membrane tension through the application of the GottliebAebischer model.53,54 Table 1 summarizes the measured tensions of the 8141 membrane in both its air-loaded and buffer-loaded states. The water-loaded tension, Twater, estimate was essentially constant between the first four modes (Table 2), displaying a rms fractional error of less than 5%, which was consistent with the intrinsic noise observed in the frequency measurement. Similar
accuracy was observed in the air-loaded membrane system. However, recorded tensions for the 8141 membrane (and for all other membranes tested) depended on the specific membrane used (Table 1), as small differences in the intrinsic tension were observed due to the variations in mounting the membrane in the REST device. Typical tension values for the other membranes used are also provided in Table 1. The tensions of these elastomeric membranes are remarkably low, lying between the surface tension of a clean air-water interface (0.072 N m-1) and the surface energy of a typical hydrophobic surface such as Teflon (0.0189 N m-1).55 Average tensions of ∼0.07 and ∼0.04 N m-1 were recorded for the airloaded and buffer-loaded 8142 membranes, respectively. This acrylic membrane is hydrophobic and, hence, is expected to have a γs0 value of the order of 0.020 N m-1, giving an intrinsic membrane tension, Tintrinsic, estimate of 0.020 N m-1 for the air-loaded system using eq 1. Thus, the surface energy γ makes a major and measurable contribution to T, permitting highly sensitive measurement of changes in the surface energy of the membrane during an adsorption process. HEWL and SDS Adsorption Studies. The adsorption isotherm for HEWL binding to the 8142 membrane is typical of all globular protein adsorption to hydrophobic polymer surfaces,56,57 remaining linear up to cb ∼ 0.0003 g L-1 before reaching a saturation surface concentration Γsat of ∼1.2 mg m-2 when cb exceeds 0.003 g L-1. We therefore applied the REST sensor to the measurement of mass loading of Alexa 532-labeled HEWL on the 8142 membrane and the time-dependent response in ∆T. Figure 4 shows an example of a simultaneous measurement of mass loading and ∆T for a bulk solution concentration of cb ) 0.00036 g L-1, which represents a subsaturating condition just below the shoulder of the isotherm. The surface fluorescence F data show that protein loading on the membrane surface reaches a steady-state concentration after ∼40 min, while changes in membrane tension continue to be observed up until a continuous flush of the sensor with pure buffer was initiated at the 152 min mark. Thus, changes in the structure and associated properties of the adlayer reflected in ∆T(t) persist long after mass loading of the sorbent has reached steady-state. This point is emphasized in Figure 5, which shows that for two identical independent experiments ∆T(t) does not reach steady state after exposure of the membrane surface to a 0.001 g L-1 solution of labeled HEWL for more than 6 h. The irreversible nature of HEWL adsorption and the prolonged changes in ∆T are in sharp contrast to the REST sensor studies of surfactant adsorption to elastomeric polymer surfaces. Figure 6 reports cb(t) and ∆T(t) data for the adsorption of SDS to the 3M 8142 membrane over a range of bulk surfactant concentrations. For each step change in the bulk SDS concentration, ∆T(t) remains closely correlated with cb(t) such that both properties reach steady state within a few minutes of each other. A small lag in ∆T(t) is generally observed, suggesting rapid equilibration of the surface structure and properties of the adlayer following mass loading. Flushing of SDS from the bulk solution of the sensor chamber results in rapid and complete desorption of bound SDS. Thus, the adsorption process is completely reversible with respect to dilution. Returning to the HEWL adsorption study described in Figure 4, we find that flushing free protein out of the bulk solution after a total contact time of 120 min results in the desorption of ∼25% (55) Chattoraj, D. K.; Birdi, K. S. Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984. (56) Elwing, H. Biomaterials 1998, 19, 397-406. (57) Norde, W.; Gonzales, F. G.; Haynes, C. A. Polym. AdV. Technol. 1995, 6, 518-525.
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Figure 6. Sensor response and bulk concentration data for the incremental additions of SDS to the mixing tank of the REST sensor assembly bearing a 3M 2000MP acrylic 8141 membrane (pH 7, 20 °C).
Figure 4. REST sensor performance: (a) response of the sensor to the addition of 0.00036 mg/mL HEWL to the chamber, showing both the measured change in tension and the measured change in surface fluorescence, and (b) comparison of the fluorescence signal with the change in bulk concentration. Figure 7. Simultaneous measurements of the changes in tension and surface fluorescence for HEWL adsorption at cb ) 0.00072 mg/mL to a 3M 2000MP acrylic 8141 membrane (pH 7, 20 °C).
Figure 5. REST sensor response repeatability: differential tension data for two experimental runs of HEWL adsorption (cb ) 0.001 mg/mL) on a 3M 2000MP acrylic 8141 membrane (pH 7, 20 °C).
of the bound HEWL, indicating that a significant fraction of the adsorbed protein molecules are characterized by extraordinarily slow desorption kinetics. The surface tension increases slightly (i.e., -∆T decreases) during the desorption process and then reaches a constant value once all reversibly bound protein molecules have been removed. Thus, when protein is present in the bulk solution, changes in ∆T(t) continue to be observed long after the mass loading of the membrane and the bulk concentration cb have reached steady state. However, they are not observed when cb ) 0, indicating that the interactions of bound protein molecules with those free in solution contribute to the prolonged change in the surface energy.
Similar results are obtained when the bulk concentration of labeled HEWL is doubled (Figure 7) such that Γ is now approaching Γsat. However, under this higher mass-loading condition, a higher percentage (∼40%) of bound protein desorbs from the membrane following the flushing of protein out of the bulk solution after 135 min of contact, indicating a concentration dependence to the kinetics of the subprocesses (e.g., protein reorientation, denaturation, and aggregation) that alter the structure of the adlayer and the associated rate of desorption. Many additional experiments with the REST sensor provided other important insights into the history dependence of HEWL adsorption to the acrylic elastomeric membrane. They include the following: (i) At all bulk protein concentrations, the degree of reversible protein binding to the membrane decreases with increasing contact time. For example, when cb ) 0.0002 g L-1, more than 90% of bound protein desorbs from the membrane after a 30 min contact period, while less than 30% desorbs after a 60 min contact period. (ii) For any cb > 0, the surface energy does not reach a constant (steady state) value, but it continues to slowly decrease with time, indicating that the adlayer remains away from equilibrium for extraordinarily long time periods (many hours), presumably due to the many configurational degrees of freedom in the sorbate macromolecule. It is important to note that this result is specific to the surface energy measurement and is not seen in the massloading measurement. It therefore would not be seen by the
A New Model of Protein Adsorption Kinetics
Figure 8. Response of the sensor to a step change in HEWL concentration from cb ) 0.00037 mg/mL and cb ) 0.00055 mg/mL. Adsorption conditions are the same as in Figure 7.
Langmuir, Vol. 23, No. 10, 2007 5597
Figure 10. Data from the REST sensor experiment shown in Figure 7 compared with the Langmuir-type surfactant absorption model utilizing the parameters listed in Table 3.
m-2 s-1) across the boundary layer is modeled as a Nernstiantype film mass-transfer process:
ΦBTL )
Figure 9. Schematic of the Langmuir-type kinetic model for SDS adsorption to the elastomeric membrane.
Dm (c - cL) ) kf(cb - cL) d b
(4)
where Dm is the solute diffusivity (m2 s-1), cL is the solute concentration in the boundary layer (mg m-3 or molecules m-3), kf is the film mass-transfer coefficient (m s-1), and d, the diffusion boundary layer thickness (m), is the distance at which solute transport by convection equals that by diffusion. The value of d depends on fluid velocity and the geometry of the flow cell, and it can be calculated.59 However, in this work, d is treated as a model parameter determined by fitting the adsorption kinetics model to the experimental data. In all cases, the fitted value of d has physically sensible values near those predicted by theory. As the binding reaction was shown to be reversible, the intrinsic rate of adsorption to the sorbent surface is effectively modeled by the classic theory of Langmuir:
many other binding-kinetics analysis systems based on the detection of mass loading. (iii) The surface energy response is sensitive to the manner in which protein is added to the sensor chamber. Sequential addition of protein to the bulk solution (Figure 8) results in rapid step changes in surface load and in a complex and more gradual change in ∆T that includes a discontinuity at the time point when the bulk protein concentration is changed. Similar results were obtained with the 3M 8141 and 8161 membranes. Thus, through its ability to simultaneously monitor surface loading and surface energy, the REST sensor provides a unique set of data that may prove useful for improving our understanding and modeling of macromolecular adsorption processes. Surfactant Adsorption Kinetics Model. To fix ideas on how surface energy data may be used to define and test models of adsorption kinetics, we first considered the relatively simple case of the reversible adsorption of SDS. As described schematically in Figure 9, the kinetics of this adsorption process can be modeled with a classic Langmuir-type model that considers molecular diffusion across the sorbent boundary layer, followed by reversible binding to the sorbent surface. We therefore assume a single equilibrium surface state, Γ1, characterized by a projected sorbate surface area a1 of 50 Å2 based on previous studies of SDS adsorption by Porcel et al.58 The flux of solute ΦBTL (kg
where e is the surface energy factor (N m-1). Tcf is a small factor to correct a slight drift in the tension signal with time that resulted in a residual positive ∆T once the surface fluorescence measurement indicated that SDS was completely removed from the surface. Equations 5 and 6 are coupled through Γ1. The simple adsorption kinetics model embodied in eqs 4-6 accurately captures ∆T(t) data measured by the REST sensor over a wide range of bulk SDS concentrations (Figure 10). The regressed model parameters listed in Table 3 show that the correction factor to ∆T is indeed very small. The regressed Γmax 1 value for SDS adsorption to the hydrophobic 3M 8142 membrane
(58) Porcel, R.; Jodar, A. B.; Cabrerizo, M. A.; Hidalgo-A Ä lvarez, R.; Martı´nRodrı´guez, A. J. Colloid Interface Sci. 2001, 239 (2), 568-576.
(59) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; John Wiley and Sons: New York, 2001.
ΦLTΓ1 ) ν1cL(1 - Γa) - ν-1Γ
(5)
where ν1 (m s-1) and ν-1 (s-1) are the forward and reverse rate constants for the binding reaction, respectively, Γ is the sorbate concentration (molecules m-2), and a is the characteristic area (m2) of interaction between the sorbate molecule and the surface. The change in tension ∆T generated by the adlayer is given by
∆T ) -e1Γ1a1 + Tcf
(6)
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Table 3. Parameters for the Langmuir-type Kinetic Model Describing the Mass Loading and Surface Energy of an Adlayer Formed by the Adsorption of SDS on the 2000MP Acrylic 8141 Membrane (pH 7, 20 °C) model parameter
value
units
d e1 ν1 ν-1 cf
0.014 6.24 × 10-21 3.6 × 10-5 2.38 4.4 × 10-26
mm N m-1 m s-1 s-1 N s-1
is similar to that (1.1 mg m-2) measured by Turner et al. for SDS binding to a hydrophobic polystyrene surface.60 Two time constants, τ1 and τ-1 (s), for the adsorption and desorption reactions, respectively, also emerge from the model analysis
τ1 )
d ν1
and
τ-1 )
1 ν-1
(7)
and show that the intrinsic rate of SDS adsorption from the boundary layer is 13 times faster than the rate of SDS desorption, which is again consistent with data from previous studies of SDS adsorption by neutron reflection.60 Thus, a simple Langmuirtype model for reversible-adsorption kinetics appears to capture the temporal features of SDS adsorption to hydrophobic polymer surfaces. We now explore how this model must change to effectively capture the more complex adsorption kinetics of globular proteins. New Model for Protein Adsorption Kinetics. Our model describing the kinetics of protein adsorption at a solid-liquid interface follows from the classic Langmuir-type adsorption kinetics model by including equations describing the rate of diffusion across the boundary layer (eq 4) and the intrinsic rate of reversible protein binding to the sorbent surface (eq 5). On their own, these equations cannot capture the slow change in surface tension that occurs during and following the relatively rapid mass loading of the interface. Nor do they capture other important characteristics of the protein adsorption process, including the progressive decrease in the rate of desorption that leads to an increase in the fraction of sorbate that appears to be irreversibly adsorbed to the surface. Previous studies of protein adsorption provide an understanding of many of the features of protein adsorption kinetics, including the ability of protein molecules in the bulk to exchange with molecules adsorbed on the surface,7,61 that must be accounted for in a meaningful model of the process kinetics. The REST data reported in this work add to that knowledge by quantifying the slow kinetic changes that occur within the adlayer and by showing that those changes require the presence of protein in the contacting bulk solution. Thus, there is a mechanism by which the molecules in the bulk can facilitate desorption of a sorbate molecule or change the energetic states of adsorbed molecules and, therefore, the overall surface energy. To capture these characteristics, we allow a given protein molecule in the adlayer to be transferred among an ensemble of unique energetic states (Figure 11), where each surface state Γk is characterized by a characteristic energy ek and a characteristic area of interaction ak between the sorbate molecule and the surface. Although the structure of the model is quite general, we assume here that each successive state is characterized by a larger area of interaction per molecule, as one might expect would occur as (60) Turner, S. F.; Clarke, S. M.; Rennie, A. R.; Thirtle, P. N.; Cooke, D. J.; Li, Z. X.; Thomas, R. K. Langmuir 1999, 15 (4), 1017-1023. (61) Joshi, O.; Lee, H. J.; McGuire, J.; Finneran, P.; Bird, K. E. Colloids Surf., B 2006, 50, 26-35.
the interaction between the protein and sorbent becomes more favorable (i.e., protein changes orientation or conformation to strengthen its interaction with the surface). As a result, the forward and reverse rates of transfer between states decrease as ak increases. Finally, to account for the observed dependence of the surface energy and sorbate exchange rate on protein in the bulk solution, the forward and reverse rates between surface states are made proportional to the free concentration of solute in the boundary layer cL. The dependence of the reverse rates of transfer on cL is what differentiates this model from others, as it allows for an off-rate from the surface while there are molecules in the bulk solution, but it eliminates protein desorption and exchange between states as cb, and therefore cL, goes to zero. Previous models by Wahlgren et al. and Daly et al. allow direct exchange between molecules in the bulk and any adsorbed molecule.3,5 In contrast, our model permits desorption through the first sorbate energy state Γ1, while any molecule in a higher adsorbed state may desorb only after it has devolved back through the intermediary states into state Γ1. In this way, our model assumes that the bulk solution molecules do not directly exchange with all the adsorbed molecules, but rather they supply the kinetic energy, through surface collisions, needed to transfer sorbate molecules between adsorbed states. While our assumption that the reverse rates of transfer between surface states are proportional to cL is new, the assumed dependence of the forward rates of transfer on cb or cL is not. Daly et al. first explored this concept to show that the reorientation rate of lysozyme adsorbed to silica was first order with respect to the bulk solution concentration.5 In its most general form, our model assumes that the ensemble of adsorbed protein molecules occupy a continuum of surface states, each characterized by a unique contact area and energy. However, to avoid an underdetermined model, we sought to define the minimum number of discrete states required to successfully model the mass-loading and surface energy response of the REST sensor. For the adsorption of HEWL to a 3M elastomeric membrane, we find that three surface states are sufficient and therefore provide the model equations for that case. The more general form of the model for larger numbers of surface states is obvious from the equations provided. Note that each solute flux ΦITJ represents a total flux and therefore includes contributions that are proportional to the surface populations as well as those proportional to cL. Equation 8 defines the net flux of molecules from the boundary layer, L, into surface state 1
ΦLT1 ) ν1cL(1 - Γ1a1 - Γ2a2 - Γ3a3) / + cL)Γ1 (8) (ν-1 - ν-1
where, for example, Γ1a1 gives the fraction of sorbent surface occupied by adsorbed protein molecules in state 1. In this state, the adsorbed protein is assumed to be in its native conformation with a1 given by the hydrodynamic radius of the protein in solution (a1 ∼ 40 Å2 for HEWL). Equation 9 gives the net flux of molecules between surface states 1 and 2 / + cL)Γ2 Φ1T2 ) (ν2 + ν/2cL)Γ1 - (ν-2 + ν-2
(9)
and eq 10 gives that between states 2 and 3 / cL)Γ3 Φ2T3 ) (ν3 + ν/3cL)Γ2 - (ν-3 + ν-3
(10)
A New Model of Protein Adsorption Kinetics
Langmuir, Vol. 23, No. 10, 2007 5599
Figure 11. Schematic defining the fluxes and adsorption states encoded in our new model describing the kinetics of protein adsorption.
The rate of change of the populations in each state is then given by
dcL 1 ) (ΦBTL - ΦLT1) dt d
(11)
dΓ1 ) ΦLT1 - Φ1T2 dt
(12)
dΓ2 ) Φ1T2 - Φ2T3 dt
(13)
dΓ3 ) Φ2T3 dt
(14)
Finally, for the three-surface-state system, ∆T is given by
Figure 12. Comparison of model predictions to the differential tension data shown in Figure 8.
3
∆T ) -
∑ekΓkak k)1
(15)
and the adsorbed-state surface fluorescence ∆F is given by 3
∆F ) f
∑ Γk k)1
(16)
where f is the slope of the fluorescence intensity versus HEWL concentration working curve. As defined in eqs 8-16, our general model of protein adsorption kinetics contains 18 parameters, one of which (f) can be determined from independent experiments. However, qualitative analysis of the trends in mass loading and ∆T(t) suggests that many of these parameters can be set equal to zero. For example, our REST sensor data indicate that changes in ∆T, and thus the forward and reverse transfer of molecules between adsorbed states, require a nonzero concentration of protein in the bulk / solution. We therefore set ν-1 , ν2, ν-2, ν3, and ν-3 equal to zero. To simplify the model further, we recognized that a1 < a2 < a3 and arbitrarily set a2 ) 1.1a1 and a3 ) 1.2a1. The remaining 10 model parameters could be fit to a set of simultaneous surface fluorescence and ∆T data acquired with the REST sensor (Figure 12). Cross correlation of fitted parameters was not observed, indicating that the model is uniquely determined by the data set. Excellent agreement with both sets of experimental data was achieved, indicating that the model can capture the response of the sensor to incremental increases in bulk concentration and to the dilution of protein from the bulk solution. Table 4 provides
Table 4. Parameters for a New Kinetic Model Describing the Mass Loading and Surface Energy of an Adlayer Formed by the Adsorption of HEWL on the 2000MP Acrylic 8141 Membrane (pH 7, 20 °C)a model parameter
value
units
time constant τ
d e1 ν1 ν-1 ν/2 / ν-2 ν/3 / ν-3 e2 e3 f
0.014 0 2.18 × 10-5 0.0151 1.61 × 10-22 9.96 × 10-23 3.43 × 10-24 1.03 × 10-23 -1.22 × 10-21 -9.12 × 10-20 0.0108
mm N m-1 m s-1 s-1 m3 s-1 m3 s-1 m3 s-1 m3 s-1 N m-1 N m-1
0.9 s 66.2 s 6.6 m 10.6 m 5.1 h 1.7 h
a The model assumes that all forward and backward rates (except for state 1 into and out of the boundary layer) are strictly proportional to the population of molecules in the boundary layer.
the complete set of model parameters for HEWL adsorption to the 3M 8142 elastomeric membrane; e1 is essentially zero, indicating that molecules in the first adsorption state have a negligible effect on the surface energy of the sensor membrane. This finding has previously been observed for the adsorption of lysozyme at the air-water interface.62 Figure 13 reports as a function of time the predicted population of protein molecules in total and in each surface state for the (62) Erickson, J. S.; Sundaram, S.; Stebe, K. J. Langmuir 2000, 16 (11), 50725078.
5600 Langmuir, Vol. 23, No. 10, 2007
Figure 13. Predicted evolution of each surface state population for the HEWL adsorption experiment described in Figure 8.
model fit shown in Figure 12 and in Table 4. The model predicts that adsorbed protein molecules transfer into state 2 relatively quickly and then more slowly into state 3. Upon flushing protein from the bulk solution, all sorbate in state 1 desorbs along with a small proportion of the molecules in state 2 that revert back to state 1 during the dilution process. All molecules in state 3 are predicted to remain irreversibly bound to the surface. The predicted model results using the parameters in Table 4 were then compared to a series of REST sensor studies carried out at different HEWL concentrations and incubation times. Small differences between the calculated and experimental trends are observed, most likely due to small differences in the properties and mounting of the membrane (a fresh membrane was used for each experiment). Nevertheless, the model clearly captures the unique features of protein adsorption kinetics, including the relatively fast mass loading, the much more gradual change in surface energy that does not cease until protein is removed from the bulk, the rapid desorption of an incubation-time-dependent fraction of bound protein when protein is removed from the bulk, and the fixing of the residual surface concentration and surface energy at constant values once the removal of reversibly bound protein and free protein is complete.
Conclusions We present data from a novel acoustically actuated resonant membrane sensor that show that the adsorption of the globular protein HEWL to an acrylic membrane surface results in changes in the surface energy of the membrane that persist long after mass loading of the protein has reached steady state. In situ measurements of adlayer formation using an optical evanescent
Clark et al.
field show that the sorbate concentration reaches steady state in less than ∼60 min. A fraction (fbound) of that adsorbed protein remains bound to the membrane following complete removal of protein from the solution phase. We find that fbound increases rapidly with time upon introduction of protein into the system, and then it increases more slowly as the contact time is extended well past the time at which the sorbate concentration reaches steady state, indicating a slow change in the structure of the adlayer that is not associated with the net loading of additional protein on the membrane. Complete removal of protein from the bulk solution results in stabilization of the surface energy to a constant value, indicating that interactions between protein in the bulk solution and protein in the adlayer are a necessary contributor to the slow changes in the adlayer structure that alter the surface energy and to the ability of adsorbed protein to desorb from the adlayer. This discovery and the γ(t) data provided by the REST sensor were used to refine previous models of protein adsorption kinetics that allow a given protein molecule in the adlayer to be transferred among an ensemble of unique structural and energetic states.3,5 These two previous models compute Γ(t), the mass loading of the sorbent, and have been shown to capture many of the unusual mass-loading effects associated with the history dependence of the protein adsorption process. Our model builds on this basic theoretical framework by making both the forward and reverse rates of transfer between surface states proportional to cL. This concept imbues the model with the ability to capture many of the unusual adsorption phenomena revealed by the REST sensor measurements, including the fixing of the residual surface concentration and surface energy at constant values when all protein in the bulk solution is removed from the system. Thus, we show that the measurement of γ(t) provides important insights into the nature of protein adsorption to solidliquid interfaces that are not directly or easily revealed from more traditional Γ(t) data and that may be used to advance theories of the adsorption process. Acknowledgment. Financial support for this research was provided by the Natural Sciences and Engineering Research Council (NSERC) Discovery and Equipment Grant programs and by the Canadian Foundation for Innovation (CFI) Canada Research Chairs Infrastructure program. The authors thank Dr. Susan Liu for assistance in the measurement and interpretation of the adsorption isotherm data and Dr. Michele Mossman for assistance in the completion of the publication of this work. Charles Haynes holds the Canada Research Chair in Interfacial Biotechnology, and Lorne Whitehead holds the NSERC/3M Industrial Research Chair in Structured Surface Physics. LA0635350
