Kinetics of Adsorption and Proteolytic Cleavage of a Multilayer

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Kinetics of Adsorption and Proteolytic Cleavage of a Multilayer Ovalbumin Film by Subtilisin Carlsberg Ladan L. Foose, Harvey W. Blanch, and C. J. Radke* Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720 ReceiVed March 5, 2008. ReVised Manuscript ReceiVed April 21, 2008 Adsorption and proteolytic activity of the enzyme subtilisin Carlsberg have been studied on an immobilized, multilayer ovalbumin film. The cross-linked multilayer substrate permits protease adsorption to be examined unencumbered by the surface inhomogeneity typically observed in monolayer studies of protease surface kinetics. Decline of the protein film was measured over time using ellipsometry. Resulting kinetic data as a function of aqueous enzyme concentration and temperature were well fit by a Langmuir-Michaelis-Menten model for surface proteolysis. We observed that both the protein degradation kinetics and the in situ adsorption data were well described by the proposed model. The temperature dependence of the kinetic rate parameter yielded an activation energy of 12 kcal/mol. Further, the apparent Langmuir adsorption equilibrium constant of the enzyme at the protein/aqueous interface was 0.11 L/mg at 22 °C, 0.034 L/mg at 36 °C, and 0.011 L/mg at 50 °C. Although enzyme adsorption at a given aqueous enzyme concentration decreased at higher temperature, the enzyme cleaved the substrate more rapidly, leading to a net increase in the ovalbumin film degradation rate. We observed that the maximum enzyme coverage on the immobilized protein surface was approximately 40% of a close-packed monolayer at ambient temperature (22 °C).

Introduction Studies of enzymes at solid/liquid interfaces are of increasing interest because of the incorporation of enzymes into a variety of commercial products and processes, including automatic dishwashing and laundry detergents, processing of paper, food, and textiles, and cleaning of medical implants and instruments.1–5 In addition, there is an increasing use of rapid enzyme-based screening and synthesis on solid supports,6–15 such as in enzyme assays for identifying substrates on microarrays and in enzymecatalyzed peptide synthesis.16–20 Aqueous-phase enzyme kinetics is a poor predictor of enzyme kinetics at an interface since heterogeneous catalysis is affected by the change in enzyme activity upon adsorption at the interface,21,22 the nature of the substrate,23,24 the intersubstrate

(1) Berg, I. C. H.; Kalfas, S.; Malmsten, M.; Arnebrant, T. Eur. J. Oral Sci. 2001, 109, 316–324. (2) Bhat, M. K. Biotechnol. AdV. 2000, 18, 355–383. (3) Ito, S.; Kobayashi, T.; Ara, K.; Ozaki, K.; Kawai, S.; Hatada, Y. Extremophiles 1998, 2, 185–190. (4) Levy, I.; Nussinovitch, A.; Shpigel, E.; Shoseyov, O. Cellulose 2002, 9, 91–98. (5) Villeneuve, P.; Muderhwa, J. M.; Graille, J.; Haas, M. J. J. Mol. Catal. B 2000, 9, 113–148. (6) Hansen, K. K.; Hansen, H. C.; Clark, R. C.; Bartlett, P. A. J. Org. Chem. 2003, 68, 8459–8464. (7) Houseman, B. T.; Huh, J. H.; Kron, S. J.; Mrksich, M. Nat. Biotechnol. 2002, 20, 270–274. (8) Kohli, R. M.; Burke, M. D.; Tao, J. H.; Walsh, C. T. J. Am. Chem. Soc. 2003, 125, 7160–7161. (9) Meldal, M. Biopolymers 2002, 66, 93–100. (10) Reents, R.; Jeyaraj, D. A.; Waldmann, H. AdV. Synth. Catal. 2001, 343, 501–513. (11) Salisbury, C. M.; Maly, D. J.; Ellman, J. A. J. Am. Chem. Soc. 2002, 124, 14868–14870. (12) Tolborg, J. F.; Petersen, L.; Jensen, K. J.; Mayer, C.; Jakeman, D. L.; Warren, R. A. J.; Withers, S. G. J. Org. Chem. 2002, 67, 4143–4149. (13) Uttamchandani, M.; Chan, E. W. S.; Chen, G. Y. J.; Yao, S. Q. Bioorg. Med. Chem. Lett. 2003, 13, 2997–3000. (14) Wu, X.; Bu, X.; Wong, K. M.; Yan, W. L.; Guo, Z. H. Org. Lett. 2003, 5, 1749–1752. (15) Zhu, Q.; Uttamchandani, M.; Li, D. B.; Lesaicherre, M. L.; Yao, S. Q. Org. Lett. 2003, 5, 1257–1260. (16) Altreuter, D. H.; Dordick, J. S.; Clark, D. S. Biotechnol. Bioeng. 2003, 81, 809–817.

distance at the surface,25 and alteration in the enzyme conformation at the interface.26 A more detailed understanding of heterogeneous enzyme reaction requires study of the adsorption and surface cleavage kinetics of the enzyme on a solid substrate. Studies of interfacial proteolysis conducted thus far employed monolayers or submonolayers of protein substrate on a surface, for example, immobilizing substrates to gold-coated glass slides22,27 or to glass beads.23,24 A difficulty with these model substrates is that the protease adsorbs both on protein-occupied sites and on solid-support sites. In addition, the nature of the surface changes over time as the enzyme cleaves the protein substrate, exposing a greater number of unoccupied sites for enzyme adsorption. This makes interpretation of protease adsorption behavior on the bound protein layer difficult. We have shown previously that an immobilized, cross-linked, multilayer protein film is a useful tool for overcoming these deficiencies in the study of protease adsorption and cleavage kinetics.28 Despite the increasing interest in understanding the mechanism of heterogeneous proteolysis, little work has been done to construct a quantitative model describing the catalytic behavior of enzymes at surfaces. We propose a generalized treatment (17) Doeze, R. H. P.; Maltman, B. A.; Egan, C. L.; Ulijn, R. V.; Flitsch, S. L. Angew. Chem., Int. Ed. 2004, 43, 3138–3141. (18) Humphrey, C. E.; Turner, N. J.; Easson, M. A. M.; Flitsch, S. L.; Ulijn, R. V. J. Am. Chem. Soc. 2003, 125, 13952–13953. (19) Ulijn, R. V.; Baraganã, B.; Halling, P. J.; Flitsch, S. L. J. Am. Chem. Soc. 2002, 124, 10988–10989. (20) Ulijn, R. V.; Bisek, N.; Flitsch, S. L. Org. Biomol. Chem. 2003, 1, 621– 622. (21) Brode, P. F., III; Rauch, D. S. Langmuir 1992, 8, 1325–1329. (22) Kim, J.; Roy, S.; Kellis, J. T., Jr.; Poulose, A. J.; Gast, A. P.; Robertson, C. R. Langmuir 2002, 18, 6312–6318. (23) Brode, P. F., III; Erwin, C. R.; Rauch, D. S.; Lucas, D. S.; Rubingh, D. N. J. Biol. Chem. 1994, 269, 23538–23543. (24) Esker, A. R.; Brode, P. F., III; Rubingh, D. N.; Rauch, D. S.; Yu, H.; Gast, A. P.; Robertson, C. R.; Trigiante, G. Langmuir 2000, 16, 2198–2206. (25) Gaspers, P. B.; Gast, A. P.; Robertson, C. R. J. Colloid Interface Sci. 1995, 172, 518–529. (26) Karajanagi, S. S.; Vertegel, A. A.; Kane, R. S.; Dordick, J. S. Langmuir 2004, 20, 11594–11599. (27) Roy, S.; Kim, J.; Kellis, J. T., Jr.; Poulose, A. J.; Robertson, C. R.; Gast, A. P. Langmuir 2002, 18, 6319–6323. (28) Foose, L. L.; Blanch, H. W.; Radke, C. J. J. Biotechnol. 2007, 132, 32–37.

10.1021/la8007014 CCC: $40.75  2008 American Chemical Society Published on Web 06/20/2008

Proteolytic ActiVity of Subtilisin Carlsberg

based on Langmuir adsorption and Michaelis-Menten kinetics29 to describe subtilisin Carlsberg proteolysis of an immobilized protein layer. In this model, adsorbed enzyme is assumed to be in equilibrium with the aqueous enzyme. The reversible adsorption step is followed by an equilibrium reaction in which the adsorbed enzyme binds to substrate at the surface, forming an enzymesubstrate complex and resulting in the cleavage of the peptide bonds present in the immobilized protein substrate. Other authors have proposed a mechanism that suggests the enzyme adsorbs from solution to form directly the enzyme-substrate complex,30–33 an unlikely scenario. A variety of techniques have been used to study protein adsorption at the solid/liquid interface, including optical waveguide light-mode spectroscopy (OWLS),34–36 ellipsometry,35,37–40 total internal reflection fluorescence (TIRF),41,42 scanning angle reflectometry,43,44 electron spectroscopy for chemical analysis (ESCA),45 atomic force microscopy (AFM),46–48 electron microscopy,49 quartz crystal microbalance (QCM) measurements,35,50 and surface plasmon resonance (SPR).22,27,32,50,51 In this work, we studied enzyme cleavage of an immobilized protein film using in situ ellipsometry. To decouple protease adsorption and cleavage events, a densely cross-linked protein film was employed that did not hydrolyze over the relevant time scale of enzyme sorption. Resulting proteolysis and protease adsorption kinetic data were fit to the Langmuir-Michaelis-Menten (LMM) model to yield parameters describing the equilibrium adsorption, cleavage kinetics, and activation energy of subtilisin Carlsberg on ovalbumin and bovine serum albumin (BSA) protein films.

Experimental Section Materials. Silicon wafers (100 mm diameter, 500 µm thickness, 〈100〉, p-type boron, single-side-polished) were purchased from International Wafer Service, Inc. A Harrick plasma cleaner/sterilizer (PDC-32G) was used to plasma oxidize the wafers. (3-Aminopro(29) Hickel, A.; Radke, C. J.; Blanch, H. W. Biotechnol. Bioeng. 1999, 65, 425–436. (30) Gutie´rrez, O. A.; Chavez, M.; Lissi, E. Anal. Chem. 2004, 76, 2664–2668. (31) Gutie´rrez, O. A.; Salas, E.; Hernańdez, Y.; Lissi, E. A.; Castrillo, G.; Reyes, O.; Garay, H.; Aguilar, A.; Garcıá, B.; Otero, A.; Chavez, M. A.; Duarte, C. A. Anal. Biochem. 2002, 307, 18–24. (32) Lee, H. J.; Wark, A. W.; Goodrich, T. T.; Fang, S.; Corn, R. M. Langmuir 2005, 21, 4050–4057. (33) Nayak, S.; Yeo, W.; Mrksich, M. Langmuir 2007, 23, 5578–5583. (34) Brusatori, M. A.; Tie, Y.; Van Tassel, P. R. Langmuir 2003, 19, 5089– 5097. (35) Hoö¨k, F.; Vo¨ro¨s, J.; Rodahl, M.; Kurrat, R.; Bo¨ni, P.; Ramsden, J. J.; Textor, M.; Spencer, N. D.; Tengvall, P.; Gold, J.; Kasemo, B. Colloids Surf., B 2002, 24, 155–170. (36) Wendorf, J. R.; Radke, C. J.; Blanch, H. W. Biotechnol. Bioeng. 2004, 87, 565–573. (37) Jonsson, U.; Lundstrom, I.; Ronnberg, I. J. Colloid Interface Sci. 1987, 117, 127–138. (38) Jonsson, U.; Malmqvist, M.; Ronnberg, I. J. Colloid Interface Sci. 1985, 103, 360–372. (39) Malmsten, M. J. Colloid Interface Sci. 1994, 166, 333–342. (40) Taylor, G. T.; Troy, P. J.; Sharma, S. K. Mar. Chem. 1994, 45, 15–30. (41) Cheng, Y. L.; Darst, S. A.; Robertson, C. R. J. Colloid Interface Sci. 1987, 118, 212–223. (42) Tilton, R. D.; Robertson, C. R.; Gast, A. P. J. Colloid Interface Sci. 1990, 137, 192–203. (43) Schaaf, P.; Dejardin, P. Colloids Surf. 1988, 31, 89–103. (44) Shirahama, H.; Lyklema, J.; Norde, W. J. Colloid Interface Sci. 1990, 139, 177–187. (45) Ratner, B. D.; Horbett, T. A.; Shuttleworth, D.; Thomas, H. R. J. Colloid Interface Sci. 1981, 83, 630–642. (46) Haggerty, L.; Lenhoff, A. M. Biophys. J. 1993, 64, 886–895. (47) Haggerty, L.; Lenhoff, A. M. Biotechnol. Prog. 1993, 9, 1–11. (48) Kim, D. T.; Blanch, H. W.; Radke, C. J. Langmuir 2002, 18, 5841–5850. (49) Gorman, R. R.; Stoner, G. E.; Catlin, A. J. Phys. Chem. 1971, 75, 2103– 2107. (50) Laschitsch, A.; Menges, B.; Johannsmann, D. Appl. Phys. Lett. 2000, 77, 2252–2254. (51) Stenberg, E.; Persson, B.; Roos, H.; Urbaniczky, C. J. Colloid Interface Sci. 1991, 143, 513–526.

Langmuir, Vol. 24, No. 14, 2008 7389 pyl)triethoxysilane (APTES; g98.0% by GC) from Fluka aminefunctionalized the silicon wafers by chemical vapor deposition (CVD). Aqueous protein solutions were prepared from distilled/ deionized water from a Millipore Milli-Q filter unit (18.2 MΩ · cm resistivity). Ovalbumin (5× crystalline, g98.0% by SDS-PAGE) was from Calbiochem. BSA (g99.0% by agarose gel electrophoresis) was from Sigma. Protein solutions (41 mg/mL) were cast onto silicon wafer supports at 3000 rpm using a Cookson P-6000 spin coater. Vapor over a 25 wt % glutaraldehyde (Sigma-Aldrich) aqueous solution cross-linked and immobilized the protein films. Subtilisin Carlsberg (Sigma, activity 10 units/mg, high-purity lyophilized powder) served as the protease. The solvent was 10 mM NaH2PO4 aqueous buffer, pH 8.1, made from Na2HPO4 · 7H2O and NaH2PO4 · H2O each procured from EMD Biosciences (g98.0%). Protein film thicknesses were measured using a Sentech SE400 ellipsometer (HeNe laser, λ ) 632.8 nm, angle of incidence φ ) 70°). Deposition of Protein Films. Formation of the immobilized, multilayer protein films is described in detail elsewhere.28 Briefly, a plasma-oxidized silicon wafer was amine-functionalized with APTES. A protein film was then spin-cast onto the functionalized silicon surface, and vapor-phase glutaraldehyde cross-linked the lysine residues in the protein film. The resulting immobilized, multilayer protein film substrate was stable in the presence of nonprotease solutions and homogeneous both laterally and in depth. For clarity, all references to the substrate refer to the protein-film substrate, whereas all references to the support refer to the silicon solid support on which the protein film is deposited. Ovalbumin films were prepared as described previously.28 Immobilized BSA films were formed on a 17.5 mm × 17.5 mm silicon wafer (the size of the platform in the ellipsometry flow cell). Samples were cross-linked with glutaraldehyde vapor for 15 h. The BSA film thickness as measured by ellipsometry in air was approximately 115 nm, corresponding roughly to 16 layers of protein on the basis of the 7 nm Stokes diameter of BSA.52 Determination of Proteolysis Rates. Proteolytic cleavage of the immobilized ovalbumin layer by subtilisin Carlsberg was determined by measuring the decrease of the film thickness with time. As described previously,28 protein substrate samples were periodically removed after exposure to the aqueous protease, rinsed in buffer and distilled/deionized water, and allowed to dry in air. The thickness of the dried films was determined by ellipsometry (Sentech SE400) and declined at a constant rate.28 Tapping-mode AFM images of the dried protein substrate before and after exposure to enzyme demonstrated uniform surface cleavage with no pitting/tunneling into the bulk of the film substrate.28 Substrate samples were reimmersed in the same protease solutions until the next measurement. The negative slope of the declining film thickness with time (-dh/ dt) gauges the rate of proteolytic cleavage. Unless noted otherwise, experiments were conducted at ambient temperature (22 °C). For rate data collected at 36 and 50 °C, all solutions were held at a constant temperature in a circulating bath (Cole Parmer Polystat temperature controller, model 12112-11). In Situ Flow Ellipsometry. To assess the adsorption/desorption behavior of the protease on top of the multilayer protein film, an in-house flow cell was constructed for in situ ellipsometry studies as illustrated in Figure 1. Cell materials include a poly(methyl methacrylate) body, precision-fused silica optical windows (Edmund Optics), and styrene-ethylene-butylene-modified block copolymer flow tubing that exhibits low protein binding (Cole Parmer). The internal volume of the flow cell was minimized (approximately 11 mL), thereby reducing the volume of enzyme solution needed in continuous experiments. To avoid trapping air bubbles near the optical windows or creating anomalous flow patterns, the inside of the cell walls were machined smooth with no protruding features. Inlet and exit ports of the cell were fitted with polyethylene frits (20 µm pore size, 3 mm thickness, Argonaut Technologies Inc.) that have the same triangular cross-sectional area as the inside of the cell. Flow distribution within the frits allows uniform cross-sectional distribution (52) Daqiq, L.; Fellows, C. M.; Bekes, F.; Lees, E. J. Texture Stud. 2007, 38, 273–296.

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Figure 1. Schematic of the in situ ellipsometry cell. (a) Cross-section of the cell orthogonal to the direction of flow, showing the optical windows (OWs), location of the inlet and outlet tubing (I/O), and flow-distribution frits (F) at the entrance and exit of the cell. (b) The platform holding the protein-coated sample (S) forms the base of the cell. The base is sealed with a rubber O-ring (O), and the sample is held in place by a sample cover (C) that exposes a 14 mm diameter circular portion of the protein-coated wafer to the flowing solution.

of the solution during axial flow through the cell. Visual experiments with fluorescein dye indicated a uniform plug-flow profile in the cell. Enzyme solution effluent from the exit port was checked for activity (fluorescently labeled BSA assay), concentration, and conformation (circular dichroism), confirming no change in the native enzyme after passing through the porous frits and no significant adsorption losses to the frit or flow-cell surfaces. In situ adsorption kinetics of subtilisin Carlsberg was measured on BSA films. The BSA film was more highly cross-linked by glutaraldehyde than ovalbumin, as BSA has a larger number of lysine residues (60 lysines per protein, comprising 9.9% of the total residues) compared to ovalbumin (20 lysines per protein, comprising 5.2% of the total residues). Given that the protein-deposition procedure likely alters the protein conformation from its native state, it is difficult to specify exactly which lysine groups are involved in cross-linking. The overall lysine density of the protein serves as a general guide for the degree of immobilization. The high cross-link density of BSA permitted protease adsorption to be studied in the absence of proteolysis, as cleavage of the immobilized BSA was strongly retarded. After cross-linking, BSA samples were rinsed for short periods of time in aqueous and enzymatic solutions to remove loosely bound protein. The rinse sequence was 15 min in 10 mM NaH2PO4 buffer, 15 min in 30 µg/mL buffered subtilisin Carlsberg, 15 min in buffer, and 5 min in distilled/deionized water, followed by drying in air. The samples were then placed onto the flow-cell platform. The height and tilt angle of the sample were aligned to give the strongest optical signal for ellipsometry. The top of the cell was screwed in place, and 10 mM NaH2PO4 buffer was pumped in at a rate of 10 mL/min. The protein film swells upon hydration. To obtain a stable baseline, the film was equilibrated in buffer for 2 h prior to commencing film-thickness measurements. The total amount of film swelling after this equilibration period was approximately 45%. The measured refractive index of the hydrated BSA film was 1.48, and the refractive index used for the buffer was 1.33. Subtilisin Carlsberg solutions of various concentrations were prepared in 10 mM NaH2PO4 buffer and checked by measuring the absorbance at 280 nm with a UV/vis spectrophotometer (E1% ) 8.6, Molecular Devices Spectramax M2). The enzyme solution was pumped into the cell at a rate of 10 mL/min for 15 min, followed by a rinse step with the buffer for approximately 30 min until the measured thickness was constant. The adsorbed mass of enzyme is calculated following the de Feijter method from the thickness of the adsorbed layer, the refractive index increment (dn/dc ) 0.18 cm3/g), and the refractive indices of the protein layer and buffer solution.53,54 (53) Fasman, G. D. Handbook of Biochemistry and Molecular Biology, 3rd ed.; CRC Press: Cleveland, OH, 1975.

Figure 2. Cleavage rate of an immobilized ovalbumin film as a function of aqueous enzyme concentration at 22 °C. The solid curve is the best fit to the LMM kinetic model.

Adsorption kinetics of subtilisin Carlsberg on the protein film was independent of flow rate. We also employed Le´veˆque theory to assess the mass transfer coefficient55 using estimates of the enzyme diffusion coefficient (10-6 cm2/s) and the shear rate (0.25 s-1). These exercises confirmed that mass transport to the protein surface was not rate limiting.

Results Proteolysis Rates. The ambient-temperature rate of proteolysis of an immobilized, multilayer ovalbumin film due to cleavage by subtilisin Carlsberg is shown in Figure 2. Each datum represents the slope of the declining film thickness in time for a protein film in the given enzyme solution. The measured kinetic rate averages over the distribution of product fragment sizes. For low enzyme concentrations, the proteolysis rate was linear in enzyme concentration. Above an aqueous-phase enzyme concentration of approximately 30 ppm, however, the proteolysis rate attained a constant value. This maximum rate results from the enzyme surface coverage reaching a maximum value at the ovalbumin/ (54) deFeijter, J. A.; Benjamins, J.; Veer, F. A. Biopolymers 1978, 17, 1759– 1772. (55) Lok, B. K.; Cheng, Y.; Robertson, C. R. J. Colloid Interface Sci. 1983, 91, 104–116.




aqueous interface, as discussed below. The solid line in Figure 2, and in Figures 3 and 4 to follow, corresponds to the proposed LMM model. Effect of Temperature on the Cleavage Rate. The effect of temperature on the rate of proteolysis of the immobilized substrate is seen in Figures 3 and 4. Of note are the significant differences in rates for 22, 36, and 50 °C. For example, at 1 µg/mL subtilisin Carlsberg, surface proteolysis of ovalbumin films at 36 °C was approximately 20% faster than at 22 °C; at 50 µg/mL, the rate increased 4-fold at 36 °C as compared to 22 °C. When the temperature was increased to 50 °C, the results were even more dramatic. At 1 µg/mL enzyme and 50 °C, subtilisin cleaved the substrate almost 4 times faster than at 22 °C, and at 50 µg/mL, the cleavage rate increased approximately 15-fold compared to that at 22 °C. In addition to an increase in the protein degradation rate with increasing temperature, we observed an increase in the enzyme concentration at which the maximum cleavage rate was achieved. For 22 °C, this occurs at approximately 30 µg/mL, whereas, at 36 °C, the maximum rate occurs at 60 µg/mL and, at 50 °C, at around 170 µg/mL. Enzyme Adsorption Isotherm. Adsorption of the protease onto immobilized, highly cross-linked 115 nm (dry thickness) BSA films was assessed by in situ ellipsometry. Figure 5 illustrates

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Figure 5. Adsorption kinetics of 30 µg/mL subtilisin Carlsberg onto a 115 nm (dry thickness) immobilized, highly cross-linked BSA film at 22 °C.

Figure 6. Adsorption isotherm of subtilisin Carlsberg on an immobilized, multilayer BSA protein film at 22 °C. The fit curve is based on Λ at 22 °C from Table 1 and a Γmax of 0.13 µg/cm2.

the sorption kinetics for a 30 µg/mL buffered solution of subtilisin Carlsberg. Upon introduction of the enzyme solution into the flow cell, the total measured surface mass, inclusive of both the protein film and adsorbed enzyme layer, increased rapidly as shown at 13 min. Within 15 min of adsorption, the adsorbed mass leveled off to the equilibrium surface concentration of enzyme. Buffer was introduced at 28 min, and the enzyme completely desorbed from the surface within 20 min. Clearly, for the short adsorption exposure times considered here, the adsorption/desorption process was reversible. Time scales for adsorption and desorption were similar for the entire range of enzyme concentrations studied. It is important to note that the five-carbon cross-linker (vapor-phase glutaraldehyde) creates a closely packed network structure that likely has a mesh size too small to allow absorption of enzyme into the bulk of the film. The reversible adsorption isotherm at 22 °C is shown in Figure 6 for subtilisin Carlsberg on the BSA multilayer film. The adsorption plateau in Figure 6 occurred at an aqueous enzyme concentration of approximately 30 µg/mL, suggesting that at this concentration the surface is saturated with the maximum equilibrium surface concentration of enzyme. We found no significant differences between adsorption of subtilisin Carlsberg on either ovalbumin or BSA. This is perhaps not surprising since both proteins are globular and have similar isoelectric points (pI

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Table 1. Fit Parameters of the Langmuir-Michaelis-Menten Model to the Kinetic Data in Figures 2–4 temp (°C)

κ (nm · L · mg-1 · h-1)

Λ (L · mg-1)

22 36 50

0.93 ( 0.07 1.5 ( 0.1 5.3 ( 0.3

0.11 ( 0.01 0.034 ( 0.003 0.011 ( 0.001

approximately 5.4). However, the highly cross-linked nature of the immobilized BSA permits enzyme-adsorption detection decoupled from cleavage kinetics. We see that the adsorption plateau of subtilisin Carlsberg on BSA coincides with the plateau concentration in Figure 2 for the cleavage rate of an ovalbumin multilayer film. Hence, the cleavage rate in Figure 2 levels off for enzyme concentrations above 30 µg/mL because a maximum enzyme surface concentration is reached. Using the value of a Stokes-Einstein radius of approximately 2.1 nm for subtilisin Carlsberg22 and assuming that the enzyme does not change size once at the interface, we approximate the projected area of an enzyme molecule as 14 nm2. Assuming a flat protein substrate surface that is fully accessible to the enzyme, the surface concentration of subtilisin Carlsberg necessary to form a close-packed monolayer is 0.33 µg/cm2. The adsorption plateau in Figure 6 occurs at roughly 0.13 µg/cm2, indicating that the enzyme coverage is 40% of a close-packed monolayer. Although part of the reason for this difference may be due to the approximations made in calculating the molecular footprint of subtilisin Carlsberg (for example, the enzyme may spread slightly upon adsorption), it is possible that lateral interactions between the enzymes prevent a close-packed surface coverage. Langmuir-Michaelis-Menten Kinetics. A LangmuirMichaelis-Menten model for enzyme adsorption and kinetics was developed to describe the proteolysis-rate data.29 Figure 7 illustrates the proposed mechanism. The subscript S denotes a surface species. E denotes enzyme in the aqueous phase, ES is the adsorbed enzyme, SS is the immobilized substrate, (ES)S is the adsorbed enzyme-substrate complex, and P is an aqueoussoluble product fragment cleaved from the protein substrate surface. Figure 5 verifies the assumption of equilibrium between the enzyme in solution and the adsorbed enzyme. It is important to note that the measured increase in mass of approximately 0.1 µg/cm2 includes the enzyme in both its adsorbed (ES) and complexed ((ES)S) forms. We neglect here lateral diffusion of the adsorbed enzyme prior to complexation with the substrate.56,57 Inclusion of one or more diffusion steps adds additional parameters, but does not change the overall form of the model. We assume that cleaved product fragments are directly released into the aqueous phase and neglect any release and readsorption of product onto the immobilized protein surface. According to the proposed Langmuir-Michaelis-Menten framework outlined in the Appendix, the protein film is cleaved at the rate (eqs A9–A11)

-

dh κ[E] ) dt 1 + Λ[E]

(1)

where [E] is the aqueous enzyme concentration, κ is a lumped rate parameter, and Λ is a lumped Langmuir equilibrium constant. As noted earlier, the measured enzyme concentration in the adsorption isotherm consists of both adsorbed enzyme and enzyme-substrate complex; hence, the Langmuir equilibrium constant in eq 1 is an apparent constant based on the total concentrations of both species. Details of the derivation are (56) Jervis, E. J.; Haynes, C. A.; Kilburn, D. G. J. Biol. Chem. 1997, 272, 24016–24023. (57) Roy, S.; Thomas, J. M.; Holmes, E. A.; Kellis, J. T.; Poulose, A. J.; Robertson, C. R.; Gast, A. P. Anal. Chem. 2005, 77, 8146–8150.

Figure 7. Schematic of enzyme adsorption onto an immobilized substrate surface, enzyme-substrate complexation, and proteolytic cleavage in the LMM model.

presented in the Appendix. Solid lines in Figures 2–4 are fits of the LMM model to the experimental rate data using “NonLinearFit” in the Mathematica 4 software statistical package. The data are well described by the model. Table 1 contains the fit parameters κ and Λ. Using Λ at 22 °C from our kinetic data and a Γmax value of 0.13 µg/cm2, we obtain the model fit to the adsorption isotherm shown by the solid line in Figure 6. There is very good agreement between the independently obtained kinetic and adsorption results.

Discussion Table 1 demonstrates that Λ decreases with increasing temperature. This indicates that, for a given aqueous enzyme concentration, enzyme adsorption at the surface is smaller than that for a lower temperature, requiring a higher aqueous enzyme concentration to achieve surface saturation. Other researchers who observed a decreased enzyme surface concentration with increasing temperature inferred that the rate of formation of product from the (ES)S complex is increased and hence that the concentration of (ES)S at the surface is smaller.32 Clearly, there is an exponential dependence on the inverse temperature of the Langmuir adsorption equilibrium constant that leads to a decreasing adsorption at higher temperature. Additionally, at higher temperatures, the entropic penalty associated with the loss of translational and rotational motion of an adsorbed enzyme overcomes some of the enthalpic contributions associated with favorable enzyme-substrate electrostatic and van der Waals interactions, resulting in a less favorable Gibbs free energy of adsorption. This reasoning accentuates the decreasing value of the Langmuir equilibrium constant at higher temperatures. There are then two possible components to the temperature effect in Figures 2–4: a decrease in enzyme adsorption with increasing temperature (for concentrations below that of surface saturation) and an increase in the reaction rate of the (ES)S complex with increasing temperature, both of which result in a reduced surface concentration of enzyme. Table 1 also reveals that the lumped rate constant, κ, increases with increasing temperature by about a factor of 5 between 22 and 50 °C. We observed that the strongest temperature dependence in the lumped rate constant results from changes in the catalytic rate constant k2, rather than in the temperature dependence of the equilibrium constants K and KL. Figure 8 shows the Arrhenius dependence of the rate constant on temperature. The linear fit of the Arrhenius expression to the data has an R2 value of 0.93. We find an apparent activation energy of approximately 12 kcal/ mol. This is comparable to the 13.7 kcal/mol activation energy reported for aqueous-phase hydrolysis of azocasein by subtilisin Carlsberg.58 As in aqueous-phase proteolysis, temperatureinduced protein conformational changes in surface proteolysis (58) Kulakova, L.; Galkin, A.; Kurihara, T.; Yoshimura, T.; Esaki, N. Appl. EnViron. Microbiol. 1999, 65, 611–617.


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Appendix: Langmuir-Michaelis-Menten Model Figure 7 illustrates the proposed Langmuir-Michaelis-Menten mechanism. We assume that the cleaved product fragments are released into the aqueous phase and neglect any release and readsorption of product onto the immobilized substrate surface. The enzyme in solution is in equilibrium with the adsorbed enzyme: KL

E + open site {\} ES

(A1)

where KL is the Langmuir adsorption equilibrium constant defined as

KL ) ΓE/[E][open site]

(A2)

and Γi denotes the surface concentration of species i. An adsorption site balance yields Figure 8. Arrhenius plot for proteolysis of immobilized ovalbumin by subtilisin Carlsberg. κ (nm · L · mg-1 · h-1) is the effective kinetic parameter in the LMM model as listed in Table 1.

may expose additional cleavage sites to the enzyme, increasing protein-film degradation.

Γmax ) [open sites] + ΓE + ΓES

(A3)

Once at the surface, the enzyme forms a complex with the substrate: K

ES + SS {\} (ES)S

Conclusions An immobilized, multilayer protein film provides a convenient means to determine independently the cleavage and adsorption kinetics of subtilisin Carlsberg at the protein/aqueous interface. Immobilized protein degradation kinetics of the substrate as a function of aqueous enzyme concentration was collected for three reaction temperatures. A Langmuir-Michaelis-Menten model was developed to describe the reversible adsorption of the protease from solution onto the surface, reversible complexation of surface enzyme to the immobilized substrate, and irreversible hydrolysis of the protein by the enzyme to release peptide fragments into solution. The resulting kinetic curves were well fit by the proposed model, yielding fit parameters describing the apparent kinetic rate constant and apparent Langmuir adsorption equilibrium constant. The resulting apparent rate constants at different temperatures provided an activation energy for the surface proteolysis reaction of 12 kcal/mol that is comparable to that found for aqueous proteolysis. The apparent Langmuir equilibrium constants decreased with increasing temperature, indicating that at higher temperatures there is less enzyme adsorbed at the surface for a given aqueous enzyme concentration. However, the surface enzymes were more active. The lumped Langmuir equilibrium constant measured from the kinetic data provided a good fit to the adsorption isotherm for subtilisin Carlsberg obtained using a flow ellipsometer. Enzyme adsorption data support the assumption that enzyme adsorption is reversible and that the protein digestion rate levels off because the enzyme reaches a surface-saturation concentration. Acknowledgment. We are grateful to the National Science Foundation Graduate Research Fellowship Program and the U.C. Berkeley Graduate Fellowship Program for fellowship support of L.L.F. Partial support of the work was provided by U.C. Discovery Grant bio03-10396 and the Procter & Gamble Co. The experimental assistance of M. Louie is acknowledged.

(A4)

where K is the equilibrium constant defined as

K ) ΓES ⁄ ΓEΓS

(A5)

Since the multilayer substrate film is homogeneous and is cleaved laterally in a uniform manner by the enzyme, we assume a constant surface concentration of the substrate, ΓS. The enzyme-substrate complex reacts to form a peptide fragment P: k2

(ES)S 98 ES + P

(A6)

where k2 is the reaction rate constant for product formation. The rate of cleavage of the substrate is given by

ν ) k2ΓES

(A7)

Finally, a mass balance on the substrate, where FS is the substrate density, yields

FS

dh ) -ν dt

(A8)

By combining the above equations, we obtain the LangmuirMichaelis-Menten model describing the change in protein film thickness, h, with time:

-

dh (k2KΓSΓmaxKL/FS)[E] ) dt 1 + (1 + KΓS)KL[E]

(A9)

The lumped parameters κ and Λ in the text follow directly as

LA8007014

κ ) k2KΓSΓmaxKL/FS

(A10)

Λ ) (1 + KΓS)KL

(A11)

Kinetics of Adsorption and Proteolytic Cleavage of a Multilayer

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