Water Interface. 2. Diffusion

are probed with the technique of fluorescence recovery after photobleaching. Upon correlating the lateral diffusion coefficients of a probe lipid and ...
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Langmuir 2000, 16, 2672-2676

Lipase Catalysis on Monolayers at the Air/Water Interface. 2. Diffusion-Controlled Kinetics on Quasi-Two-Dimension Keiji Tanaka, Steven P. Mecca, and Hyuk Yu* Department of Chemistry, University of WisconsinsMadison, Madison, Wisconsin 53706 Received July 13, 1999. In Final Form: November 5, 1999 Homogeneous exoplasmic leaflets of biomembrane are mimicked by lipid monolayers at the air/water interface. The reaction rates of lipase (Pseudomonas cepacia) catalyzed hydrolysis of a substrate (umbelliferone stearate) on L-R-dilauroylphosphatidylcholine/cholesterol mixed monolayers at the air/ water interface are examined as a function of cholesterol composition, which is to vary the dynamics of the system. Lateral mobility as a measure of dynamics of phospholipids and adsorbed lipase molecules are probed with the technique of fluorescence recovery after photobleaching. Upon correlating the lateral diffusion coefficients of a probe lipid and lipase with the interfacial hydrolysis kinetics, we show for the first time that the catalytic reactions on the monolayers are diffusion-controlled. Moreover, our results are in a quantitative agreement with the two-dimensional reaction dynamics theory of Torney and McConnell.

Introduction Chemical reactions in solutions occur in a very different way from those in gases because the encounter frequency of reactants is considerably less than that in a gas. Besides, encountering particles stay together for longer periods of time than those in a gas under the influence of surrounding solvent environment. If the chemical step of such a reaction is faster than other various sequential steps, its reaction rate is governed by the rate at which the reactants diffuse through the medium, that is, the reaction kinetics is diffusion-controlled.1 It has been widely accepted that elementary reactions such as ion pair association in dilute aqueous solutions are a typical example of this.1 The heterogeneous chemical reaction is an intriguing issue for this aspect because sequential steps basically take place on two dimensions. For example, in the case of the dehydrogenation of ethane on a platinum catalysis, the reaction involves the four sequential steps: adsorption of ethane to Pt, diffusion of ethane on Pt, reaction, and desorption of products. If the diffusion of reactants on a solid surface is a rate-limiting step, this becomes a case of a two-dimensional diffusion-controlled reaction. The chemical reaction on two dimensions can be seen in a completely different, biological, system as well. A biological membrane is a self-assembly in which lipids form a matrix, and a variety of proteins are embedded in it.2-4 In such a membrane, the lipids play the role of quasi-twodimensional solvent, and thus biological membranes can be regarded as a quasi-two-dimensional smectic viscous continuum.2 Phospholipid monolayers at the air/water interface are often regarded as a well-represented model system of a hemi-leaflet of a bilayer membrane.5 The monolayer technique has been employed for more than 6 decades in the study of enzymatic reactions at the interface.6-15 A (1) Rice, S. A. Chemical Kinetics, Vol 25, Diffusion-Limited Reactions; Elsevier: Amsterdam, 1985; p 3. (2) Singer, S. J.; Nicolson, G. L. Science 1972, 175, 720. (3) Jacobson, K.; Sheets, E. D.; Simson, R. Science 1995, 268, 1441. (4) Simons, K.; Ikonen, E. Nature 1997, 387, 569. (5) Gennis, R. B. Biomembranes, Molecular Structure and Function; Springer-Verlag: New York, 1989; p 36. (6) Hughes, A. Biochem. J. 1935, 29, 437. (7) Lagocki, J. W.; Boyd, N. D.; Law, J. H.; Ke´zdy, F. J. J. Am. Chem. Soc. 1970, 92, 2923. (8) Colacicco, G. Nature 1971, 233, 202.

distinctive feature of the monolayer technique is the controllability of surface pressure, areal mass density, composition, and subphase viscosity. When a surface active lipolytic enzyme is injected beneath the lipid monolayer, it adsorbs spontaneously to the monolayer, manifesting enzymatic activity which is greater than that in bulk solution by several orders of magnitude, commonly ascribed to a conformational change of the enzyme at the interface.16,17 Our focus is to elucidate how the enzymatic hydrolysis kinetics at the interface is modulated by the dynamics in a fluid monolayer. Since we can gain access to the in-plane lateral diffusion of the reactants by fluorescence recovery after photobleaching (FRAP) technique,18-22 our intent is to explore a correlation, if any, between the lateral diffusion and the interfacial kinetics. By the lateral diffusion we mean a quasi-two-dimensional translational diffusion, for monolayers are interfacial objects with a finite thickness. Thus, in our experiment, the monolayer composed of an enzyme and lipids, which are not substrates toward the enzyme but rather function solely as a matrix of quasi-twodimensional viscous continuum, is prepared at the air/ water interface, and then a surface active substrate is injected beneath. The point is to mimic the processes taking place on the extracellular side of the cell membranes. The difference between the previous works (9) Verger, R. Methods Enzymol. 1980, 64, 340. (10) Verheij, H. M.; Slotboom, A. J.; de Haas, G. H. Rev. Physiol. Biochem. Pharmacol. 1981, 91, 91. (11) Brockman, H. L. Lipase; Elsevier: Amsterdam, 1984; p 1. (12) Thuren, T.; Wilcox, R. W.; Sisson, P.; Waite, M. J. Biol. Chem. 1991, 266, 4853. (13) Hall, D. G. Biochem. J. 1992, 287, 73. (14) Goodman, D. M.; Nemoto, E. M.; Evans, R. W.; Winter, P. M. Chem. Phys. Lipids 1996, 84, 57. (15) Ransac, S.; Ivanova, M.; Verger, R.; Panaiotov, I. Methods Enzymol. 1997, 286, 263. (16) Brzozowski, A.; Derewenda, U.; Derewenda, Z. S.; Dodson, G. G.; Lawson, D. M.; Turkenburg, J. P.; Bjorkling, F.; Huge-Jensen, B.; Patkar, S. A.; Thim, L. Nature 1991, 351, 491. (17) van Tilbeurgh, H.; Egloff, M.-P.; Martinez, C.; Rugani, N.; Verger, R.; Cambillau, C. Nature 1993, 362, 814. (18) Rubenstein, J. L. R.; Smith, B. A.; McConnell, H. Proc. Natl. Acad. Sci. U.S.A. 1979, 76, 15. (19) Peters, R.; Beck, K. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 7187. (20) Kim, S.; Yu, H. J. Phys. Chem. 1992, 96, 4034. (21) Tamada, K.; Kim, S.; Yu, H. Langmuir 1993, 9, 1545. (22) Almeida, P. F. F.; Vaz, W. L.; Thompson, T. E. Biochemistry 1992, 31, 1, 6739.

10.1021/la990925w CCC: $19.00 © 2000 American Chemical Society Published on Web 01/13/2000

Lipase Catalysis on Monolayers

referred to earlier and our experiment is that we relate the kinetics to the dynamic characteristics of the constituents of the monolayer. The phospholipid of our choice is L-R-dilauroylphosphatidylcholine (DLPC), since its bilayer has a gel-liquid crystal transition temperature of 271.4 K23 and, hence, is in a liquid-expanded state of the monolayer at the temperature of our experiment, 296.2 ( 0.5 K. Cholesterol, which is one of three principal components of animal cell membranes,24 is used as the second component of the lipid in order to vary the in-plane lateral diffusion coefficients of the monolayer constituents, which are now well documented for such an effect on bilayers22,25 and monolayers.26,27

Langmuir, Vol. 16, No. 6, 2000 2673 per lipase and was assumed to be small enough to have a negligible effect on the lateral diffusion coefficient of the intact lipase; we checked earlier that the intact and labeled lipases gave rise to the same surface pressure isotherms. This was in agreement with the report by Roberts and Tombs.29 For FRAP measurements, the labeled lipase was incorporated to the mixed monolayers by its equilibrium partitioning after a lipase solution injection into the subphase. The labeled-lipase fraction in the monolayers was less than 1 mol %. Fluorescence Recovery after Photobleaching. The instrumental setup and the data analysis method were reported earlier in detail.20 A set of recent modifications of the signal acquisition step is also described elsewhere.30 Briefly, the lateral diffusion coefficient, D(2), is deduced from

1/τ ) D(2) q2

(1)

Experimental Section Materials. DLPC and 1-acyl-2-[12-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]phosphatidylcholine (NBD-PC) is employed here as a fluorescent lipid probe (Avanti Polar Lipids). Cholesterol was purchased from Sigma. Umbelliferone stearate (UMB-C18) used as a surface active substrate for the enzymatic catalysis was synthesized.28 UMB-C18 belongs to a class of fatty acid phenolic esters which upon hydrolysis gives rise to a fluorogenic phenoxide, umbelliferone (UMB). All of these were stored at 253.2 K just prior to use and then used without further purification after thawing at room temperature for more than 1 h. HPLC grade chloroform and acetone (Aldrich) were used as the spreading solvent for DLPC/cholesterol mixture and the injection solvent for UMB-C18, respectively. DLPC/cholesterol mixed solutions with total concentration of 0.1-0.2 mM were prepared by mixing each in chloroform. The concentration of UMB-C18 solution was 1.5-2.5 mM. The fluorescent probe content in the mixed monolayer for FRAP measurement was 1 mol %. Phosphate buffer solutions at pH of 7.0, which are composed of 9.13 × 10-2 M dibasic anhydrous sodium phosphate, 3.87 × 10-2 M monobasic sodium phosphate, and 0.1 M sodium chloride, were used as the subphase of monolayers. The water used was the house deionized, further purified by a Milli-Q system with the initial resistivity of greater than 17 MΩ. Lipase Labeling. Crude lipoprotein lipase LPL 200S, which is mixture of glycine and lipase, from Pseudomonas cepacia was obtained from Amano International Enzyme Co. This mixture was purified by following the method published elsewhere.28 Modified McIlvane buffer composed of 0.115 M dibasic sodium phosphate and 1.31 × 10-2 M citric acid in Millipore water was used as a solvent after pH adjusted to 8.0 with 0.1 M sodium hydroxide solution. The purified lipase solution was stored at 253.2 K to preserve enzyme activity. The lipase was labeled with fluorescein isothiocyanate isomer I (FITC) from Aldrich through aqueous medium accessible lysine residues, to confer fluorescence for the FRAP measurement. A labeling procedure, slightly modified from the published method20 was used. Initially, the enzyme solution from the purified fraction was added to a flask containing 10 wt % FITC, and 0.1 M sodium hydroxide solution was added to raise pH of the mixture to 10.0, which corresponds to maximum FITC solubility. The solution was stirred for 2 h at 263.2 K to minimize protein denaturation, then the the products were obtained by size exclusion chromatography on a Sephadex G-25 fine gel column (Pharmacia Fine Chemicals). Since the labeled enzyme and free dye are easily visible on the column, labeled lipase was collected directly into a flask and the solution concentration determined. Individual lipase solutions were stored at 253.2 K after division into 1 mL fractions. The label content was approximately two dye molecules (23) Mabrey, S.; Sturtevant, J. M. Proc. Natl. Acad. Sci. U.S.A. 1976, 73, 3862. (24) Houslay, M. D.; Stanley, K. K. Dynamics of Biological Membranes; Wiley: New York, 1982; p 196. (25) Smith, L. M.; Rubenstein, J. L. R.; Parce, W.; McConnell, H. M. Biochemistry 1980, 19, 5907. (26) Merkel, R.; Sackmann, E. J. Phys. Chem. 1994, 98, 4428. (27) Tanaka, K.; Manning, P. A.; Lau, V. K.; Yu, H. Langmuir 1999, 15, 600. (28) Tanaka, K.; Manning, P. A.; Yu, H. Langmuir 2000, 16, 2665.

where τ is the relaxation time of the difference signal between the depletion profile and recovery profile of the unbleached and bleached regions by bleaching pulse at 488 nm from an argon ion laser, respectively, and q ()2π/p) is the spatial wavevector of the Ronchi ruling fringe with a spacing of p, imaged on the illuminated area 473 µm in diameter. Under these conditions, we can deduce the lateral diffusion coefficient in a range 5 × 10-6 to 5 × 10-10 cm2‚s-1. To attenuate the surface convective flow effect in the area of focal point of the viewing microscope, a cone-shaped Teflon barrier with platinum ring tip was used. If the convective flow is not arrested or attenuated greatly, smoothly decaying signals cannot be obtained. Monolayer Preparation and Kinetic Protocol. The Langmuir trough made of Teflon has two compartments9 with an area of 67.4 cm2 and a volume of 350 mL each, which was housed within an acrylate box for humidity control. The relative humidity within the box was kept at 70% or above, and the temperature was controlled at 296.2 ( 0.5 K during all measurements. The surface tensions of the bare and monolayer-covered surfaces were determined by the Wilhelmy technique using a sandblasted platinum plate. The detail experimental protocol is described in the accompanying paper.28 The DLPC/cholesterol mixed monolayer with the surface pressure range of 3.3-5.0 mN‚m-1 was prepared on one of the compartments by the successive addition method. The initial surface pressure of the DLPC/cholesterol mixed monolayers was adjusted to obtain a constant lipase surface concentration after a lipase solution injection into the subphase, depending on the cholesterol content in the mixed monolayer. This is because the packing density in monolayers depends on the cholesterol fraction in the monolayer.27 A lipase solution was injected beneath the monolayer, and an equilibrium partitioning of the lipase is allowed to reach. The equilibrium surface pressure Πeq after lipase adsorption to the DLPC/cholesterol mixed monolayer was not sensitive to the cholesterol fraction up to 30 mol % cholesterol, and its value was 25.4 ( 0.5 mN‚m-1. To isolate the preformed, enzyme imbedded monolayer from possible effects of lipase in bulk subphase on the interfacial hydrolysis, the monolayer was then transferred to the another compartment with the aid of a pair of Teflon barriers under the constant Πeq. Subsequently, the hydrolysis reaction of UMB-C18 was initiated by injecting its solution into the water subphase, which was being gently stirred by a magnetic stirring bar. The monolayer subphase is circulated through a spectrophotometric cell placed in a fluorometer (MK2 fluorimeter, Optical Technology Devices). The excitation and emission wavelengths were fixed at 367 and 454 nm, respectively.

Results and Discussion Kinetics. Hydrolysis Reaction Rates. According to the interfacial Michaelis-Menten kinetic model which is modified from the classical one after taking into account the fact that a reaction takes place only on the monolayer,28 (29) Roberts, G. A.; Tombs, M. P. Biochim. Biophys. Acta 1987, 902, 327. (30) Ma, J. Ph.D. Dissertation, University of WisconsinsMadison, 1998.

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Figure 1. Substrate concentration dependence of the initial hydrolysis rate on the DLPC monolayer. The abscissa is expressed in the substrate bulk concentration. The solid and broken lines are drawn in the context of the interfacial Michaelis-Menten model and merely to indicate the trend.

the reaction rate of lipase-catalyzed hydrolysis is monitored as a function of substrate concentration at different surface densities of enzyme on the lipid monolayer. Our kinetic model has four distinct steps; they are (1) the substrate adsorption from bulk phase to the monolayer, (2) substrate-enzyme encounter via in-plane diffusion, (3) hydrolysis catalysis by the lipase, and (4) spontaneous desorption of the products into the subphase. In the accompanying article, the substrate and enzyme concentration dependences of the initial hydrolysis rate are reported.28 Since the anomalous behavior was observed in the higher substrate concentration region than those reported before, however, we re-examined the relation between the substrate concentration [UMB-C18] and the initial hydrolysis rate Vo. Figure 1 shows a plot of [UMBC18] vs Vo. Here, DLPC monolayer without cholesterol was used. Measurements were carried out under the conditions of a constant temperature at 296.2 ( 0.5 K, surface pressure of 25 ( 0.5 mN‚m-1, and lipase surface concentration [lipase]σ of 1.08 × 10-2 molecule‚nm-2. The partitioning of the UMB-C18 from the bulk subphase to the monolayer was not large despite its surface activity. For instance, at [UMB-C18] ) 100 nM, the surface concentration [UMB-C18]σ, estimated by accounting for the increment of total surface area to maintain the constant lateral pressure, is 1.97 × 10-2 molecule‚nm-2, provided that the area per molecule of UMB-C18 remains at 0.24 nm2 as determined from its surface pressure isotherm. The results plotted in Figure 1 make it clear that there are two regimes. In regime I, roughly bordered by the substrate concentration at 150 nM, the initial hydrolysis rate Vo increased linearly with the substrate concentration, consistent with the Michaelis-Menten kinetics. The turnover number obtained from the Lineweaver-Burk plot, i.e., 1/Vo vs 1/ [UMB-C18], was 166 s-1, which is much larger than that in bulk solution. A detailed discussion about this number was given in the accompanying article.28 The solid line for regime I in Figure 1 is drawn according to the interfacial Michaelis-Menten model with the turnover number of 166 s-1. When the substrate concentration exceeds 150 nM, Vo clearly deviates from the solid line. In the concentration region of 150-250 nM, the relation between [UMB-C18] and Vo cannot be accounted for by the Michaelis-Menten type kinetics because the line extrapolated to [UMB-C18] ) 0 does not go through the origin. Once it goes beyond this crossover region identified by the shaded area in Figure 1 and reaches to a higher concentration region, however, the linear dependence of Vo on [UMB-C18] is

Tanaka et al.

Figure 2. Cholesterol fraction dependence of the hydrolysis reaction rate on DLPC/cholesterol mixed monolayers: (b) [UMB-C18] ) 100 nM as regime I; (O) [UMB-C18] ) 300 nM as regime II.

Figure 3. Lateral diffusion coefficient of a probe lipid and labeled lipase in DLPC/cholesterol mixed monolayers as a function of cholesterol content: (0) probe lipid; (9) labeledlipase. The solid lines are drawn to guide the eye.

recovered, presumably with different rate constants for the elemental steps. This region is designated as regime II. We truncate the examination of Vo at about 400 nM since the monolayer was found to be no longer homogeneous as noted by appearance of opaque flakes visible by the naked eye. We defer to later our proposal to explain the two regimes of the initial rate Vo. We now turn to the cholesterol effect on Vo at two fixed concentrations of substrate, [UMB-C18] ) 100 and 300 nM, representing regimes I and II, respectively. The results are displayed in Figure 2, where the left-hand and right-hand ordinates stand for regimes I and II, respectively. The experimental condition of the hydrolysis reaction was the same as before, and the monolayer homogeneity at the experimental surface pressure of 25 mN‚m-1 was confirmed by epifluorescence microscopy. In both regimes, Vo decreases monotonically with the cholesterol fraction in the mixed monolayer though its dependence differs in the two. For example, at 30% cholesterol, Vo retardations relative to 0% cholesterol are by 56% and 23% for regimes I and II, respectively. The larger absolute magnitude of Vo in regime II in comparison with that in regime I at a given cholesterol fraction is attributed to the large amount of the substrate feed, as shown in Figure 1. Dynamics. Lateral Diffusion Coefficients. As the crux of this study, we present the cholesterol effect on monolayer dynamics, the lateral diffusion coefficients, designated as D(2) for convenience, of the lipid probe and lipase in Figure 3. Since the intact substrate, UMB-C18, is nonfluorescent by 488 nm wavelength incident light (argon ion laser), its lateral diffusion was not accessible

Lipase Catalysis on Monolayers

experimentally. Therefore, the lateral diffusion coefficient D(2) of lipids or substrate is assumed to be the same as the fluorescent phospholipid probe, NBD-PC although the cross-sectional area of NBD-PC is slightly larger than that of UMB-C18. On the other hand, the FITC-labeled lipase was used to deduce D(2) of lipase. The D(2) of NBD-PC decreases progressively as cholesterol composition is increased. Incorporation of cholesterol enhances the extended conformation of phosphatidylcholine lipid tails,31,32 resulting in an increase in the viscosity of monolayers. Thus, a decrement of D(2) with the cholesterol composition is attributed to the increase in the in-plane viscosity. The details of lateral diffusion coefficients of NBD-PC in the DLPC/cholesterol mixed monolayer have been reported earlier.27 On the other hand, there is a dearth of reports dealing with the lateral diffusion of well-characterized protein in the model membrane, monolayers and bilayers, although membrane dynamics of more realistic system have been vigorously examined.33-36 Since many factors such as the surface viscosity, domain formation, extracellular influences, and specific interactions may affect the diffusion coefficient of integral and/or peripheral proteins in cell membranes, it is difficult to gain clear insight into the dominant factors controlling the lateral mobility of biological macromolecules in membranes from such a study, though those are of pivotal important for biomedical applications. Hence, it is worthwhile here to evaluate the diffusion coefficient of well-characterized protein, lipase,37 in the homogeneous DLPC/cholesterol mixed monolayers, which does not involve any of the above-mentioned complexity. As shown in Figure 3, the D(2) values of labeledlipase in the DLPC monolayer and in 30 mol % cholesterol mixed monolayer were 4.32 × 10-8 and 1.37 × 10-8 cm-2, respectively, and decreased progressively in about the same fashion as the probe lipid, as cholesterol composition is increased. The difference of D(2) between the probe lipid and the labeled lipase at a given cholesterol fraction is about an order of magnitude or more for the entire range of cholesterol composition examined here. Such a difference can be quantitatively accounted for by applying the hydrodynamic theory of Hughes et al.38 based on the difference of the cross-sectional radii of labeled lipase and NBD-PC at the interface. Thus, it seems reasonable to claim here that the lateral mobility of biological macromolecules in homogeneous membranes is regulated only by the size of diffusant if there is no specific interaction between diffusant and environment. Finally, it should be reminded that the simple decrement of the D(2) of the lipids and enzyme with the cholesterol fraction (Figure 3) is qualitatively in agreement with the cholesterol dependence of the initial hydrolysis rate Vo (Figure 2). Coupling of Kinetics with Dynamics. We finally come to combine the lateral diffusion coefficient with the enzymatic hydrolysis rate on the monolayers by using the strictly two-dimensional diffusion-controlled reaction dynamics theory by Torney and McConnell.39 In the case (31) Leathes, J. B. Lancet 1925, 208, 853. (32) Yeagle, P. L. Choelsterol in Model Membranes; CRC Press: Boca Raton, FL, 1993; p 1. (33) Berk, D.; Hochmuth, R. Biophys. J. 1992, 61, 9. (34) Storrie, B.; Kreis, T. E. Trends Cell Biol. 1996, 6, 321. (35) Kitani, K.; ZsNagy, I. Int. Hepatol. Commun. 1996, 5, 236. (36) Salome, L.; Cazeils, J. L.; Lopez, A.; Tocanne, J. F. Eur. Biophys. J. Biophys. 1998, 27, 391. (37) Schmid, R. D.; Verger, R. Angew. Chem., Int. Ed. Engl. 1998, 37, 1608. (38) Hughes, B. D.; Pailthorpe, B. A.; White, L. R. J. Fluid Mech. 1981, 110, 349. (39) Torney, D. C.; McConnell, H. M. Proc. R. Soc. London 1983, A387, 147.

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Figure 4. Normalized initial hydrolysis rates by using the data set from Figure 2. The symbols are the same as those given in Figure 2. The solid and dashed lines are drawn according to eq 2 of the two-dimensional diffusion-limited reaction dynamics theory of Torney and McConnell.

of an irreversible reaction, A + B f P, its rate function k(t) decreases asymptotically to zero as (ln t)-1, and it is given as follows

k(t) )

{

4πRD(2) z-1 - γz-2 -

(

)

}

π2 - γ2 z-3 + O(z-4) 6

(2)

with

z ) ln(16βD(2)tl-2)

(3)

{ (1 -R R)}

(4)

and

β ) exp π

Here R, γ, and t are the reaction probability of the reactants upon encounter, Euler’s constant, and the reaction time, respectively, while D(2) is the two-dimensional diffusion coefficient and is estimated from the sum of the observed lateral diffusion coefficients of the two species, the probe lipid and labeled lipase. The quantity designated by l in eq 3 is a parameter related to the radius of reaction circle R, equal to 2R exp(γ). The interfacial cross-sectional radii of UMB-C18 and lipase are 0.28 and 3.01 nm,20 respectively, both of them being evaluated from surface pressure-area isotherms; hence R is taken to be 3.29 nm. The contribution of higher order term, O(z-4), of eq 2 is less than 1% for the time scale of our experiment and is hence ignored. Figure 4 shows the cholesterol content dependence (via the experimentally observed lateral diffusion coefficients) of the normalized initial hydrolysis rate by Voo in pure DLPC without cholesterol. The solid and dashed lines are drawn according to eq 2 with R ) 1.0 and 0.1, respectively. It appears clear that our results in regime I are in good agreement with the theoretical prediction of Torney and McConnell. Thus, we conclude that the substrate adsorbs to the interface, randomly diffuses to lipase, and is hydrolyzed by the enzyme at the interface (Figure 5a) in regime I, and its reaction rate is diffusion-controlled in the monolayer. Whereas in the case of regime II, though the hydrolysis rate is still sensitive to the cholesterol composition, its effect is not as great as that in regime I. Since the bulk substrate concentration is rather large in this regime, it is plausible that there are many substrate molecules which are directly accessible to lipase. We thus propose that two mechanisms might be operative in regime II wherein the catalyzed hydrolysis reaction proceeds by a combination of an interfacial diffusion-controlled process

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Tanaka et al.

diffusion control mechanism is greatly overwhelmed by the bulk mechanism. Noting that our results in Figure 4 are independent of R in the theory, we claim that no fitting parameter is necessary once the normalization is allowed to focus on the diffusion retardation effect by cholesterol. In other reported cases of the diffusion-controlled reaction on solid surfaces,42,43 however, at least one fitting parameter is required.

Figure 5. A schematic illustration of the enzymatic hydrolysis mechanism proposal at the interface: (a) pristine interfacial mechanism; (b) hybrid interface-bulk mechanism.

and a direct access process to the vicinity of the enzyme; hence we call it the hybrid interface-bulk mechanism (Figure 5b). If indeed such is the case, then the hybrid mechanism should be sensitive to the subphase viscosity, if the diffusion to the enzyme site is controlling, in addition to the in-plane monolayer viscosity, or it could be entirely reaction-controlled. In any event, if the bulk mechanism happens to be dominant at higher substrate concentrations, then its dependence on the lateral diffusion coefficient should be attenuated compared to the case of a pristine interfacial mechanism of regime I. We formulate this proposal in an attempt to accommodate all our findings. It is possible that if the enzyme kinetics at the interface using monolayers, micelles, emulsions, and vesicles are studied in a higher substrate concentration region, the reaction rate might turn out to be reactioncontrolled40,41 because the pathway of the interfacial

Conclusions Chemical kinetics of the lipase-catalyzed hydrolysis on the DLPC/cholesterol mixed monolayers at the air/water interface with various cholesterol fractions were studied. The hydrolysis reaction rate monotonically decreases with the increasing cholesterol content in the mixed monolayer. The lateral diffusion coefficient of lipid analogue and labeled lipase, which represents a quasi-two-dimensional dynamics due to a finite thickness of monolayers, is proved by means of the FRAP technique, and decreases with the increase in the cholesterol fraction. The D(2) of the lipase is slower than that of the probe lipid by a decade or more due to its larger cross-sectional area on the surface. Combining the lateral diffusion coefficient of reactants with chemical kinetics on monolayers, we have directly shown that the enzyme catalysis on uniphasic binary monolayers of DLPC/cholesterol is diffusion-controlled and the results are in quantitative agreement with a strictly two-dimensional reaction dynamics theory of Torney and McConnell. To the best of our knowledge, this is the first report of such an investigation. Acknowledgment. This work was partially supported by the Eastman Kodak Professorship and NSF grants (DMR9203289 and DMR9711226) awarded to H.Y. We are grateful for helpful discussions with Professor George Zografi. The choice and synthesis of the lipase substrate, umbelliferone stearate, were made by Drs. David D. Manning and Patricia A. Manning, to whom we are deeply indebted. LA990925W

(40) Berg, O. G.; Yu, B.-Z.; Rogers, J.; Jain, M. K. Biochemistry 1991, 30, 7283. (41) Berg, O. G.; Cajal, Y.; Butterfoss, G. L.; Grey, R. L.; Alsina, A.; Yu, B.-Z.; Jain, M. K. Biochemistry 1998, 37, 6615.

(42) Trigiante, G.; Robertson, C. R.; Gast, A. P. J. Colloid Interface Sci. 1999, 213, 81. (43) Wang, H.; Harris, J. M. J. Am. Chem. Soc. 1994, 116, 5754.