Polymer Binary Monolayers: Lateral Diffusion

To show that the diffusion-controlled reaction kinetics on monolayers is of ...... that diffusion-controlled kinetics of interfacial enzyme catalysis ...
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Langmuir 2002, 18, 797-804

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Lipase Activity on Lipid/Polymer Binary Monolayers: Lateral Diffusion-Controlled Enzyme Kinetics Keiji Tanaka† and Hyuk Yu* Department of Chemistry, University of WisconsinsMadison, Madison, Wisconsin 53706 Received June 25, 2001. In Final Form: September 18, 2001 This is a follow-up study to our recent reports of lipase catalysis on uniphasic binary monolayers of L-R-dilauroylphosphatidylcholine (DLPC) and cholesterol. The earlier studies were undertaken to show that the reaction kinetics on monolayers of ester hydrolysis catalyzed by an interface active enzyme, lipase, is closely correlated to the lateral dynamics, i.e., the hydrolysis of a lipase substrate is a diffusion-controlled process, whereby the rates were quantitatively analyzed in terms of a theory of purely two-dimensional diffusion-controlled reactions. In so establishing, cholesterol was used as the second component to retard the lateral diffusion coefficient of DLPC to different extents. On the other hand, phospholipids and cholesterol are being found to form “condensed complexes” even in homogeneous monolayers, hence the finding of the diffusion-controlled processes might well be construed to be unique to the phospholipid-cholesterol system. To show that the diffusion-controlled reaction kinetics on monolayers is of more general validity, i.e., not system-specific, we chose a completely different second component to constitute a binary homogeneous monolayer system by which we can vary the lipid diffusion coefficient. The second component is a synthetic polymer, poly(tert-butyl methacrylate) (PtBMA), well-known for its surface activity on the air/water interface, and is demonstrated to form uniphasic monolayers with DLPC at the air/aqueous buffer (pH 7) interface. Upon completing the entire set of measurements for the diffusion coefficients and the hydrolysis rates with the same substrate, umbelliferone stearate, we reached the conclusions that what we found with DLPC/ cholesterol are not unique to the system but equally applicable to DLPC/PtBMA, whereas the polymer is not likely to exert the same sort of retardation effect on monolayer dynamics by specific interactions that result in condensed complexes of phospholipid and cholesterol.

Introduction This is to report a study of lipase catalyzed hydrolysis reaction kinetics on binary monolayers of a phospholipid and a synthetic polymer. This parallels our earlier studies 1,2 with the same kind of kinetics on binary monolayers of the identical phospholipid, L-R-dilaurylphosphatidylcholine (DLPC), and cholesterol. In these studies, we established that the kinetics is diffusion-controlled. As the second component, cholesterol was chosen for its wellknown interactions with the lipid molecules to retard the lateral mobility. The point of another binary monolayer with a synthetic polymer as the second component springs directly from the fact that cholesterol interacts specifically with phospholipids on monolayers to form “condensed complexes”. This issue is being actively explored by McConnell and co-workers.3-5 In the context of such condensed complexes, our observations with the phospholipid/cholesterol binary system might be construed as so specific to the system that they are of no general validity relative to the diffusion-controlled kinetics of lipase on monolayers. Here, we focus on the pivotal issue of nonspecificity of the second component, provided it retards the lipid mobility and forms uniphasic monolayers across a composition range of interest with DLPC. As long as it affects the lateral mobility of the lipid monolayers, quite possibly † Present address: Department of Applied Chemistry, Faculty of Engineering, Kyushu University, Fukuoka 812-8581, Japan.

(1) Tanaka, K.; Manning, P. A.; Yu, H Langmuir 2000, 16, 2665. (2) Tanaka, K.; Mecca, S. P.; Yu, H. Langmuir 2000, 16, 2672 (3) Keller, S. L.; Anderson, T. G.; McConnell, H. M. Biophys. J. 2000, 79, 2033. (4) Anderson, T. G.; McConnell, H. M. J. Phys. Chem. B 2000, 104, 9918. (5) Radhakrishnan, A.; Anderson, T. G.; McConnell, H. M. Proc. Nat. Acad. Sci. U. S. A. 2000, 97, 12422.

due to enhanced lateral viscosity of the monolayers without any apparent interactions with the lipid molecules, we would have produced a counter example to the requirement of specific interactions. Such a claim could be made compelling if the chosen polymer has no pendant hydrocarbon chains of any significant length to interact with alkyl chains of DLPC. The choice of polymer is poly(tertbutyl methacrylate), PtBMA, without a long pendant chain but with a roughly spherical tertiary butyl group. The polymer has been known to form insoluble monolayers at the air/water interface6-9 and it forms homogeneous monolayers with DLPC (see below). This study is undertaken to show that a case can be made for the diffusioncontrolled processes involving lipase-catalyzed hydrolysis reaction without requiring specific interactions resulting in condensed complexes. Turning to a generic issue of diffusion-controlled kinetics,10,11 we start from the importance of such reaction processes on monolayers. In bulk solutions, it has been widely accepted that elementary reactions such as ion pair association in dilute aqueous solutions are the typical examples of this.11 However, the kinetics of chemical reactions on surfaces have not been systematically studied thus far despite its pivotal importance to those governed by heterogeneous catalysis. Further, heterogeneously catalyzed chemical reactions are ubiquitous in a whole host of chemical and biological processes, particularly in cellular signal transduction and molecular recognition.12,13 (6) Kawaguchi, M.; Sauer, B. B.; Yu, H. Macromolecules 1989, 22, 1735. (7) Kim, S.; Yu, H. J. Phys. Chem. 1992, 96, 4034. (8) Sacchetti, M.; Yu, H.; Zografi, G. Langmuir 1993, 9, 2168. (9) Sadrzadeh, N.; Yu, H.; Zografi, G. Langmuir 1998, 14, 151. (10) Smoluchowski, M. V. Phys. Z. 1916, 17, 585. (11) Rice, S. A. Chemical Kinetics, Vol. 25, Diffusion-Limitted Reactions; Elsevier: Amsterdam, 1985. (12) Weng, G. Z.; Bhalla, U. S.; Iyengar, R. Science 1999, 284, 92.

10.1021/la010965b CCC: $22.00 © 2002 American Chemical Society Published on Web 01/10/2002

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To examine chemical reactions on surfaces vis-a`-vis those in solutions, lateral homogeneity in macroscopic length scales is required just as in homogeneous solutions. Such can be realized with liquid surfaces with a molecularly smooth area in macroscopic length scales. Hence, the dynamics of either the reactants or the products, can be regarded as uniform in macroscopic length scales, not affected by any local chemical potential wells on liquid surfaces. A liquid surface can easily reach its thermodynamic equilibrium state defined by capillarity. The surface roughness of water generated by the spontaneous capillary wave is extremely small and its value deduced by X-ray or neutron reflectivity is 0.3-0.4 nm.14,15 Also, all molecules on the water surface are at the same chemical potential, and they can be controlled to have more or less the same orientation and accessibility depending on lateral pressure; such a control is not easily obtained on solid surfaces.16 These specific advantages are taken here in choosing the air/aqueous buffer interface as a suitable matrix for carrying out chemical reactions. We choose binary monolayers as the reaction medium. Lipid monolayers at the air/water interface are often taken as a well-represented model of homogeneous hemi-leaflets of bilayered phospholipid membranes17 (biomembranes for short). As for the structure of biomembranes, the earlier simple picture of cell membranes as homogeneous fluid mosaic of phospholipids, membranous proteins, and carbohydrates on exoplasmic side18 has undergone a substantial modification.19 The currently accepted representation is a complicated one of lateral heterogeneities arising from microdomains consisting of complexes of sphingolipids and sphingomyelins with cholesterol which function as rafts for the transport of some membrane constituents or as relay stations in intracellular signal transduction.20,21 Since the chemistry and kinetics on the leaflets is expected to be influenced by these microdomains, we have to understand, first as a benchmark, what controls the kinetics of enzymatic catalysis on homogeneous hemileaflets. Hence, we choose DLPC monolayers in “fluid state” at the air/buffer interface. Since the thickness of a monomolecular film on the liquid surface is generally a few nanometers, the system amounts to a quasi-twodimension with a finite uniform height. As in the previous studies, we adopt umbelliferone stearate (UMB-C18) as the lipase substrate that is spread with pure DLPC and DLPC/PtBMA binary solution with tBMA fraction up to 25 mol %. Thus, the objective of this study is to examine the monolayer dynamics and the hydrolysis kinetics of UMB-C18 on uniphasic binary monolayers composed of DLPC and PtBMA. Although there has been emphasis on phase behavior22-24 of binary (13) Bhalla, U. S.; Iyengar, R. Science 1999, 283, 381. (14) Braslau, A.; Deutsch, M.; Pershan, P. S.; Weiss, A. H.; AlsNielsen, J.; Bohr, J. Phys. Rev. Lett. 1985, 54, 114; Braslau, A.; Pershan, P. S.; Swislow, G.; Ocko, B. M.; Als-Nielsen, J. Phys. Rev. A 1988, 38, 2457. (15) Ma, J.; Yu, H.; Clarson, S. J.; Satija, S.; Maliszewskyj, N. Macromolecules 2001. Submitted for publication. (16) Davies, J. T.; Rideal, E. K. Interfacial Phenomena, 2nd ed.; Academic Press: San Diego, 1963. (17) Gennis, R. B. Biomembranes, Molecular Structure and Function; Springer-Verlag: New York, 1989; pp 36-84. (18) Singer, S. J.; Nicolson, G. L. Science 1972, 175, 720. (19) Jacobson, K.; Sheets, E. D.; Simson, R. Science 1995, 268, 1441. (20) Simons, K.; Ikonen, E. Nature 1997, 387, 569. (21) Varma, R.; Mayor, S. Nature 1998, 394, 798. (22) Naumann, C.; Dietrich, C.; Lu, J. R.; Thomas, R. K.; Rennie, A. R.; Penfold, J.; Bayerl, T. M. Langmuir 1994, 10, 1919. (23) Winterhalter, M.; Burner, H.; Marzinka, S.; Benz, R.; Kasianowicz, J. J. Biophys. J. 1995, 69, 1372. (24) Majewski, J.; Kuhl, T. L.; Kjaer, K.; Gerstenberg, M. C.; AlsNielsen, J.; Israelachivili, J. N.; Smith, G. S. J. Am. Chem. Soc. 1998, 120, 1469.

Tanaka and Yu

mixtures of lipid and synthetic polymer at the air/water interface, there is a dearth of studies dealing with dynamics of lipid/polymer monolayers. Thus, this is the first systematic report of this kind to the best of our knowledge. Experimental Section Materials and Surface Pressure Measurements. DLPC and 1-acyl-2-[12-[(7-nitro-2-1,3-benzoxadiazol-4-yl)amino]dodecanoyl]phosphatidylcholine (NBD-PC), used as a fluorescent lipid probe, were purchased from Avanti Polar Lipids. Monodisperse PtBMA with the number-average molecular weight of 10kDa was purchased from Polyscience, Inc. Umbelliferone stearate (UMB-C18), used as a surface active substrate for the enzymatic catalysis, was synthesized by following the method published elsewhere.1 UMB-C18 belongs to a class of fatty acidphenolic esters which upon hydrolysis produces a fluorogenic phenoxide, umbelliferone (UMB). All of these were stored at 253.2 K prior to use and then used without further purification after thawing at room temperature for more than 1 h. Crude lipoprotein lipase LPL 200S, a mixture of glycine and lipase from Pseudomonas cepacia, was obtained from Amano International Enzyme Co. The mixture was purified by following our method published elsewhere.1 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 for lipase after pH adjusted to 8.0 with 0.1 M sodium hydroxide solution. The purified lipase solution was then frozen and 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.1 The label content was approximately two dye molecules per lipase, and was assumed to be small enough to have a negligible effect on the lateral diffusion coefficient of the intact lipase. HPLC grade chloroform and acetone from Aldrich were used as the spreading solvent for monolayers and the injection solvent for UMB-C18, respectively. DLPC/PtBMA binary solutions with a total concentration of 0.17 mM were prepared by mixing each in chloroform. The concentration of UMB-C18 solution was 1.01.5 mM. Phosphate buffer at pH 7.0, consisting of 9.13 × 10-2 M dibasic anhydrous sodium phosphate, 3.87 × 10-2 M monobasic sodium phosphate and 0.1 M sodium chloride, was used as the subphase of monolayers. For water, what we used was the house deionized water that was further purified by a Milli-Q system with the initial resistivity of greater than 17 MΩ. Π-A measurements were carried out in a Teflon trough with a surface area of 67.9 cm2, which was housed in an acrylate box for humidity control. The monolayer surface mass density for all Π-A measurements was varied by the successive addition method at a controlled room temperature (296.2 ( 0.5 K), under the assumption that spread components form insoluble monolayers without any desorption from the surface into the subphase. The relative humidity within the box was kept at 80% or above during all measurements. The surface tension of the bare and monolayer-covered surface were determined by the Wilhelmy technique using a sandblasted platinum plate. The surface tension, γ, was observed as a function of time by a Cahn electrobalance until the time dependence, dγ/dt, reached approximately 10-3 mN(m s)-1, which is our operational benchmark of apparent equilibrium state. Lateral Diffusion by Fluorescence Recovery after Photobleaching. Lateral diffusion coefficients, D(2), of a probe lipid and labeled enzyme were determined by the fluorescence recovery after photobleaching (FRAP) measurements. The instrumental setup and the data analysis method were reported earlier in detail.7 A set of recent modifications of the signal acquisition step is also described elsewhere.25 Briefly, D(2) is deduced from

1/τ ) D(2) q2

(1)

where τ is the relaxation time of the difference signal between the depletion profile and recovery profile of the unbleached and (25) Ma, J., Ph.D. Dissertation, University of WisconsinsMadison, 1998.

Lipase Activity on Lipid/Polymer Binary Monolayers bleached regions following a 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 p, imaged on the illuminated area of 473 µm in diameter. Under these conditions, we can deduce the lateral diffusion coefficient in a range 5 × 10-2 to 5 × 102 µm2 s-1. All binary monolayers composed of DLPC and PtBMA were prepared by the successive addition method in a Teflon trough with an upper surface area of 62.0 cm2 at 296.2 ( 0.5 K. The fluorescent probe, NBD-PC, content in the mixed monolayer was less than 1 mol %. As a typical instance of enzyme catalyzed reaction on the monolayers, a binary monolayer of DLPC and PtBMA with a known compostion was formed at a given surface pressure and then lipase solution was injected beneath the DLPC/ PtBMA monolayers. The adsorbed lipase amount on the monolayer was adjusted to approximately 1.08 × 10-2 molecules nm-2 which was deliberately made the same as the lipase surface concentration for hydrolysis reaction. To attenuate the surface convective flow effect in the vicinity of the focal point of the viewing microscope, a cone-shaped Teflon barrier with a platinum ring tip was used. If the convective flow is not arrested or attenuated greatly, smoothly decaying signals could not be obtained. Kinetic Protocol. Since the details have been described in our previous publication,1 for the sake of brevity, we restrict ourselves only to a broad outline. We perform kinetic studies on a Langmuir trough made of Teflon, having two compartments,17 each with an area of 67.4 cm2 and a volume of 350 mL. The DLPC/PtBMA binary monolayer with the surface pressure range of 5.0-6.4 mN m-1 was prepared on one of the compartments by the successive addition method. The initial surface pressure of the binary monolayers was adjusted to obtain a constant lipase surface concentration, upon a lipase solution injection into the subphase, which in turn depends on the PtBMA content in the monolayer. A lipase solution was injected beneath the monolayer and the partitioning was allowed to equilibrate. The equilibrium surface pressure Πeq after lipase adsorption to the monolayer was not so sensitive and its value was 25.5 ( 0.5 mN m-1. To isolate the preformed, enzyme imbedded monolayer from possible effects of lipase in bulk subphase, the monolayer was then transferred to the adjacent 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 subphase liquid is circulated through a spectrophotometric cell placed in a fluorimeter (MK2 fluorimeter, Optical Technology Devices). The excitation and emission wavelengths were fixed at 367 and 454 nm, respectively.

Results and Discussion Before we get to the central point of this report, namely, the catalytic hydrolysis kinetics of a lipase substrate, we need to address several pivotal issues beforehand. They are the monolayer properties of the binary system, the mixing behavior of DLPC and PtBMA on the binary monolayer, and the lateral diffusion of a probe lipid and labeled lipase on the monolayer, as a function of its composition. For fear of distracting the reader from the central point, we need to abbreviate the discussion of these three issues, but without glossing them over as ancillary. Surface Pressure-Area Isotherms of Binary Monolayers. We start with the presentation of the experimental isotherms at the air/buffer interface. Figure 1 shows the surface pressure-area isotherms, Π-A isotherms, for pure DLPC, pure PtBMA, and their binary system. The calculation of molar composition and the mean area were made on the basis of repeating unit of PtBMA as in the case of pure PtBMA. Hence, the polymer composition in the binary monolayer is expressed as mol % of tBMA. The inset of Figure 1 displays the tBMA composition dependence of average area A per segment in the monolayers at surface pressures of 5 and 10 mN m-1; we refer by a segment either a DLPC molecule or a repeating unit of the polymer, tBMA.

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Figure 1. Surface pressure-area (Π-A) isotherms of DLPC/ tBMA uniphasic binary monolayers at room temperature (296 ( 0.5 K): (b) pure DLPC, (O) 5 mol % tBMA, (2) 10 mol % tBMA, (4) 15 mol % tBMA, (9) 25 mol % tBMA, (0) 50 mol % PtBMA, (1) 75 mol % tBMA, and (3) tBMA. The subphase employed is a buffer composed of 9.13 × 10-2 M Na2HPO4, 3.87 × 10-2 M NaH2PO4, and 0.1 M NaCl with pH adjusted to 7.0. The inset shows tBMA content dependence of isobaric area per segment: (b) Π ) 5 mN m-1 and (2) Π ) 10 mN m-1, where solid and broken lines denote the ideal mixing at 5 and 10 mN m-1, respectively.

The replicability of Π at a given area is about equal to or better than 0.5 mN m-1 while the precision of Π determination for a given monolayer is better than 0.05 mN m-1. The isotherms as displayed in Figure 1 are grouped into 3 types: Group I, those of pure DLPC and tBMA composition up to 25 mol %; Group II, tBMA composition at 50 mol %; Group III, those with 75 and 100 mol % of tBMA. For Group I, the collapse pressure (45 mN m-1 for pure DLPC) and collapse area (0.5 nm2 segment-1 for pure DLPC) decrease progressively with increasing tBMA content. The onset of monolayer collapse, as observed by flattening of Π with respect to A, is reproducibly determined without a long wait, e.g., 24-48 h, for equilibriation. As judged by the epi-fluorescence microscopy, there seems to be no detectable heterogeneity. We hasten to add however that the length scale of detection preclude observing any microphase separation that is finer than 0.5 µm. For Group II, Π determination above 30 mN m-1 was not feasible because it did not equilibriate even after 48 h upon spreading; hence we report only up to 30 mN/m. We speculate that this must arise from slow mixing of the two components at this composition in addition to instability of the binary monolayer at 50 mol % at Π g 30 mN m-1 since PtBMA has the collapse pressure of only 15 mN m-1. Once crossing over this threshold, 25-50 mol %, Group III monolayers appear stable and the equilibriation time is as short as those for Group I. With respect to Group III monolayers, we further note that the surface pressure increases more abruptly than other monolayers in the vicinity of the lift-off specified by Π > 0 within the detection limit. The limiting area for tBMA is estimated as 0.34 nm2; this is customarily determined by extrapolating the linear range of Π-A isotherm to Π ) 0. The value for tBMA so obtained is different from the reported value6,9,26 of 0.27 nm2. Also, the slope of Π-A isotherm, dΠ/dA, hence the static elasticity, s ) -A(∂Π/∂A)T for pure PtBMA monolayer in this study is smaller than those reported previously by a factor of about 0.6. The difference between the two in terms of experimental protocol is that in this study a phosphate buffer at pH 7.0 is used instead of pure water as the subphase. Since PtBMA should be stable at pH 7.0, it seems reasonable to envisage that the phosphate buffer used here is a better solvent for PtBMA than pure water. (26) Similar discrepancies of the limitting area and the slope of Π-A isotherm between on pure water and phosphate buffer at pH 7.0 were obtained by using poly(vinyl acetate).

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We thus conclude that the limiting area discrepancy is attributable to the solvent quality of the subphase. DLPC-PtBMA Mixing Behavior on Binary Monolayers. We now come to the underlying thermodynamics of the observed isotherms. The area per segment corresponding to the isotherm lift-off point, becomes monotonically smaller with increasing tBMA fraction; the isotherm progressively shifts toward the ordinate as the tBMA fraction increases. A part of this reduction is expected as tBMA segment, with a smaller projected molecular cross section compared to that of DLPC, is incorporated into the monolayer. An additional reduction in the occupied area beyond the smaller projection of tBMA is clearly shown in the inset of Figure 1. The straight lines connecting the two limits represent the ideal mixing. The excess area of mixing ∆AE, which stands for a measure of nonideality of a binary monolayer, analogous to ∆VE for a bulk nonideal solution, is expressed by eqs 2 and 3:27

∆AE(Π) ) A(Π) - Ao12

(2)

Ao12 t X1Ao1 + X2Ao2

(3)

where A(Π) and Ao12 are, respectively, the calculated area per segment at a given Π assuming insoluble monolayers, and the calculated average area per segment assuming the ideal mixing. Also, Aoi and Xi (i ) 1,2) are the area per molecule or segment of pure components and mole fraction in the monolayer, respectively, and subscripts of 1 and 2 refer to DLPC and tBMA, respectively. Hence, ∆AE is a function of monolayer composition and Π, and for mixed monolayers either in ideally miscible or completely immiscible state, ∆AE is zero. Deviations from the ideal mixing rule, eq 3, indicate miscibility and interactions between the two components. Since ∆AE for DLPC/PtBMA mixed monolayers at all composition is negative, it is to be expected that DLPC and PtBMA are miscible with some attractive intersegment interactions. As stated in the above, the miscibility was confirmed by epi-fluorescence microscopic observation of DLPC/PtBMA monolayers containing 1 mol % fluorescence dye, NBD-PC. To present the miscibility more quantitatively, the molar excess Gibbs free energy of mixing, ∆G h E(Π), is calculated from the results displayed in the inset of Figure 1, according to the procedure by Goodrich:28

∆G h E(Π) )

∫0Π∆AE dΠ

(4)

Figure 2 shows ∆G h E(Π) values for the mixed monolayers as a function of tBMA fraction at two different surface h E(Π) < 0 for pressures. As it should be from ∆AE < 0, ∆G all compositions. The plot of ∆G h E(Π) vs tBMA fraction is concave upward regardless of surface pressure. The critical composition, which is specified as the composition corresponding to minimum ∆G h E(Π), is skewed toward the lower tBMA composition side, as usually seen in phase diagrams of polymer solutions or polymer blends.29 Hence, the asymmetry of ∆G h E(Π) relative to binary composition is likely ascribed to the asymmetry of mixing entropy arising from the fact that segments of one component, tBMA, are covalently bonded to one another by virtue of their being a part of a polymer. At all compositions, ∆G h E(Π) becomes more negative with increase in the surface (27) Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Wiley-Interscience: New York, 1966. (28) Goodrich, F. C. Proc. 2nd Int. Congr. Surf. Activity 1957, 85. (29) Koningsveld, R.; Stockmayer, W. H., Nies, E. Polymer Phase Diagrams; Oxford University Press: New York, 2001.

Figure 2. Molar excess Gibbs free energy ∆G h E as a function of tBMA fraction at two surface pressures: (b) Π ) 5 mN m-1 and (2) Π ) 10 mN m-1. Solid curves are drawn to guide the eye, and a horizontal broken line denotes ∆G h E ) 0 corresponding to the ideal mixing.

Figure 3. Lateral diffusion coefficient D(2) of a probe lipid, NBD-PC, in the binary monolayers as a function of surface pressure at different tBMA compositions, and the symbols are the same as in Figure 1.

pressure, indicating that the attractive interactions between the two components are greater at larger lateral pressures. Parenthetically, ∆G h E(Π) for the present binary system of DLPC/PtBMA at the same surface pressure is much smaller than that for monoolein/PtBMA binary mixture reported previously,9 whose miscibility is explained in terms of hydrogen bonding between lipid hydroxyl groups and ester groups of the polymer. Since the hydrophilic headgroup of DLPC is zwitterioninc, it is plausible that the excellent miscibility for DLPC/PtBMA mixtures at the air/water interface is induced by attractive interactions between the hydrophilic headgroups and the ester groups of the polymer side chain. Lateral Diffusion of a Probe Lipid. We now come to the issue of molecular mobility on the binary monolayer. To gain access to monolayer mobility of DLPC/PtBMA binary monolayer, the lateral diffusion coefficients D(2) of a probe lipid, NBD-PC, dispersed in the monolayer were determined with the FRAP technique. Results at each composition were reproduced in three independent trials. In every case, the profile of the fluorescence difference signal was best fit by a single exponential; we take this as evidence for a grossly averaged center of mass diffusion for the lipids (A ≈ 0.4 nm2) within the binary monolayers, averaged over a displacement length that exceeds the cross sectional size of lipids by 4 orders of magnitude, i.e., 34 µm for the fringe spacing versus (0.4)1/2 nm. We have earlier established that the diffusion coefficient at a given Π is not probe specific with two different probes.7 Figure 3 displays the surface pressure dependence of the diffusion coefficient at different tBMA fractions. Here, we restrict our discussion to Group I monolayers, homogeneous binary monolayers with tBMA fractions up to 25 mol %, containing 1 mol % of NBD-PC, that can reach apparent equilibrium without long wait. The data points shown for Π ) 0, correspond to the diffusion coefficients obtained at the lift-off points of all isotherms. For pure DLPC monolayer, the surface pressure reaches the liftoff point from the LE/gas coexistence region and the

Lipase Activity on Lipid/Polymer Binary Monolayers

Langmuir, Vol. 18, No. 3, 2002 801 Table 1. Two Fitting Parameters Extracted from the Plots Shown in Figure 4: the Mean Occupied Area ao and the Slope βa* at Different tBMA Fractions

D(2)/D(2)o

-1

Figure 4. A semilogarithmic plot of vs af in accord with the free area model, eq 6(see text); the symbols are the same as in Figures 1 and 3. All solid lines indicate the best fitted ones with ao and βa* of eq 6 as the fitting parameters and collected in Table 1.

monolayer moves into the LE state, and D(2) decreases sharply with increasing surface pressure. Also, incorporation of tBMA into the lipid monolayer exerts an additional influence; that is, D(2) decreases progressively as tBMA is added. In the case of the DLPC/PtBMA monolayer with 25 mol % tBMA, D(2) reaches an asymptotic limit of 25 µm2 s-1 at Π ) 20 mN m-1. The collapse pressure for the DLPC/PtBMA monolayer at this composition is substantially lower than those of other mixed monolayers, as shown in Figure 1. Hence, it is probable that the free area of this monolayer at 25 mol % tBMA is almost neglibly small at Π g 25 mN m-1. The asymptotic behavior of D(2) with respect to surface pressure can be seen even for pure DLPC monolayer when Π is higher than 35 mN m-1. Since these findings are consistent with our previous results using a different viscosifier, cholesterol,30 it can be considered that the decrement of D(2) with increasing surface pressure and/or tBMA fraction can be attributed to increasing the monolayer viscosity. We will shortly return to the viscosity effect. The surface pressure dependence of D(2) in pure DLPC at the air/water interface has been studied by Peters and Beck,31 and our previous results for the DLPC monolayer were coincident with theirs.7,30,32 Here, the free area model by Sackmann, Tra¨uble, and co-workers,33,34 is applied to analyze the retardation profile of D(2) in the homogeneous DLPC/PtBMA mixed monolayers. The lateral diffusion coefficient, D(2) of a rigid cylinder with a cross-sectional area ao is expressed as follows:

D(2) ) R exp(-βa*/af)

(5)

where R is a factor representing the diffusant geometry and its local velocity, af is the free area per molecule defined as af ) A - ao, a* is the critical free area for a step displacement, and β is a factor accounting for the overlap of free area (0.5 < β < 1.0). The preexponential factor, R, in eq 5 can be replaced by Do(2),

D(2) ) Do(2) exp (-βa*/af)

(6)

where Do(2) has the meaning of a hypothetical diffusion coefficient of a probe lipid with the same ao in the limit of infinite dilution at the air/water interface, namely, D(2) of a diffusant with ao at af ) ∞. Figure 4 shows a (30) Tanaka, K.; Manning, P. A.; Lau, V. K.; Yu, H. Langmuir 1999, 15, 600. (31) Peters, R.; Beck, K. Proc. Natl. Acad. Sci. U. S. A. 1983, 80, 7187. (32) Tamada, K.; Kim, S.; Yu, H. Langmuir 1993, 9, 1545. (33) Tra¨uble, H.; Sackmann, E. J. Am. Chem. Soc. 1972, 94, 4499. (34) Galla, H. J.; Hartmann, W.; Theilen, U.; Sackmann, E. J. Membr. Biol. 1979, 48, 215.

tBMA/mol %

ao/nm2

βa*/nm2

0 (DLPC) 5 10 15 25

0.42 ( 0.03 0.40 ( 0.01 0.37 ( 0.01 0.36 ( 0.02 0.35 ( 0.01

0.230 ( 0.004 0.226 ( 0.004 0.170 ( 0.004 0.161 ( 0.005 0.153 ( 0.002

a Equation 6 is the basis of the plots in Figure 4 to deduce a and o βa* where D(2) ) Do(2) exp(-βa*/af) with af ≡ A - ao.

semilogarithmic plot of D(2)/Do(2) vs af-1. Since the experimental uncertainties for D(2) at the lift-off point are much larger than those at finite Π for all compositions, Do(2) extrapolated from a semilogarithmic plot of D(2) vs af-1 on the basis of eq 5 is used here. Solid lines in Figure 4 indicate the best semilogarithmically fitted lines with ao as a fitting parameter. It should be noted that all solid lines go through the origin within experimental errors, indicating validity of eq 6. We collect in Table 1 the values of ao so chosen with the uncertainties representing the fitting range within 95% confidence limit, and the linear slope, βa* obtained from the slopes in Figure 4 with one standard deviation. The magnitudes of Do(2), ao, and βa* for pure DLPC monolayer are 119 µm2 s-1, 0.42 nm2, and 0.230 nm2, respectively, which are in good agreement with those by Peters and Beck31 and ours reported earlier.7,30,32 Briefly we touch on the significance of the two parameters. Both ao and βa* decrease with increasing tBMA fraction. In terms of the hydrodynamic model of HughesPailthrope-White (HPW),35 D(2) of a diffusant is inversely proportional to the monolayer viscosity η, as will be seen shortly; hence, it seems reasonable to conclude that the decrease in the lipid diffusion coefficient with increasing tBMA fraction arises from the “condensation effect” on DLPC by tBMA which in turn incrementally enhances the in-plane lateral (quasi-two-dimensional) viscosity of the mixed monolayer. Actually, in our parallel experiment using monoolein/PtBMA monolayers, it was observed that the in-plane lateral viscosity of lipid monolayers increased by incorporating polymer, PtBMA, although the lipid used was not DLPC.36 Also, the decrements in the values of ao and βa* with increasing tBMA fraction are abruptly changed at tBMA fraction of 10 mol %, and then remain almost constant. Thus, it might be surmised that the surface viscosity of DLPC/PtBMA binary monolayer is drastically changed at this tBMA fraction. Comparing the free area analysis of the DLPC/PtBMA monolayers with the DLPC/cholesterol monolayers reported previously,30 it is interesting that the unique composition where the values of ao and βa* change drastically is not restricted to cholesterol but the same is true for the DLPC/PtBMA system, perhaps indicating that it is not “viscosifierspecific”. A more conclusive study of the relation between the monolayer viscosity and tBMA composition for this system as well as the DLPC/cholesterol monolayers will be carried out soon with our surface canal viscometer.37,38 Lateral Diffusion of Lipase. As alluded to earlier, the focus of this report is to correlate kinetics of enzyme catalyzed reaction on monolayers with its monolayer dynamics, and thus both, kinetics and dynamics, must be (35) Hughes, B. D.; Pailthorpe, B. A.; White, L. R. J. Fluid Mech. 1981, 110, 349. (36) Sadrzadeh, N. J. Ph.D. Dissertation, University of WisconsinMadison, 1996. (37) Sacchetti, M.; Yu, H.; Zografi, G. Rev. Sci. Instrum. 1993, 64, 1941. (38) Sacchetti, M.; Yu, H.; Zografi, G. J. Chem. Phys. 1993, 99, 563.

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Figure 5. Lateral diffusion coefficient of NBD-PC and FITClabeled lipase in the binary monolayer as a function of tBMA composition: (b) NBD-PC and (O) FITC-lipase. The solid curve for D(2) of FITC-lipase is drawn by scaling down D(2) of NBDPC by a factor of 4.2 (see text for the explanation of the factor).

carried out under the same condition. Although D(2) in the binary monolayers in homogeneous state has been presented thus far, it might be different from the diffusion behavior of a probe molecule in the binary DLPC/PtBMA monolayers containing a small amount of lipase, which is the necessary component for the hydrolysis reaction. Hence, D(2) of NBD-PC- and FITC-labeled lipase in the binary monolayers are determined here under the same lipase concentration in the monolayers, and this is the same as that for the hydrolysis reaction. Also, the lateral diffusion coefficient D(2) of the lipid or the substrate is assumed to be the same as that of NBD-PC, for we are compelled to do so since D(2) of intact substrate, UMBC18, is not accessible experimentally due to the absence of fluorescence emission by 488 nm wavelength incident light. For D(2) measurements of lipase, the FITC-labeled lipase is used to confer fluorescence on lipase molecules in lieu of intact lipase which is nonfluorescent. Figure 5 shows tBMA content dependence of the diffusion coefficients in the DLPC/PtBMA monolayers containing a lipase surface concentration of 1.08 × 10-2 molecules nm-2, which has been determined separately.1 Since the diffusion measurements are made after an equilibrium partitioning of the lipase from bulk subphase to the monolayer is reached, the surface pressure at the measurement is 25.5 ( 0.5 mN m-1. Incorporation of lipase into the DLPC/ PtBMA mixed monolayers does not alter the phase state, that is, homogeneous state, at this surface pressure range. As before, D(2) of NBD-PC decreases progressively as tBMA composition is increased. Since this trend is in good agreement with the D(2) retardation by tBMA in the binary monolayers without lipase, it seems likely that the observed decrease in D(2) with the composition is mainly due to the increase in in-plane viscosity. As shown in Figure 5, D(2) of the labeled-lipase decreases progressively in about the same fashion as the probe lipid as tBMA fraction is increased. To account for the difference of D(2) between the probe lipid and the labeled-lipase at a given tBMA fraction, the HPW hydrodynamic model35 is referred. In a quasi-two-dimensional viscous continuum with a steady shear viscosity η, sandwiched between the upper and lower Newtonian fluids with the viscosities η′ and η′′, D(2) of an isolated cylinder with a radius a and height h is given by

Figure 6. Hydrodynamic model of Hughes, Pailthorpe, and White (HPW) for lateral diffusion of an isolated cylindrical diffusant immersed in a thin flat viscous continuum: (a) an illustration of HPW model, (b) an expanded view of imbedded cylinder in (a), (c) possible insertion states of lipase into the lipid monolayer at the air/water interface.

defined as

Λ() ≡ [{ln(2/) - γ + (4/π) (1/2)2ln(2/) + O(2)}] (8) where γ is Euler’s number and

 ≡ (a /h)[(η′+ η′′)/η]

(9)

(7)

An illustration of the model specification is presented in Figure 6a and b. As given by eqs 7-9, D(2) is a function of η, η′, η′′, a, and h. Since the DLPC/PtBMA monolayer is at the air/buffer (pH 7) interface (η′ and η′′ are constants), the difference of D(2) for NBD-PC and that for the labeled lipase at a given tBMA fraction (η is fixed) may be rationalized in terms of the differences in a and h. Assuming that lipase has a disk shape in the monolayer with its h estimated to be 2.91 nm from its cross-sectional radius of 3.01 nm and hydrodynamic radius of 2.70 nm,7 while a and h of the probe lipid can be taken as 0.44 and 1.6 nm,39 respectively. Using these values as the parameters in eqs 7-9, D(2) of lipase can be estimated at approximately 1/3 of that for NBD-PC. The data shown in Figure 5 differ by more than a factor of 3. In fact, the solid curve drawn over the lipase diffusion coefficients is obtained by scaling the lipid diffusion coefficient by a factor of 4.2 to give the best fit. It is possible to account for this scaling factor difference of 3 to 4.2. While the HPW model is predicated on the insertion state of a diffusant to be exactly coincident in height with the sandwiched viscous continuum (case I in Figure 6c), such does not hold true for the lipase insertion state; as mentioned in the above, the height of lipase might be larger than that of the lipid layer (case II in Figure 6c). Also, other lipase insertion states such as cases III 40 and IV are entirely possible. In such cases, an additional hydrodynamic drag between the part of lipase being out of the lipid layer and water subphase should be taken into account in the theory, although no such attempt has yet been made. At any rate, we could invoke such an additional viscous drag to account for the scaling factor difference of 3 to 4.2. Enzyme Catalyzed Hydrolysis Reaction. We now turn to discuss the kinetics of lipase catalyzed hydrolysis reaction of UMB-C18 on DLPC/PtBMA binary monolayers at the air/buffer interface. Since the kinetic analysis follows very closely that in the previous study with cholesterol,2

where Λ() is a reduced friction coefficient that is a monotonically decreasing function of the parameter ,

(39) Thoma, M.; Schwendler, M.; Baltes, H.; Helm, C. A.; Pfohl, T.; Riegler, H.; Mo¨hwald, H. Langmuir 1996, 12, 1722. (40) Gidalevitz, D.; Huang, Z.; Rice, S. A. Proc. Acad. Sci. U.S.A. 1999, 96, 2608.

D(2) )

kT 4π(η′ + η′′) ‚ a ‚ Λ()

Lipase Activity on Lipid/Polymer Binary Monolayers

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Figure 7. Initial rate of hydrolysis Vo of umbelliferone stearate, a lipase substrate, on the binary monolayer as a function of tBMA fraction. Solid curve is drawn to guide the eye. The inset is a plot of Vo vs the sum of lateral diffusion coefficients of NBD-PC and labeled lipase obtained at different tBMA fractions.

Figure 8. Normalized initial hydrolysis rates Vo by that in pure DLPC Voo using the data set shown in Figure 7. The solid curve is drawn according to eq 10 for the two-dimensional diffusion-limited reaction dynamics theory of Torney and McConnell.

with the discussion will be rather brief in order to avoid the repetition. Our kinetic model has four distinct steps: (1) the substrate adsorption from bulk phase to the monolayer, (2) substrate-enzyme encounter via in-plane diffusion, (3) hydrolysis catalyzed by the lipase, and (4) spontaneous desorption of the products in the subphase.2 In Figure 7 is shown the effect of tBMA composition of the binary monolayer on the initial hydrolysis reaction rate, Vo, at a fixed substrate bulk concentration, [UMB-C18] ) 100 nM. Measurements were carried out at a constant temperature of 296.2 ( 0.5 K, surface pressure of 25.5 ( 0.5 mN m-1, and lipase surface concentration [lipase]σ of 1.08 × 10-2 molecules nm-2. The partitioning of the UMBC18 from the bulk subphase to the monolayer was not large despite its known surface activity. 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.7 The monolayer homogeneity at the experimental surface pressure of 25 mN m-1 was confirmed by the epifluorescence microscopy. The turnover number of this hydrolysis reaction on DLPC monolayers at 25 mN m-1 was 166 s-1, which was much larger than that in bulk solution.2 The Vo decreases monotonically with tBMA fraction. The retardation profile of Vo by tBMA is similar in shape to those of D(2) with tBMA composition shown in Figure 5. Thus, it is qualitatively obvious that Vo is governed by the lateral mobility of the reactants. This can be seen clearer when Vo is replotted as a function of the sum of D(2)s of a lipid and lipase, as shown in the inset of Figure 7. We note with emphasis that our subsequent analysis of the kinetics is based on the assumption that the diffusion coefficient of one of the reactants, UMB-C18, is the same as that of the lipid probe whereas that of the other reactant, lipase, is deduced separately by the experiment with the labeled lipase. We finally come to combine the lateral diffusion coefficients of the reactants with the enzymatic hydrolysis rates on the monolayers, using the two-dimensional diffusion-controlled reaction dynamics theory of Torney and McConnell.41 The rate function k(t) for an irreversible reaction, A+B f P, 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 (10)

z ) ln(16βD(2)tl-2)

(11)

{ (1 -R R)}

(12)

and

β ) exp π

Here R, γ, and t are the reaction probability of the reactants upon encounter, Euler’s number, and the reaction time, respectively, while D(2) 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 11 is a parameter related to the radius of reaction circle R and equals 2R exp γ. The interfacial cross-sectional radii of UMB-C18 and lipase both evaluated from surface pressure-area isotherms are 0.28 and 3.01 nm,22 respectively, hence R is taken to be 3.29 nm. The contribution of the higher order term, O(z-4), of eq 10 is less than 1% for the time scale of our experiment, and is therefore ignored. Figure 8 shows the tBMA content dependence of the normalized initial hydrolysis rate, where Voo is in pure DLPC without tBMA. The solid line is drawn according to eq 9 with R ) 1.0. Actually, the prediction of Vo/Voo is not sensitive to the choice of R. It appears clear that our results are in good agreement with the theoretical prediction of Torney and McConnell. Thus, we should like to conclude that the substrate adsorbs to the interface, randomly diffuses to lipase and is hydrolyzed by the enzyme at the interface, with its reaction rate controlled by diffusion in the monolayer. Our result is contrary to the kinetics of enzymed catalyzed reaction at the interface observed by using vesicles, which are reaction-controlled.42,43 We surmise that the discrepancy in the two is based on the effective substrate concentration, since we have observed that the reaction kinetics on the monolayer can be reaction-controlled at higher substrate concentrations.1 This is because many substrate molecules are directly accessible from the subphase to lipase by not diffusing to the monolayer at large. Noting that our results in Figure 8 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 tBMA. In other reported cases of the diffusioncontrolled reaction on solid surfaces,44,45 however, at least one fitting parameter is required. (41) Torney, D. C.; McConnell, H. M. Proc. R. Soc. London 1983, A387, 147. (42) Berg, O. G.; Yu, B.-Z.; Rogers, J.; Jain, M. K. Biochemistry 1991, 30, 7283. (43) Berg, O. G.; Cajal, Y.; Butterfoss, G. L.; Grey, R. L.; Alsina, A.; Yu, B.-Z.; Jain, M. K. Biochemistry 1998, 37, 6615.

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Conclusions The lateral diffusion coefficients of a probe lipid and of lipase from Pseudomonas cepacia are examined on the uniphasic DLPC/PtBMA binary monolayers at different compositions at the air/buffer (pH 7) interface. Both diffusion coefficients decrease with increase in the surface pressure and tBMA fraction, and the diffusion coefficient of the lipase is slower than that of the probe lipid by a factor of approximately 1/4. These results are discussed on the basis of the free area model and the hydrodynamic model of Hughes, Pailthorpe, and White. Parallel with the diffusion studies, the chemical kinetics of a lipase catalyzed hydrolysis reaction on the binary monolayers was investigated. The hydrolysis reaction rate monotonically decreases with the tBMA content. Combining the lateral diffusion coefficients of the reactants with the chemical kinetics, we have directly shown that the enzyme (44) Gaspers, P. B.; Gast, A. P.; Robertson, C. R. J. Colloid Interface Sci. 1995, 172, 518. (45) Wang, H.; Harris, J. M. J. Am. Chem. Soc. 1994, 116, 5754.

Tanaka and Yu

catalysis on the uniphasic binary monolayers of DLPC/ PtBMA is diffusion-controlled and the results are in quantitative agreement with a strictly two-dimensional reaction dynamics theory of Torney and McConnell. Thus, we put forth the claim that diffusion-controlled kinetics of interfacial enzyme catalysis is not limited to our previous biomimetic system, DLPC/cholesterol,1,2 but perhaps a general phenomenon on monolayers with [UMB-C18] ) 100 nM in the subphase. Acknowledgment. This work was partially supported by the Eastman Kodak Professorship and NSF grants (DMR9711226 and DMR0084301) awarded to H.Y. We are grateful for helpful discussions with Prof. George Zografi and our colleagues Thorsteinn Adalsteinsson and Hunkyun Pak. 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. Finally, K.T. is indebted to Brian Yablon for his careful reading of the manuscript. LA010965B