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Langmuir 2008, 24, 10950-10960
Molecular Packing Tunes the Activity of KluyWeromyces lactis β-Galactosidase Incorporated in Langmuir-Blodgett Films Eduardo M. Clop, Pedro D. Clop, Julieta M. Sanchez, and Marı´a A. Perillo* Quı´mica Biolo´gica-Biofı´sica Quı´mica, Departamento de Quı´mica/ ICTA, Facultad de Ciencias Exactas, Fı´sicas y Naturales and UniVersidad Nacional de Co´rdoba, AVenida Ve´lez Sarsfield 1611, X 5016GCA Co´rdoba, Argentina ReceiVed May 30, 2008. ReVised Manuscript ReceiVed July 11, 2008 Functional consequences of constraining β-Gal in bidimensional space were studied at defined molecular packing densities and constant topology. Langmuir-Blodgett films, LB15 and LB35 composed of dipalmitoyl phosphatidylcholine and K. lactis β-Gal, were obtained by transferring Langmuir films (L) initially packed at 15 and 35 mN/m, respectively, to alkylated glasses. The β-Gal-monolayer binding equilibrium, mainly the adsorption rate and affinity, depended on the initial monolayer’s surface pressure (lower for higher πi). At πi ) 15 and 35 mN/m, the surface excess (Γ) followed downward parabolic and power-law tendencies, respectively, as a function of subphase protein concentration. Γ values in L roughly reflected the protein surface density chemically determined in LBs (0-7.5 ng/mm2 at πi ) 0-35 mN/m and [β-Gal]subphase ) 0-100 µg/mL). The β-Gal-catalyzed hydrolysis of o-nitrophenyl-galactopyranoside showed a Michaelian kinetics in solution as well as in LB15. KM, KM,LB15, Vmax, and Vmax,LB15 were 5.15 ( 2.2 and 9.25 ( 6 mM and 39.63 and 0.0096 ( 0.0027 µmol/min/mg protein, respectively. The sigmoidal kinetics observed with LB35 was evaluated by Hill’s model (K0.5 ) 9.55 ( 0.4 mM, Vmax,35 ) 0.0021 µmol/min/mg protein, Hill coefficient n ) 9) and Savageau’s fractal model (fractal constant Kf ) 9.84 mM; reaction order for the substrate gs ) 9.06 and for the enzyme ge ) 0.62). Fractal reaction orders would reflect the fractal organization of the environment, demonstrated by AFM images, more than the molecularity of the reaction. Particular dynamics of the protein-lipid structural coupling in each molecular packing condition would have led to the different kinetic responses.
1. Introduction Biological environments are heterogeneous media. In these kinds of systems the kinetics of enzyme-catalyzed reactions may be modulated through several mechanisms affecting, e.g., the distribution of enzymes and/or substrates between the different compartments and the supramolecular organization of the substrate (in the case of amphipathic and self-organized substrates).1-3 The accompanying molecular crowding may be affecting the probability of enzyme-substrate collisions due to the excluded volume and the thermodynamic activity of water due to its structuring at surfaces.4 The enzyme binding to a nonsubstrate surface can modulate the enzyme conformation and activity.5-9 Moreover, the reaction confinement to dimensionally restricted spaces such as a percolation matrix, channel, or surface can cause significant effects on the reaction mechanism and rate.7,10-13 * To whom correspondence should be addressed. (1) De Tullio, L.; Maggio, B.; Hartel, S.; Jara, J.; Fanani, M. L. Cell. Biochem. Biophys. 2007, 47, 169–77. (2) Perillo, M. A.; Yu, R. K.; Maggio, B. Biochim. Biophys. Acta 1994, 1193, 155–64. (3) Perillo, M. A.; Guidotti, A.; Costa, E.; Yu, R. K.; Maggio, B. Mol. Membr. Biol. 1994, 11, 119–26. (4) Ellis, R. J. Trends Biochem. Sci. 2001, 26, 597–604. (5) Davies, S. M.; Epand, R. M.; Kraayenhof, R.; Cornell, R. B. Biochemistry 2001, 40, 10522–31. (6) Sanchez, J. M.; Perillo, M. A. Colloids Surf. B: Biointerfaces 2000, 18, 31–40. (7) Sanchez, J. M.; Perillo, M. A. Biophys. Chem. 2002, 99, 281–95. (8) Sanchez, J. M.; Perillo, M. A. Colloids Surf. B: Biointerfaces 2002, 24, 21–31. (9) Johnson, J. E.; Cornell, R. B. Mol. Membr. Biol. 1999, 16, 217–35. (10) Savageau, M. A. J. Theor. Biol. 1995, 176, 115–24. (11) Aon, M.; O’Rourke, B.; Cortassa, S. Mol. Cell. Biochem. 2004, 101, 4447–4452. (12) Lindenberg, K.; Sheu, W.-S.; Kopelman, R. Phys. ReV. A 1991, 43, 7070 LP–7072. (13) Sanchez, J. M.; Ciklic, I.; Perillo, M. A. Biophys. Chem. 2005, 118, 69–77.
Monomolecular reactions are not affected by dimensionality restrictions due to their unitary kinetic order. This is a reasonable assumption because, in these cases, dimensionality restrictions are not expected to affect the probability that an isolated molecule exhibits spontaneous cleavage or conformational change. However, dimensionality restrictions have a greater influence in collision probabilities and, hence, in the rate of a bimolecular reaction. A fractal kinetics may arise in restricted reaction conditions when the potential-energy surface that has to be explored during the reaction possesses fractal properties.14 In those cases, kinetic orders will reflect the fractal dimension of the surface where the reaction is taking place.10 In previous works we demonstrated that β-galactosidase from Escherichia coli (β-Gal), which is a soluble protein, could be modulated in heterogeneous media. This modulation was dependent on the enzyme interaction with lipid/water interfaces and exerted at different levels, e.g., the enzyme conformation and reaction mechanism included an apparent effect associated with the partition of one of the reaction products (o-nitrophenol) between the membrane and the water phases.13 Localization of this substance within the polar headgroup region of the membrane15 also played a significant role in the modulation of the hydrolytic reaction mechanism. The type of β-Gal/bilayer interaction (adsorption or penetration) depended on the membrane composition, organization, and topology and differentially modulated the activity of the enzyme toward a soluble substrate.7,8 In membranes, the organization is defined by several properties in a combined manner, mainly the packing and mobility of its molecular components and the topology of its surface. In a tridimensional system such as a liposome, typically used as a (14) Kurzynski, M. FEBS Lett. 1993, 328, 221–4. (15) Sanchez, J. M.; Turina, A. D.; Perillo, M. A. J. Photochem. Photobiol. B 2007, 89, 56–62.
10.1021/la801679m CCC: $40.75 2008 American Chemical Society Published on Web 09/04/2008
ActiVity of KluyVeromyces lactis β-Galactosidase
biomembrane model, these properties are mutually affected. Conversely, use of phospholipid monolayers self-organized at the air-water interface allows one to maintain a constant planar topology and control the molecular packing.16 Moreover, the monolayer can be transferred to an alkylated glass to obtain a planar supported, Langmuir-Blodgett (LB), film conserving the molecular organization of the original floating monolayer.17,18 In the present paper we investigated the effect of the lateral molecular packing at constant planar topology on the activity of β-Gal incorporated to dipalmitoylphosphatidylcholine (dpPC) monolayers packed at different initial surface pressures (πi) and transferred at constant π to an alkylated glass. The kinetics of β-Gal adsorption as well as LB films preparation are described. Then the catalytic reaction occurring at the solid/liquid interface between the transferred proteolipidic monolayer and water was analyzed. The enzymatic assay was based on conversion of a soluble substrate reagent to a soluble colored product. A qualitative change, from hyperbolic to sigmoidal behavior, was found in the reaction kinetics upon π increasing from 15 to 35 mN/m. A fractal kinetic model was tested as one possible hypothesis to explain the experimental data, and its results were analyzed in conjunction with atomic force microscopy (AFM) images.
2. Materials and Methods 2.1. Materials. The enzyme β-Gal from KluyVeromyces (Saccharomyces) lactis [EC 3.2.1.23] was from Maxilat 2000, (specific activity 1.3 UI/mg protein; 1UI ) 1 µmol/min of ONP formed at 37 °C); o-nitrophenol-β-D-galactopyranoside (ONPG) was obtained from Sigma Chemical Co. (St. Louis, MO). Lipids were purchased from Avanti Polar Lipids (Alabaster, AL). Other reagents and solvents used were analytical grade. 2.2. Preparation of the Hydrophobic Glass Surface. The procedure was essentially that described by von Tscharner and McConnell.19 Borosilicate glasses 18 × 18 × 0.15 mm (coverslips) were submitted to the following treatments: (a) washing with hot 1% P/V SDS and sonication (Test Laboratory TB02 sonicator, Argentina) at 80 W, 40 kHz; (b) washing with distilled water; (c) washing with sulfochromic solution (33 mM K2CrO7 in 3.75 H2SO4) for 15 min; (d) washing with distilled water; (e) sonication with 3 mM NaOH for 15 min; (e) rinse with bidistilled water for 20 min; (f) dry at 110-150 °C for at least 30 min; (g) immersion in the alkylation mixture (80% v/v hexadecane (purity 99% v/v), 12% v/v Cl4C, 8% v/v Cl3CH, and 0.1% v/v octadecyl trichlorosilane) and shake for 10-15 min, and (h) rinse three times with Cl3CH for 5 min. 2.3. Langmuir-BlodgettFilms. 2.3.1. LangmuirFilmPreparation. Monomolecular layers of dpPC at the air-water interface were prepared following the Langmuir technique and monitored as described previously.20,21 Between 5 and 30 µL of a chloroformic solution of phospholipid was spread with a microsyringe onto an unbuffered aqueous surface in a trough with an initial area of 247.5 cm2; about 5 min was allowed for evaporation of chloroform. Lateral surface pressure (π) was measured by the Wilhelmy plate method using a roughened platinum plate (a platinized Pt foil 5 mm wide × 20 mm long × 0.025 mm thick). The surface pressure (π) was obtained by means of a computer-controlled commercial device (Minitrough II, KSV Instruments Ltd., Finland) enclosed in a Plexiglas box to reduce surface contamination. Before each experiment the trough was rinsed and wiped with 70% v/v ethanol and several times with bidistilled water. The absence of surface(16) Gaines, G. Insoluble Monolayers at Liquids-Gas Interfaces; Interscience Publishers: New York, 1966. (17) Hollars, C. W.; Dunn, R. C. Biophys. J. 1996, 75, 342–353. (18) Zasadzinski, J. A.; Viswanathan, R.; Madsen, L.; Garnaes, J.; Schwartz, D. K. Science 1994, 263, 1726–1732. (19) von Tscharner, V.; McConnell, H. M. Biophys. J. 1981, 36, 421–7. (20) Perillo, M. A.; Polo, A.; Guidotti, A.; Costa, E.; Maggio, B. Chem. Phys. Lipids 1993, 65, 225–38. (21) Garcia, D. A.; Perillo, M. A. Biophys. Chem. 2002, 95, 157–64.
Langmuir, Vol. 24, No. 19, 2008 10951 active compounds in pure solvents and the subphase solution (bidistilled water) was checked before each run by reducing the available surface area to less than 10% of its original value after enough time was allowed for adsorption of possible impurities that might have been present in trace amounts. Symmetric compression was achieved with two moving barriers at a constant rate of 7.5 cm2 min-1. Reproducibility was within (0.01 nm2 and (1 mN/m for molecular area and surface pressure, respectively. Temperature was maintained at 22 ( 1 °C with a circulating water bath. The initial surface pressure (πi) was set between 0 and 35 mN/m. The aqueous protein solution (β-Gal or bovine serum albumin (BSA)) was injected in the subphase under the monolayer at the desired final concentration. The penetration kinetics was studied as explained below (see section 2.4). 2.3.2. Monolayer Transference to an Alkylated Glass and Topography EValuation through Atomic Force Microscopy. Monolayers were transferred to hydrophobic glasses at a constant surface pressure. This computer-controlled process started after the protein was injected in the subphase, completed its penetration in the monolayer, and the surface pressure reached the plateau level. It is important to note that the transferring of the monolayer to the hydrophobic glass began with the support in the air above the film. When the glass was first dipped through the film the lipids adhered to the hydrophobic surface with their tails, and when the support was extracted a second layer was deposited. The result was a double layer but with the polar heads of the two leaflets inside. Then the protein injected in the subphase could not adsorb from the solution directly on the surface of the alkylated glass. The software was fed with numerical values of the geometrical parameters of the coverslip to allow calculation of the film-covered surface. While the alkylated glass passed across the interface, the monolayer was transferred to it, inducing a decrement in the surface pressure that was sensed by the surface balance and immediately compensated by an automatic barrier movement. This resulted in a reduction in the monolayer area equivalent to the area transferred. The relationship between this value and the total glass area represents the cumulative transfer (CT). Other parameters useful to evaluate the evolution of the experiments are the relative transference (RT) and the relative transference ratio (TR). The former informs about the barrier movement and is represented by a straight line with ordinate values ranging from 0 to 1. The latter is similar to the former except that the whole alkylated glass length is divided in several sections of 1 mm each, where the software calculates the mean relative transference, as an enzyme source. LB films were stored at 4 °C for not more than 2 days in a humid environment until used. In this condition, but not in a dry atmosphere, the enzyme activity was preserved. The topographic structure of LB films was evaluated by atomic force microscopy (AFM)22 using Multimode NanoScope IIIa AFM equipment. Analyses were made with the LB films immersed in bidistilled water under tapping mode conditions at 2 Hz scan frequency using a 100 µm piramidal quartz cantilever, which had a nominal value of spring constant 0.32 N/m, integral gain IG ) 0.33 and proportional gain PG ) 0.78. The microscopic images were flattened (planar fitting) using the software provided by the manufacturer, and then they were analyzed with n-Surf Beta version 1.0 to evaluate the height profile and topological dimension. 2.4. Protein Penetration in the Monolayer from the Subphase. 2.4.1. Surface Pressure-Dependent Protein Adsorption to the Monolayer-Water Interface. These experiments were performed at constant surface area using a circular Teflon trough (4.5 cm diameter and 0.5 cm depth, 15.9 cm2 available area). The initial surface pressures (πi) was set between 0 and 35 mN/m (the later is close to the equilibrium lateral pressures of bilayers).23 The increase in π as a function of time was measured up to a plateau (πmax). The value of ∆πmax ) πmax - πi, induced by β-Gal or BSA penetration into the monolayer, was measured after injection of 20 µL of 34.65 mg/mL β-Gal or 18 mg/mL BSA in the subphase. Then ∆πmax values (22) Cross, B.; Ronzon, F.; Roux, B.; Rieu, J.-P. Langmuir 2005, 21, 5149– 5153. (23) Marsh, D. Biochim. Biophys. Acta 1996, 1286, 183–223.
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were plotted against πi and a straight line was fitted; the maximal π allowing protein penetration (πcutoff) was determined from the intersection of this line with the abscise axis. 2.4.2. Effect of Subphase Concentration on β-Gal Adsorption to the Monolayer-Water Interface. (a) Binding Affinity. The kinetics of β-Gal incorporation in dpPC monolayers was studied by recording the changes in π vs time, monitored as described above. These experiments were performed within a concentration range of β-Gal ranging from 15 to 75 µg/mL. The rate constants for the adsorption and desorption processes at/from the monolayer-water interface were determined from a plot of ∆π (πt - πi,) vs t (the time elapsed after enzyme injection in the subphase) and analyzed according to a single-exponential model represented by eq 1
∆π = [1 - exp(-t ⁄ τ)]
(1)
and the time constant (τ) values could be determined for each individual enzyme concentration in the subphase. Then the rate constants for the adsorption (ka) and desorption (kd) processes were obtained by fitting eq 2 to the plots of τ vs enzyme concentration
1 ) kd + ka[enzyme] τ
(2)
Finally, eq 3 allowed calculation of the association binding constant (Kb),24,25 as follows
Kb )
ka kd
(3)
(b) Extent of Binding. The quantity of enzyme bound to the monolayer-water interface was determined from the Gibbs adsorption equation as a surface excess (Γ) representing a surface molecular density according to eq 4:16
c ∂γlip Γ)RT ∂c
(4)
where Γ is the amount of β-Gal per unit area, c is the protein concentration in the subphase, γlipis the surface tension of dpPC monolayer (calculated from γlip ) γw - π, at a particular molecular area, being γw the surface tension of water at 25 °C). An ideal behavior of protein in solution was assumed, so the β-Gal activity coefficient was equal to unity. 2.5. Determination of Protein Concentration. Protein concentration was determined according to the method of Lowry,26 with the following modifications, to allow solubilization of proteins incorporated in LB films. Alkylated glasses, covered with the LB film, were immersed in a solution containing 50 µL of SDS 3% p/v and 0.5 mL of 0.63 mM EDTA-Cu2+ and sonicated for 15 min at a 80 W power, 40 kHz frequency, and room temperature. After 30 min incubation at room temperature, 50 µL of Folin-Ciocalteau, diluted to one-half, was added, and 1 h later and the absorbance was measured at 750 nm. Bovine serum albumin was used as the standard. 2.6. Determination of Enzyme Activity and Kinetic Parameters. The method applied was essentially that of Wallenfels and Malhotra.27 The incubation system contained 1 mL of 0.1 M sodium phosphate pH 6.8 buffer with 0-20 mM ONPG. After incubation at 37 °C for 10 min, the hydrolysis reaction was stopped by addition of 0.2 mL of 1.4 M sodium carbonate. The absorbance of the ONPx formed was determined at 420 nm by spectrophotometry (molar extinction coefficient of ONPx ε420 ) 4530 M-1 cm-1). Possible effects of the polarity of the medium on the ONP extinction coefficient value (due to partitioning of ONP toward the membrane) were taken into account. The assays were performed in independent triplicates (different beta(24) de Matos Alves Pinto, L.; Malheiros, S. V.; Lino, A. C.; de Paula, E.; Perillo, M. A. Biophys. Chem. 2006, 119, 247–55. (25) Bordi, F.; Cametti, C.; Motta, A.; Diociaiuti, M.; Molinari, A. Bioelectrochem. Bioenergy 1999, 49, 51–6. (26) Lowry, O. H.; Rosebrough, N. J.; Farr, A. L.; Randall, R. J. J. Biol. Chem. 1951, 193, 265–75. (27) Wallenfels, K.; Malhotra, O. P. AdV. Carbohydr. Chem. 1961, 16, 239– 98.
Gal-LB film preparations were used for the repetitions). The enzymatic activity in the supernatant of LB films was analyzed for possible enzyme solubilization. Nonenzymatic substrate hydrolysis with enzyme free glasses was not checked. The plot of the initial reaction rate (V) vs the substrate concentration (S) was fitted to the Michaelis-Menten equation (eq 5) to determine the kinetic parameters Vmax (maximal reaction rate) and KM (Michaelis constant).
V)
VmaxS KM + S
(5)
In cases where the kinetics showed a sigmoidal behavior, both a Hill equation28 and a fractal analysis were applied. The former was represented by eq 6
(
log
)
V ) n log K0.5 + n log S Vmax - V
(6)
In the Hill plot, log[V/(Vmax - V)] vs log S, the hyperbolic kinetics (Michaelian) would be associated with slope ) 1 and in sigmoidal kinetics with slope > 1. The Hill plot would also allow distinguishing between the allosteric and the fractal kinetics because log[V/(Vmax - V)] vs log [S] produces a straight line in the case of allosteric kinetics and two straight lines with different slopes in fractal kinetics. The intersection of both lines occurs at x ) log(Kf) (Kf is the fractal Michaelis constant). At S < Kf the cooperative effect will be evidenced with a Hill number given by gs/ge with gs and ge the being the reaction order for the substrate and enzyme, respectively.10 Equations 7 and 8 summarize the law for fractal kinetics
( ) ( )( S Kf
gs
)
V V 1Vm Vm
Kmeff ) Kf2(ge-1)⁄gs
)
-ge
(7) (8)
where Kmeff is the effective Michaelis’s constant. Kinetic data (V vs [S]) represented in a log-log plot (see Figure 9b) allow determining three of the four parameters characterizing the fractal kinetics: two asymptotes provide estimations of Vmax and Kf and the slope at low S gives an estimation of gs. When the exponents gs ) ge ) 1, which is the condition for homogeneous systems, eq 7 reduces to the traditional Michaelis-Menten’s equation. The fractal constant Kf is a function of ET; hence, the forth parameter ge can be either determined from the slope of a secondary plot of Kf vs ET or, as done in the present work, calculated by solving eq 8. 2.7. Image Analysis and Fractal Dimension Estimation. The fractal dimension of protein dots distribution in AFM images were calculated by the box counting method29 with the commercial software Benoit 1.2 (Trusoft). The box dimension is defined as the exponent Df in the equation N(d) ≈ 1/dDf where N(d) is the number of boxes of linear size d necessary to cover the data set of points distributed in a 2D plane. In the definition of box dimension, a box is counted as occupied and enters the calculation of N(d) regardless of whether it contains one point or a relatively large number of points. 2.8. Statistical Calculations. The least-squares method was applied to fit functions through a regression analysis. Two-way ANOVA was used to compare the effect of molecular packing on the values of the enzymatic parameters. Student’s t test was applied to compare individual averages. The propagation error method was used to evaluate the error associated to variables calculated from other ones determined experimentally.30,31 (28) Segel, I. H. Enzyme Kinetics: BehaVior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems; Wiley Classics Library: New York, 1993. (29) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: New York, 1983. (30) Sokal, R.; Rohlf, F. Introduction to biostatistics; W. H. Freeman & Co.: New York, 1987.
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Figure 1. Protein penetration in monomolecular layers of dpPC. (Upper panels) Variation of surface pressure as a function of time after injection of BSA (a) and β-Gal (b) in the subphase at different πi and at final concentrations of 40 and 77.6 µg/mL, respectively. (Lower panels) Change in the surface pressure (∆π ) πmax - πι) as a function of πi measured from data shown in the upper panels (BSA (c) and β-Gal (d)). See Materials and Methods section for details. Arrows point to the πcutoff value.
3. Results 3.1. Protein Adsorption to the Monolayer-Water Interface. This experiment was done with both β-Gal and BSA. The latter was used as a reference model of a monomeric protein. After injection of the protein in the aqueous subphase the surface pressure started to increase. This phenomenon may involve two effects: (a) protein adsorption to the free air-water interface (at πι ) 0 mN/m) or incorporation to the lipid monomolecular layer at the air-water interface (at πι > 0 mN/m) and (b) protein unfolding either subsequently or simultaneously with the adsorption/penetration process (Figure 1a and 1b). It was noticeable that when the protein adsorbed to a lipid-free interface (πi ) 0 mN/m) the maximal surface pressure measured was πmax ) 24 mN/m. Between 7 and 25 mN/m πmax was independent from πi and the values reached with BSA and β-Gal were similar (28 mN/m). At higher πi (between 25 and 35 mN/ m), in the presence of β-Gal, πmax increased up to 41 mN/m. These experiments were performed at a subphase protein concentration of 78 µg/mL; lower concentrations led to lower πmax. Protein penetration into dpPC monolayer, measured as ∆πmax, decreased with increasing molecular packings (the higher the πi the higher the packing) with a cutoff initial pressure πi,cutoff = 26 and 37 mN/m for BSA and β-Gal, respectively (Figure 1c and 1d). The time constants τ for enzyme penetration in dpPC monolayers were determined by fitting eq 1 to the ∆πt vs β-Gal concentration plot. Here ∆πt represents the difference between π at time t (πt) minus πi. In Figure 2a typical results of the temporal variation of ∆πt obtained at 15 mN/m, at different β-Gal subphase concentrations, are shown. The values of 1/τ, at each of the πi tested, were plotted as a function of enzyme concentration (Figure 2b), and straight lines were obtained (eq 2). Their slopes represented the rate constants for the adsorption (ka) which were higher for the lowest initial surface pressure (ka,15 ) 4 × 10-4 M-1 · s-1 and ka,35 ) 2.4 × 10-5 M-1 · s-1 for monolayers packed at πi 15 and 35 mN/m, respectively). The (31) Green, J. R.; Margerison, J. D. Statistical Treatment of Experimental Data; Elsevier: New York, 1978.
Figure 2. Kinetics of β-Gal binding to the dpPC monolayers packed at different initial lateral pressures. (a) Temporal variation of surface pressure change (∆πt ) πt - πi) at increasing enzyme concentrations in the subphase (from bottom to top 15, 30, 45, 60, 75 µg/mL) in a typical experiment at πi ) 15 mN/m. Solid lines represent the fitness of eq 1 to each π-time curve. This allowed determining τ values. (b) τ values were calculated from experiments similar to a but performed at two different πi (15 and 35 mN/m); their reciprocals determined at each πi were plotted as a function of the β-Gal concentration in the subphase, and eq 2 was fitted to determine association and dissociation rate constants from the slope and the y axis intercept, respectively.
ordinates represented the rate constants kd for the protein desorption processes from the monolayer/water interface (kd,15 ) 0.031 s-1 and kd,35 ) 0.02 s-1 for monolayers packed at πi ) 15 and 35 mN/m, respectively). Finally, from eq 3 the equilibrium binding constants of β-Gal at 15 and 35 mN/m resulted in Kb,15 ) 1.3 × 10-2 M-1 and Kb,35 ) 1.2 × 10-3 M-1, respectively. From the comparison of the association and
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Figure 4. Temporal evolution of the dpPC-protein monolayer transference from the air-water interface to an alkylated glass at a constant surface pressure: CT, cumulative transference; TR, relative transfer ratio; RT, relative transference (see section 2.3.2).
Figure 3. Surface excess (Γ) due to β-Gal interaction with dpPC monolayers as a function of enzyme concentration in the subphase and at different inicial surface pressures. (a) After injection of β-Gal in the subphase, the monolayer π increased from the initially set value (15 or 35 mN/m) up to a plateau (πmax). The surface tension at πmax was calculated (γlip ) γw - πmax) and plotted against the β-Gal concentrations in the subphase. (b) Data from panel a were used to calculate the surface excess (Γ) (eq 4) at each of the two initial surface pressures assayed (15 mN/m, solid lines; 35 mN/m, dotted lines). Γ represents the surface concentration of β-Gal. (O) Results from chemical determination of protein content in LB films at each πi were also included to facilitate comparison with calculated data.
dissociation rate constants it follows that the higher affinity of β-Gal for the lower packed monolayer was more strongly influenced by the higher association rate (ka,15 = 17 × ka,35) than by the dissociation processes (kd,15 = 1.55 × kd,35). The value of πmax was dependent on the enzyme concentration in the subphase under the phospholipid monolayer. Transformation of πmax values into surface tension values γi allowed describing the phenomenon on a quantitative basis following Gibbs adsorption equation. In Figure 3a it is shown that, at πi ) 15 mN/m, γlip decreased as a function of β-Gal concentration in the subphase. However, at πi ) 35 mN/m, the decrease in γlip as a function of β-Gal concentration was very low up to a subphase concentration of 60 µg protein/mL and exhibited an abrupt decreasing tendency at higher protein concentrations. Calculation of the molecular surface excess Γ from these data by the means of eq 4 (Figure 3b) highlights a qualitatively different behavior of protein adsorption at the two molecular packings assayed. At 15 mN/m, Γ15 increased up to approximately 25 µg/mL with a Γ15,max ) 0.0123 molecules/Å2 and decreased at higher concentrations. At 35 mN/m, Γ35 increased slightly, remaining near 0.001 molecules/Å2 up to approximately 40 µg/mL, and at higher concentrations it suddenly increased. The protein surface density determined in LB35 films obtained from similar monolayers was included in Figure 3b to facilitate comparison between both models, Langmuir and LB films. 3.2. Preparation and Evaluation of Langmuir-Blodgett Films. The transference process of the monolayer toward the alkylated glass started once the surface pressure stabilized after protein injection in the subphase. Figure 4 shows a real-time recording of the transference at constant pressure. The cumulative
Figure 5. Sequential film transference to an alkylated glass from a single monolayer. (a) Maximal cumulative film transference from the same monolayer to successive glasses is shown: first layer (O) and second layer (b). β-Gal incorporated to the free air-water interface (0 mN/m) (a) or penetrated into the lipid monolayer initially packed at 15 (b) or 35 mN/m (c).
transference reached values close to 1 (100%) not only for the first (Figure 4a) but also for the second layer (Figure 4b), although, in the latter, the cumulate transference showed values initially lower with respect to the former. The attempts to transfer a third layer were unsuccessful because of a generalized destabilization of the film (data not shown). The efficiency of the transference process was irregular and tended to decrease in the successive samples prepared from a single monolayer of pure protein (πi ) 0 mN/m) (Figure 5a), but it was more regular with mixed lipid-protein monolayers prepared at πi ) 15 (Figure 5b) and 35 mM/m (Figure 5c). The mean percent transference and its corresponding standard error were taken as a measure of the transference quality (Table 1). According to this information, the percent of the alkylated glass area covered with film as well as the reproducibility of the LB film obtained from a single monolayer tended to increase as a function of the molecular packing of the starting Langmuir-type
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Table 1. Langmuir Film Transference to a Solid Hydrophobic Glass at a Constant Initial Surface Pressurea % transference mean ( s.e.m. (% CV) πi (mN/m) 0 15 35
1st layer
2nd layer
74.8 ( 10.8 (14) 60.3 ( 2.9 (5) 79.9 ( 1.7 (2)
73.9 ( 12.5 (17) 50.9 ( 8.5 (17) 77.9 ( 2.6 (3)
a πi: initial surface pressure of the dpPC monolayer at the air-water interface. Values shown are the average of the percent film transference to several glasses from a single monolayer and expressed as mean ( s.e.m. (% CV). s.e.m.: standard error of the mean. %CV: percent coefficient of variation.
Figure 6. Effect of initial surface pressure (a) and protein concentration in the subphase (b) on the amount of protein transferred to form the Langmuir-Blodgett films. Protein surface concentration was determined by the Lowry method applied to the material extracted from the LB film. (a) Constant initial surface pressure was πi ) 35 mN/m. Symbols represent the mean ( s.e.m. of independent duplicates. (b) β-Gal concentration in the subphase was 77.6 µg/mL.
lipid film. This was illustrated by the higher mean transference and lower percent variation coefficient (%CV) values recorded at higher π (Table 1). The amount of β-Gal transferred increased as a function of the protein concentration in the subphase (Figure 6a). The amount of β-Gal transferred also increased as a function of Langmuir film’s πi (Figure 6b). This behavior could not be extended to other proteins. As an example: the transference of BSA was less dependent on the initial surface pressure (not shown). The AFM indicated that hydrophobic glasses could actually be film coated as shown by the significantly different images obtained with the clean glass used as a control (Figure 7a) compared with the LB15 and LB35 samples (Figures 7b and 7c). The LB films had a uniform and flat appearance. In LB15, the lipid phase appeared as round dots, clearer than the background probably corresponding to submicrometer condensed domains17 (Figure 7b). In LB35 lipid domains were not resolved, so the background was smoother than that of the control glass (lower roughness value) (Figure 7f). Consequently, the root-mean-square roughness of each LB varied in the following order LB35 < Control < LB15 (Figures 7d-f). Protein molecules were visible as bright areas in the AFM images. In accordance with the
chemical quantitation of the amount of transferred protein (Figure 6a) the protein density observed in the LB35 (Figure 7c) was higher than in LB15 (Figures 7b) (19 × 10-9 and 4 × 10-9 molecules/Å2, respectively) (Table 2). Some of the bright dots observed in Figure 7c exhibited a size close to that of K. lactis β-Gal as that (5.2 nm radius) estimated from its molecular weight (220.7 kD).32 Others, significantly bigger, would be protein aggregates. The amount of protein transferred at 15 mN/m (coming from a Langmuir film in liquid expanded phase, LE) to form the LB15 film was slightly less than at 35 mN/m (becoming from a Langmuir film in liquid condensed phase, LC) to form the LB35 film. The film topography in all the conditions tested as well as the bright dots (protein molecules?) distribution was noneuclidean. In Figure 8a and 8c we analyzed the distribution of bright dots above a height threshold of 3 and 15 nm, respectively, remaining after eliminating the rough background of height fluctuations. The box counting method29 was applied, and the slopes of the log-log plots shown in Figures 8d-f revealed that the control exhibited a homogeneous distribution of heights fluctuation that filled the whole plane and accordingly was characterized by D ) 2 (Figure 8d). On the contrary, the dimension of protein distribution in LB15 surfaces was Df,15 ) 0.48 (Figure 8e), and LB35 exhibited a Df,35 ) 0.78 (Figure 8f) (a typical fractal distribution). 3.3. Kinetics of ONPG Hydrolysis Catalyzed by K. lactis β-Gal Incorporated in a LB Film. The rate of the reaction catalyzed by the β-Gal in LB films prepared for monolayer packed at an initial surface pressure of 35 mN/m and 78 µg protein/mL in the subphase increased as a function of the incubation time, maintaining a straight-line behavior up to 3 h of incubation (not shown). When the enzyme was incorporated at an initial surface pressure of 15 mN/m the kinetics of ONPG hydrolysis followed a Michaelian behavior however, at 35 mN/m the kinetics suffered a qualitative change toward a sigmoidal behavior (Figure 9a). In the case of LB15 a nonlinear regression analysis allowed fitting the Michaelis-Menten equation to the experimental data and Vmax and KM values were calculated. With LB35 a cooperative mechanism was assumed and a Hill equation was fitted to the experimental data and Vmax, K0.5 and the Hill coefficient (n) value were determined. Results are summarize in Table 2. As an alternative hypothesis, we assumed the possibility that the sigmoidal behavior could be explained by the coupling of the reaction kinetics to the topology of the environment where it was taking place. Hence, the fractal Savageau’s model was applied (Figure 9b). The reaction order for the enzyme was a noninteger number (ge ) 0.62) (Table 2) of the same magnitude as well as the fractal dimension of protein distribution in the film (Figure 8, Table 3). In turn, the reaction order for the substrate gs ) 9.06 was coincident with the value of the Hill coefficient.
4. Discussion In the present work, we described for the first time the preparation of mixed lipid-protein LB films containing β-Gal through the transference, in controlled molecular packing conditions, of a mixed lipid-protein monomolecular layer from the air-water interface toward a solid hydrophobic glass. The protein retained its enzymatic activity, but the kinetics depended on the supramolecular organization of the environment where the protein was inserted. (32) Uversky, V. N. Biochemistry 1993, 32, 13288–13298. (33) Tello-Solis, S. R.; Jimenez-Guzman, J.; Sarabia-Leos, C.; Gomez-Ruiz, L.; Cruz-Guerrero, A. E.; Rodriguez-Serrano, G. M.; Garcia-Garibay, M. J. Agric. Food Chem. 2005, 53, 10200–10204.
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Figure 7. Atomic force microscopy images of dpPC-β-Gal mixed Langmuir-Blodgget films: (a) Silanized glass; (b) LB15; (c) LB35.
The β-Gal from K. lactis is a heterodimer.33 In solution, the enzyme exhibits a Michaelian behavior characterized by hyperbolic V vs S curves, which indicates the absence of allosteric interactions between active sites located in each protomer. 4.1. Interaction of β-Gal-Monomolecular Layer at the Air-Water Interface. We demonstrated the effective enzyme incorporation in the lipid monolayer. This was supported by the temporal evolution of the lateral surface pressure of free or lipid occupied air-water interfaces after enzyme injection in the subphase that was dependent on both the initial surface pressure and the protein subphase concentration (Figure 1). Similarly to what happened with many other proteins,2,6-8 β-Gal interacted with monolayers inducing a deformation (∆π > 0) that was inversely proportional to the initial molecular packing (πi). It should be noted that ∆π was mainly dependent on the initial π since πmax acquired only one of two possible values, 28 mN/m at πi < 25 and 41 mN/m at πi g 35 mN/m. This suggested that β-Gal accessed the interface and penetrated in it to an extent related with the lipid compressibility and the water/monolayer partition coefficient of the protein. A twodimensional phase transition of dpPC occurs at 10 mN/m. Above this π value highly compressible liquid expanded (LE) and slightly compressible liquid condensed (LC) domains coexists in the monolayer, which can be observed through epifluorescence microscopy.34,35 It is possible that only those protein molecules partitioned within the LE domains could suffer a significant (34) Kruger, P.; Losche, M. Phys. ReV. E 2000, 62, 7031–43. (35) Nag, K.; Keough, K. M. Biophys. J. 1993, 65, 1019–26.
unfolding process that lead to monolayer deformation and π increase. Moreover, the proportion of LE domains decreases with the increase in the transference of matter from LE to LC throughout the bidimensional phase transition process, and as a result, the degree of monolayer expansion due to the protein unfolding at the interface would decrease as πi grows up. The characteristic value of πmax ) 28 mN/m reached when injection started at low πi was close to typical values for collapse of protein components in protein-lipid mixtures.36 Even though, if the protein was injected at πi > 28 mN/m it could still induce a positive ∆π up to a πcutoff value for β-Gal prenetration in a lipidic monolayer of 37 mN/m (Figure 1d). Hence, this suggested that the protein molar fraction and/or the protein unfolding in β-Gallipid mixed monolayers packed at 28 mN/m < π > 37 mN/m would be lower than at π < 28 mN/m. This behavior was concentration dependent as shown by the surface excess (Figure 3b). Hence, Γ15 reached a maximum at 25 µg/mL and decreased at higher concentrations, suggesting a saturation, instabilization, and collapse of the lipid-protein mixture at the composition reached at the interface in these conditions. In turn, Γ35 increased slightly at least up to [β-Gal] ≈ 40 µg/mL. This was consistent with the proposed phase separation/protein unfolding characteristics of the lipid-protein mixture at π > 28 mN/m. The subsequent sudden increase in Γ35 at higher [β-Gal] suggested the possibility of a multilayer-type protein binding to the interface. However, this multilayered structure would have not remained (36) Oliveira, R. G.; Calderon, R. O.; Maggio, B. Biochim. Biophys. Acta 1998, 1370, 127–37.
ActiVity of KluyVeromyces lactis β-Galactosidase
Langmuir, Vol. 24, No. 19, 2008 10957 Table 3. Kinetic Parameters of ONP Hydrolysis Catalyzed by K. lactis β-Gal in solution or Incorporated in LB Filmsa sample water LB15 LB35 LB35
kinetic model
K (mM)
Vm (µmol/min/mg)
gs
ge
Michaelis-Menten Michaelis-Menten Hill fractal
5.15 ( 2.2 9.25 ( 6.0 9.60 ( 0.4b 9.84 ( nd
39.63 ( 5.49 0.0096 ( 0.0027b 0.0021 ( 0.0001b c 0.0021 ( nd
1 1 9 9.06
1 1 1 0.62
a β-Gal was in solution (water), incorporated to Langmuir films packed at initial surface pressures of 15 or 35 mN/m and transferred at constant π to a solid hydrophobic glass to form the corresponding Langmuir-Blodgett film (LB15 and LB35, respectively). With LB35 the reaction exhibited sigmoid kinetics and was evaluated with two kinetic models. K should be interpreted as KM or in the case of LB35 as K0.5 or Kf depending on the model applied (Hill or fractal, respectively). b Significantly different from the free enzyme (p < 0.05). c Significantly different with respect to the LB15 (p < 0.05).
Figure 8. Kinetics of ONPG hydrolysis catalyzed by K. lactis β-Gal organized in mixed lipid-enzyme LB films. (a) Enzyme incorporated into LB films prepared from dpPC monolayers packed at initial surface pressures of 15 (b, LB15) or 35 mN/m (O, LB35). Symbols represent the mean ( s.e.m. of independent duplicates. Lines represent the nonlinear regression analysis by the least-squares method applied to fit the Michaelis-Menten equation (LB15) or a 3-parameter Hill model (LB35) to the experimental data. (b) ONPG hydrolysis kinetics using LB35 as the enzyme source was represented in a log-log plot and analyzed under Savageau’s fractal kinetics model. Fractal (Kf) and effective (KMeff) constants as well as gs estimation are indicated. Table 2. Protein Surface Density in Langmuir Films Packed at Initial Surface Pressures of 15 and 35 mN/m and in Langmuir-Blodgett Films Derived from Thema23 (πi) (mN/m) sample 15 15 15 35 35 35 35b
L15 LB15 LB15 L35 LB35 LB35 MLV
data source dγ vs [Protein]subphase Lowry AFM dγ vs [Protein]subphase Lowry AFM
protein surface density (molecules/Å2) 6 × 10-3 2.02 × 10-4 4 × 10-9c,d 0.23 3 × 10-4 19 × 10-9c,d 1.05 × 10-5e
a L, Langmuir film consisting of insoluble dpPC monolayer at the air-water interface. LB, Langmuir-Blodgett film. MLV, multilamellar vesicles. Subindexes indicate the initial surface pressure (πi) in mN/m. The protein subphase concentration was 77.6 µg/mL. b Approximate equilibrium surface pressure of bilayers. c Calculated considering a 1 mg/mL lipid concentration, 1 µm diameter MLVs that exposed 25% of the total lipid, a dpPC molecular area of 70 Å2 at the equilibrium surface pressure of a bilayers and a membrane-water partition coefficient for β-Gal Pm/w ) 1122, according to data taken from ref 13. d They might be aggregates; hence, they should be expressed as spots/Å2. e From the Stokes radio of K. lactis β-Gal in the native and the unfolded states (52 and 147 Å, respectively)32 its area/molecule is 8500 and 6.7 × 104 Å2/molecules, respectively. On the other hand, smaller (r ) 500 Å) and bigger (r ) 2000 Å) spots exhibited average surface areas of 0.780 × 106 and 1.25 × 107 Å2/spot, respectively; hence, the mean molecular density per spot in LB35 is ca. 90-1470 or 12-195 molecules/spot for native and unfolded, respectively.
after the Langmuir film transference to the solid support as shown by the straight line behavior exhibited by the increase in the protein transferred at 35 mN/m (LB35) as a function of πi (Figure 6a). This suggested the need for a certain molecular density (and possibly settlement of a molecular network of lipids) to allow protein stabilization at the lipid-water interface. LE domains
Figure 9. Kinetics of ONPG hydrolysis catalyzed by K. lactis β-Gal incorporated in Langmuir-Blodgett films. (a) Specific activity vs substrate concentration analyzed according to Michaelis-Menten’s ((b) LB15) or Hill’s ((O) LB35) models. (b) Kinetics with β-Gal in LB35 films analyzed according to Savageau’s fractal model.
are present in the dpPC monolayers at all pressures above the bidimensional phase transition and do not coalesce until the collapse pressure is reached. In addition, the length of the LE-LC interdomain contour lines increases as LC domains grow.34,35,37 This is particularly noticeable in the case of dpPC because, due to its molecular chirality, lobulated domains with a fractal dimension emerge at the supramolecular organizational level. Accordingly, based on the information presented and the results obtained in the present work (Figures 3b and 6), it is possible to suggest that for the protein binding to the interface, the existence of LC domains is needed; however, the protein would bind mainly at the LE-LC boundary line. The binding process would allow relaxation of the line tension,38 so that the binding of protein molecules at the LE-LC boundary would be energetically favorable. From the LE-LC boundary the protein would start its expansion toward the LE domain which would be expressed as an increase in the lateral pressure. The amount of protein adsorption on the LE film was less than on the LC film (Figure 6b). This may be due to the fact that β-Gal (37) Theumer, M. G.; Clop, E. M.; Rubinstein, H. R.; Perillo, M. A. Colloids Surf. B: Biointerfaces 2008, 64, 22–33. (38) Netz, R. R.; Andelman, D.; Orland, H. J. Phys. II Fr. 1996, 6, 1023–1047.
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is adsorbed onto the dpPC membrane by hydrophobic interactions and that hydrophobic interactions between β-Gal and dpPC are greater in the liquid-condensed film, similarly to the behavior of other proteins.39 It is important to note that the physical meaning of Kb involves contributions from the protein unfolding and binding affinity. This explains the fact that although the affinity of β-Gal for the lipid-water interface was higher at lower π (Kb,15 > Kb,35 (Figure 2), the amount of protein transferred followed the opposite trend (Figure 6b; see below for discussion). 4.2. Preparation of LB Films. To our knowledge, there is just one study cited in the literature investigating the kinetic behavior of a β-galactosidase adsorbed on a solid support. In that case an enzyme from Aspergillus oryzae was transferred to a methylated silica support in the absence of phospholipids, and the process of adsorption was made from a solution circulating at a constant flow and with a laminar steady-state regime. Thus, a protein molecular assembling reached organizational characteristics remaining unknown for the experimenter.40 In our work, we used a modified silica support through the covalent binding of hydrocarbon chains of 18 carbon atoms length. That surface was covered with the proteolipidic preassembled film which had been self-organized at the air-water interface and transferred to the alkylated glass at a known and constant molecular packing. Each LB film was composed of two stable monomolecular layers (Figure 5, Table 2). Increasing the number of layers unstabilized the system as a whole. This behavior would be related with repulsive electrostatic forces established between the polar head groups of the third and fourth molecular layers in addition to the repulsive effect of hydration forces,41 which had already been described as a technical limitation of Langmuir-Blodgett film formation.42 Something similar happened with the number of samples (not more than 20) that could be prepared from each monomolecular layer at the air-water interface. The latter could be due to the complexity of the system and its high dependence on initial conditions. Each time the alkylated glass crossed the interface, the monolayer suffered a perturbation that at certain point could not be compensated by the automatic movement of the barriers. Although finally this would lead to a catastrophic and irreversible phenomenon of monolayer destabilization and collapse, a significant amount of samples could be prepared from the same monolayer. The reproducibility of the molecular transference to successive alkylated glasses from a single monolayer, in terms of the amount of transferred monolayer, was higher in the case of the more packed monolayers and impaired for the transference of a second layer, particularly at low pressures (Figure 5, Table 1). The amount of β-Gal transferred to the alkylated glass increased as a function of the protein concentration in the subphase (Figure 6a). The later result (coming from a chemical measurement of the protein in the LB film) was partially in accordance with Gibbs adsorption equation, from which we calculated the surface density of β-Gal in the original Langmuir film (Figure 3b). Although, up to 40 µg/mL, in both the Langmuir and the LB35 film, we found a direct dependence between Γ and the protein concentration in the subphase, two differences between Langmuir and LB films may be highlighted. In LB35, on one hand, the slope of the curve was markedly higher than the initial slope of the Γ35 vs β-Gal concentration curve in Langmuir films, and, on the (39) Yokouchi, Y.; Tsunoda, T.; Imura, T.; Yamauchi, H.; Yokoyama, S.; Sakai, H.; Abe, M. Colloids Surf. B: Biointerfaces 2001, 20, 95–103. (40) Tsung, E. F.; Tilton, R. D. J. Colloid Interface Sci. 1999, 213, 208–217. (41) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: New York, 1989. (42) Charitat, T.; Bellet-Amalric, E.; Fragneto, G.; Graner, F. Eur. Phys. J. B 1999, 8, 583–593.
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other hand, the sudden increase at high protein concentrations in the subphase was not observed. The former may be due to adsorption of soluble protein molecules from the subphase during glass immersion, an assumption that is in accordance with the nonzero ordinate of the plot in Figure 6b. Note that this was a stable protein binding considering the negligible enzymatic activity measured in the supernatants obtained after incubation of such LB films in buffer (not shown). On the contrary, the above-mentioned possible multilayer-type protein binding to Langmuir films that lead to a high Γ35 did not remain stable after being transferred; hence, it did not appear as a steep increase in protein density as quantified by the Lowry method in LB35. Table 2 summarizes the protein surface density in the floating monolayer in LBs films and in multilamellar vesicles (MLVs) as determined through different methods such as dγ vs [β-Gal], protein chemical measurement and atomic force microscopy images analysis. 4.3. Kinetics of β-Gal Catalyzed Hydrolysis of ONPG. 4.3.1. Enzyme Kinetics in Solution. In solution, the kinetics of hydrolysis of a soluble substrate (ONPG) catalyzed by β-Gal from K. lactis was Michaelian. The values of the kinetic parameters determined in aqueous medium and without addition of activator ions were KM ) 5.15 ( 2.2 mM and Vmax ) 39.63 ( 5.59 µmol/min/mg protein (intrinsic activity Vmax/KM ) 7.69 (µmol/min/mg protein) µM-1)) reflected an affinity, a maximum reaction rate and an intrinsic activity lower than those reported previously in the presence of 0.1 M KCl and 2 mM MgCl2 (KM ) 2 mM; Vmax ) 91 µmol/min/mg protein; Vmax/KM ) 45.5 (µmol/min/mg protein) µM-1).43 4.3.2. Enzyme ActiVity at Interfaces. The β-Gal from A. oryzae self-organized as a single monolayer on a surface of methylated silica in the absence of lipids without changing the michaeliantype kinetics and inducing a decrease in the kcat rate constant by a factor of 10 as well as in the KM by a factor of 4.5. Thus, the enzyme intrinsic activity, represented by the relationship kcat/KM fell 45 times due to adsorption if compared with the enzyme in solution.40 The enzyme surface density reached on this type of surface was approximately 0.8 mg/m2 at an enzyme bulk concentration of 16 µg/mL. When our β-Gal from K. lactis was organized in a two-layersLB film packed at an initial lateral pressure of 15 mN/m it showed a michaelian kinetics, the KM was 1.8 times smaller, kcat fell 4128 times, and the intrinsic activity kcat/KM was 0.001 (7700 times lower than that of the same enzyme in solution). The behavior of the enzyme incorporated into the monolayer originally packaged up to 35 mN/m was worse than that observed at 15 mN/m: kcat decreased 18 871 times, K0.5 increased 1.85 times, and the intrinsic activity kcat/K0.5 was 0.0002 (5 times smaller than the same enzyme in LB15). This low specific activity suggested at least three possible explanations for the main effect induced by the supramolecular organization of the protein environment: (a) a reduction in the accessibility of the substrate to the enzyme active site, (b) an enzyme unfolding with a lost of the active site conformation during the process of incorporation to the interface, explained above, and/or (c) a selective decrease of β-Gal interface binding with respect to other contaminant proteins. Moreover, an overestimation of protein concentration cannot be excluded.44 However, adsorbed enzymes should not be considered in isolation; rather their function must be interpreted in terms of the molecular and supramolecular structure of the adsorbed layer. (43) Giacomini, C.; Irazoqui, G.; Batista-Viera, F.; Brena, B. M. J. Mol. Catal. B: Enzym. 2001, 11, 597–606. (44) Knight, M. I.; Chembers, P. J. Mol. Biotechnol. 2003, 23, 19–28.
ActiVity of KluyVeromyces lactis β-Galactosidase
Currently, the most realistic step is to explain changes in the enzyme function due to adsorption rather than to describe the absolute activity. In doing so it is essential to characterize the molecular structure of the adsorbed layer in as much detail as possible. 4.4. Sigmoidal Kinetics of β-Gal in LB Films. β-Gal is not intrinsically allosteric since its kinetic behavior in solution has always been described as michaelian (e.g., Table 3). However, when we incorporated the K. lactis β-Gal within the membrane structure in the LB35 film, it exhibited a sigmoidal behavior (Figure 9a). Reactions that occur in spaces characterized by noneuclidian (fractals) geometries may reveal an increase in the kinetic order if compared with the same reaction in solution. In these circumstances, the reaction order would not match the molecularity of elementary reaction steps but would reflect the fractal dimension of the surface where it occurs, leading to an overall sigmoidal kintetics. The AFM images revealed the topographical characteristics of the thin film covering the hydrophobic glass as well as the fractal distribution of protein molecules (Figures 7 and 8), which may support a fractal hypothesis to explain the sigmoidal kinetics. However, other theoretical models may account for the sigmoidal behavior of β-Gal in LB35 such as (a) direct and (b) indirect allosteric modulation and (c) low water activity based phenomenons. (a) The direct allosteric modulation model involves the existence of several interacting binding sites located in the same protein and the condition that the ligand binding to one site affects the intrinsic binding affinity of other sites (cooperativity). Since this β-Gal is an oligomeric protein, arguments appear to consider this hypothesis. The local concentration of protein molecules at the lipid-water interface would contribute to formation of aggregates or could modify interactions between the active sites in the different monomers of β-Gal, which might allow an allosteric behavior. (b) In the case of indirect allosteric modulation, there is a cooperativity without apparent ligand binding to a protein. The solute induces a change in the membrane pressure profile, thereby affecting the protein conformational equilibrium.45 Such a phenomenon might be perfectly but misleadingly modeled by both the Hill equation and the Monod-Wyman-Changeaux (MWC) model at the limit of infinite number of sites and very low affinity.28 Accordingly, in order to distinguish between direct and indirect models it is necessary but not sufficient to demonstrate the existence of several binding sites in a protein. Both phenomena could coexist in the case of membrane-bound proteins. The LB accumulation of reaction product molecules (the membranewater partition coefficient of ONP is Pm/w ) 5013) could have altered the gradient of membrane lateral pressure and thus facilitated the shift toward protein conformations of greater affinity, triggering an indirect allosteric mechanism. (c) The binding of water molecules to the extra protein surface exposed during the allosteric transition from the low affinity to the high affinity conformational state was interpreted as the limiting stage of the cooperative reaction.46 Moreover, in the case of surface active enzymes, the dehydration accompanying hydrophobic interactions was associated with the allosteric coupling between the membrane-binding (regulatory) site and the catalytic center and with the enzyme interfacial activation.47 (45) Cantor, R. S. Biophys. J. 1999, 77, 2643–2647. (46) Salvay, A. G.; Grigera, J. R.; Colombo, M. F. Biophys. J. 2003, 84, 564–70. (47) Tatulian, S. A. Biophys. J. 2003, 84, 1773–1783.
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Therefore, the spatial position of β-Gal within the hydrophobic core of LB films would be stabilized by desolvation of the macromolecular surface (hydrophobic interactions), even when electrostatic interactions or specific binding of lipids were substantial,48 and this condition of the protein hydration state could have contributed to the cooperative behavior. Although at this point this hypothesis is rather speculative since no experiments on the hydration/dehydration state are reported in this study, it is important to state the relevance for them to be taken into account in future investigations. Probably, all these mechanisms operating in conjunction may explain the sigmoidal kinetics of β-Gal incorporated and confined in LB35 films.
5. Conclusions Here we demonstrated that β-Gal was effectively incorporated in the lipid monolayer and could be successfully transferred to an alkylated glass under controlled and constant molecular packing and planar topology conditions. The binding affinity of β-Gal for the lipid monolayer depended on the molecular packing that affected mainly the association process. The amount of protein incorporated in the monolayer and remaining in LB films was also dependent on π and might be correlated with the surface ratio between LE and LC film domains. If compared with the behavior in solution, a marked decrease in enzyme activity for β-Gal in LB films may be due to a decrease in the accessibility of the soluble substrate to the enzyme active site and a partial protein unfolding and inactivation at the interface. A qualitative change, from hyperbolic to sigmoidal behavior, was found in the reaction kinetics upon π increasing from 15 to 35 mN/m. The fitness of a fractal kinetic model was tested, and a plausible hypothesis was found to explain our findings. Fractal reaction orders would reflect the fractal organization of the environment, demonstrated by AFM images, more than the molecularity of the reaction. Particular dynamics of the protein-lipid structural coupling in each molecular packing condition would have led to the different kinetic responses.
6. Abbreviations LB, Langmuir-Blodgett films; ONPG, o-nitrophenyl β-Dgalactopyranoside; ONP, o-nitrophenol; ONPx, o-nitrophenoxide; BSA, bovine serum albumin; SDS, sodium dodecylsulfate; MLV, multilamellar vesicle; sPC, soybean phosphatidylcholine; D, dielectric constant; KM, Michaelis-Menten constant; Vmax, maximal velocity; Vo, initial velocity; s.e.m., standard error of the mean; ANOVA, analysis of variance; %CV, percent variation coefficient.
7. Appendix Fractal Kinetic Analysis According to Savageau’s Theory.10 Dimensional restrictions would not affect monomolecular reactions with unitary kinetic orders. However, they would affect molecular collisions, which in turn would affect bimolecular reactions with a high probability. This situation would be expressed as kinetic orders that do not represent the molecularity of the reaction but the dimension of the space where it is occurring. Fractal dimensions are represented by noninteger numbers. Fractallity in enzymatic reactions can be suspected when (a) the kinetics is nonmichaelian, (b) the kinetics exhibits a sigmoidicity that resembles a cooperative behavior between binding sites even when there is just one binding site, (c) the kinetic order with respect to total enzyme concentration is higher than 1, and (d) (48) Lomize, A. L.; Pogozheva, I. D.; Lomize, M. A.; Mosberg, H. I. BMC Struct. Biol. 2007, 7, 44.
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KM seems to be a function of ET (decreases with increasing ET). In the present work, we tested a fractal model based on the theoretical frame developed by Savageau10 to describe the kinetics of samples exhibiting a Hill number above 1. Given a typical enzymatic reaction k1
k2
E + S {\} ES 98 E + P k-1
where E, S, ES, and P refer to the enzyme, substrate, enzyme-substrate complex, and product concentrations, power laws provide a group of equations to describe the kinetic mechanism of Michaelis-Menten (eqs 7 and 8)
d(ES) ) R1SgsEge - (β1 + R2)(ES) dt dP ) Vp ) R2(ES) dt
(7a)
(
)( )(
R2 + β1 V Vm V R1 R2 R2 R2
)
(8a)
-ge
(9)
where Vm is the maximal velocity. If Kf is defined as a fractal Michaelis constant given by
(
R2 + β1 Kf ) R1
)( ) 1 gs
Vm R2
1-ge gs
gs
)
V V 1Vm Vm
(10)
then the law for fractal kinetics can be expressed as follows
)
-ge
(11)
Note that eq 11 reduces to the traditional Michaelis-Menten equation when the exponents gs ) ge ) 1, which is the condition for homogeneous systems. Different from what happens with classical enzyme kinetics where KM is independent of ET, Kf is a function of ET. Kinetic data represented in a log-log plot allow determining three of the four parameters characterizing the fractal kinetics: two asymptotes provide estimations of Vm and Kf, and the slope at low S gives an estimation of gs. The fourth parameter ge can be either determined from the slope of a secondary plot of Kf vs ET or, as done in the present work, calculated by solving eq 12
Kmeff ) Kf2(ge-1)⁄gs
where ge and gs are the kinetic orders with respect to the free enzyme and free substrate, respectively, and rate constants typically used in classical kinetics k(i) were changed by R1 and R2 for the direct reactions and β1 for the reverse reaction. Under quasi-stationary state conditions, eq 7 becomes 0 and after applying the mass balance for total enzyme concentration (ET ) E + ES), the system of eqs 7 and 8 can be solved for S and expressed as a function of the reaction rate V
Sgs )
( ) ( )( S Kf
(12)
A characteristic of fractal kinetics is the sigmoidal shape of the V vs S plot, which is evidenced by the Hill plot log[V/(Vm - V)] vs log S. In this plot the hyperbolic kinetics (michaelian) would be associated with a slope ) 1 while in sigmoidal kinetics with slope > 1. The Hill plot would also allow one to distinguish between the allosteric and the fractal kinetics because the log [V/(Vm - V)] vs log [S] produces a straight line in the case of allosteric kinetics and two straight lines with different slopes changing when the concentration of substrate equals log (Kf) (where Kf is the fractal Michaelis constant).10 At S < Kf the cooperative effect will be evident with a Hill number given by gs/ge. Acknowledgment. This work was supported by grants from CONICET, SeCyT-UNC, Agencia Co´rdoba Ciencia, and ANPCyT. E.M.C. and P.D.C. are graduate students from the Doctorado en Ciencias Biolo´gicas, FCEFyN, UNC, and fellowships holders from Conicet and Foncyt, respectively. J.M.S. and M.A.P. are career members of CONICET (Argentina). LA801679M
