Hydrolysis of fluid supported membrane islands by phospholipase A2: Time-lapse imaging and kinetic analysis

Journal of Colloid and Interface Science 301 (2006) 107–115 www.elsevier.com/locate/jcis

Hydrolysis of fluid supported membrane islands by phospholipase A2 : Time-lapse imaging and kinetic analysis Adam Cohen Simonsen ∗ , Uffe Bernchou Jensen, Per Lyngs Hansen MEMPHYS, Center for Biomembrane Physics, Physics Department, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark Received 3 March 2006; accepted 20 April 2006 Available online 12 June 2006

Abstract The activity of phospholipase A2 (PLA2 ) which catalyzes the hydrolysis of phospholipids into free fatty acids and lysolipids, depends on the structure and thermodynamic state of the membrane. To further understand how the substrate conformation correlates with enzyme activity, model systems that are based on time-resolved membrane microscopy are needed. We demonstrate a methodology for preparing and investigating the dynamics of fluid supported phospholipid membranes hydrolyzed by snake venom PLA2 . The method uses quantitative analysis of time-lapse fluorescence images recording the evolution of fluid bilayer islands during hydrolysis. In order to minimize interactions with the support surface, we use double bilayer islands situated on top of a complete primary supported membrane prepared by hydration of spincoated lipid films. Our minimal kinetic analysis describes adsorption of enzyme to the membrane in terms of the Langmuir isotherm as well as enzyme kinetics. We use two related models assuming hydrolysis to occur either at the perimeter or at the surface of the membrane island. We find that the adsorption constant is similar for the two cases, while the estimated turnover rate is markedly different. The PLA2 concentration series is measured in the absence and presence of β-cyclodextrin which forms water soluble complexes with the reaction products. The results demonstrate the versatility of double bilayer islands as a membrane model system and introduces a new method for quantifying the kinetics of lipase activity on membranes by directly monitoring the evolution in substrate morphology. © 2006 Elsevier Inc. All rights reserved.

1. Introduction Secretory phospholipase A2 (PLA2 ) is a class of enzymes that catalyze the hydrolysis at the sn-2 position of glycerophospholipids, producing fatty acid (FA) and lysophospholipids (lysoPC). The hydrolysis products have significant influence on various physiological functions such as inflammation [1,2]. More specifically, fatty acids can have important roles as messengers and as precursors for the eicosanoid hormones. The other product, lysophospholipids have important roles in the physical perturbation and remodeling of membrane structure. They can also serve as precursors of the bioactive phospholipid, platelet activating factor (PAF) and conversely PAF can be converted to lysoPC’s by PAF-acetylhydrolase which is a specific subfamily of PLA2 [3]. * Corresponding author. Fax: +45 6550 4048.

E-mail address: [email protected] (A.C. Simonsen). 0021-9797/$ – see front matter © 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2006.04.060

Although extensively studied over more than the last 30 years, the modification and degradation of biomembranes by PLA2 is still an incompletely understood process. In particular more information is needed on how the membrane morphology is modulated during the action of PLA2 and how this morphology during hydrolysis depends on the membrane phase state (fluid, solid, liquid-ordered). Much useful information on PLA2 activity has been obtained in the past with techniques such as pH-stat titration [4], (first-order) monolayer trough [5], zero-order trough measurements [6,7] and fluorescence spectroscopy [8]. However, in order to establish a link between membrane morphology (on a nm–µm scale) and PLA2 activity it is necessary to obtain time-resolved imaging of the hydrolysis process and to apply a quantitative analysis to these imaging data. Although it has been observed that PLA2 binds uniformly to the surface of a fluid phospholipid bilayer [9], the activity of PLA2 is strongly influenced by the lipid bilayer phase behavior [10]. At the main phase transition temperature of the lipid

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bilayer, PLA2 displays a maximum activity [11,12] and this is believed to be associated with the formation of small-scale lipid lateral domains. It also suggests more generally that PLA2 may be particularly active at domain interfaces, membrane boundaries or other structural defects [13]. This hypothesis has been verified by atomic force microscopy (AFM) imaging of the hydrolysis of supported solid state lipid bilayers by PLA2 [14,15] which shows that the bilayer is hydrolyzed from the perimeter of holes. Based on these investigations Nielsen et al. [14] proposed that the rate of product formation is proportional to the length of the perimeter. Our recent work [16] indicates that this hypothesis is also valid for fluid supported membranes hydrolyzed by PLA2 . In this work it was shown that during hydrolysis, a fluid supported POPC membrane exhibits a rich and not previously described dynamic behavior which is quite different from the behavior of solid membranes. This is caused by the dynamic interplay between line tension which minimizes the membrane perimeter and hydrolysis which degrades the membrane. Thus, it is possible to observe both the formation and decay of membrane holes as well as Rayleigh instabilities in membrane rims. For supported membranes, it is known that the support may have a substantial effect on the bilayer and consequently could affect the enzyme dynamics. The presence of the support changes the lipid diffusion rates and alters the general behavior of the membrane compared to free standing membranes. The interactions have strongest effects on the lower leaflet of the bilayer, and consequently the two leaflets may have separate phase transitions [17] and different lateral lipid mobilities [18]. Investigations have shown that double bilayer structures provide better model systems for biophysical studies of membranes [19]. The intermembrane interactions are considerably reduced compared to the interaction between the membrane and the support. This is for example demonstrated in the ability of the top bilayer to form the ripple phase [20], which is seldom found in the lower bilayer. Recently, we have developed a procedure to prepare supported bilayers based on hydration of spin-coated lipid films [21]. We have found that by carefully controlling the degree of hydration of the dry lipid film, this procedure allows fluid supported double lipid bilayers to be prepared at physiological salt concentrations. We have used time-lapse fluorescence imaging to visualize the PLA2 catalyzed hydrolysis of the lipids of the double bilayer islands, and we present a kinetic model based on Michaelis–Menten kinetics to describe these results. Analysis of the fluorescence data using this kinetic model allows us to estimate the turnover number per enzyme as well as the adsorption equilibrium constant describing the enzyme– membrane interaction. It has recently been shown [22,23] that PLA2 catalyzed hydrolysis can be measured in the presence of beta-cyclodextrin (βCD) which forms water soluble complexes with the reaction products without being tensioactive or forming complexes with phospholipids. In order to ensure that the decrease in area of the membrane islands is quantitatively reflecting the reaction progress we have measured the PLA2 concentration series also in the presence of βCD. A comparison with the measurements made without βCD sug-

gests that the adsorption of enzyme to the membrane is decreased by βCD while the measured reaction rate is largely unaffected. 2. Materials and methods 2.1. Materials 1-Palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC, lyophilized powder) was purchased from Avanti Polar Lipids and 1,1 -dioctadecyl-3,3,3 ,3 -tetramethylindocarbocyanin perchlorate (DiI-C18 ) from Molecular Probes. β-Cyclodextrin (βCD, MW = 1135, >99%), 4-(2-hydroxyethyl)piperazine-1ethanesulfonic acid (HEPES, >99.5%), 4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid sodium salt (HEPES sodium salt, >99.5%), CaCl2 (>99.5%) were all from Sigma while NaCl (>99.5%) and ethylenediaminetetraacetic acid (EDTA, >99%) were from Merck. Hexane and methanol (Sigma) were HPLC grade. Milli-Q water (18.3 M cm) was used throughout for all work in aqueous phases. Snake venom PLA2 (42 µM aqueous stock solution) from Agkistrodon piscivorus piscivorus was a gift from R.L. Biltonen, University of Virginia. HEPES buffer (10 mM HEPES, 150 mM NaCl, 30 µM CaCl2 and 10 µM EDTA) was prepared at pH 8.0 by mixing appropriate amounts of HEPES and HEPES sodium salt. Muscovite mica (75 × 25 × 0.2 mm sheets) was from Plano GmbH, Germany. 2.2. Preparation of double membrane islands The preparation of fluid membrane islands is an extension of the methodology we recently developed [21] for preparing single supported membranes by hydration of spincoated lipid films. The present version of the method consists of two steps: (1) Fabrication of a dry spincoated lipid film followed by (2) controlled hydration/annealing of the film. To prepare a dry spincoated POPC film on mica we used a stock solution of 10 mM POPC containing 0.7% DiI-C18 in hexane/methanol (97:3 volume ratio). A droplet (30 µl) of this lipid stock solution was then applied to freshly cleaved mica with a size 10 × 10 mm and immediately thereafter spun on a Chemat Technology, KW-4A spin-coater at 3000 rpm for 40 s. This created a dry multilayered lipid film with the orientation of the lipids as shown in Fig. 1A. The sample was then placed under vacuum in a desiccator for 10–15 h to ensure complete evaporation of solvents. The dry spin coated film was subsequently hydrated by immersing the sample in HEPES buffer followed by heating in an oven to 80 ◦ C for 3 h. The sample was then placed on the fluorescence microscope (see below) and flushed vigorously with 80 ◦ C buffer. By monitoring the response of the lipid film while washing, the removal of lipid layers could be accurately controlled. Typically, only the center of the sample was flushed and this completely removed all but the lowest bilayer in this region (Fig. 1B). Some distance away from the flushed region, lipid multilayers where present, while in the transition zone one could routinely localize round double bilayer islands situated on top of the lowest

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2.4. Image analysis Image analysis of the fluorescence time series was automated with procedures written in MatlabTM using the Image Processing Toolbox. Briefly, the procedure consists of a manual first step where the user marks a specific membrane island in the first frame of the sequence. All subsequent frames are then cropped to only contain this island. By using the Matlab command “graythresh” all images are auto-converted to black/white and the time dependent island area A(t) and perimeter length L(t) are then computed from the b/w images of the island (see also Fig. 2). The rate of area decrease dA/dt is computed by numerical differentiation of A(t). A box-type smoothing of A(t) was applied before differentiation to remove noise, but without affecting the numerical value of dA/dt . Curve fitting and plotting was done in Igor Pro 5.01. 3. Results and discussion 3.1. Fluid bilayer islands during hydrolysis

Fig. 1. Sample preparation methodology. The structure (A) of a dry spincoated lipid film with oriented multilayers. The double membrane islands originate from the bilayer M2 created during spincoating. Fluorescence image (B) of the hydrated, spincoated POPC film. After hydration/annealing at 80 ◦ C the center region of the image has been flushed with 80 ◦ C buffer. In this center region (1) holes in the lower bilayer are visible while further away from the center an intact bilayer (2) and a double bilayer (3) are localized. In the transition zone between the first and the second bilayer round bilayer islands (4) on top of a complete lower bilayer are routinely found.

bilayer. Once such a region with round bilayer islands had been localized, the sample was allowed to cool to 20 ◦ C and to relax for at least 1 h prior to the addition of PLA2 . 2.3. Fluorescence microscopy Epi-fluorescence microscopy of the lipid film was performed with the sample placed with the lipid side facing up in a microscope chamber (Lab-Tek Brand Products, Naperville, IL, 2-chamber unit, 2 ml volume) on a Nikon TE2000 inverted microscope and using a 20× long working distance objective. Fluorescence excitation was done with a halogen lamb and using a G-2A filtercube (Nikon). Images were recorded with a high sensitivity CCD camera (Sensicam em, 1004 × 1002 pixels, PCO-imaging, Kelheim, Germany) and operated with Camware software (PCO). Lipid hydrolysis was initiated by completely exchanging the HEPES buffer in the microscope chamber with a HEPES buffer containing PLA2 without drying or moving the sample. Images were recorded at 10–20 s intervals, depending on the concentration of PLA2 in the chamber. A total of 550–570 images where recorded pr. experiment. All experiments were conducted at room temperature.

By the procedure displayed in Fig. 1, a region of the sample can systematically be created and localized that contains round double bilayer islands. An example of one such region is shown in Fig. 2A. The mica support in this area is completely covered with a primary lipid bilayer. A number of lipid bilayer islands with varying sizes are situated on top of this membrane. The fluidity of the bilayers allows the shape of these islands to be governed by line tension acting as a contracting force around the perimeter. For a given membrane area (fixed) line tension minimizes the perimeter resulting in circular or semi-circular islands. Deviations from a circular shape are also observed as shown in Fig. 2C. In such cases, islands are pinned to the underlying membrane at certain discrete points thereby preventing the membrane from completely relaxing to a circular shape. The system in Figs. 2A and 2B is prepared in the presence of 880 µM βCD while the island shown in Fig. 2C is absent of βCD. The qualitative features of the system (sample preparation, hydrolysis, etc.) are identical in the two types of systems and we observe both pinned and unpinned islands in both cases. The contours shown in Fig. 2B reveal the time evolution of the island boundaries in Fig. 2A upon exposure to 100 nM PLA2 at time t = 0 s. It is well known from previous studies [6,24,25] that the hydrolysis of bilayers by PLA2 exhibit a lagburst phenomenon where the hydrolysis changes from an initial low to high activity [14,25]. In our recent work, this phenomenon was also observed in fluid supported POPC bilayers [16]. In contrast to these previous findings, the hydrolysis of the double bilayer islands proceeds immediately with no detectable lag phase. This is observed by the immediate decrease (shrinking) of the double bilayer islands within a time of maximum 20 s after addition of the enzyme. During the shrinkage induced by hydrolysis, the shape of the islands continues to be governed by line tension as well as possible pinning points. The circular islands in Fig. 2B remain circular during hydrolysis. There is a slight overall movement of the islands during the course of the reaction (∼1.5 h), caused by convection in the fluid phase.

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The pinned island in Fig. 2C behaves somewhat differently during hydrolysis. In this case the membrane perimeter length is minimized under the constraint of the pinning points, some of which are marked with ∗ in Fig. 2C. During hydrolysis, the pinning can be lifted and new pinning points may become detectable which leads to relaxations of the membrane to a new optimal shape. The dynamics of the relaxation processes is de-

termined by line tension, the viscoelastic properties of the membrane as well as intermembrane forces. The membrane therefore does not immediately relax to a new equilibrium structure and it should be remembered that the membrane shape is set both by relaxations and by hydrolysis which runs concurrently. We observe a difference in the time-scales for hydrolysis of the first (lower) and the second (upper) bilayer. At PLA2 concentrations below approximately 100 nM, no apparent hydrolysis is observed in the lower bilayer on the time scale of an experiment (<2 h). Above 100 nM, hydrolysis in the burst mode is observed in the lower bilayer after a lag-time of around 1500 s and in accordance with our previous work on this system [16]. There may be several possible explanations to this difference. It is documented that mica-supported membranes have considerable interactions with the support and that these interactions can even induce a decoupling of the main phase transition between the upper and the lower membrane leaflets [17]. The interactions are most likely electrostatic in nature and it is quite possible that they can also restrict the ability of PLA2 to orient favorably at the membrane edge in order to catalyze hydrolysis. This effect is expected to be considerably smaller for the second bilayer which has less interaction with the underlying surface and more conformational freedom. In the kinetic analysis of hydrolysis of the upper bilayer islands (see below) we assume as a first approximation, that hydrolysis of the upper and lower bilayers are not strongly coupled and can be treated independently. Also for this reason, we analyze the imaging data only in time-regimes where no significant hydrolysis is observed in the lower bilayer. 3.2. Kinetic models for PLA2 catalyzed bilayer island hydrolysis We now describe a minimal kinetic model for the bilayer island hydrolysis that allows quantitative analysis of the image sequences. We refer to the outline in Fig. 3 for details. The model comes in two versions: Case (I), assuming that PLA2 activation occurs at the island perimeter and case (II) assuming the activation to occur uniformly over the island surface.

Fig. 2. Typical fluorescence image (A) of round POPC double bilayer islands before the onset of PLA2 hydrolysis. The black inserts (B) show the boundary contours of the individual islands during hydrolysis by 100 nM PLA2 in the presence of 880 µM βCD as detected by the image processing algorithm. The time interval between the displayed contours is 300 s, but the full sequence is recorded with a time resolution of 10 s. Example of a non-round island (C) and the corresponding boundary contours during hydrolysis (25 nM PLA2 , no βCD).

Fig. 3. Model for PLA2 catalyzed hydrolysis of a fluid membrane island. Shown is the perimeter activated case of the model where the enzyme E (PLA2 ) is assumed to be activated around the perimeter L(t) of the membrane island. The area-activated version of the model describes the complementary situation where the enzyme is assumed to be activated uniformly over the island area A(t).

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Case (I) is explained below and case (II) then follows by simple analogy. Fig. 3 summarizes the reaction scheme [26]. The enzymatic reaction is treated in terms of standard Michaelis–Menten kinetics. To obtain the simplest model, we treat the adsorption of enzyme to the membrane in terms of the Langmuir isotherm which simply relates the total occupancy θ of enzyme sites at the perimeter to the bulk enzyme concentration E0 : bE0 θ (E0 ) = 1 + bE0

(1)

on with b = kkoff being the ratio between the on and off rates for the enzyme at the perimeter sites. The Langmuir isotherm is valid independently of the spatial dimension of the system (1D–3D). A requirement for using the Langmuir isotherm is that E0 is effectively unchanged when enzyme binds to the membrane. We have checked that this is fulfilled by considering a version of the isotherm which explicitly takes into account the number of surface site. The time dependent length of the perimeter around the island is denoted L(t), and therefore we can write the total number of enzymes at the island perimeter (NEp ) as:

L (2) = N E ∗ + NES d with d being the width of an enzyme molecule. The last equality in (2) states that enzymes at the perimeter exist as either an enzyme/substrate complex (ES) or as a free state without substrate (E ∗ ). The interconversion between these two states is governed by the rate constants k1 and k−1 . In accordance with the standard Michaelis–Menten derivation we now write the rate of change of the enzyme/substrate complex:

NEp = θ (E0 ) ·

d[ES] = −kcat [ES] − k−1 [ES] + k1 [S][E ∗ ] dt = −kcat [ES] − k−1 [ES] + k1 [E ∗ ].

(3)

Enzyme concentrations at the island perimeter are generally defined as number of enzymes per perimeter length of the island, so that for example [ES] = NLES . The last equality in Eq. (3) follows from the assumption that the substrate concentration seen by an enzyme at the perimeter is constant and it is therefore absorbed in the new constant k1 = [S]k1 . This relation is expected to hold if the hydrolysis products are removed from the bilayer during reaction, so that the lipid density remains constant. Applying the conventional steady-state assumption (d[ES]/dt = 0) to Eq. (3) now allows us to isolate [ES]: [ES] =

k1 kcat + k−1

[E ∗ ] =

[E ∗ ]  KM

,

(4)

where the modified Michaelis–Menten constant is defined as  = (k + k )/k  . According to Eq. (2) we can now make KM cat −1 1 the substitution [E ∗ ] = [Ep] − [ES] and isolate [ES] again: [ES] =

[Ep]  + 1. KM

(5)

We now turn to the overall reaction rate for perimeter activated case which can be written as the rate of generation of

lysolipids (LPC):  kcat dNLPC  = kcat NES =  · NEp .  dt Perimeter KM + 1

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(6)

We now apply Eq. (2) which gives the final expression for the reaction rate:  kcat L(t) dNLPC  =  · θ (E0 ) ·  dt K +1 d Perimeter

M

L(t) . (7) d Here we have defined the apparent rate constant KC = kcat /  ). The connection to the image data can now be made (1 + KM when the rate of hydrolysis is written in terms of the area change of the membrane island, with a being the area per lipid in the membrane:  2 dA L(t) dNLPC  =− · (t) = KC · θ (E0 ) · (8) dt Perimeter a dt d or  KC · a · θ (E0 ) dA  = · L = αPerimeter · L, −  (9) dt Perimeter 2d = KC · θ (E0 ) ·

0) . where we have introduced the parameter αPerimeter = KC ·a·θ(E 2d This derivation is valid to the extent that the reaction progress is entirely reflected in an area decrease of the membrane island. This is only strictly true if the hydrolysis products are removed from the bilayer during reaction. This assumption is thus equivalent to the one made when defining k1 and is ensured when βCD is present. When analyzing image sequences taken at different enzyme concentrations (E0 ) we derive two main parameters: The Langmuir isotherm constant b and the rate constant KC . Knowledge of kcat can be inferred only in  =0 the limit where k1  k−1 and k1  kcat in which case KM and KC = kcat . This is equivalent to a situation where all enzymes adsorbed to the perimeter exist as the transition state complex (ES) with the substrate, which may or may not be the case. However, we can determine the apparent rate KC regardless of whether this limit is reached. The analysis of the area-activated situation proceeds analogously. Note, that in this case concentrations of enzymes on the membrane surface are calculated as number per area. Also the total number of enzymes at the surface (NEA ) now becomes:

NEA = θ (E0 ) ·

A = N E ∗ + NES d2

(10)

with d 2 approximating the effective footprint area pr enzyme adsorbed to the membrane surface. Thus we get for the reaction rate in the area activated case:  A(t) dNLPC  = KC · θ (E0 ) · 2 . (11)  dt Area d Similarly, the rate of area decrease is proportional to the area:  KC · a · θ (E0 ) dA  = · A = αArea · A, −  (12) dt Area 2d 2 0) . The reaction rates obtained where we define αArea = KC ·a·θ(E 2d 2 for the two limiting cases in Eqs. (9) and (12) are proportional to

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the perimeter in case (I) and proportional to the area in case (II). The data analysis now consists of extracting the following quantities: Perimeter L(t), area A(t) and rate of area change dA dt (t) from the image sequence, for each membrane island. By subdA sequently considering the plots ( dA dt , L) and ( dt , A) we can determine the slopes αPerimeter and αArea and thereby determine b and KC . Finally, the adsorption equilibrium constant can be used to estimate the standard free energy of adsorption, G◦ad . From equilibrium thermodynamics the standard free energy is related to the equilibrium constant by G◦ad = −kB T ln b,

(13)

where kB is the Boltzmann constant and T is the temperature. 3.3. Kinetic analysis of the fluorescence time-series In order to test the proposed model and to obtain estimates of the rate constant KC and the adsorption equilibrium constant b, the area A and perimeter length L of a number of lipid bilayer islands were measured as a function of time for a range of different enzyme concentrations. We have analyzed a total of 43 islands in the presence of βCD and 28 islands in the absence of βCD. Concentration ranges of PLA2 were 1–600 nM and 1–300 nM, respectively. The behavior of the system in the presence and absence of βCD is qualitatively similar, but with quantitative differences as discussed below. One significant difference between the two systems is that DiI-C18 is not removed from the islands in the absence of βCD which leads to an increase in brightness (fluorescence emission per area) from an island as the area decreases, but the probe is not removed. We do not observe such an intensity increase in the presence of βCD meaning that the βCD partly or completely removes the fluorescence probe along with the products of the hydrolysis. Figs. 4A and 4B shows the time evolution of the parameters L(t) and A(t) for the 4 islands indicated in Fig. 2A. The rate of area decrease −dA/dt in Fig. 4C was determined by numerical differentiation of A(t). All islands analyzed in the image sequences showed a monotonic decrease in L(t) and A(t). However, in cases where the islands where constrained by pinning points, the time evolution of L(t) may contain discrete jumps to lower values when the island relaxes to a new and more round shape. On the other hand, in the same time sequences A(t) shows a smooth behavior without jumps, since the area is not affected by relaxations in the shape of the island. For PLA2 concentrations above 100 nM where the lower bilayer is being hydrolyzed after a lag phase, only data recorded during this lag phase is used and presented. This is done to minimize interference effects between hydrolysis of the lower and the upper bilayer. The time evolution of the island decay can now be analyzed in terms of the two kinetic models that assume PLA2 activation to occur either at the membrane perimeter or at the membrane surface. This is done by plotting the rate of area decrease −dA/dt against the membrane perimeter L or against the area A. Another possibility for the analysis would have been to assume a specific (circular) shape of the islands and to solve

Fig. 4. Typical time evolution of the characteristic parameters related to islands no. 1–4 indicated on Fig. 2 during hydrolysis initiated at t = 0 s (100 nM PLA2 ). Shown is the island perimeter L(t) (A), the decrease in the island area A(t) (B) and the rate of area change −dA/dt (C).

the kinetic equations for A(t) and L(t). Since most of the islands are close to circular this leads to virtually identical results (not shown) compared to the present analysis where no specific shape is assumed and where we only consider how the perimeter or the area relates to the decay of membrane area. Fig. 5 shows such plots for the 4 islands indicated in Fig. 2A. In both of these cases, the data fall on approximately straight lines in agreement with Eqs. (9) and (12). The quality of the fit is slightly better for the area-activated as compared to the perimeter-activated case. However, this difference is small and we cannot exclude either of the models based on the quality of the fits alone. dA The slope of the ( dA dt , L) and ( dt , A) yields the constants αPerimeter and αArea , respectively. The α values indicated in Fig. 5 are of similar magnitude, as expected. Moreover it is a general observation that there is no systematic correlation between the measured slopes and the initial size of the islands. This is the case both in the presence and absence of βCD. We can therefore conclude that variations in α can primarily be attributed to variations in the bulk enzyme concentration rather that variations in the initial area of the bilayer island. The values of α determined as described above are plotted against the PLA2 enzyme concentration to derive the relevant

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Fig. 5. Plots of the rate of area decrease −dA/dt vs island perimeter (A) and of −dA/dt vs island area (B) for the 4 islands shown in Fig. 2 (100 nM PLA2 ). The two plots correspond to case (I) and case (II) of the kinetic analysis. The plots above no. 1 have in both (A) and (B) been displaced vertically for clarity. The slope of a line equals the parameter α and the value is indicated for each line (island).

adsorption and kinetic parameters. The plots in Fig. 6 show results in the absence of βCD while results in Fig. 7 show the corresponding results in the presence of 880 µM βCD. It is generally observed that the spread in the data points is larger for the system in the absence of βCD as compared to the system containing βCD. There is also a tendency towards a larger spread in the αArea points compared to the αPerimeter points. An adsorption isotherm of the type in Eq. (1) (constant · θ (E0 )) was fitted to the α values in Figs. 6 and 7, as indicated. The constant determines the saturation limit of the α values with respect to an increasing PLA2 concentration corresponding to the limit θ → 1 as E0 → ∞. From the definition of α one then finds the apparent rate constant KC by invoking the linear extension d of an enzyme as well as the effective area a pr. lipid in the membrane. For POPC, we used the values a = 0.6 nm2 [27] and d = 3 nm [28], respectively. The values determined for the adsorption constant, the rate constant KC and the adsorption free energy are reproduced in Table 1. There are several things to be noted regarding these results. We carried out experiments in the presence of βCD in order to establish a situation where the reaction progress would be entirely reflected in the area decrease of the islands. It is well known that long chain fatty acids and LysoPC’s have some affinity towards the membrane and therefore cannot expect this assumption to hold without βCD added. The value of the apparent rate constant KC for the perimeter activated case is of the order 200 s−1 whereas the value found for the area activated case is about 5000 times smaller. This is consistently found both in the absence and presence of βCD. As evident from Table 1 it is clear that the measured rate constant KC is relatively unaffected

113

Fig. 6. The concentration dependence of α for the PLA2 catalyzed hydrolysis of POPC islands in the absence of βCD. Shown is the analysis according case (I) (A) and case (II) (B) and a least squares fit to the Langmuir isotherm (Eq. (1)).

Fig. 7. The concentration dependence of α for the PLA2 catalyzed hydrolysis of POPC islands in the presence of 880 µM βCD. Shown is the analysis according case (I) (A) and case (II) (B) and a least squares fit to the Langmuir isotherm (Eq. (1)).

by the presence of βCD whereas the characteristic adsorption concentration (1/b = concentration at half saturation) increases about ten fold in the presence of βCD. This indicates that the effect of βCD is to effectively reduce the affinity of PLA2 towards the membrane substrate. One mechanism by which this can occur is by depletion of negatively charged reaction prod-

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Table 1 Table of the kinetic parameter KC and the isotherm parameter 1/b which equals the concentration of half coverage in the Langmuir isotherm. Shown is also the free energy of adsorption calculated from Eq. (13) 1/b (nM) No βCD

Perimeter activated Area activated

880 µM βCD

Perimeter activated Area activated

1.28 ± 0.57 5.77 ± 6.28 86.0 ± 36.2 74.9 ± 34.7

ucts (fatty acids) from the reaction sites on the membrane. This would lead to a decreased binding of PLA2 , since it is well known that the presence of negative charges in the membrane strongly promotes the association of positively charged snake venom PLA2 . Another possible mechanism is that a simple competition exists between βCD and PLA2 on gaining access to the substrate sites where the enzyme is activated and where hydrolysis products are released. Regarding the magnitude of the adsorption free energy, Tatulian [29] estimates a binding constant of 2 × 105 M−1 for adsorption of snake venom PLA2 to negatively charged membranes. This value corresponds to a standard free energy of adsorption of −30 kJ/mol. Other studies [30] have estimated the standard free energy of adsorption of snake venom PLA2 to large unilamellar vesicles of DPPG to −1.8 kJ/(mol lipid) and DPPC to −0.9 kJ/(mol lipid). With 20 lipids involved in the binding process these values corresponds to −36 and −18 kJ/mol enzyme. Our values for G◦ are thus of the same magnitude as these literature values. The value determined for the apparent rate constant KC is very different in the perimeter and the area activated cases, although the plots in Fig. 5 are linear in both cases. The main explanation for this is geometrical, since the membrane surface is two-dimensional and the boundary is one-dimensional the corresponding maximum number of binding sites is very different in these two cases. KC is defined as the apparent turnover pr enzyme and consequently this number will depend on the maximum number of binding sites in the two geometries. Literature values of kcat based on pH-stat titration are in close agreement with the perimeter activated analysis and not with the area activated analysis. Thus for DMPM (1,2-dimyristoyl phosphatidylmethanol) vesicles kcat is determined [31,32] to be in the range 300–450 s−1 depending on the NaCl concentration. Using snake venom PLA2 , Nielsen et al. [14] considered the small channels in a supported DPPC membrane as formed by single enzymes and thereby estimated an effective hydrolysis rate of 88 s−1 per enzyme. Grandbois et al. [15] performed similar experiments with bee venom PLA2 and estimated the hydrolysis to 88 ± 30 s−1 per enzyme. The fact that we obtain higher KC values than these may be due to the difference in the rate of hydrolysis between fluid and solid membranes as previously measured in GUV’s [9]. Overall, a comparison of the numbers in Table 1 with literature values, indicates that PLA2 in the present system is perimeter activated. The width, d of the enzyme is used for determining KC and b, and therefore the accuracy of this value is important. However, as the enzyme carries bound counter ions and water molecules in solution, the value of d might be somewhat larger

KC (s−1 )

G◦ad (kJ/mole)

241.3 ± 17.3 0.0610 ± 0.0113

−49.8 ± 1.1 −46.2 ± 1.8

192.5 ± 27.2 0.0266 ± 0.004

−39.6 ± 0.9 −39.9 ± 0.9

than the crystal structure size of 3 nm (22 × 30 × 42 Å [28]). If the dimension of the enzyme is a low limit value then KC is also a lower estimate (see Eqs. (9) and (12)). An additional finding in this work was the absence of a lag period for the fluid lipid bilayer islands, both in the presence and absence of βCD. The lag phase is thought to be associated with the generation of membrane structural defects which can be generated by the hydrolysis products [25]. Since βCD removes these products from the membrane, there must be other defects that mediate an instant activation of the enzyme upon binding to the membrane. Also we note that the KC values in Table 1 suggest activation on the island perimeter. Interestingly is has been found that PLA2 instantaneously hydrolyzes highly curved small unilamellar vesicles [30], and as the perimeter of the bilayer islands are highly curved, this is speculated to be the reason for the absence of a lag phase. 4. Conclusion In this work, we have acquired time-lapse fluorescence data of the PLA2 -catalyzed hydrolysis of fluid supported POPC bilayer islands. The islands are secondary supported membranes situated on top of a primary membrane and are prepared in a straightforward manner upon hydration of a spincoated lipid film. Upon addition of PLA2 to the fluid cell we observe immediately a shrinking of the membrane island area. By quantitative image analysis of the fluorescence time series we determine the time dependent decrease in membrane area and perimeter length for a wide range of PLA2 concentrations, both in the presence and absence of βCD which forms soluble complexes with the reaction products. We apply a simple model for the enzyme kinetics that combines enzyme adsorption to the perimeter or area of the membrane island with the hydrolysis step. From the analysis we determine the Langmuir adsorption isotherm describing the equilibrium adsorption of enzyme to the membrane as well as the apparent kinetic rate constant. Comparing with kinetic data of the literature our results are fully consistent with enzyme activation at the perimeter of the island rather than uniformly over the island surface. The results show that βCD effectively decreases the binding of PLA2 to the membrane and that this is most likely due to removal of negatively charged reaction products from the membrane. Our study demonstrates a new experimental methodology for quantitatively probing the response of fluid membranes to external perturbations such as the action of lipases. The kinetic analysis, although simple, yields useful dynamic information and it can be applied to other membrane/lipase systems, includ-

A.C. Simonsen et al. / Journal of Colloid and Interface Science 301 (2006) 107–115

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