Kinetic analysis of phospholipase A2 activity toward mixed micelles and its implications for the study of lipolytic enzymes.

A detailed kinetic scheme is proposed for the action of phospholipase A2 on mixed micelles of phospholipid and surfactant: see article. where E is the enzyme, A is the mixed micelle, and B is the phospholipid substrate in the mixed micelle. This scheme takes into account quantitatively the involvement of the lipid-water interface in the action of this enzyme toward substrate in macromolecular lipid complexes. The kinetic equation for this scheme is derived and four simplifying assumptions which are necessary for its practical application are described. Kinetic data are reported for the action of cobra venom phospholipase A2 (Naja naja naja) on 1,2-dipalmitosyl-sn-glycero-3-phosphorylcholine in mixed micelles with the nonionic surfactant Triton X-100, and these data are analyzed in terms of the kinetic equation presented. At 40 degrees, pH 8.0, and in the presence of 10 mM Ca2+, V was found to be about 4 X 10(3) mumol min(-1) mg of protein(-1). KsA, which is the dissociation constant for the enzyme-mixed micelle complex, is about 5 X 10(-4) M. KmB, the Michaelis constant for the catalytic step, which is (k-2 + k3)/k2, is 1 to 2 X 10(-10) mol cm-2. This kinetic treatment, together with the fact that the mixed micelle system allows the concentration of the substrate in the lipid-water interface to be varied, has made possible the quantitative separation of the association of a lipolytic enzyme with the lipid-water interface (expressed as KsA) and the binding to the substrate in the interface (reflected in the KmB term). The implications of this kinetic scheme for the analysis of phospholipase A2 from other sources acting on other aggregated forms of phospholipid and for the study of other phospholipases and lipases is considered.


Phospholipase
Al, as well as other lipolytic enzymes, act in uiuo on substrates that are part of macromolecular aggregates.
For in uitro kinetic studies, several forms of the substrate have been employed including monolayers (l), micelles of phospholipids containing short chain fatty acids (2), monomers (3), ether-water complexes (4), and mixed micelles with surfactants (5). All of the studies have suggested that the lipid-water interface of these macromolecular aggregates plays an important role in enzymatic activity, although the precise function of the interface has not been elaborated. The presence of an interface sets lipolytic enzymes apart from "normal" enzymes, and an understanding of its functioning is crucial before the detailed catalytic mechanisms of this class of enzymes can be established. The Triton X-100-phosphatidylcholine mixed micelle system allows a direct kinetic investigation of the interaction of the enzyme and the lipid-water interface, because it provides a system in which the concentration of substrate in the interface can be varied and the activity can be followed by standard kinetic techniques.
We have now developed a kinetic scheme which accounts for an interfacial requirement of phospholipase A,; the theoretical and experimental kinetic analyses of this scheme are presented. We also discuss the implications of these results for other lipolytic enzymes and for analyzing phospholipase A, activity toward other types of interfaces.
The studies described here were conducted with a homogeneous preparation of phospholipase A, derived from cobra venom (Baja naja naja) which is described in the accompanying paper (6). Given the general scheme shown in Fig. 2, it is possible that E associates with A and moves around its surface until it binds to B forming EAB or that E comes on and off A rapidly and only forms EAB when it collides with A in such a way that B is in the correct position for forming EAB. Both possibilities are compatible with the scheme; the distinction between them depends on the magnitude of the relevant rate constants. In either case, EA binds to B to form EAB and B is the phospholipid present in the surface of the mixed micelle. It should be noted that we use the word surface to indicate the region of the micelle in which the catalytic reaction takes place and this may extend beyond the Stern or palisade layer into the hydrophobic region. Since the phospholipid is constrained to this two-dimensional surface, its concentration must be expressed in terms of its concentration in the surface. The scheme presented in Fig. 2 is summarized in Equation 3.
The kinetic equation for this scheme is derived under "Appendix" and is shown in Equation 4.
It should be noted that this equation is formally the same as that considered by Cleland (10) for a soluble, bisubstrate enzyme displaying an equilibrium ordered initial velocity pattern (pp. 9-10 of Ref. 10). In our case, the micelle is kinetically analogous to a cofactor such as a metal ion which is required to bind before the substrate and is not altered by the reaction.
It is useful to consider the expression for u as a function of (A) when (B) is held constant; this expression is given in    Practical Considerations-In order to apply the above considerations to the action of phospholipase A, toward mixed micelles of phosphatidylcholine and Triton X-100, it is necessary to vary both (A) and ( y, and n are not known accurately at any concentration of P and T, and they would be difficult to determine precisely. However, by applying the simplifying assumptions given below, it is possible to deal with the kinetic data.
1. The size and aggregation number of mixed micelles are constant as (A) is varied. Thus, x and y are also constant as (A) is varied at constant (B). This assumption arises from the fact that the aggregation number of pure micelles of nonionic surfactants does stay roughly constant over a large concentration range above the critical micelle concentration (111, although no data are available on mixed micelles.
2. Only 1 enzyme molecule can bind to a finite segment of a micelle and n, which defines the size of that segment, is constant under all experimental conditions. 3. The average surface area per molecule of phosphatidylcholine and Triton X-100 in mixed micelles is the same, that is x = y. There are no experimental data available for these values in mixed micelles, but the limited data available for Triton and phosphatidylcholine in separate structures are consistent with this assumption.
Interfacial tension measurements of Triton X-100 in isooctane-water interfaces suggest that the average surface area is about 85 A' (12). Monolayer studies with both natural and synthetic phosphatidylcholines suggest that phospholipase A, acts maximally when the surface pressure is such that the average surface area of the phospholipid molecules is about 80 to 90 A* (13, 14). Although the average surface area of Triton X-100 and phosphatidylcholine molecules in mixed micelles is undoubtedly different, it is not likely that they differ greatly.
4. For simplicity, the average surface area per molecule of both phospholipid and Triton X-100 is assumed to remain constant as their molar ratio is varied. Thus, n and y are constant as (B) is varied. This assumption implies that to a first approximation, the size of the mixed micelles does not vary with changes in composition of Triton X-100 and phospholipid.
Because we have found that the size and polydispersity of mixed micelles do vary with molar ratio of Triton X-100/ phospholipid (15), this simplifying assumption is not completely valid and is taken into account below.
These assumptions allow Equations 1 and 2 to be simplified as shown in Equations 9 and 10, respectively. These results suggest that kinetic experiments should be conducted holding either A' or B' constant. For practical purposes, it is easiest to prepare a stock mixture of Triton X-100 and phospholipid at a constant mole fraction, B', and various amounts of that mixture can be used to vary A' in each assay. This method was used to obtain the data reported here. The normal way to conduct kinetic experiments, if Triton X-100 were thought to be an activator and/or inhibitor of the enzyme, would be to hold the Triton X-100 concentration constant and vary the phospholipid concentration. However, results obtained in this manner would be difficult to interpret in terms of the kinetic equation presented above because both A' and B' would be varied simultaneously.

AND DISCUSSION
Kinetic Data-Kinetic studies on phospholipase A, action toward dipalmitoyl phosphatidylcholine in mixed micelles with Triton X-100 and with a saturating concentration of Ca'+ present were conducted. Replots are shown in Fig. 4. The points appear to be somewhat curved, but a reasonable straight line could be drawn for the l/v intercept plot which intersects on the l/u axis (which is l/v) within a small range of its value determined at the point of intersection in the original plot. This procedure was employed to minimize the effects of curvature and obtain a rough value of xK,,,~; this problem will be considered below. Similarly, a reasonable straight line passing through the origin could be drawn in the slope replot, and the value of nK,*/x is similar to that obtained in the original plot. there was greater scatter of points; therefore, lines were drawn Fig. 3 "USUS z/n'. a minimum value for it by assuming that the enzyme is a spherical or somewhat ellipsoidal to a progressively more perfect sphere and that 2 enzyme molecules associated with a ellipsoidal shape as the mole fraction increases, then the micelle cannot be closer than their diameters. This would imply that the micellar binding site cannot be less than the projection of the enzyme's cross-sectional area onto the micellar surface. This cross-sectional area can be calculated from the partial specific volume and the molecular weight of the enzyme as discussed elsewhere (6). This gives n = 3.6 x 10" cm* mol-'of binding sites. Note that this corresponds to about 7 molecules of Triton X-100 and/or phospholipid.
Using these values of x and n, KSA is about 7 x lo-' M and K,B is about 1.8 x 10-l' mol cm-'.
Validity of Assumptions-When the data were considered as surface area per molecule would decrease due to the decreasing average curvature of each molecule.
increase by the same amount as B' changes, the results shown Because the precise quantitative effect on x and y is not known, assumption 4 was employed in the evaluation of the in Fig. 6b are obtained. It is clear that the curvature is much results. Since it appears that the lack of linearity in the plots shown in Fig. 5 is most likely due to the crudeness of more pronounced in Fig. 66 than in Fig. 5, and that the values assumption 4, the following considerations were applied to the data. If it is assumed that x and y decrease by a factor of 2 as used in Fig. 6a give rise to a more linear plot and are probably the mole fraction, B', goes from 0.077 to 0.33, reasonable more correct. This is the same as assuming that the average straight lines intersecting on the l/u axis could be drawn as shown in Fig. 6a. Conversely, if it is assumed that x and y surface area per molecule at a mole fraction of 0.077 is about 85 A*, and it decreases proportionally to 42.5 A* at a mole fraction of 0.33. This is a reasonable range for the surface area of these molecules. It should be noted that the values of x used in obtaining Fig. 6a resulted from simply varying x by a factor of 2 in a regular manner; no attempt was made to determine precise they are comprised of about 150 monomers and are spherical.

though B' was varied at constant values of A', the results
Since it appears unlikely that this number of hydrophobic groups could pack in a purely spherical manner, the micelles shown in Fig. 5 were obtained.
It was not possible to draw are probably at least somewhat ellipsoidal, but it is clear that the much larger structures formed at larger mole fractions straight lines through the data because the experimental must be on the average quite ellipsoidal. Similar changes in shape of mixed micelles of Triton X-100 and sphingomyelin points clearly curve upwards. We discussed above the fact that have been suggested on the basis of experimental measurements (17). Furthermore, we have found on gel chromatogra-assumption 4 was not valid since the average size of mixed phy that two main populations of micelles occur at lower molar ratios (termed mixed micelles and quasi-mixed micelles) (15).

micelles (and thus presumably the area per mblecule) does
It may be that the proportion of larger micelles is merely vary with the mole fraction of phospholipid in the mixed micelle. We have found that mixed micelles at a mole fraction of about 0.09 are about the same size as pure Triton X-100 micelles (15). The precise structure of Triton X-100 micelles is not known but Kushner and Hubbard (16) have suggested that values of x that would give the best fit to straight lines. A linear replot of the slopes in Fig. 6a is obtained as shown in  Fig. 3 were replotted using the same assumption for the values of x and y used in Fig. 6a as shown in Fig. 8, and the replots are shown in Fig. 9. The value of V, KIA, and K,s differ by less than a factor of 2 from those obtained in Fig. 4 and agree closely with those obtained from Figs. 6a and 7. Since the values obtained after invoking the decreasing as the molar ratio is increased, and the enzyme may correction to assumption 4 are probably more correct, we will have different activities toward each type of micelle. If this is consider these latter data as the kinetic constants, although the case, however, it would express itself in a change in the similar values can be obtained by using assumption 4 directly. 2 average structure of the mixed micelle with molar ratio. Thus, Assumption 3 stated that x = y. The linearity of the plot in if the average shape of the mixed micelles changes from a Fig. 3 is also rather insensitive to this assumption as shown in the plots in Fig. 10, where it was assumed that the average 1 I I I I surface area of Triton X-100 is either twice or one-half that of the phospholipid. Lines were drawn as in Fig. 3. Replots are not 6-obviously less linear than the original plots, and the kinetic parameters do not v'ary greatly. Also, plots of l/u uersus l/(B) at constant (A) do not significantly alter the apparent curvature in Fig. 5. Thus, even if assumption 3 is not completely valid, it does not affect our results significantly.
In summary, the data presented here are consistent with the kinetic scheme presented in Fig. 2 and Equation 4 considering all of the simplifying assumptions required; however, the *It should be noted that K,* and K,,," in Equation 4 are constants, but in the mixed micelle system, it is possible that variations of x and y with (B) cause changes in the physical state of the interface and I I I L I consequently affects these constants and this is responsible for the -6 -3 0 3 6 9 12 15 curvature in the plots. When (B) is less than 0.09, x and y should be   high that data cannot be obtained at concentrations in the immediate vicinity of the K,,,s, and this makes the precise determination of the K," unreliable. Further refinements in the assay system are required to determine these constants more accurately and to test the model more definitively.
Conclusions and Implications for Study of Lipolytic Enzymes-We have developed a kinetic equation to analyze the activity of phospholipase A, toward phospholipid-Triton X-109 mixed micelles. The scheme upon which this equation is based is not radically different from schemes that others have presented for other forms of the substrate as recently reviewed by Brockerhoff and Jensen (19). In summarizing the kinetic results obtained by others, the phospholipase A,-phospholipid system was treated as if it was a single substrate reaction containing two intermediate complexes (19). This treatment yields a rate equation in which only an apparent K, could be determined.
KaA and K,s were not separated out of the apparent K, and thus little can be concluded about the interfacial binding of the enzyme or the subsequent Michaelis complex formation.
In order for a water-soluble enzyme to act on a substrate localized in a large lipid aggregate, the enzyme probably first associates with the lipid-water interface. There- The rate equation now has the same form as a simple monosubstrate Michaelis-Menten reaction. Pancreatic phospholipase A, does demonstrate such kinetics when acting on these micelles. This illustrates the problem mentioned above, in that K.* and K,w cannot be separated without additional independent data. With the introduction of Triton X-100 into the micelles, (B) becomes less than l/x and is no longer constant. This dilution of the phospholipid in the interface has been described as a "surface dilution phenomenon" (5). This in turn forces the use of the complete kinetic equation, Equation 4, and allows the determination of K,w and KeA. Verger et al.
(1) have also suggested a scheme similar to the one presented in Fig. 2 to explain the action of pancreatic phospholipase A8 toward monolayers and micelles of phospholipid, and their analysis provides information about the enzyme-interface interaction.
However, their experiments did not lead to a determination of the kinetic constants equivalent to KaA and K,w defined here.
We have found in preliminary experiments with phospholipase C' and a solubilized form of the membrane-bound enzyme phosphatidylserine decarboxylase (18) acting on mixed micelles of Triton X-100 and phospholipid that the kinetic results are also analyzable with the scheme and equation presented here. It is also possible that triglyceride lipases act in a fashion similar to phospholipase A,. However, analyzing the triglyceride substrate in this manner would be difficult since as generally studied, triglyceride lipases act on lipid emulsions in which only a fraction of the triglyceride substrate is at the lipid-water interface where it is exposed to the enzyme. Thus, the dependence of total surface and the