Specific contribution of different phospholipid surfaces to the activation of prothrombin by the fully assembled prothrombinase.

This paper addresses, in thermodynamic and kinetic terms, the reasons for the acidic lipid specificity of the human prothrombinase complex. We obtained, from the measured lipid titrations of the initial rates of prothrombin activation, the empirical binding constants for prothrombinase assembly on different membranes. These favored assembly on phosphatidylserine (PS)- as opposed to phosphatidylglycerol (PG)-containing membranes. In addition, we have used full time courses of prothrombin activation, in conjunction with a calculation of the equilibrium distribution of factor Xa between four enzymatic forms, to obtain the intrinsic kinetic constants of the prothrombinase assembled on PS- or PG-containing membranes. The resulting values of kcat, Km, and kcat/Km increased as acidic lipid content increased, and kcat/Km reached a plateau at 12 mol % PS and 50 mol % PG. Using the measured assembly and kinetic constants, the observed shapes of the phospholipid titration curves of human prothrombin activation were interpreted. We conclude that the difference in activity of prothrombinase assembled on PS- versus PG-containing membranes results both from the different binding properties of factors Xa and Va to these surfaces and from the different intrinsic activities of the prothrombinase when assembled on different membranes.

Not all negatively charged phospholipid membranes furnish catalytic surfaces that are equally effective for prothrombin activation. Jones et al. (1985) demonstrated that phosphatidylserine (PS)'-containing vesicles were able to support thrombin-generating activity at much lower concentrations than were phosphatidylglycerol (PG)-containing membranes.
More recently,  reported that PS-containing membranes retained their procoagulant activity even when the membrane had a net positive surface charge, whereas PG-containing membranes did not. These observations suggest a degree of phospholipid specificity in the prothrombinase complex. At least one source of this specificity may reside in differences in the abilities of PS-and PGcontaining membranes to assemble the prothrombinase complex (Cutsforth et al., 1989).' In addition, we have shown recently that prothrombin is structurally altered when bound to PS-as opposed to PG-containing membranes Lentz et al., 1991). These observations suggest that the phospholipid surface may alter in a lipid-specific fashion at least one component (the substrate) of the catalytic complex, thereby leading to different intrinsic catalytic properties of the enzyme assembled on different acidic lipid surfaces.
At least two factors make it difficult to establish the intrinsic catalytic activities of the prothrombinase assembled on different membranes.
First, activation of prothrombin to thrombin requires that two peptide bonds be hydrolyzed by the prothrombinase complex. If Arg273-Thr274 is cut first, prethrombin 2 is produced; if A~-p -I l e~'~ is cleaved first, meizothrombin is formed. The proteolysis catalyzed by the full prothrombinase (Xa. Va. membrane) is much more rapid than any competing proteolytic event, and proceeds almost exclusively through the partially enzymatically active intermediate meizothrombin, producing almost none of the inactive intermediate, prethrombin 2 (Rosing et al., 1980.
In order to avoid buildup of the meizothrombin intermediate, we have chosen to work at low prothrombin concentrations. Under these conditions, it has been shown that meizothrombin does not accumulate, and that the product of proteolysis is primarily thrombin . Thus, appropriate choice of conditions has allowed us to focus in this report on the net thrombin-forming activity of the prothrombinase.
A second complication is that factor Xa interacts with factor Va, with acidic lipid membranes, and with membranebound factor Va with roughly comparable binding constants. Thus, although most studies have reported saturating kinetic Prothrombinase Phospholipid Specificity 3227 behavior at high concentrations of membranes or factor Va (Nesheim et al., 1979b;Rosing et al. 1980), not all factor Xa is expected to be incorporated into membrane-bound prothrombinase even under saturating conditions. We have attempted to deal with this assembly issue by utilizing available binding constants to model the equilibrium distribution of factor Xa between membrane-bound and solution forms with or without associated factor Va.
For both PS-and PG-containing membranes, we have measured the initial velocity of prothrombin activation as a function of both phospholipid concentration and as a function of negatively charged lipid content. We have used these initial velocity titration curves, along with an equilibrium binding algorithm (see Appendix (Powers and Lentz (1993); pp. 3234-3237 of this issue), to estimate the empirical equilibrium constant for assembly of the full prothrombinase on different membranes. This constant favored assembly on PS-containing membranes. In addition, we have analyzed complete progress curves of thrombin generation to obtain apparent kinetic constants and corrected these for the fraction of factor Xa associated with membrane-bound factor Va to establish the Michaelis-Menten kinetic constants for the surface-assembled prothrombinase. These indicated that the enzyme assembled on a PS-containing surface had an enhanced catalytic ability relative to enzyme assembled on a comparable PGcontaining membrane. Thus, the PS specificity of the prothrombinase, as reflected in phospholipid titration curves, appears to arise both from enhanced assembly and from enhanced catalytic ability on PS relative to PG-containing surfaces.

EXPERIMENTAL PROCEDURES
Materials-Bovine brain phosphatidylserine (PS), l-palmitoyl-2oleoyl-3-sn-phosphatidylcholine (PC), and 1,2-dioleoyl-3-sn-phosphatidylglycerol (PG) were purchased from Avanti Biochemicals. Dansylarginine-N-(3-ethyl-1,5-pentanediyl)amide (DAPA) was generously provided by Dr. Roger Lundblad. All chemicals were ACS reagent grade or the best available grade; all solvents were HPLC grade. Small, unilamellar vesicles with various phospholipid compositions were prepared in 20 mM Tris, 0.15 M NaCI, pH 7.4, by sonication and fractionated by centrifugation (Lentz et al., 1980(Lentz et al., , 1982. Phospholipid concentration was determined by analysis of inorganic phosphate (Chen et al., 1956). Human plasma was obtained from the North Carolina Memorial Hospital Blood Bank as waste material from the plasmapheresis unit. Human prothrombin, factor X, and factor V were isolated from human plasma by published procedures (Dahlback, 1980;Cutsforth et al., 1989). Factor X was activated with a purified fraction of Russel's viper venom factor Xactivating protein which had been covalently linked to agarose beads (Jesty and Nemerson, 1976). Factor V was activated by 1.25 ng/ml factor V-activating protein isolated from Russell's viper venom (Kisiel and Canfield, 1981) in situ. The concentration of factor Va was determined by the "thromboplastin" assay in terms of the clottingtime of factor V-deficient plasma standardized against the clotting time of pooled, normal, human plasma (Nesheim et al., 1981b).
Kinetic Measurement with DAPA-The fluorescence intensity of DAPA, a specific fluorescent inhibitor of thrombin, is greatly enhanced when bound to the active site of thrombin or its partially activated form, meizothrombin (Nesheim et al., 1979a;Hibhard et al., 1982). DAPA provides a convenient method not only for continuously monitoring the progress of prothrombin activation but also for preventing any feedback reactions catalyzed by newly formed product (Nesheim and Mann, 1983;Malhotra et al., 1985;Krishnaswamy et al., 1986Krishnaswamy et al., , 1987. Fluorescence intensity measurements were carried out with an SLM 48000TM fluorescence spectrophotometer (SLM Aminco). Excitation wavelength was 280 nm (band pass, 4 nm) and emission wavelengths were from 515 to 550 nm with a 515-nm cutoff filter. Reaction temperatures were maintained a t 37 "C using a refrigerated, circulating water bath. All buffers were filtered through a 0.45-pm filter to reduce scattered light artifacts. When phospholipid concentration was varied, reaction mixtures (1.0 ml in a continuously stirred cuvette) contained 20 mM Tris, 0.15 M NaCI, pH 7.4, 5 mM CaCI2, 0.1 nM factor Xa, 1.2 nM factor Va, and 500 nM DAPA and variable concentrations of phospholipid. The reaction mixtures were equilibrated for 3 min, allowing the prothrombinase to be fully assembled, before initiating proteolysis by the addition of prothrombin to a final concentration of 120 nM. When prothrombin concentration was varied, the mixtures contained 10 WM phospholipid, and the final concentrations of prothrombin were adjusted between 10 and 500 nM.
Treatment of Kinetic Data-Despite the complexity of the prothrombinase reaction, most previous studies (Nesheim et al., 1979b;Nesheim and Mann, 1983;Malhotra et al., 1985) have assumed a Michaelis-Menten reaction mechanism, with the substrate prothrombin approaching the assembled prothrombinase complex from solution. This is also the assumption made here. However, there is not universal acceptance of this view. Rosing et al. (1980) and Nesheim et al. (1981a) postulated that the dramatic decrease in the apparent K,,, for factor Xa-catalyzed conversion of prothrombin to thrombin which occurs in the presence of phospholipid is a consequence of concentrating the substrate on the phospholipid surface from whence it would have more ready access to the prothromhinase active site. On the other hand, Pusey and Nelsestuen (1983) observed that the K,,, for the fully assembled prothrombinase was independent of the prothrombin density at the surface, from which they concluded that substrate approach must be from the aqueous phase. Van Rijn et al. (1984) concurred that, in the presence of factor Va, the source of the substrate for the prothrombinase was the aqueous solution. In agreement with this position, Higgins et al. (1985) observed that alterations in membrane "fluidity" had no discernible effect on the prothrombinase catalytic properties. Most recently, Giesen et al. (1991) have examined the prothrombinase assembled at very low density (about 0.3 fmol cm-') on supported bilayers. At these very low surface densities, these authors interpreted a delay in thrombin generation as well as an anomalously large k,,,/K,,, to suggest that the substrate is "funneled" to the prothrombinase active site by the membrane surface. Thus, despite some uncertainty associated with the absolute values of the kinetic constants reported by these authors, their data do favor the "bound substrate model" at the extremely low surface densities of their experiments. However, a t surface densities typical of most kinetic experiments (and probably of physiological conditions), Giesen et al. (1991) agree that the influence of surface diffusion of substrate (prothrombin) would not be kinetically resolved, and the prothrombinase would be expected to behave according to the simple Michaelis-Menten model with substrate approaching from solution, as we have assumed.
Initial velocities of prothrombin activation were calculated from the initial portion of the progress curves of fluorescence intensity versus time. Fluorescence intensity at the completion of the reaction (infinite time) was considered to represent quantitative conversion of prothrombin to thrombin and was used to convert the fluorescence intensity change per unit time into units describing thrombin active site formation as a function of time. As noted in the Introduction, we have chosen reaction conditions for which meizothrombin does not accumulate and prothrombin is the major product. Therefore, the integrated Henri-Michaelis-Menten analysis was applied to determine the apparent K,,, and V, , , of prothrombin activation to thrombin from the whole time course of the proteolysis reaction as described previously (Nesheim et aL, 1979b). The Lineweaver-Burk method (Rosing et al., 1980;Krishnaswamy et al., 1987) was also used to obtain the apparent K , and VmaX of prothrombin activation from initial rates determined at different prothrombin concentrations. The kcat of prothrombin activation was calculated according to the equation, kc,, = V,.,/([Xa],.F), where VmaX is the apparent kinetic constant obtained from the above analysis, [Xa], is the nominal enzyme concentration, and F is the fraction of Xa bound to Va on the phospholipid surface in the reaction mixture. This fraction was calculated using an algorithm described in the Appendix (Powers and Lentz (1993); see pp. 3234-3237 of this issue). Using binding constants obtained from the literature, this algorithm calculates the distribution of factor Xa between four species: aqueous Xa, aqueous XaVa, membrane-bound Xa, and membrane bound XaVa. creased to a stable, limiting value after a period of time. This value was considered to be indicative of the binding of DAPA to the active site of thrombin generated in any given reaction mixture, and was used to convert units of fluorescence intensity to units of thrombin active-site concentration. Initial velocities of prothrombin activat.ion were measured in units describing generation of thrombin active site as a function of time (see "Experimental Procedures"). This method of monitoring active-site formation is essentially that first described by Nesheim et al. (1979b) and is valid as long as insignificant amounts of other DAPA-binding prothrombin proteolysis products, prethrombin 2 and meizothrombin, are produced. Under our conditions, where high concentrations of fully assembled prothrombinase are formed, prethrombin 2 is not expected to form in detectable amounts (Rosing et al., 1980), a prediction that we have verified by analysis of proteolysis products using gel electrophoresis (data not shown). DAPA detects active sites on meizothrombin with ca. 25 mol % greater sensitivity than it does the active site of thrombin (Nesheim and Mann, 1983). This is not a significant complication as long as meizothrombin is not present at concentrations approaching that of thrombin in our reaction mixtures. At the low prothrombin concentrations used in our experiments, meizothrombin is reported to accumulate at a much slower rate than that at which thrombin accumulates (Rosing and Tans, 1988). This expectation is supported by the shape of our DAPA-binding time courses (Fig. 1). Formation of significant quantities of meizothrombin is characterized by a n initial increase followed by a decrease in fluorescence intensity (Krishnaswamy et al., 1986(Krishnaswamy et al., , 1987, which we did not observe under our conditions. Phospholipid Dependence of the Rate of Prothrombin Activation-From time courses such as shown in Fig. 1, the initial velocity of prothrombin activation was determined as a function of both composition and concentration of membrane vesicles containing acidic phospholipid. The results are shown in Figs. 2A and 2B, for PS-and PG-containing vesicles, respectively. For membranes of all acidic lipid contents considered, a minimal or critical concentration of phospholipid was required in order to observe significant rates of thrombin formation. This is qualitatively similar to our previous report, of a critical phospholipid concentration required to observe any thrombin formation in a crude assay system containing much higher levels of factor Xa (Jones et al., 1985). Consistent with our previous results (Jones et al., 1985), for a fixed acidic lipid content, this critical concentration was always greater for PG-as compared to PS-containing membranes (compare im,, 1 1

FIG. 2. Phospholipid dependence of the initial velocity of prothrombin activation using PS-containing vesicles ( A ) and PC-containing vesicles ( B ) .
The values of the initial velocity were determined from the initial slopes of time courses such as shown in  Figs. 2A and 2 B ) . This confirms that PS-containing vesicles possess greater ability to activate prothrombin than PGcontaining ones. For both types of acidic lipid membrane, at a given total lipid concentration, the initial velocity of prothrombin activation increased as the content of negatively charged phospholipid increased. Comparison of Figs. 2A and 2B demonstrates that it required membranes containing 50 mol % PG to provide a surface as effective as provided by membranes containing 25 mol % PS. It is not evident from these results, however, whether the enhanced effectiveness of PS-as compared to PG-containing membranes is due to better assembly of the prothrombinase complex or to enhanced activity of the assembled complex.
Empirical Equilibrium Dissociation Constants for Assembly of the Prothrombinase on Different Membranes-Lipid titration curves such as shown in Fig. 2 contain a great deal of information about the assembly and activity of the prothrombinase complex. It is shown in the Appendix that the shapes and peak heights of lipid titration curves shown in Fig. 2 were reflective of three key parameters: the kinetic constants (mainly kcat) for activation of prothrombin by the assembled prothrombinase, the Kd for factor Va binding to membranes, and the effective Kd values for binding of factor Xa to Va. PL, i.e. for assembly of the prothrombinase (see Appendix). This means that the titration curves contain sufficient information that at least one of these three parameters can be obtained by fitting calculated initial rate titrations obtained using the calculated equilibrium concentration of prothrombinase (see Appendix) to our experimental titration curves.
There is in the literature an initial estimate of Kd for formation of the bovine Xa.Va. PL complex obtained by a functional binding assay utilizing 20/80 PS/PC membranes (Nesheim et al., 1979b). Although this estimate is roughly consistent with another estimate by a crude direct binding assay (van de Waart et al., 19841, there were three concerns about our ability to use it. First, the species difference is of concern: our work is with human proteins; reported values are for bovine proteins. Second, analysis of the functional binding data by Nesheim et al. (197913) did not take into account the competition for factor Xa between phospholipid membrane and the species Va. PL. This competition would be expected to lower the apparent binding constant. Third, we did not expect the effective binding constant for assembly of the prothrombinase to be the same for PS-and PGcontaining membranes nor for membranes containing different surface concentrations of acidic phospholipid.
For these reasons, we have adjusted the Kd for factor Xa binding to Va.PL to obtain a best least-squares fit of calculated initial rates (see Appendix) to our own lipid titration experiments. As pointed out in the Appendix, kcat influenced only the height of the peak and not its position nor the position of the rising or falling edges. Thus, by normalizing each titration data set to the peak initial rate, we removed the dependence of the titration curves, and t.he Kd values derived therefrom, on kcat. With the Kd for factor Va binding to membranes held constant, the position and shape of the rise of the normalized titration curves was sensitive mainly t o the value of Kd for Xa binding to Va.PL. A simple onedimensional grid search yielded a best estimate of the desired K d (stoichiometry fixed a t 1:l) for each of the membrane compositions considered. The resulting Kd values, summarized in Table I, indicate a slight preference for assembly of the prothrombinase on PS-as compared to PG-containing membranes. It should be noted that the procedure we used to obtain these values is essentially the same as used by Nesheim et al. (1979b) to obtain their estimate of the effective binding constant for prothrombinase assembly, except that we have varied the phospholipid component of the complex, while they varied either the factor Va or factor Xa components. There is close agreement between the Kd obtained from our data with human proteins and 25 mol % PS membranes (5.0 x 10"' M) and the value derived using our analysis from the data of Nesheim et al. for 20 mol % PS membranes and bovine proteins (5.2 X 10"' M). Thus, the thermodynamic behavior of the human and bovine systems appear to be similar. These values were somewhat smaller than that obtained by Nesheim et ai. (1979b, 7.2 X M), perhaps because our analysis, unlike that of Nesheim et al. (1979b), takes into account directly the competition between Va.PL and PL for factor Xa.
If the content of negatively charged phospholipid was high, both PS-and PG-containing vesicles showed the previously demonstrated (Nesheim et al., 1979b;Rosing et al., 1980;Pusey et al., 1983) inhibitory effects of high phospholipid 12.8 f 6.4 Data are obtained by the best least-squares fit of calculated initial rates (see Appendix) to the normalized initial rates acquired from the phospholipid titration experiments (see Fig. 2). concentration (Fig. 2, A and B ) . The reason for this will be examined in the "Discussion." Apparent Kinetic Parameters for the Prothrombinase Assembled on Different Membranes-There are two routes to determining from our data the kinetic constants of the prothrombinase complex assembled on different membranes. First, data such as those shown in Fig. 1 were transformed and replotted according to the integrated Henri-Michaelis-Menten equation (Segel, 1975;Nesheim et al., 1979b). One such plot is presented in Fig. 3, where data encompassing the reaction from 10 to 90% completion are presented. For each membrane considered, a linear relationship with a positive slope (K,,,/VmaX) and a positive vertical intercept (1/VmaX) was obtained, indicating that the prothrombinase complex can be characterized, a t least formally, by the apparent kinetic parameters K, and V, , , . These are summarized for various PS/ PC concentrations in Table 11. Lineweaver-Burk analysis was also performed on initial rate data obtained a t different prothrombin concentrations to confirm the results obtained by the integrated Henri  Table 111).

TABLE I1
Phospholipid concentration dependence of kinetic parameters of prothrombin activation for 2575 PS;PC vesicles The reaction conditions are given in the legend of Fig. 1 with the DhosDholiaid concentration varied as indicated. values obtained by these two methods agreed well (see 25% PS:PC data in Table 111).
In any prothrombinase reaction mixture, there exist at least four possible proteolytic species capable of catalyzing the activation of prothrombin: factor Xa bound to factor Va on the phospholipid surface (Xa. Va. PL), the aqueous binary complex of factor Xa and factor Va (Xa. Va), factor Xa bound to a phospholipid surface (Xa.PL), and free aqueous factor Xa (Xa). The fraction of each species will vary with the composition and concentration of phospholipid vesicles in the reaction mixture (see Appendix). Among the enzyme species, Xa . Va. PL, the fully assembled prothrombinase, is reported t o activate prothrombin to thrombin about 1,000 times more rapidly than any of the other enzyme species (Nesheim et al., 1979b;Rosing et al., 1980). The usual method for calculating kcat is to divide the observed V,,, by the nominal enzyme concentration, [Xa]. Because factor Xa is distributed between four different enzyme species, the concentration of the most active prothrombinase species, Xa. Va. PL, may not be equal to the nominal factor Xa concentration. It was our hypothesis that this would account for the variation of apparent kcat values with the concentration of acidic phospholipid incorporated into the reaction mixture as shown in Table 11. To test this hypothesis, kcat was calculated according to the equation given under "Experimental Procedures," wherein F is the fraction of the enzyme, factor Xa, present in species Xa . Va. PL, with F calculated as described in the Appendix.
The corrected values of kcat thus obtained were reasonably constant over a wide range of phospholipid concentrations (see Table 11).
We note that our K, values do not show the lipid concentration dependence reported by Rosing et al. (1980). The concentration dependence reported by Rosing et al. (1980) may have been due to a decrease in the concentration of free substrate (prothrombin) at higher phospholipid concentrations. Van Rijn et al. (1984) have reported that the prothrombinase displays an intrinsic K, independent of phospholipid concentration if it is calculated on the basis of free prothrombin concentration. The integrated Michaelis-Menten analysis involves the ratio of substrate concentrations at time t and zero time (see Fig. 3, abscissa label). Since the fraction of substrate free in solution is not expected to vary over most of the course of prothrombin proteolysis, it is not surprising that the integrated Michaelis-Menten analysis did not produce the phospholipid-dependence of K , reported by Rosing et al. (1980). When kinetic parameters are obtained by Lineweaver-Burk analysis, however, it is often necessary to correct for the K,,, and kcat were obtained as described for Table 11.
Data are derived from the Lineweaver-Burk plot in the insert of Fig. 3. fraction of substrate remaining in solution; Fig. 4 illustrates this for data taken from Rosing et al. (1980). Under conditions where the great majority of prothrombin was free in solution, kinetic constants obtained by the integrated Michealis-Menten and the Lineweaver-Burk methods agreed (see 25/75 PS/ PC data in Table 111).
The kinetic parameters for prothrombin proteolysis under all conditions considered are listed in Table 111. The values are given as the average (with standard deviation) of at least seven experiments performed over a range of phospholipid concentrations (e.g. as shown in Table I1 for 25/75 PS/PC). The value of kcat increased faster than the K , as the content of negatively charged phospholipid increased, leading to an increase in the turnover number, kCat/K,, to a limiting value of 1.15 to 1.30 n"' s-'. In agreement with the observations of Pusey and Nelsestuen (1983) and van Rijn et al. (1984), vesicles containing only 6 mol % PS were quite active. An increase to 12 mol % PS content provided a nearly maximally active membrane surface as evidenced by the value of kcat/Km. In contrast to PS-containing membranes, PG vesicles with 12  Rosing et al. (1980). This simulation was carried out by calculating the fraction of factor Xa assembled into the full prothrombinase (see Appendix) then using the kinetic constants contained in Table  111 for the membrane-bound prothrombinase to predict the dependence of initial ). Straight lines were drawn through the simulated data. The simulation showed qualitatively the behavior seen by Rosing et al. (1980); quantitative agreement was not expected, since our kinetic constants, not those of Rosing et al. (1980), were used to calculate initial rates. B, replot of adjusted kinetic data taken from Fig. 10 of Rosing et al. (1980), with open and closed symbols as indicated in A. From our calculations (Appendix), we obtained the concentration of prothrombin free in solution as well as the fraction of factor Xa assembled into prothrombinase. The initial rates observed by Rosing et al. (1980) were normalized to obtain initial rates per mol of assembledprothrombinase. A single line through both data sets was obtained by linear regression to give kcat = 1280 min" and K,,, = 0.055 pM.

Prothrombinase Phospholipid Specificity 3231
mol % PG were barely active (data not shown). Increasing the vesicle PG content caused a slow rise in the value of kcat/ K , to a maximum of 1.38 to 1.42 nM" s" a t 50 mol % PG, roughly the kcat/K, value seen with membranes containing only 12 mol % PS. Although membranes containing low concentrations of PG were clearly less effective in promoting the activation of prothrombin than membranes of comparable PS content, membranes containing high concentrations of P G supported a prothrombinase complex with a turnover number comparable and perhaps even greater than observed for the prothrombinase assembled on PS-containing membranes. Overall, it is evident from the kinetic parameters in Table 111 that these two types of surfaces differ in their abilities to support the activity of the assembled prothrombinase complex.
The other independent route to information about prothrombinase kinetic parameters is through the interpretation of lipid titration curves such as shown in Fig. 2. As noted in the Appendix, the maximal or peak initial velocity observed for a given type of membrane was sensitive to the kinetic constants (basically kc,, since K,,, did not vary with lipid concentration) of the prothrombinase assembled on that membrane. Using binding constants from this laboratory (Cutsforth et al. (1989) and Table I) and from the literature, the concentration of prothrombinase complex assembled on different membranes under our in vitro reaction conditions was calculated as described in the Appendix. In order to calculate from these concentrations the initial velocities of prothrombin activation expected under different conditions, the Michaelis-Menten constants for the prothrombinase assembled on different membranes were needed. K,,, and k,,, values obtained from our integrated Michaelis-Menten analysis (Fig. 3, as summarized in Table 111) were used to calculate, at each phospholipid concentration, the initial rate of thrombin generation. Agreement of the calculation with experiment (shown in Fig. 5 for 25:15 PS:PC and 2 5 3 5 PG:PC) was very good. When the kc,, values were varied to obtain the best fit of calculated to measured lipid titration curves, the agreement with experiment was not improved significantly.

DISCUSSION
Interpretation of Phospholipid Titration Curves-In this paper, we have used phospholipid titration of the protein components of the prothrombinase complex to obtain information about the phospholipid dependence of both the assembly of the complex as well as the activity of the assembled complex. Given the central role of these lipid titration curves in this study, it is appropriate to comment first on the suspected origin, as indicated by our computational analysis, of the shape of these curves. Our analysis allows estimation of the concentration of each of the four factor Xa-containing enzymes (Xa, Xa. Va, Xa. PL, Xa. Va. PL) that can exist in a prothrombinase reaction mixture as well as the concentrations of membrane-bound and free aqueous prothrombin (see Appendix). The variation with phospholipid concentration of the fraction of each enzyme species and of free substrate is shown in Fig. 6, A and B, for 2 5 3 5 PS:PC and 2 5 7 5 PG:PC, respectively. It is clear from published rates (Nesheim et al., 1979b;Rosing et al., 1980) that formation of the species Xa. Va. P L is the overwhelming determinant of the initial velocity of thrombin formation. It can be seen from Fig. 6A that the fraction of total factor Xa involved in the fully assembled prothrombinase (Xa.Va.PL, large open circles in the figure), closely mimicked the PS titration curve shown in Fig. 2 4 . The factor Va binding constant was the principal determinant of our ability to simulate the rising part of the phospholipid  titration curves shown in Fig. 2. According to our calculations, as acidic lipid vesicles were added to a prothrombinase reaction mixture (log[PL] about -8 to -9), factor Va bound to these membranes and "condensed" (see  and Krishnaswamy (1990)) factor Xa, which would not have bound to such low concentrations of membranes in the absence of factor Va. Thus, the difference in the abilities of PS-uersus PG-containing membranes to "activate" prothrombinase (see Fig. 2, A and B ) apparently reflected, at least in part, their different binding affinities for factors Va and Xa.
Our calculations also suggested that, as the concentration of phospholipid was increased, the fraction of factor Xa associated with active prothrombinase first increased and then decreased. According to our calculations, this occurred because the excess phospholipid surface began to be an effective competitor with bound factor Va for available factor Xa (see the increase in Xa. PL indicated by large open triangles in Fig. 6). The disappearance of free prothrombin from solution (open squares in Fig. 6) may also have contributed to the loss of prothrombinase activity a t very high phospholipid concentration (Pusey and Nelsestuen, 1983), but the near perfect coincidence of the 25% PS data from Fig. 2A with the fraction of Xa . Va. P L in Fig. 6A make it clear that substrate depletion was not the major contributor to PS-containing-membrane inhibition of the prothrombinase, as least as predicted by our simulation of the equilibrium between prothrombinase components. This is further illustrated by the fact that adjusting the prothrombin binding constant had almost no effect on the fit of the simulated titration to experiment but that a slight adjustment of the factor Xa binding constant produced an excellent fit to the high phospholipid portion of the PSinhibition curve (see Fig. 5). It appears that substrate depletion plays a somewhat more significant role in explaining the observed inhibition by high concentrations of PG-containing membranes as the drop in prothrombinase activity in However, prothrombinase assembly still accounted for the major features of the PG titration curve shown in Fig. 2B up to M phospholipid. It has also been suggested that phospholipid inhibition of the prothrombinase occurs uia the dilution of substrate on the membrane surface (Nesheim et al., 1984). Even though the prothrombinase behaves like a Michaelis-Menten enzyme with substrate approach from solution, it appears that binding to the membrane serves to "funnel" the substrate to the prothrombinase active site (Giesen et al., 1991). However, the observed inhibition of prothrombinase activity does not correlate with a decrease in calculated prothrombin surface concentration, as is evident from Fig. 6, wherein is plotted the surface concentration of bound prothrombin (closed squares). Consideration of the results for 25 mol % PG shows that the surface concentration of prothrombin (Fig. 6B, closed squares) dropped much more rapidly from 10 pM to 1 mM phospholipid than did the observed initial rate of prothrombin activation (Fig. 2B, closed circles).
Kinetic Constants for the Assembled Prothrombinase-The kinetic constants obtained here by a combination of experimental and theoretical approaches are summarized in Table  111. These are best compared to those of van Rijn et al. (1984) who employed the chromogenic substrate H-D-phenylalanyl-L-arginine-p-nitroanilide dihydrochloride at 37 "C to follow prothrombin activation. We found similar K , values, but kcat values at high acidic lipid content were about 2-3 times larger than reported by van Rijn et al. The disagreement in kcat values is not surprising, as our kinetic constants are corrected for the fraction of factor Xa incorporated into active prothrombinase enzyme. If we correct the reported kinetic constants of van Rijn et al. for the fraction of factor Xa present as Xa.Va.PL under their reaction conditions, we obtain a kcat value (146 s-') for 25% P S membranes much closer to that reported here (203 s" in Table 11). That this kcat is slightly lower than ours might reflect inhibition in van Rijn's reaction mixture by a substrate-depletion mechanism, as discussed above. The worse agreement for PG-containing membranes (66 s" corrected compared to our 30 s" in Table 11) is very difficult to rationalize but helps to explain why van Rijn et al. found little difference in the activity of prothrombinase as assembled on PS-uersus PG-containing membranes, a result in clear conflict with our present and previous results (Table 11; Jones et al., 1985). A more recent paper from the same laboratory does report a difference between PS-and PG-containing membranes .
It is worth pointing out that the turnover numbers (kcat/ K,) obtained from the corrected kinetic constants for the fully assembled prothrombinase are quite large (Table 111), being roughly lo9 M" s-'. Giesen et al. (1991) have estimated that the theoretically maximal value that could be expected for diffusion controlled approach from solution of the substrate to the prothrombinase active site would be 1.8 x lo9 "1 s-l . The fact that the measured values so closely approach this theoretical limit suggests that the membrane plays a significant role in orienting and directing the prothrombin substrate to the membrane-associated active site of the prothrombinase. This could result from surface diffusion as suggested by Giesen et al. or could result from less severe orienting effects of the membrane as the substrate approaches the active site. Our results can not distinguish between these two possibilities.
The Role of Specific Phospholipids in the Prothrombinase-Specific acidic lipid membranes contribute to prothrombinase activity in two distinct ways. Acidic membranes clearly serve to assemble the components of the prothrombinase enzyme  and differ in their abilities to do this according to their affinities for factors Va and Xa. That PS-containing membranes interact more favorably with factors Xa and Va is documented elsewhere (Cutsforth et al., 1989).' It is not surprising, then, that the empirical constants for the assembly of the Va. Xa. PL complex ( Table I) also reflect a preference for assembly on PS-containing membranes. Thus, preferential assembly apparently accounts for at least part of the enhanced effectiveness of PS-containing membranes in thrombin formation.
Specific acidic lipid membranes may also alter the properties of either the bound enzyme components (factor Xa and factor Va) or the bound substrate (prothrombin). On the basis of the results summarized in Figs. 24 and 2B and Table 111, we must conclude that acidic lipid molecules somehow contribute to altering the kinetic properties of the assembled prothrombinase complex; a conclusion that depends on our ability to determine the distribution of prothrombinase components through the equilibrium calculations outlined in the Appendix. Thus, the lower initial rates seen for 2575 PG:PC membranes in Fig. 2B as compared to 25:75 PS:PC membranes (Fig. 2 A ) reflect the much lower corrected kcat observed for prothrombinase assembled on 25:75 PG:PC uersus 25:75 PS:PC membranes (see Table 111). For PS-containing vesicles, the ratio of kcat/Km reached a plateau at 12 mol % PS (Table  111). Any further increase in PS content increased both kcst and K, but the ratio of these remained constant. This is reflected in the comparable peak heights observed for 12 and Prothrombinase Phospholipid Specificity 3233 25 mol % P S vesicles in the lipid titration curves in Fig. 2 4 . A decrease in P S content below 12 mol % resulted in a decrease in kc,, and K,, but, in this case, the ratio of $,JK,,, decreased, as did the peak height for 6 mol % PS vesicles in Fig. 2.4. This behavior suggests that the composition of negatively charged membranes is crucial for prothrombinase activity. Thus, it may not be a coincidence that procoagulant membrane vesicles released from collagen-stimulated human platelets contain about 10 mol % PS and 2 mol % phosphatidic acid and efficiently support blood coagulation (Crawford, 1985;Sandberg et al., 1985).
There are several possible reasons for this improved catalytic ability on PSversus PG-containing membranes. First, the enzyme constituents (factors Va and Xa) may be altered in different ways when binding to these two types of surfaces. Second, the interaction between these two proteins may be different on a PS-containing as opposed to a PG-containing surface. Third, the substrate, prothrombin, may be altered in lipid-specific ways when binding to an acidic lipid surface and this may affect its conformation in the prothrombinase active site. It should be noted that, although the prothrombinase behaves kinetically as if prothrombin approaches from solution, it appears from the most recent data (Giessen et al., 1991; see also "Treatment of Kinetic Data" under "Experimental Procedures") that membrane-bound prothrombin is rapidly "funneled" by the membrane surface to the active site of the enzyme. Recent results from our laboratory Lentz et al., 1991) provide evidence that prothrombin undergoes a conformational change on binding to acidic lipid membranes, and that the nature and extent of this change is different for PS-as compared to PG-containing membranes. This could account at least partly for the enhanced catalytic activity of PS-assembled prothrombinase as compared to PG-assembled prothrombinase. Other factors may also contribute, and much remains to be done to reveal them.