Full Time Course Kinetics of the Streptokinase-Plasminogen Activation Pathway*

Background: We previously proposed a mechanism for plasminogen (Pg) activation by streptokinase (SK). Results: We tested the mechanism using new discontinuous assays that resolved the full time courses of all the reaction species. Conclusion: Analysis of the results independently validates the proposed SK-Pg activation pathway. Significance: The assays can be applied to SK-Pg activation in other contexts. Our previously hypothesized mechanism for the pathway of plasminogen (Pg) activation by streptokinase (SK) was tested by the use of full time course kinetics. Three discontinuous chromogenic substrate initial rate assays were developed with different quenching conditions that enabled quantitation of the time courses of Pg depletion, plasmin (Pm) formation, transient formation of the conformationally activated SK·Pg* catalytic complex intermediate, formation of the SK·Pm catalytic complex, and the free concentrations of Pg, Pm, and SK. Analysis of full time courses of Pg activation by five concentrations of SK along with activity-based titrations of SK·Pg* and SK·Pm formation yielded rate and dissociation constants within 2-fold of those determined previously by continuous measurement of parabolic chromogenic substrate hydrolysis and fluorescence-based equilibrium binding. The results obtained with orthogonal assays provide independent support for a mechanism in which the conformationally activated SK·Pg* complex catalyzes an initial cycle of Pg proteolytic conversion to Pm that acts as a trigger. Higher affinity binding of the formed Pm to SK outcompetes Pg binding, terminating the trigger cycle and initiating the bullet catalytic cycle by the SK·Pm complex that converts the residual Pg into Pm. The new assays can be adapted to quantitate SK-Pg activation in the context of SK- or Pg-directed inhibitors, effectors, and SK allelic variants. To support this, we show for the first time with an assay specific for SK·Pg* that fibrinogen forms a ternary SK·Pg*·fibrinogen complex, which assembles with 200-fold enhanced SK·Pg* affinity, signaled by a perturbation of the SK·Pg* active site.

Streptokinase (SK) 2 from Streptococcus pyogenes is a human host-specific, potent virulence factor in group A streptococcal infections, estimated to account for 500,000 deaths/year globally (1). SK from Streptococcus equisimilis used in the present studies is a group C streptococcal protein responsible for the potentially fatal infection in horses called strangles (2). S. equisimilis SK is most homologous (ϳ90%) to phylogenetic cluster 1 SKs from S. pyogenes (3,4). SK subverts the fibrinolytic system by specific binding to the catalytic domain of plasminogen (Pg) and by induction of non-proteolytic activation of the Pg zymogen by the molecular sexuality mechanism (5)(6)(7)(8)(9). SK inserts its NH 2 -terminal Ile 1 -Ala 2 into the NH 2 -terminal binding cleft of the Pg catalytic domain such that Ile 1 forms a salt bridge with Pg Asp 194 (chymotrypsinogen numbering) that induces conformational expression of the substrate binding site and the oxyanion hole required for proteolytic activity (5)(6)(7)(8)(9). Although there is no crystallographic proof of this mechanism for SK, solution studies provide ample evidence for it, and for the conformational activation of prothrombin by the Staphylococcus aureus activator, staphylocoagulase, crystal structure evidence is available (10).
Conformational activation of Pg in formation of the SK⅐Pg* complex initiates the ultimate conversion of Pg into the proteolytically activated product, plasmin (Pm) by a unique mechanism. The activated SK⅐Pg* complex binds another Pg molecule and cleaves it to Pm. Pm binds SK with very high affinity (K D ϭ 11-19 pM (11)(12)(13)), and formation of the SK⅐Pm complex is accompanied by expression of an exosite that assists in binding of Pg as a substrate of the SK⅐Pm complex, enabling proteolytic Pg activation into Pm, whereas Pm itself does not activate Pg (11,14,15). There are two modes of SK-Pg/Pm binding, one in the catalytic mode in SK⅐Pg* and SK⅐Pm complexes and the second in the substrate mode in the SK⅐Pg*⅐Pg and SK⅐Pm⅐Pg product-forming ternary complexes. The crystal structure of SK bound to the catalytic domain of Pm (Pm (5)) shows that SK interacts with Pm through three independently folded ␤-grasp domains, ␣, ␤, and ␥, that are connected through two flexible linking sequences. In solution, SK has no stable domain structure (16), but when bound to the Pm catalytic domain, it organizes into a structure resembling a three-sided crater surrounding the Pm active site at the bottom (5).
Binding of Pg/Pm to SK in both the catalytic and substrate modes is enhanced by interactions with lysine-binding sites (LBS) of primarily the 1, 4, and 5 kringle domains of Pg/Pm that are inhibited by the lysine analog, 6-aminohexanoic acid (6-AHA) (11-13, 17, 18). Formation of the SK⅐Pg* and SK⅐Pm catalytic complexes is enhanced 12-14-fold in affinity by the COOH-terminal Lys 414 residue of SK binding to a Pg/Pm kringle that has not been definitively identified (13), whereas recent studies suggest that it may be kringle 4 (19). Binding of Pg in the substrate mode is mediated by interaction of Arg 253 , Lys 256 , and Lys 257 of the SK 250-loop in the ␤-domain with kringle 5 of the substrate Pg (20 -22). The dual modes of Pg as catalyst and substrate result in unique steady-state kinetics as a function of SK concentration (17,18). At low concentrations of SK, Pg binds preferentially in the catalytic mode to form SK⅐Pg*, which proteolytically activates free Pg to Pm at a rate that increases to a maximum as the SK concentration is increased. At higher SK concentrations, the rate of Pm formation decreases, approaching zero, reflecting depletion of free Pg to function as the substrate (17,18).
Continuous assays in the presence of a chromogenic substrate developed for steady-state kinetics of the SK-Pg activation mechanism allowed resolution of conformational formation of SK⅐Pg* from proteolytic Pm generation. Development of active site-fluorescently labeled Pg analogs enabled quantitation of the binding of SK to [Glu]Pg, [Lys]Pg, and Pm in the absence of proteolysis (11-13, 17, 18). These approaches demonstrated that (a) the affinity of SK for native [Glu]Pg is comparatively weak (K D ϳ130 nM) and LBS-independent, (b) [Lys]Pg binds SK more tightly (K D ϳ10 nM) and is partially LBS-dependent, and (c) Pm binds with very high affinity (K D ϭ 11-19 pM) and is partially LBS-dependent. On this basis, a unified mechanism for the SK-Pg activation pathway was postulated ( Fig. 1) (18). Rapid and reversible formation of the SK-[Lys]Pg* complex is the initiating event, followed by binding of substrate [Lys]Pg and its proteolytic activation to [Lys]Pm in the first catalytic cycle (Fig. 1, trigger). Because Pm binds SK in the catalytic mode with 500 -900-fold higher affinity than [Lys]Pg, it displaces SK from SK⅐Pg*, forming SK⅐Pm, which initiates the second catalytic cycle (Fig. 1, bullet). Depending on the SK and Pg concentrations, only a few turns of the triggering cycle are required to deplete SK, which shuts off the triggering cycle, and the tightly bound SK⅐Pm complex activates the residual Pg to Pm.
The goal of the present work was to evaluate this mechanism for the SK-[Lys]Pg activation pathway by full time course kinetics under conditions where the distribution of reaction intermediates and products is dictated by the SK concentration. New chromogenic substrate assays that are orthogonal to those used previously were developed that distinguish between the reactants, intermediates, and products, using three different quenching conditions designed on the basis of the previously determined properties of the reaction species (11,12,17,18). The results of quantitative characterization of the activation species over a 4 -50 nM range of SK concentration exhibited behavior that supported the mechanism (Fig. 1). We propose that the structural organization of SK during Pg binding triggers conformational Pg activation and expression of the Pg sub-strate binding site and serves to order the reactions of the initial catalytic cycle of Pg activation catalyzed by SK⅐Pg*. The subsequent differentially higher affinity of SK for Pm compared with Pg binding in the catalytic mode directs the formation of the second SK⅐Pm catalytic complex that propagates complete activation of free Pg to Pm. In addition, we show that the assays developed can be applied to investigate the mechanism through which fibrinogen regulates [Lys]Pg activation by SK.

Protein Purification and Characterization
Native SK was purified from outdated therapeutic SK (S. equisimilis strain H46A; Diapharma) by affinity chromatography on SulfoLink gel (Pierce) to which Pm was linked though its active site by N ␣ -((acetylthio)acetyl)-D-Phe-Phe-Arg-CH 2 Cl as described (11,12,23). Human [Glu]Pg carbohydrate form 2 was purified from normal plasma by published procedures (12,17,(23)(24)(25)(26)(27). Activation of 10 M [Glu]Pg to [Lys]Pm with 90 FIGURE 1. The previously hypothesized mechanism of Pg activation by SK. The first step of the trigger catalytic cycle is rapid binding of SK to the catalytic domain of Pg and conformationally induced activation of Pg in the SK⅐Pg* catalytic complex. The affinity of SK⅐Pg* formation is enhanced by LBS interactions mediated by the SK COOH-terminal Lys 414 residue with a Pg kringle (not shown). SK⅐Pg* binds a second Pg molecule in the substrate mode and proteolytically activates it to Pm. The substrate interaction is facilitated by interaction of Arg 253 , Lys 256 , and Lys 257 in the SK ␤-domain with kringle 5 of Pg bound in the substrate mode (not shown). Free Pm and free Pg compete for SK in the catalytic mode, where the formation of SK⅐Pm is highly preferred over SK⅐Pg* because of its 500 -900-fold higher affinity. This results in transition of the catalytic complexes from SK⅐Pg* to SK⅐Pm as the sole catalyst, terminating the trigger cycle and initiating the bullet cycle. The SK⅐Pm catalytic complex, similarly stabilized by LBS interactions mediated by Lys 414 (not depicted), binds free Pg as the substrate (aided by the LBS of kringle 5; not depicted) and proteolytically converts the remaining free Pg to Pm. The figure was reproduced in modified form from Ref. 18 with permission. units/ml urokinase (Calbiochem) was performed in 10 mM MES, 10 mM HEPES, 150 mM NaCl, 20 mM 6-AHA, and 1 mg/ml polyethylene glycol (PEG) 8000 at pH 7.4 and 25°C (11). For maximum stability, 10 -20 M Pm was stored in equal volumes of glycerol and 5 mM HEPES, 300 mM NaCl, 5 mM 6-AHA, 1 mg/ml PEG 8000, pH 7.4, quick frozen in a dry ice/2-propanol bath, and stored at Ϫ80°C. Dilutions for assays were typically ϳ1000-fold, and the carryover of ϳ2.5 M 6-AHA had no significant effect on the initial rates. Pm active site-blocked with D-Phe-Phe-Arg-CH 2 Cl (FFR-Pm) was prepared as described (11). Purified ␣ 2-antiplasmin (AP) was purchased from Molecular Innovations (Novi, MI). Protein concentrations were determined from the absorbance at 280 nm using the following absorption coefficients ((mg/ml) Ϫ1 cm Ϫ1 ) and molecular weights: [Glu]Pg, 1.69 and 92,000; [Lys]Pg, 1.69 and 84,000; [Lys]Pm, 1.9 and 84,000 (27)(28)(29); SK, 0.81 and 47,000 (30); AP, 0.70 and 70,000 (31,32); human fibrinogen (Fbg), 1.51 and 170,000 (protomer concentration) (33)(34)(35)(36).

Assays for Full Time Course Kinetics
Three assays were developed to quantitate SK-[Lys]Pg reaction species: SK Free , Pg Free , Pm Free , SK⅐Pg*, SK⅐Pm, and Pm Total (Pm ϩ SK⅐Pm).
Prior to starting the full time course assays at a given SK concentration, the activity of the Pm stock was determined from at least two initial rate measurements of 50 M VLK-pNA hydrolysis as described below and the protein concentration from the 280-nm absorbance. The Pm concentration was stable under the storage conditions described above at 81 Ϯ 2% (range) active for the duration of the studies.
Assay 1, Pm Total ϭ Pm Free ϩ SK⅐Pm-Discontinuous assays were performed by incubating [Lys]Pg and SK for various times and quenching the reaction by the addition of 200 nM FFR-Pm and 10 mM 6-AHA for 2 min to dissociate the SK⅐Pg* complex and to inhibit additional Pm formation, respectively. Control assays containing known concentrations of Pm or SK⅐Pm in the presence of 10 mM 6-AHA were inhibited 20 Ϯ 2% compared with assays without 6-AHA. The rates for this assay were corrected for the 6-AHA effect, which is most likely due to weak inhibition of the Pm catalytic site in a non-competitive (39) or, more recently, a competitive mechanism (40). FFR-Pm had no effect on the rates for Pm or SK⅐Pm. Prequenched reactions in which [Lys]Pg was preincubated with 200 nM FFR-Pm, 10 mM 6-AHA, and VLK-pNA and the assay initiated with SK resulted in Pm Total rates representing Ͻ0.5% of the Pm Total maximum rate. Such prequenching was used to define the rates at time 0 in the full time course experiments. Pm Total concentrations were calculated using a rearrangement of the Michaelis-Menten equation, where [E] o is the total Pm formed at each quench time, [S] o is the VLK-pNA concentration, and v obs is the measured initial velocity. The previously published kinetic parameters (K m ϭ 140 Ϯ 10 M and k cat ϭ 16.9 Ϯ 0.5 s Ϫ1 ) for Pm were used (11). The kinetic parameters for SK⅐Pm previously determined are K m ϭ 300 Ϯ 50 M and k cat ϭ 34 Ϯ 2 s Ϫ1 (11). At 50 M VLK-pNA, the calculated initial rate for SK⅐Pm is 9.2% greater than that of free Pm, which was within the experimental error of the parameters. For all Pm preparations used in the current studies, the active Pm concentration was calculated from the initial rate using the kinetic constants above that were obtained with Pm preparations that were active site-titrated with p-nitrophenyl-pЈ-guanidinobenzoate or fluorescein mono-p-guanidinobenzoate (11).

Assay 2, SK⅐Pm-SK-[Lys]
Pg reactions were quenched with 200 nM FFR-Pm and 100 nM AP for 30 s to dissociate the SK⅐[Lys]Pg* complex and to inactivate free Pm, respectively. This is possible because SK⅐Pm is resistant to inactivation by AP (41). FFR-Pm and AP at the concentrations used had no effect on the rates of VLK-pNA hydrolysis by SK⅐Pm. Control assays showed that 20 nM Pm was Ն97% inactivated by 50 nM AP after 30 s under these conditions. Prequenched reactions in which [Lys]Pg was preincubated with 200 nM FFR-Pm, 100 nM AP, and VLK-pNA and the assay was initiated with SK resulted in SK⅐Pm rates of VLK-pNA hydrolysis Ͻ0.5% of the SK⅐Pm maximum activity.
For determination of SK⅐Pm and Pm Free , additional results were necessary because of the high affinity of SK for Pm (K D ϭ 11-19 pM) (11)(12)(13). Titrations of 7.8 and 20 nM active Pm with SK were performed using the quenching conditions for Assay 2. The rates as a function of SK concentration were normalized to the maximum rate at saturating SK concentration and fit simultaneously by the quadratic binding equation to obtain the fitted maximum rates and the stoichiometric factor, with K D fixed at 12 pM. Pm preparations typically show stoichiometric factors of 1.3 mol of SK/mol of Pm, despite active site titration and high purity by SDS-PAGE (11). In the present case, a value of 1.42 Ϯ 0.03 mol/mol was obtained. This value was rather high for two reasons. First, assuming that the SK is fully active and that Pm was 81 Ϯ 2% active accounts for a stoichiometric factor of 1.23 mol of SK/mol of active Pm. Second, fitting of the two titrations simultaneously with the quadratic binding equation used the active concentrations of Pm, which increased the stoichiometric factor from 1.23 to the value of 1.42 given above. The purpose of performing the analysis in this way was to obtain a single factor to correct the rates in Assay 2, because these rates only measure active species. The rates obtained in Assay 2 at subsaturating SK concentrations were multiplied by 1.42 to adjust for the slope of the linear part of the titration with SK. Pm Free was calculated by subtracting the concentration of SK⅐Pm (Assay 2) from Pm Total (Assay 1).
Assay 3, SK⅐Pm ϩ SK⅐Pg*-This assay is based on the protection of SK⅐Pg* and SK⅐Pm from inactivation by AP (41,42). SK-[Lys]Pg reactions were quenched by the addition of 100 nM AP for 30 s to inactivate Pm Free . Prequenched reactions in which [Lys]Pg was preincubated with 100 nM AP and VLK-pNA and the assay was initiated with an excess of SK resulted in rates representing the maximum concentration of SK⅐Pg* formed.
To obtain a different measurement of SK⅐Pg*, 7.8 or 20 nM [Lys]Pg, 100 nM AP, and 50 M VLK-pNA were titrated with 0 -90 nM SK. These prequenched reactions inactivated any Pm Free , leaving SK⅐Pg* as the only active species. The continuously monitored initial rates of 50 M VLK-pNA hydrolysis were linear, indicating no significant Pg activation, which would have produced parabolic progress curves (13,17,18,20). The maximum rates at saturating levels of SK were normalized to the maximum Pg concentrations determined from the fit by the quadratic binding equation. The rates measured for Assay 2 (SK⅐Pm) were subtracted from those obtained in Assay 3 (SK⅐Pm ϩ SK⅐Pg*) to obtain the rate for SK⅐Pg*. SK⅐Pg* concentrations were calculated using new kinetic parameters for VLK-pNA extended to 10 mM substrate (4.3 ϫ K m ), K m ϭ 2.32 Ϯ 0.14 mM and k cat ϭ 40.8 Ϯ 0.8 s Ϫ1 .

Additional Corrections
For progress curves that converted all of the Pg to Pm, the averaged maximum rates from Assay 2 (SK⅐Pm) near the end of the reactions were normalized to the maximum rates from Assay 3 (SK⅐Pm ϩ SK⅐Pg*). This assumed that at the plateau of SK⅐Pm formation near the end of the full activation reactions, the concentration of the transiently formed SK⅐Pg* complex was completely depleted, such that the rates from Assays 2 and 3 would be equivalent, as shown by the results. The maximum correction was Յ7% for all of the full-activation experiments.

Fitting of the Mechanism for the SK-[Lys]Pg Activation Pathway
Five time course data sets at different SK concentrations, titrations of SK⅐Pg* formation at 7.8 and 20 nM Pg, and an SK titration of 1 nM SK⅐Pm formation in the presence of 10 mM 6-AHA were fit simultaneously by numerical integration and least squares fitting of the mechanism below with KinTek Explorer version 3.0 (43,44).
Pg binding to SK in the catalytic mode to form the conformationally activated SK⅐Pg* complex is represented as a single, rapid equilibrium step with dissociation constant K D ϭ k Ϫ1 /k 1 (Equation 2). The second step is binding of Pg as the substrate of the SK⅐Pg* catalytic complex (K S ϭ k Ϫ2 /k 2 ; Equation 3) to generate Pm with catalytic rate constant k Pg (Equation 4). This reaction is bimolecular with a rate constant of k Pg /K S because the Pg concentration of 20 nM used in the kinetic studies was apparently much lower than the K S , as shown by the inability of the mechanism to fit this parameter. Pm generated in Equation 4 binds tightly to SK in the catalytic mode even in the presence of 10 mM 6-AHA (Equation 5). The SK⅐Pm catalytic complex then recognizes free Pg as its substrate (KЈ S ϭ k Ϫ4 /k 4 ) (Equation 6) and converts it proteolytically into Pm (Equation 7), which is also a bimolecular reaction with rate constant k Pm /KЈ S , because the [Lys]Pg concentration used was much lower than the value of KЈ S of 270 nM determined previously (18).

Fitting Strategy
Initial constraints for fitting were made on the basis of the two cycles catalyzed first by SK⅐Pg* (Equations 2-4) and second by SK⅐Pm (Equations 5-7). The on-and off-rate constants for SK binding to Pg, k 1 and k Ϫ1 (Equation 2), were set to vary in a fixed ratio (a feature of the software), as were Pg substrate bind- OCTOBER 11, 2013 • VOLUME 288 • NUMBER 41 ing k 2 and k Ϫ2 , and the catalytic rate constant k Pg with all three varied in a different fixed ratio. The analogous SK⅐Pm k 3 and k Ϫ3 , the Pg substrate binding k 4 and k Ϫ4 , and k Pm were set to vary in a separate fixed ratio. All separate binding steps were initially assigned 1 nM Ϫ1 s Ϫ1 on-rate constants. Initial parameters for the fit were those determined here. Because few values of rate or affinity are available for Pg substrate binding to SK⅐Pg* and SK⅐Pm, an off-rate constant to yield a KЈ S value of 270 nM previously determined was used (18). Later in the analysis, an off-rate constant for Pg substrate binding to SK⅐Pg* was identified by the lowest dissociation constant (2 M) that did not alter detectably the fit of the most sensitive progress curves, and the parameters for this step were fixed at this value. In the final analysis, the constants for Pg substrate binding to SK⅐Pm and the bimolecular rate constant (k Pm /KЈ S ) were constrained as a group to vary in a constant ratio. All other constants were fitted (see Table 1).

SK⅐Pg*⅐Fbg Ternary Complex Experiments
Prequenching of mixtures of 5 nM [Lys]Pg with 100 nM AP and 50 M VLK-pNA in the absence and presence of fixed concentrations of Fbg was followed by preincubation for 2 min before initiation of the assay by increasing SK concentrations. For a titration of 1 nM [Lys] at a fixed SK concentration of 60 nM, mixtures of [Lys]Pg, Fbg, and VLK-pNA were prequenched with AP in the same way except that the Fbg concentration was varied. The results were analyzed by non-linear least squares fitting by an iterative model using SCIENTIST software. The equations for the dissociation constants K A , K B , and K C , the two k cat /K m values for the two active product-forming complexes (SK⅐Pg* and SK⅐Pg*⅐Fbg), and the mass balance equations were simultaneously solved by the software. K D, calc. was calculated from detailed balance, K D, calc. ϭ K A ϫ K B /K C . K C was fixed at its determined value. 3

Assays for SK-[Lys]Pg Full Time Course Kinetics-Chromo-
genic substrate (VLK-pNA) initial rate assays were developed to selectively measure the concentrations of plasmin, Pm Total ϭ Pm Free ϩ SK⅐Pm (Assay 1), SK⅐Pm (Assay 2), and SK⅐Pm ϩ SK⅐Pg* (Assay 3), based on the previously determined properties of these SK-[Lys]Pg activation intermediates and products (11,12,17,18). Different combinations of 200 nM active siteblocked Pm, prepared with D-Phe-Phe-Arg-CH 2 Cl (FFR-Pm), a 10 mM concentration of the Pg/Pm kringle-binding lysine analog 6-AHA, or 100 nM AP, the rapid and irreversible physiological serpin inhibitor of Pm, were used to quench the reactions.
For Assay 1, quenching with FFR-Pm and 6-AHA dissociated the transiently formed, conformationally activated SK⅐Pg* complex and inhibited Pm formation. This assay was based on a 10 -20-fold weakening of the 10 nM K D of SK⅐Pg* formation, in which Pg is bound in the catalytic mode to SK, by 10 mM 6-AHA blocking the LBS of a Pg kringle. This prevents the affinityenhancing interaction with the COOH-terminal Lys 414 residue of SK (13,17,18). FFR-Pm binds in the catalytic mode to SK with a K D value of 11-19 pM, 500 -900-fold tighter than SK⅐Pg* (11)(12)(13)17). Binding of SK to Pm is similarly weakened by 10 mM 6-AHA blocking the Lys 414 -kringle interaction, but Pm still maintains an LBS-independent 0.2-0.3 nM K D value for SK (11)(12)(13). The net effect of quenching with 6-AHA and FFR-Pm is dissociation of SK⅐Pg* and sequestering of free SK in the SK⅐FFR-Pm inactive complex. One consequence, however, is that the use of 10 mM 6-AHA as a quenching reagent only in Assay 1 results in 10 -20-fold weakening of SK binding to Pm. Although this might affect the distribution of Pm Free and SK⅐Pm measured in Assay 1, it does not affect the concentration of Pm Total . Previous studies show that the off-rate constant for displacement of Pm by FFR-Pm is ϳ0.0008 s Ϫ1 , slow enough for the dissociation of Pm to be negligible in the 2-min quench time (45). In any case, only Pm Total appears in the conservation equations used to calculate SK Free , Pg Free , and Pm Free . This might also affect the reaction pathway to a small extent.
Assay 2 measures the SK⅐Pm complex by quenching with 200 nM FFR-Pm and incubation with 100 nM AP for 30 s before initiating the assay by substrate addition. The SK⅐Pg* complex is dissociated by FFR-Pm due to the much higher affinity of SK for FFR-Pm compared with SK⅐Pg*, as described above. Pm (10 nM) was Ն99% inactivated by 100 nM AP, whereas SK⅐Pm is protected from inactivation by AP (41), leaving SK⅐Pm the only active species.
An additional calibration was required for determination of the concentrations of SK⅐Pm and Pm Free . Titrations of 7.8 and 20 nM active Pm with SK were performed with quenching as described for Assay 2 ( Fig. 2A). The titrations were normalized to the maximum rates at saturating SK and fit by the quadratic binding equation with the stoichiometric factor and fitted maximum rate as parameters and the value of KЈ D fixed at 12 pM (11). Stoichiometric factors for SK binding to Pm are often as high as 1.3 mol of SK/mol of Pm, although Pm preparations were pure by SDS-PAGE and active site-titrations were performed (11). In the present case, a value of 1.42 Ϯ 0.03 mol of SK/mol of active Pm was obtained ( Fig. 2A). This value incorporates the 81 Ϯ 2% activity of the Pm preparation in the stoichiometric factor and the use of the active Pm concentration in the 7.8 and 20 nM acceptor concentrations for fitting the titrations with SK. The analysis was done in this manner to obtain a single factor based on only the active concentrations of Pm and SK⅐Pm to correct the rates in Assay 2. The rates obtained with Assay 2 at subsaturating SK concentrations were multiplied by 1.42 to adjust the slope of the linear part of the titrations, and the concentration of Pm Free was obtained by subtracting SK⅐Pm (Assay 2) from Pm Total (Assay 1). Titrations with SK using the same preparation of Pm were done in the presence of 10 mM 6-AHA and quenched with AP (Fig. 2B). Titration of 1 nM Pm with SK gave a KЈ D value of 0.33 Ϯ 0.14 nM, corresponding to a ϳ25-fold lower affinity than the mean value of 13 pM in the absence of 6-AHA (11)(12)(13).
Assay 3 measures the sum of SK⅐Pm and SK⅐Pg* concentrations by quenching with 100 nM AP, because both complexes are protected from inactivation by AP, whereas Pm Free is inactivated (41,42). Titrations of prequenched mixtures of 7.8 or 20 nM [Lys]Pg with 100 nM AP and 50 M VLK-pNA were initiated by the addition of increasing concentrations of SK (Fig. 2C). The titrations were fit simultaneously by the quadratic binding equation to the data normalized to the total Pg concentration obtained from the fit because it was not possible to determine the maximum independently from the data as done for SK⅐Pm. Fitting of the normalized data in this way did not change the K D value or the relative error in the fitted parameters, which were SK⅐Pg* maximum concentrations of 7.8 Ϯ 0.7 nM, 20 Ϯ 1 nM, and a K D value of 9 Ϯ 2 nM (Fig. 2C). The K D value was indistinguishable from K D values of 9 -10 nM determined previously by competitive equilibrium binding of native and fluorescently labeled [Lys]Pg (13,17). The concentration of SK⅐Pg* was determined from the rate obtained in Assay 3 using new kinetic parameters determined for VLK-pNA. The results supported the capacity of Assay 3 to quantitate SK⅐Pg*, albeit with significant experimental error due to its 6.3-fold lower chromogenic substrate activity (k cat /K m ) compared with SK⅐Pm.
Assay Stability and Reproducibility-The stability and reproducibility of the assays were investigated by incubation of 10 nM Pm or SK⅐Pm with the quenching components as a function of time (Fig. 3, A and B). Pm and SK⅐Pm were each incubated with FFR-Pm, 6-AHA, AP, or 6-AHA and a combination of AP, FFR-Pm, and 6-AHA for up to 60 min before the chromogenic substrate assay. The concentrations of quenching components were 100 nM FFR-Pm, 10 mM 6-AHA, and 50 nM AP. Assays containing 10 mM 6-AHA were inhibited 20 Ϯ 2%, probably due to inhibition of the Pm active site at the low concentration of 50 M VLK-pNA (39,40), for which the rates were corrected. The assays showed reasonable reproducibility to within 12-14% of the means (Fig. 3, A and B) for all of the results over the 60-min time courses, which were 3-fold longer than the SK-[Lys]Pg full activation time.    Five full time course experiments were fit globally by combined numerical integration and least squares fitting of the mechanism (Equations 2-7) (43,44). Additional data included the SK⅐Pm activity titration in the presence of 6-AHA (Fig. 2B) and two SK⅐Pg* activity titrations (Fig. 2C). A representative full time course experiment at 11.7 nM SK and 20 nM [Lys]Pg is shown in Fig. 4A along with the global fit for the concentrations of six deconvoluted activation species: SK Free , Pg Free , Pm Free , SK⅐Pg*, SK⅐Pm, and Pm Total (Fig. 4, B-G). At time 0, the measured values of the concentrations of SK Free , Pg Free , and SK⅐Pg* were 5.0, 13.3, and 6.6 nM, respectively, from which a K D value of 10 nM was calculated, in reasonable agreement with the K D (6 nM) from the global analysis. There were obvious lags in the time courses of Pg Free , Pm Free , SK⅐Pm, and Pm Total , which were accounted for by the sequential generation of Pm for all of the Pm species and the faster release of Pg Free from total depletion of SK Free and SK⅐Pg*. As can be seen from these reactions at subsaturating SK concentration with respect to that of Pg, the activation process catalyzed by SK⅐Pg* ceases when this complex is fully depleted at ϳ300 s and one SK equivalent of SK⅐Pm has been formed, which remains constant, whereas Pm Free and Pm Total approach completion. The concentration of Pm Total at the end of the reactions (19.6 nM; mean of 5 points at 600 -1080 s) was distributed as 43% Pm Free and 57% SK⅐Pm, where the latter value corresponded to the initial 58% ratio of [SK] o to [Pg] o . The calculated K D value for SK binding to Pm at the end of the reactions was 310 pM, in good agreement with the global fit value of 290 pM. This substantiated the assumption that minimal dissociation of SK⅐Pm by FFR-Pm occurred in the 2-min quenching time for Assay 1 because the off-rate constant is ϳ0.0008 s Ϫ1 (45).
The global fit of the five full time course and three titration data sets (715 assays) is shown in Fig. 5, A-H, with the parameters listed in Table 1. The results show how the pathway of Pm formation is initially accelerated at substoichiometric SK concentrations (Fig. 5, A and B) and subsequently inhibited at higher SK concentration (Fig. 5, D and E). At subsaturating SK, one equivalent of SK⅐Pm is formed and is stable after that, and the activation reaction continues until all of the Pg is converted to Pm Free and SK⅐Pm (Fig. 5, A and B). At equimolar (20 nM) SK and Pg concentrations, generation of SK⅐Pm and Pm Total coalesces, and this is maintained at higher SK concentrations, although the rate of Pm Total formation decreases (Fig. 5, C-E). Over the high SK concentration range, SK⅐Pg* increases at time 0 until all Pg is bound in SK⅐Pg*, and Pg Free is reduced to an undetectably low concentration (Fig. 5E). SK⅐Pm continues to be formed, whereas the concentration of Pm Free is undetectably low, until all of the remaining SK⅐Pg* is converted into SK⅐Pm (Fig. 5E) (Fig. 6). This is distinct from the use of Assay 3 in prequenched reactions from which SK⅐Pg* was measured and Pm formation was blocked. Quenching with only AP inactivated the generated Pm Free and yielded the sum of the catalytic complexes weighted by their contribution to VLK-pNA hydrolysis. The resulting curve at 5 nM [Lys]Pg and 10 nM SK exhibited a small lag as SK⅐Pg* was depleted, approaching a final plateau as SK⅐Pm became the sole catalyst (Fig. 6A). At higher SK concentration (40 nM), the rate of transition was slower and reached the same end point. The addition of the two curves in Fig. 6 to the experimental data set required minor changes in the output equations to account for the amplitude of the biphasic reactions, which arose from the disappearance of SK⅐Pg* and appearance of SK⅐Pm. Two amplitude factors were added to give f1 ϫ [SK⅐Pg*] ϩ f2 ϫ [SK⅐Pm]. Amendment of the data set and the mechanism by the addition of the amplitude factors had no effect on the fitted parameters or experimental error compared with those obtained from the global analysis. The fitted amplitude factors, with all other parameters in Table  1 fixed, correspond to the rates of VLK-pNA hydrolysis by SK⅐Pg* (f1) and SK⅐Pm (f2), which were 0.828 and 4.13 nM s Ϫ1 , respectively. The ratio of the rates was 5 Ϯ 6 (2 ϫ S.E.), with the large error due to that for the SK⅐Pg* complex. The ratio was indistinguishable from the value of 5.6 calculated from the amplitudes, chromogenic substrate concentration, and the kinetic parameters for SK⅐Pg* and SK⅐Pm using the Michaelis-Menten equation.
Simulation of the mechanism over a 100-fold range of SK concentration starting at equimolar [Lys]Pg (5 nM) showed relatively rapid transition of SK⅐Pg* to SK⅐Pm with a reduced final maximum amplitude due to ϳ20% of the Pg being converted into Pm Free that was inactivated by AP quenching and the remaining ϳ80% SK⅐Pm. The transition was slower at 50 nM SK and exceedingly slow at 500 nM, where the rates representing SK⅐Pg* depletion and SK⅐Pm formation were linear. This behavior is explained by the sequestering of Pg Free in SK⅐Pg* by excess SK. This sequestering inhibits both catalytic cycles by depleting Pg Free needed to bind to the catalytic complexes in the substrate mode.

Mechanism of the Effector Function of Fibrinogen on SK-[Lys]
Pg Activation-The SK-Pg activation mechanism is regulated by fibrinogen and fibrin through a SK⅐Pg*⅐fibrin(ogen) ternary complex (46 -50). To demonstrate further the utility of the assays developed, Assay 3 was used in the prequenching design with AP to examine binding of Fbg to the SK⅐Pg* complex. The results show titrations with SK of 5 nM [Lys]Pg measured by the initial velocity of 50 M VLK-pNA hydrolysis by SK⅐Pg* in the absence and presence of four fixed concentrations of Fbg (Fig. 7A) and a titration with Fbg of 1 nM [Lys]Pg and SK fixed at 60 nM (Fig. 7B). The titrations with SK produced a family of hyperbolic curves with increasing amplitudes up to 1-2 M Fbg (Fig. 7A), whereas the Fbg titration showed an apparently tighter interaction. The results (Fig. 7, A and B) were simultaneously fitted by a minimal random addition ternary complex mechanism (Fig. 7C). K A , K B , and the bimolecular rate constants (k cat /K m ) for the active SK⅐Pg* binary complex and the SK⅐Pg*⅐Fbg ternary complex for VLK-pNA hydrolysis were fit-  Table 1. The concentrations of reaction species were measured or calculated and were analyzed as described under "Experimental Procedures."

TABLE 1 Summary of kinetic and binding constants from global fitting of SK-[Lys]Pg full time courses and activity titrations for SK⅐Pg* and SK⅐Pm
Listed are the individual reaction steps and corresponding equations under "Experimental Procedures." Parameters are listed with their global fit values. Error in the parameters was propagated and represents 2 ϫ S.E. F represents parameters that were fixed at the listed values. Constraint C1 is indicated for parameters that were grouped and varied in a fixed ratio. Fitting was performed as described under "Experimental Procedures."

Reaction step Parameters Global fit values Constraints
Streptokinase-Plasminogen Activation Pathway OCTOBER 11, 2013 • VOLUME 288 • NUMBER 41 ted parameters (Table 2). K C , the dissociation constant for Pg binding to Fbg, was fixed at its determined value of 19 M for the analysis. 3 K D, calc. , the dissociation constant for SK binding to the Pg⅐Fbg binary complex, forming the ternary SK⅐Pg*⅐Fbg complex, was calculated from detailed balance. The results show that the affinity of SK⅐Pg* for Fbg is increased 200-fold over that of Pg binding to Fbg, and likewise, the affinity of SK binding to the Pg⅐Fbg complex to form the ternary complex is increased 200-fold over SK binding to Pg in the absence of Fbg (Table 2). We also compared the kinetic parameters for VLK-pNA hydrolysis by SK⅐Pg* with those for SK⅐Pg*⅐Fbg formed at saturating SK (500 nM) and Fbg (2 M) concentrations (Table 2) (data not shown). K m was decreased 2.3-fold, and k cat increased 1.4-fold. k cat /K m from these parameters increased 3.2-fold in the ternary complex, the same as the 3.1-fold determined under bimolecular conditions (Fig. 7C and Table 2). This demonstrated that there was a significant increase in the specificity constant due to the presence of Fbg in the ternary complex, signaling a perturbation in the conformationally activated SK⅐Pg* catalytic site accompanying Fbg binding.
Although it has been known for a long time that an SK⅐Pg*⅐Fbg ternary complex is formed, this conclusion was inferred from descriptive studies, including native gel electrophoresis (50), kinetic studies that were not quantitated (49), or qualitative studies using bacteria (48,51). A few kinetic studies have been done that showed Fbg stimulation of [Lys]Pg activation by SK of 2-or 5.6-fold, which were attributed to other aspects of the SK-Pg mechanism or to entirely different mechanisms (46,47). It should be noted that we eliminated various sequential mechanisms that included formation of a ternary SK⅐Pg*⅐Fbg complex, all of which failed to fit the results. None have addressed the mechanism presented here quantitatively, which establishes for the first time the random addition ternary complex mechanism that greatly facilitates assembly of the [Lys]Pg binding to Fbg was fixed at 19,000 nM based on unpublished results. 3 Fitted parameters K A and K B (nM) and the bimolecular rate constants for VLK-pNA substrate hydrolysis (k cat /K m in M Ϫ1 s Ϫ1 ) are shown for SK⅐Pg* and SK⅐Pg*⅐Fbg. VLK-pNA substrate is shown as S in the green oval, and the product (pNA) is the P in the orange oval. K D, calc. (nM) was calculated using detailed balance. Assays were performed and analyzed as described under "Experimental Procedures." SK⅐Pg*⅐Fbg complex and has broad significance in streptococcal pathogenesis.

DISCUSSION
The results obtained by new assays that are orthogonal to those used previously provide independent support for the validity of the mechanism of the SK-initiated [Lys]Pg activation pathway previously proposed (17,18). The previous studies were based on continuous steady-state kinetics in the presence of a chromogenic substrate and on competitive equilibrium binding experiments with the native proteins using active sitefluorescein-labeled Pg/Pm analogs as binding probes. Importantly, the kinetic and binding parameters from the global fit of the full time courses and activity-based binding experiments are within 2-fold of those determined previously (11,12,17,18). The bimolecular rate constants for Pm generation by the SK⅐Pg* and SK⅐Pm catalytic complexes previously determined were 0.5 Ϯ 0.05 and 1.16 Ϯ 0.04 M Ϫ1 s Ϫ1 , respectively, whereas here they were 1.17 Ϯ 0.17 and 2.4 Ϯ 0.4 M Ϫ1 s Ϫ1 , respectively. The reason for this relatively small difference is not known, but it may be due to differences in the assumptions made here for the discontinuous assays and those in the previous studies from analysis of continuous parabolic assays in the presence of chromogenic substrate.
Specific molecular events are thought to dictate the sequential pathway of [Lys]Pg activation by SK. The trigger catalytic cycle depends on (a) conformational rearrangement of the disordered domain structure of SK in solution into the ordered structure it forms on binding of Pg and plasmin seen in the SK⅐Pm crystal structure (5, 16); (b) induced conformational activation of Pg by SK NH 2 -terminal insertion (7-9); (c) engagement of the LBS of a Pg kringle, probably kringle 4, by SK Lys 414 that increases affinity of SK⅐Pg* formation (13,45); (d) expression of the exosite on SK⅐Pg* that mediates Pg substrate binding, as shown for Pm (11); and (e) engagement of LBS interactions with kringle 5 mediated by Arg 253 , Lys 256 , and Lys 257 in the SK ␤-domain that enhance Pg substrate binding (20). Although required, the order in which events c, d, and e occur has not been completely defined.
The second, bullet cycle depends on intermolecular cleavage of Pg bound to SK⅐Pg* in the substrate mode to form Pm in the trigger cycle. Free Pm and free Pg bind competitively to SK in the catalytic mode. Pm has the advantage over Pg in competitive catalytic complex formation, binding SK with 500 -900fold higher affinity than [Lys]Pg, which results in transition of the catalytic complexes from SK⅐Pg* to SK⅐Pm as the reactions proceed. This transition is important because it is at the junction of the catalytic cycles. Because Assay 1 contained 10 mM 6-AHA, the affinity difference between [Lys]Pg and Pm for SK was reduced to ϳ30-fold, nevertheless sufficient to support transition to the SK⅐Pm complex. Once sufficient Pm is produced to bind all of the SK, the trigger cycle stops, and SK⅐Pm is the only catalytic complex. SK⅐Pm binding of Pg as substrate is also thought to be facilitated by the same residues in the ␤-domain used by SK⅐Pg* (20) and produces Pm at a ϳ2-fold faster bimolecular rate constant than SK⅐Pg*, ultimately converting all of the remaining Pg to Pm. The off-rate constant for dissociation of the SK⅐Pm complex is ϳ0.0008 s Ϫ1 (t1 ⁄ 2 ϳ900 s (45)), suggesting that the SK⅐Pm complex may not dissociate significantly during the full time course of the bullet catalytic cycle.
Rapid reaction kinetics of SK binding to active site-labeled Pm demonstrate a three-step mechanism of rapid encounter complex formation followed by two sequential affinity-enhancing conformational changes (45). Comparison of the effects of kringle ligands and a SK Lys 414 deletion mutant identified the encounter complex as the primary source of the LBS dependence of SK⅐Pm catalytic complex formation, whereas the two conformational changes are less affected. The first step in the binding pathway requires on-rate constants of Ն1 nM Ϫ1 s Ϫ1 , indicating near-diffusion controlled encounter complex formation (45). Remarkably, the fitted rate constant for SK⅐Pm formation determined here was 1.2 nM Ϫ1 s Ϫ1 (Table 1). This suggests that the initial step in the SK⅐Pm catalytic cycle is fast compared with the fitted value of 0.1 nM Ϫ1 s Ϫ1 for SK⅐Pg*, and the engagement of Lys 414 with a Pm kringle occurs before the tightening conformational changes of SK⅐Pm.
Concerning the role of SK as a virulence factor in streptococcal infections, generation of Pm is critical for dissemination of the bacteria through tissues by directly cleaving extracellular matrix proteins, indirectly activating metalloproteinases, and dissolving fibrin barriers established in the initial host response to infection (52)(53)(54)(55). The SK-Pg activation mechanism is regulated by fibrinogen and fibrin through a SK⅐Pg⅐fibrin(ogen) ternary complex and by Pg-binding group A streptococcal M-like protein (PAM) that is covalently bound to the bacterial cell wall (46 -50, 53, 54, 56).
PAM mediates Pg and Pm binding through two type a, continuous repeat sequences near the NH 2 terminus of its ␣-helical, dimeric coiled-coil structure, which extends into solution about 500 Å from the LPXTG motif near the COOH terminus Listed are the fitted dissociation constants for the ternary complex mechanism (Fig.7C) (designated T under "Source") K A and K B were fitted, the dissociation constant K C was fixed (F under "Constraint") at its determined value, and K D, calc. was calculated from detailed balance. The fitted bimolecular rate constants for VLK-pNA hydrolysis by the SK⅐Pg* and SK⅐Pg*⅐Fbg complexes in the ternary complex mechanism are also listed. The kinetic parameters (K m , k cat , and k cat /K m ) determined independently from initial velocities of VLK-pNA substrate hydrolysis as a function of substrate concentration are listed as v obs versus ͓S͔ o (up to 10 mM) for the SK⅐Pg* complex containing 5 nM ͓Lys͔Pg at saturating SK concentration (500 nM). The SK⅐Pg*⅐Fbg complex at saturating SK (500 nM) and Fbg (2 M) are also listed (data not shown). Error in the parameters was propagated and represents 2 ϫ S.D. Experiments were performed and analyzed as described under "Experimental Procedures" and "Results." that links PAM to the cell wall (57)(58)(59). Direct binding of Pm or SK⅐Pg*-generated Pm bound to PAM results in coating of the bacterial surface by proteolytically active PAM⅐Pm complexes that are resistant to inactivation by AP, allowing the bacteria to spread rapidly through fibrin barriers and the extracellular matrix like proteolytic chain saws. Other members of the M protein superfamily lack the Pm-binding motifs, but a subset of them, including M1, bind Fbg specifically through the b-type repeats (53,54,57,58,60). This begins what is called the indirect pathway of Pm generation through formation of the SK⅐Pg*⅐Fbg ternary complex (48,61), which is resistant to inactivation by AP and, we now know, intrinsically assembles with 200-fold higher, subnanomolar affinity compared with SK⅐Pg*. Whether the Pm generated by the SK⅐Pg*⅐Fbg⅐M-protein quaternary complex remains bound through the picomolar affinity of formation of the SK⅐Pm catalytic complex and many other unanswered questions will require much further investigation. The assays developed here may be similarly extended to investigate the mechanisms of allelic variants of SK (3,4,62) and other pathogenic effectors of SK-Pg activation.