Analysis of the Kinetics of Prothrombin Activation and Evidence That Two Equilibrating Forms of Prothrombinase Are Involved in the Process*

Prothrombinase cleaves prothrombin at Arg271 and Arg320 to produce thrombin. The kinetics of cleavage of five recombinant prothrombins were measured: wild-type prothrombin (WT-II), R155A/R284A/R271A prothrombin (rMZ-II), R155A/R284A/R320A prothrombin (rP2-II), S525C prothrombin labeled with fluorescein (WT-II-F*), and R155A/R284A/R271A/S525C prothrombin labeled with fluorescein (rMZ-II-F*). rMZ-II and rP2-II are cleaved only at Arg320 and Arg271, respectively, to yield the intermediates meizothrombin and prethrombin-2, respectively. WT-II-F* and rMZ-II-F* were labeled at Cys525 with fluorescein; cleavage was monitored by enhanced fluorescence. Activation kinetics of WT-II, rMZ-II, and rP2-II indicated that the catalytic efficiency of cleavage at Arg320 was increased by 30,000-fold by the cofactor factor Va, as was the conversion of prothrombin to thrombin. However, factor Va increased cleavage at Arg271 only by 34-fold. Although WT-II competitively inhibited cleavage of WT-II-F*, rMZ-II or rP2-II did not inhibit completely even at saturating concentrations. However, rMZ-II and rP2-II together inhibited WT-II-F* cleavage competitively. Both WT-II and rMZ-II competitively inhibited rMZ-II-F* cleavage, whereas rP2-II did not. A model of prothrombin activation that includes two equilibrating forms of prothrombinase, each recognizing one of the cleavage sites, is quantitatively consistent with all of the experimental observations. Therefore, we conclude that the kinetics of prothrombin activation can be described by a “ping-pong”-like mechanism.

The coagulation cascade culminates in the activation of prothrombin to thrombin. This reaction is carried out by the multicomponent complex prothrombinase, which comprises the serine protease factor Xa, the activated protein cofactor factor Va, calcium ions, and an appropriate cell membrane or phospholipid surface (1)(2)(3)(4)(5). Factor Xa alone can slowly generate thrombin by an extremely inefficient reaction; however, the rate of this reaction is enhanced by 5 orders of magnitude by incorporation of factor Va, Ca 2ϩ , and the procoagulant surface (5).
Two bond cleavages are required for thrombin formation, one at Arg 271 and one at Arg 320 . Therefore, two activation path-ways are possible during prothrombin activation, yielding the intermediates fragment 1.2:prethrombin-2 (F1.2:Pre2) 1 and meizothrombin. Cleavage at Arg 271 first produces the intermediate F1.2:Pre2, whereas cleavage at Arg 320 first produces the intermediate meizothrombin. In the absence of factor Va, the accumulation of the intermediate F1.2:Pre2 is observed (6 -8).
In the presence of fully assembled prothrombinase, however, accumulation of the intermediate meizothrombin is observed (9), suggesting that factor Va directs the reaction toward the meizothrombin pathway.
The first objective of this study was to determine the effects of factor Va on cleavage at Arg 271 and Arg 320 in prothrombin. Three recombinant prothrombin derivatives were prepared for this purpose (see Fig. 1). These were WT-II, which can be cleaved at both Arg 271 and Arg 320 to produce thrombin (10); the derivative rMZ-II, which can be cleaved only at Arg 320 to produce the intermediate meizothrombin (10), and the derivative rP2-II, which can be cleaved only at Arg 271 to produce the intermediate F1.2:Pre2. These mutants, in addition to meizothrombin and F1.2:Pre2, allowed us to isolate each individual step of the overall reaction and to determine the catalytic efficiency of all bond cleavages involved in prothrombin activation.
Two additional recombinant prothrombin derivatives were used to carry out competition assays between each of the three recombinant prothrombin derivatives (see Fig. 1). The derivative WT-II-F* is an active-site mutant of prothrombin in which the active-site serine was mutated to cysteine, which was subsequently labeled with fluorescein (11). The derivative rMZ-II-F* is the rMZ-II derivative with the active-site serine-tocysteine mutation labeled with fluorescein. Both of these mutants displayed an increase in fluorescence intensity upon activation and therefore allowed us to monitor their activation specifically in the presence of WT-II, rMZ-II, and rP2-II as competitors. As will be shown, the competition studies suggest that prothrombinase exists in two equilibrating forms, one catalyzing cleavage at Arg 271 and the other at Arg 320 . icillin/streptomycin/Fungizone mixture, and reduced glutathione were obtained from Invitrogen. Baby hamster kidney cells and the mammalian expression vector pNUT (12) were graciously provided by Dr. Ross MacGillivray (University of British Columbia). Methotrexate (David Bull Laboratories, Vaudreuil, Quebec, Canada) and vitamin K (Sabex, Boucherville, Quebec) were purchased at Kingston General Hospital. For enzyme-linked immunosorbent assay, horseradish peroxidase-conjugated sheep anti-human prothrombin was from Affinity Biologicals (Ancaster, Ontario). Benzamidine, Russell's viper venom, DEAE-cellulose, benzamidine-Sepharose, phosphatidyl-L-serine, phosphatidyl-Lcholine, XAD-2 resin, and Sephadex G-25 were obtained from Sigma. Q-Sepharose Fast Flow anion-exchange resin, Cibacron blue-Sepharose, and CNBr-activated Sepharose 4B were from Amersham Biosciences (Uppsala, Sweden). 5-Iodoacetamidofluorescein was purchased from Molecular Probes, Inc. (Eugene, OR). IODO-BEADS were obtained from Pierce. 125 I was obtained from ICN Pharmaceuticals Ltd. (Montreal, Canada). Echis (carinatus) pyramidium venom was purchased from Latoxan (Rosans, France). Purified ecarin was prepared from the venom by a modification of the procedure described previously (13). Briefly, ϳ70 mg of lyophilized venom was dissolved in 20 ml of 0.05 M Tris-HCl (pH 8.0). The solution was clarified by centrifugation and treated with 2 mM diisopropyl fluorophosphate for 1 h at room temperature, followed by incubation with 5 M Phe-Phe-Arg-chloromethyl ketone for 1 h at room temperature. The sample was then applied to a 20-ml DEAE-cellulose column equilibrated with 0.05 M Tris-HCl (pH 8.0). The column was washed with the equilibration buffer until the absorbance of the eluent was zero at 280 nm. Ecarin was eluted with a NaCl gradient (0.05 M Tris-HCl and 0 M NaCl to 0.05 M Tris and 0.25 M NaCl). Fractions were assayed for ecarin activity (13) in the presence and absence of calcium ion. Fractions containing ecarin-like activity (both calcium ion-dependent and -independent) were pooled and loaded onto a 2-ml Cibacron blue-Sepharose Column. The column was washed with 0.05 M Tris-HCl and 0.1 M NaCl (pH 8.0) until the absorbance of the eluent was zero at 280 nm. Calcium ion-dependent ecarin-like activity was found in the flow-through fractions. Calcium ion-independent ecarin was eluted with 0.05 M Tris-HCl and 0.25 M NaCl (pH 8.0). Ecarin-containing fractions were assayed for activity in the presence and absence of calcium ion. Calcium ion-dependent and -independent fractions were pooled separately and ammonium sulfate-precipitated (80% saturation). Ecarin was stored in 0.05 M Tris-HCl (pH 8.0) and 0.02% sodium azide at 4°C. The fluorescent inhibitor dansylarginine-N-(3-ethyl-1,5-pentanediyl)amide (DAPA) was prepared as described previously (14). Phospholipid vesicles (75% PC and 25% PS (PCPS)) were prepared as described by Bloom et al. (15). Human prothrombin (16), thrombin (17), factor Xa (16), and factor Va (18) were prepared as described previously. F1.2:Pre2 was made by incubating human prothrombin (10 M) with an equal volume of factor Xa-Sepharose in the presence of 10 M DAPA at room temperature for 3 h. The sample was filtered through 0.2-m filters and subsequently incubated with 0.1 volume of benzamidine-Sepharose at room temperature for 10 min to remove traces of thrombin and factor Xa, followed by 0.2-m filtration. Meizothrombin was formed by treating prothrombin with purified Ca 2ϩ -independent ecarin in 0.02 M Tris, 0.15 M NaCl, and 5 mM CaCl 2 in the presence of 5 M DAPA. F1.2:Pre2 and meizothrombin were freshly prepared for each experiment and were used within 10 min. Factor Xa-Sepharose and 125 I-labeled human prothrombin were prepared as described previously (19).

Methods
DNA Construction and Mutagenesis-The cDNAs for rMZ-II (10) and for WT-II-F* (11) had been prepared previously in our laboratory. The cDNA for rMZ-II-F* was prepared as described previously for WT-II-F*, except that the starting template was that for rMZ-II instead of WT-II, and the DNA polymerase used was Pfx. For the production of the rP2-II cDNA, pBluescript SK ϩ containing full-length rMZ-II cDNA was digested with HindIII, SacI, and PstI. The HindIII/SacI fragment spanned nucleotides 307-1076 and was excised to facilitate the amino acid substitution of Ala 271 with Arg 271 and the insertion of a BsiWI restriction site. The primers used were 5Ј-GAAGGGCGTACGGC-CACA-3Ј with the T7 promoter primer (Stratagene) and 5Ј-TGTGGC-CGTACGCCCTTC-3Ј with the T3 promoter primer (Stratagene). The SacI/PstI fragment spanned nucleotides 1076 -1583 and was excised to facilitate the amino acid substitution of Arg 320 with Ala 320 and the insertion of a NarI restriction site. The primers used were 5Ј-ATC-GACGGCGCCATTGTG-3Ј with the T7 promoter primer and 5Ј-CA-CAATGGCGCCGTCGAT-3Ј with the T3 promoter primer. Each PCR product was ligated into the EcoRV site of pBluescript SK ϩ and then cut with the appropriate restriction endonuclease along with that for the newly introduced site. Digested fragments were ligated at their new restriction sites and subcloned into pBluescript SK ϩ . The presence of mutations and correct PCR amplifications were verified by DNA sequence analysis using the T3 and T7 promoter primers. The mutated fragments were ligated into the cDNA for rMZ-II. The resulting cDNA was subcloned into the pNUT vector and prepared for expression as described previously (11). Cell culture, transfection, and selection was carried out as described previously (11).
Recombinant Protein Purification-Recombinant prothrombins were purified as described previously (11). Briefly, stored media were thawed at 4°C and loaded onto XAD-2 (2.5 ϫ 15 cm) and Q-Sepharose (1.4 ϫ 8 cm) columns in tandem at either 4 or 21°C. The XAD-2 column was used to remove indicator dye in the medium. Adsorbed prothrombin was eluted from the Q-Sepharose with 0.02 M Tris-HCl and 0.5 M NaCl (pH 7.4). Protein-containing fractions were identified using a Bio-Rad assay and pooled. Fluorescent labeling of mutants containing free cysteine residues was performed directly on this pooled fraction by adding a 30-fold molar excess of 5-iodoacetamidofluorescein from a 20 mM stock solution of 5-iodoacetamidofluorescein in N,N-dimethylformamide and incubating the sample for 2 h at room temperature in the dark. Prothrombin pools were subjected to barium citrate adsorption by the addition of sodium citrate to a final concentration of 0.025 M, followed by the addition of 1.0 M BaCl 2 solution, with stirring, to a final concentration of 0.08 M. The solution was stirred at 4°C for 1 h and centrifuged. The resulting pellet was washed and solubilized as described previously (11). The sample was then dialyzed against 0.02 M Tris-HCl and 0.15 M NaCl (pH 7.4) and subjected to anion-exchange chromatography on a fast protein liquid chromatography Mono Q HR 5/5 column (Amersham Biosciences) at 4°C. The protein was eluted with a 0 -30 mM CaCl 2 gradient in 0.02 M Tris-HCl and 0.15 M NaCl (pH 7.4) (total volume of 30 ml; flow rate of 0.5 ml/min). This was performed to separate protein that was fully ␥-carboxylated (10). The first peak was pooled, and protein concentrations and labeling efficiencies (where applicable) were determined by absorbance readings at 280 and 495 nm, respectively.
Activation of Prothrombin Derivatives in the Absence of Factor Va-Substrates were activated at various concentrations in the presence of 50 M PCPS and 5 M DAPA in 0.02 M Tris-HCl, 0.15 M NaCl, 5 mM CaCl 2 , and 0.01% Tween 80. Reactions were started at room temperature by the addition of 20 nM factor Xa. In the cases of WT-II, rMZ-II, and F1.2:Pre2, reactions were allowed to proceed for 10 min, at which time an aliquot was removed and diluted into a 96-well plate that had been pretreated with 0.02 M Tris-HCl, 0.15 M NaCl, and 1% Tween 80. Wells contained a sufficient volume of S2238 (H-D-phenylalanyl-L-pipecolyl-L-arginine-p-nitroaniline dihydrochloride) so that the final concentration was 400 M. Absorbance at 405 nm was read over time in a Spectromax Plus spectrophotometer (Molecular Devices) at room temperature. Initial rates of S2238 hydrolysis were determined and compared with a thrombin standard curve. In the case of rP2-II, aliquots were removed from activation reactions and diluted into 2 volumes 0.2 M acetic acid. Aliquots were concentrated, and reduced samples were subjected to SDS-PAGE on 5-15% polyacrylamide minigels according to Neville (20). Densitometry was carried out to determine the amount of prethrombin-2 produced at each time point. In the case of meizothrombin activation, reactions were carried out in a 96-well plate that had been pretreated with 0.02 M Tris-HCl, 0.15 M NaCl, and 1% Tween 80 and monitored in a Spectra Max Gemini fluorescence plate reader (Molecular Devices) at excitation and emission wavelengths of 280 and 545 nm, respectively, with a 515-nm emission cutoff filter in the emission beam. Initial rates of activation for all substrates were calculated and plotted versus the substrate concentration. The data are plotted as the means Ϯ S.D. of at least three experiments. The K m and k cat values were determined by nonlinear regression of the data to the Michaelis-Menten equation using the NONLIN module of SYSTAT (SPSS Inc., Chicago, IL).
Activation of Prothrombin Derivatives in the Presence of Factor Va-Substrates were activated at various concentrations in the presence of 50 M PCPS, 20 nM factor Va, and 5 M DAPA in 0.02 M Tris-HCl, 0.15 M NaCl, 5 mM CaCl 2 , and 0.01% Tween 80. In the case of WT-II, rMZ-II, F1.2:Pre2, and meizothrombin, reactions were carried out in 96-well plates that had been pretreated with 0.02 M Tris-HCl, 0.15 M NaCl, and 1% Tween 80. Reactions were started at room temperature by the addition of 0.02 nM factor Xa and monitored in the Spectra Max Gemini fluorescence plate reader at excitation and emission wavelengths of 280 and 545 nm, respectively, with a 515-nm emission cutoff filter in the emission beam. In the case of rP2-II, aliquots were removed from activation reactions and diluted into 2 volumes of 0.2 M acetic acid. Aliquots were concentrated, and reduced samples were subjected to SDS-PAGE on 5-15% polyacrylamide minigels. Densitometry was carried out to determine the amount of prethrombin-2 produced at each point. Initial rates of activation for all substrates were calculated and plotted versus the concentration of substrate. The data are plotted as the means Ϯ S.D. of at least three experiments. The K m and k cat values were determined by nonlinear regression.
Time Courses of Prothrombin, Meizothrombin, and Thrombin during Prothrombin Activation-Unlabeled prothrombin (1 M) was activated in the presence of a trace amount of 125 I-prothrombin (150,000 cpm) with 50 M PCPS, 20 nM factor Va, 0.035 nM factor Xa, and 5 mM CaCl 2 in 0.02 M Tris-HCl, 0.15 M NaCl, and 0.01% Tween 80. The reaction was started at room temperature by the addition of factor Xa. Aliquots were removed from the reaction, diluted into 2 volumes of 0.2 M acetic acid, and concentrated. Reduced samples were subjected to SDS-PAGE on a 5-15% polyacrylamide gel. The gels were fixed in 50% methanol, 20% ethanol, and 6% trichloroacetic acid for 2 h and then stained with Coomassie Blue and destained. Bands were excised and counted in an Amersham Biosciences Minigamma 1275 ␥-counter. The experiment was performed twice, and three gels were analyzed. The data are plotted as the means Ϯ S.D. of three results.
Competition Experiments and Mathematical Modeling of Prothrombin Activation-Studies of prothrombin activation indicated that the substrates rMZ-II and rP2-II only partially inhibited prothrombin activation (see below). This phenomenon could not be rationalized by any conceivable equilibrium model that involved only one form of prothrombinase because, in such a model, competing substrate at a sufficiently high concentration would occupy all of the enzyme, thereby completely inhibiting prothrombin activation. Therefore, the following model was constructed to account for partial inhibition by rMZ-II and rP2-II. The model includes two equilibrating forms of prothrombinase, designated E and EЈ, as indicated in Equation 1.
One of these forms (E) catalyzes cleavage at Arg 320 . Thus, it catalyzes conversion of prothrombin (P) to meizothrombin (M), F1.2:Pre2 (P2) to thrombin (T), and rMZ-II (rMZ) to rMZ-IIa(rMZa). The other form (EЈ) catalyzes cleavage at Arg 271 and thereby catalyzes conversion of prothrombin to F1.2:Pre2, meizothrombin to thrombin, and rP2-II (rP2) to rP2-IIa(rP2a). In this model, once a particular form of the enzyme catalyzes its corresponding bond cleavage, it releases the product and reverts to the other form of the enzyme. In this sense, the model is similar to the classical "ping-pong" mechanism of enzyme kinetics. The proposition that E and EЈ can equilibrate is included in the model to account for the fact that rMZ-II, rP2-II, meizothrombin, and F1.2:Pre2 can be completely activated. This could not happen if the two forms of the enzyme could not interconvert spontaneously.
Each form of the enzyme is presumed to interact with its substrate (

S) in an equilibrium binding interaction such that [E][S] ϭ K[ES] and [EЈ][S] ϭ K[EЈS]
. The enzyme-substrate complexes then turn over to product at rate r, where r ϭ k [ES] or r ϭ k [EЈS]. The term k is the turnover number. Each reaction rate can therefore be expressed in terms of the free enzyme forms according to . Each specific reaction is allowed its own k and K values. These are shown in Equations 2 and 3.
The rate of thrombin formation (r) is the sum of the rates of conversion of the intermediates meizothrombin and F1.2:Pre2 to thrombin (Equation 4).
To express the rate of the reaction in terms of the prothrombin concentration, steady states with respect to the levels of the intermediates are assumed, such that their rates of formation from prothrombin and subsequent conversion to thrombin are equal. Thus, for meizo- . The rate of prothrombin activation then can be expressed in terms of the prothrombin concentration according to Equation 5.
To further develop the rate equation, the conservation of enzyme is considered. Because some experiments were carried out in the presence of rMZ-II and rP2-II as competing substrates, the interactions of E and EЈ with them are also accounted for in the conservation equation.
The steady states in meizothrombin and F1.2:Pre2 are again invoked to eliminate terms containing them from the conservation equation.
The conservation of enzyme is then given according to Equation 8.

Division of Equation 5 by Equation 8 and then division of the numerator and denominator of the resulting equation by [E] yield Equation 9
, which gives the rate per total concentration of enzyme.
The ratio [EЈ] [E] in Equation 8 can be eliminated by assuming a steady state in [E] (and therefore [EЈ]). Thus, the rates of formation and removal of E are presumed equal. This is expressed in Equation 10.
Invoking steady states in the levels of the intermediates allows for simplification of Equation 10 to give Equation 11.

Equation 11 is then solved for the ratio [EЈ]/[E]
, which is given in Equation 12.
The right-hand side of Equation 12 is substituted for [EЈ]/[E] in Equation 9. When this is done, Equation 13 is the result, with the terms k cat , K m , a 1 , a 2 , a 3 , b 1 , b 2 , b 3 , c, and ␤ given in Equations 14 -23.
Equation 13 predicts that, in the absence of competing substrates ([rMZ-II] ϭ 0, [rP2-II] ϭ 0), prothrombin activation kinetics will conform to the Michaelis-Menten equation , with k cat and K m defined in Equations 14, 15, and 23. It also predicts that the competing substrates rMZ-II and rP2-II will inhibit prothrombin only partially. With rMZ-II, for example, as [rMZ-II] is raised without bounds (in the absence of rP2-II), Equation 13 predicts that prothrombin activation will occur at a non-zero rate, rϱ ϭ a 1 [P]/(a 2 ϩ a 3 [P]). Thus, at saturation with respect to [rMZ-II], a finite rate of prothrombin activation will be expected. Furthermore, its value will depend on the prothrombin concentration. The same behavior is predicted with rP2-II, By analogous reasoning, the rate of rMZ-II activation in the presence of rP2-II is given in Equation 24, with k cat , K m , g 1 , g 2 , and g 3 given in Equations 25-29.
Similarly, the rate of activation of rP2-II with rMZ-II as a competing substrate is given in Equation 30, with k cat , K m , h 1 , h 2 , and h 3 given in Equations 31-35. r/͓E͔ T ϭ k cat ͓P2͔/͑K m ϩ ͓P2͔͒ (Eq. 39) Equations 36 and 39 indicate that the kinetics of activation of meizothrombin and F1.2:Pre2 also will conform to the Michaelis-Menten equation.

Characterization of Recombinant Prothrombin
Derivatives-Three recombinant prothrombin derivatives were prepared to determine the effects of factor Va on cleavage at Arg 271 and Arg 320 in prothrombin (Fig. 1). Two additional recombinant prothrombin derivatives were used to carry out competition assays between each of the three recombinant prothrombin derivatives (Fig. 1). The recombinant prothrombins WT-II, rMZ-II, and rP2-II were activated with prothrombinase, and aliquots were subjected to SDS-PAGE under reducing conditions (Fig. 2). Activation of WT-II produced the intermediates expected when cleavage occurs at both Arg 271 and Arg 320 . Activation of rP2-II produced the intermediate F1.2:Pre2 only, indicating a single cleavage at Arg 271 . Finally, activation of rMZ-II produced the intermediate meizothrombin, indicating a single cleavage at Arg 320 . Activation of WT-II-F* and rMZ-II-F* was also carried out and analyzed in two ways. In the first, fluorescence intensity was monitored throughout the reaction. In the second, aliquots were removed and subjected to SDS-PAGE. The change in fluorescence observed was coincident with cleavage, and the expected cleavage patterns were obtained (data not shown).
Kinetics of Activation of Prothrombin Derivatives in the Absence and Presence of Factor Va-The Initial rates of activation of rMZ-II to meizothrombin, rP2-II to F1.2:Pre2, meizothrombin to thrombin, and F1.2:Pre2 to thrombin were measured in the absence and presence of factor Va at various substrate concentrations. These data were fit to the Michaelis-Menten  (Table I). In the absence of factor Va, the catalytic efficiencies for conversion of rMZ-II to meizothrombin and of rP2-II to F1.2:Pre2 indicated that cleavage at Arg 271 was ϳ50-fold more efficient than cleavage at Arg 320 . The catalytic efficiencies for conversion of meizothrombin to thrombin and of F1.2:Pre2 to thrombin indicated that, when prothrombin was initially cleaved at Arg 271 to produce F1.2:Pre2, subsequent cleavage at Arg 320 represented the rate-limiting step of thrombin formation, as the catalytic efficiency of cleavage was 100-fold lower for this second step. Additionally, the catalytic efficiency of cleavage at Arg 271 in meizothrombin was 10-fold greater than that in rP2-II. These data rationalize the accumulation of the intermediate F1.2:Pre2 and the lack of detectable meizothrombin accumulation when prothrombin is activated in the absence of factor Va.
In the presence of factor Va, the kinetic parameters determined for cleavage at Arg 271 in rP2-II and at Arg 320 in rMZ-II were indistinguishable from each other and were very similar to that obtained for the overall conversion of prothrombin to thrombin. Because the activation of WT-II to thrombin was monitored by DAPA fluorescence, the rates of activation of prothrombin to thrombin could be overestimated somewhat. This is because the increase in DAPA fluorescence is due to the formation of both meizothrombin and thrombin, and the meizothrombin-DAPA complex is 30% more fluorescent than the thrombin-DAPA complex (9). Nonetheless, these results suggest that, with rMZ-II and rP2-II, neither of the cleavages required for prothrombin activation is rate-limiting. They also suggest that, in the presence of factor Va, prothrombin activation would be expected to proceed through both pathways at equal rates. However, this does not appear to be the case, as will be shown when the catalytic efficiencies of cleavages in prothrombin are compared with those of cleavages in the derivatives and intermediates (see below).
The increase in catalytic efficiency of each cleavage upon the addition of factor Va was also calculated. Efficiency of cleavage for the overall conversion of prothrombin to thrombin was enhanced by 39,700-fold by factor Va. Cleavage at Arg 320 was enhanced by 20,600-fold (with rMZ-II as the substrate) or by 27,200-fold (with F1.2:Pre2 as the substrate), whereas cleavage at Arg 271 was enhanced only by 453-fold (with rP2-II as the substrate) or by 34-fold (with meizothrombin as the substrate). Therefore, cleavage at Arg 271 is not nearly as dependent upon factor Va as cleavage at Arg 320 .
Activation of 125 I-Prothrombin in the Presence of Factor Va-Prothrombin that had been labeled with 125 I was activated in the presence of factor Va and subjected to SDS-PAGE. The time courses of prothrombin, meizothrombin, and thrombin during the reaction are shown in Fig. 3. Fig. 3 illustrates that the decline in the concentration of prothrombin during the reaction was nearly first-order at this prothrombin concentration. The intermediate meizothrombin first increased to a maximum at 6 min, followed by a steady decline. The intermediate F1.2:Pre2 was not observed. The thrombin concentration in the first 300 s is shown in the inset and appeared to rise immediately upon initiation of the reaction, without the lag that is characteristic of a mechanism with an obligatory intermediate. Because this lag did not occur, the time course of thrombin formation suggests that some direct conversion of prothrombin to thrombin occurred without equilibration of free intermediates with the prothrombinase complex, thereby indicating a channeling phenomenon (19). In addition, these data indicate that the catalytic efficiency for conversion of prothrombin to meizothrombin is much larger than that for conversion of prothrombin to F1.2:Pre2. This can be appreciated by comparing the initial rates of meizothrombin and thrombin accumulation. The initial rate of meizothrombin accumulation was less than or equal to the initial rate of meizothrombin formation from prothrombin. Because F1.2:Pre2 did not accumulate, the initial rate of thrombin formation was greater than or equal to the rate of F1.2:Pre2 formation from prothrombin. Because the initial rate of meizothrombin accumulation was much greater than that of thrombin accumulation, the catalytic efficiency of cleavage at Arg 320 in prothrombin must be considerably greater than that of cleavage at Arg 271 . This is in contrast to the nearly identical catalytic efficiencies measured with rMZ-II and rP2-II.

Activation of WT-II-F* and rMZ-II-F* in the Presence of WT-II, rMZ-II, and rP2-II-
The prothrombin derivative WT-II-F* is an active-site mutant of prothrombin in which the active-site serine was mutated to a cysteine, which was subsequently labeled with fluorescein. The prothrombin derivative rMZ-II-F* is the rMZ-II mutant with the same active-site mutation. Both mutants displayed an increase in fluorescence intensity upon activation and therefore allowed us to monitor their activation specifically in the presence of WT-II, rMZ-II, and rP2-II as competitors. Fig. 4 illustrates the inhibition of WT-II-F* activation observed in the presence of WT-II, rMZ-II, or rP2-II at various concentrations. Simple competitive inhibition was observed when WT-II-F* was activated in the presence of WT-II. The substrates rMZ-II and rP2-II did not, however, exhibit simple competitive inhibition when activated in the presence of WT-II-F*. In both cases, inhibition was not complete, even at saturating levels of competitor. In addition, the extent of inhibition was dependent upon the starting concentration of WT-II-F*. However, when both rMZ-II and rP2-II were added together as competitors, inhibition was competitive. As illustrated in Fig. 5, cleavage of rMZ-II-F* was inhibited competitively by both WT-II and rMZ-II. However, inhibition by rP2-II was not complete, and the extent of inhibition was dependent upon the starting concentration of rMZ-II-F*.  (Table I) The k cat /K m value for prothrombin activation is given by the ratio of Equations 14 and 15, (k cat /K m ) P ϭ (k Ϫ1 /(k 1 ϩ k Ϫ1 ))(k/ K) 320(P) ϩ (k 1 /(k 1 ϩ k Ϫ1 ))(k/K) 271(P) ϭ 0.262 Ϯ 0.024, where (k/K) 320(P) and (k/K) 271(P) are the respective intrinsic catalytic efficiencies of cleavages at Arg 320 and Arg 271 in prothrombin.
If the catalytic efficiencies of cleavage at Arg 271 and Arg 320 in prothrombin were the same as those in the prothrombin derivatives, then the k cat /K m ratio for prothrombin, as indicated by the above equations, would be expected to equal the sum for the prothrombin derivatives, which is 0.513. However, the experimentally determined value (0.262) is only about one-half of the expected value. Thus, the intrinsic catalytic efficiency of cleavage at one or possibly both of the bonds in prothrombin is not equal to that for cleavage at the same bonds in the prothrombin derivatives.
That this is so is evident in the data of Fig. 3. As shown, meizothrombin was clearly produced and transiently accumulated, but F1.2:Pre2 did not. If the k cat /K m values for both cleavages were approximately equal, as they are in the derivatives, one would expect F1.2:Pre2 to accumulate with a time course similar to that of meizothrombin. Even channeling through the F1.2:Pre2 pathway would not account for the lack of this intermediate because if channeling were to occur so that F1.2:Pre2 did not accumulate, the initial rate of thrombin formation would equal or exceed the rate of meizothrombin formation, which clearly is not the case. Thus, the difference in catalytic efficiencies of cleavages at Arg 271 and Arg 320 in prothrombin compared with the derivatives appears to lie with cleavage at Arg 271 . If one assumes that cleavage at Arg 320 in prothrombin proceeds with the same efficiency as it does with the derivatives, one can calculate the intrinsic catalytic efficiency of cleavage at Arg 271 in prothrombin relative to that in the derivatives. Using the above equations to eliminate k Ϫ1 /(k 1 ϩ k Ϫ1 ) and k 1 /(k 1 ϩ k Ϫ1 ) yields (k cat /K m ) P ϭ (k cat /K m ) 320(d) ((k/K) 320(P) /(k/K) 320(d) ) ϩ (k cat / K m ) 271(d) ((k/K) 271(P) /(k/K) 271(d) ). Assuming that (k/K) 320(P) ϭ (k/K) 320(d) and letting R ϭ (k/k) 271(P) /(k/K) 271(d) yields (k cat / K m ) P ϭ (k cat /K m ) 320(d) ϩ R((k cat /K m ) 271(d) ). Thus, R ϭ (0.262 Ϫ  0.252)/0.262 ϭ 0.038, i.e. the intrinsic catalytic efficiency of cleavage at Arg 271 in prothrombin is only 3.8% of that of cleavage at Arg 271 in meizothrombin and rP2-II. Why this should be the case is not revealed by these studies. These studies suggest, however, that in the activation of prothrombin, under the conditions of our experiments, cleavage at Arg 320 occurs first to form meizothrombin. This is an event that, in effect, creates the second cleavage site at Arg 271 . This site is then cleaved with an efficiency roughly equal to that of the initial cleavage at Arg 320 . Thus, under these conditions, prothrombin activation appears to occur with an ordered sequence of cleavages, with the bond at Arg 320 cleaved first to produce meizothrombin, as indicated previously by Krishnaswamy et al. (9,21).
Estimation of the Rate Constants for Bond Cleavage and for Equilibration of the Two Forms of Prothrombinase-Analysis of the k cat /K m ratios above indicates that the intrinsic catalytic efficiency (k/K) of cleavage at Arg 271 in prothrombin is only 3.8% of that of cleavage at Arg 320 in prothrombin and at Arg 271 or Arg 320 in the prothrombin derivatives. If the further simplifying assumptions are made that the low catalytic efficiency is due to a low turnover (low k) rather than weak binding (high K) and that all other k and K values are the same, then the rate constant for bond cleavage (k) and the rate constants for the E and EЈ interconversions (k 1 and k Ϫ1 ) can be calculated. These can be calculated from the k cat values for cleavage at Arg 320 (average k cat for cleavage of rMZ-II and F1.2:Pre2) and Arg 271 (average k cat for cleavage of rP2-II and meizothrombin) and for cleavage of prothrombin. The relevant equations are as follows: k cat(320) ϭ k Ϫ1 k/(k Ϫ1 ϩ k), k cat(271) ϭ k 1 k/(k 1 ϩ k), and k cat(P) ϭ (k Ϫ1 k ϩ 0.038k k 1 )/(2k Ϫ1 ϩ 1.038k). These are obtained by applying the above assumptions to Equations 40,37,and 14,respectively. Utilizing the k cat values from Table I and solving these equations by iteration yield the following values: k ϭ 344/s, k 1 ϭ 214/s, and k Ϫ1 ϭ 166/s. These values indicate that the concentrations of E and EЈ at equilibrium are such that [EЈ]/[E] ϭ k 1 /k Ϫ1 ϭ 1.29, i.e. the concentrations of the two forms are about equal in the absence of substrate. These values also indicate that the k cat values for bond cleavage are limited by the rate constants for interconversion of E and EЈ, i.e. the kinetics of prothrombin activation are determined in part by the rate constants for interconversion of the two enzyme forms. These low values of k 1 and k Ϫ1 (relative to the rate constant for cleavage) are also responsible for the partial inhibition of prothrombin activation by the single cleavage derivatives. If the k 1 and k Ϫ1 values were very high relative to k, the partial inhibition phenomenon would not exist because E and EЈ would very rapidly equilibrate. This can be argued formally by allowing k Ϫ1 and k 1 to approach infinity in Equation 13. Under these circumstances, this equation becomes r ϭ II] and [rP2-II] in the numerator and therefore describes simple competitive inhibition of prothrombin activation by rMZ-II and rP2-II. DISCUSSION Two recombinant prothrombins labeled with fluorescein were utilized in these studies. Both mutants displayed an increase in fluorescence intensity upon activation. Their activation was monitored specifically in the presence of WT-II, rMZ-II, and rP2-II as competitors. Although WT-II was a competitive inhibitor of WT-II-F*, rMZ-II or rP2-II did not inhibit cleavage of WT-II-F* completely, and the extent of inhibition was dependent upon the starting concentration of WT-II-F*. When both rMZ-II and rP2-II were added together, however, the inhibition observed was competitive. In the case of rMZ-II-F*, both WT-II and rMZ-II behaved as competitive inhibitors, whereas rP2-II did not. Numerous models of prothrombin activation kinetics were investigated to rationalize these data. No model that included only a single form of prothrombinase was consistent with the data. The data instead were consistent with a ping-pong-like model of kinetics in which prothrombinase exists in two equilibrating forms, each specific for a unique site in prothrombin (Fig. 6). The form of the enzyme that cleaves at Arg 320 has been designated E, and the form that cleaves at Arg 271 has been designated EЈ. This model is like the classical ping-pong model in that two enzyme forms are involved, and the enzyme is converted to its alternate form after a catalytic event. However, the model differs from the ping-pong model in that the two forms of the enzyme spontaneously interconvert in the absence of substrate. This is so because if cleavage had to occur to convert E to EЈ or vice versa, activation reactions containing rP2-II or rMZ-II alone, with the substrate in excess over the enzyme, would not go to completion, as they did in these studies.
Ping-pong-type kinetics have been identified in several other mammalian systems. Some examples include cholesterol oxidase, which is a monomeric flavoenzyme that catalyzes the oxidation and isomerization of cholesterol to cholest-4-en-3one. Two forms of the enzyme have been identified, and the kinetics of the reaction have been shown to follow a ping-pong mechanism (22). Lipoamide dehydrogenase is a flavoprotein that catalyzes the reversible oxidation of hydrolipoamide by NAD ϩ , also through a ping-pong kinetic mechanism (23). NADPH-cytochrome P450 oxidoreductase is a membranebound protein that is associated with the endoplasmic reticulum and nuclear envelope of most eukaryotic cells and that transfers electrons from NADPH to FAD and then to any number of cytochromes P450 through a nonclassical (two-site) pingpong mechanism (24).
In the case of prothrombinase, other published data suggest the existence of two forms of the enzyme. The actual cleavage sites in prothrombin are spatially distinct, being separated by as much as 36 Å (25), with one site requiring extensive reorganization before factor Xa can dock (26). Thus, separate forms of the enzyme may be required to cleave these two sites. The ability of factor Xa to cleave the two sites is affected differently by both factor Va (21) and PCPS (27). Rapid kinetics, stoppedflow studies by Walker and Krishnaswamy (27) suggest that two distinct types of enzyme-substrate interactions are required for the two cleavage sites involved in prothrombin activation. Additionally, factor Xa has been shown to behave differently both as an enzyme (1)(2)(3)(4)(5) and as a target for antithrombin/heparin (11, 28 -36) when it is complexed with some or all of the prothrombinase components. For example, the half-life of factor Xa in the presence of antithrombin and heparin is increased by Ͼ100-fold when factor Xa is incorporated into the prothrombinase complex in the presence of prothrombin. Although this protection is profound, it is not complete. Conceivably, this protection could be due to the dynamics of the equilibrium between E and EЈ, with one form being more susceptible to inhibition than the other.
In the absence of factor Va, cleavage at Arg 271 was ϳ50-fold more efficient than cleavage at Arg 320 . Thus, cleavage at Arg 320 appears to be the rate-limiting step. Additionally, the catalytic efficiency of cleavage at Arg 271 in meizothrombin was 10-fold  Fig. 4. Initial rates of rMZ-II-F* activation were calculated and plotted versus the concentration of inhibitor. The lines correspond to global fits of the data to the appropriate rate equations as outlined under "Experimental Procedures." For competition of rP2-II against rMZ-II-F*, see Equation 24. greater than that in rP2-II. These data rationalize the accumulation of the intermediate F1.2:Pre2 and the lack of detectable meizothrombin accumulation when prothrombin is activated in the absence of factor Va.
In the presence of factor Va, the estimated values for the catalytic efficiencies of cleavage at Arg 271 and Arg 320 in prothrombin are 0.0961 ϫ 10 8 and 2.52 ϫ 10 8 M Ϫ1 s Ϫ1 , respectively. The value for cleavage at Arg 320 in prothrombin, in which the bond at Arg 271 is intact, is very similar to that for the Arg 320 bond in F1.2:Pre2 (1.98 ϫ 10 8 M Ϫ1 s Ϫ1 ), in which the bond at Arg 271 is not intact. Thus, the catalytic efficiency of cleavage at Arg 320 does not depend on whether the bond at Arg 271 has been cleaved. In contrast, the catalytic efficiency of cleavage at Arg 271 in meizothrombin (2.3 ϫ 10 8 M Ϫ1 s Ϫ1 ), in which the bond at Arg 320 has been cleaved, is 24-fold greater than the estimated value for cleavage at the same bond in prothrombin, in which the bond at Arg 320 is intact. This suggests that, in prothrombin, with factor Va as a component of prothrombinase, the bond at Arg 271 is not readily available for cleavage until after the bond at Arg 320 is cleaved. Curiously, the Arg 271 bond in rP2-II is cleaved with high efficiency (2.91 ϫ 10 8 M Ϫ1 s Ϫ1 ). However, this mutant has an alanine rather than an arginine residue at position 320. Perhaps it interacts with prothrombinase in a way that had the bond at position 320 been cleavable, it would have been cleaved. Although this bond was not cleaved because it could not be, perhaps the interaction with prothrombinase was sufficient to produce high efficiency cleavage at Arg 271 . A similar phenomenon exists in the absence of factor Va. In this case, the catalytic efficiency of cleavage at Arg 320 in rMZ-II (1.5 ϫ 10 4 M Ϫ1 s Ϫ1 ), in which the bond at Arg 271 is intact, is very similar to the value for cleavage at this bond in F1.2:Pre2 (7.3 ϫ 10 3 M Ϫ1 s Ϫ1 ), in which the bond at Arg 320 is not intact. In contrast, the catalytic efficiency of cleavage at Arg 271 in meizothrombin (6.76 ϫ 10 6 M Ϫ1 s Ϫ1 ), in which the bond at Arg 320 is not intact, is 11-fold greater than that of cleavage at this bond in rP2-II (0.64 ϫ 10 6 M Ϫ1 s Ϫ1 ), in which the bond at Arg 320 is intact. Thus, either with or without factor Va, the catalytic efficiency of cleavage at Arg 320 appears to be minimally affected by the state of cleavage at Arg 271 . In contrast, the catalytic efficiency of cleavage at Arg 271 is strongly influenced by the state of cleavage at Arg 320 , such that it increases by about an order of magnitude if the bond at Arg 320 is cleaved. In the presence of factor Va, the catalytic efficiency of cleavage at Arg 271 is nearly identical to that at Arg 320 once cleavage at Arg 320 has occurred. This has also been inferred by Krishnaswamy et al. (21).
Factor Va enhances the catalytic efficiency of prothrombin activation by a factor of 39,700 compared with that obtained with factor Xa, PCPS, and Ca 2ϩ only. This effect is not expressed equivalently for the two bond cleavages. The magnitude of the effect on cleavage at Arg 320 ranges from 20,600-to 27,200-fold, depending on whether rMZ-II or F1.2:Pre2, respectively, is the substrate. In contrast, the magnitude of the effect on cleavage at Arg 271 ranges from only 34-to 453-fold, depending on whether meizothrombin or rP2-II, respectively, is the substrate. Taking F1.2:Pre2 and meizothrombin as the natural substrates for prothrombinase, the best estimates for the enhancement of catalytic efficiencies by factor Va are 27,000-fold for cleavage at Arg 320 and 34-fold at Arg 271 .
Prothrombin interacts with prothrombinase at exosites that are separate from the active site of factor Xa. These exosites may mediate substrate recognition and/or cleavage (37)(38)(39)(40)(41). In addition, x-ray crystallographic studies of prethrombin-2 indicate that the residues preceding the Arg 320 -Ile 321 bond require extensive rearrangement to be successfully docked into the active site of factor Xa (26). Such features are not observed for the identical residues preceding the Arg 274 -Thr 275 bond in bovine meizothrombin-des-F1 (25). If incorporation of factor Va into the prothrombinase complex is necessary to reorder the residues preceding Arg 320 in human prothrombin, perhaps factor Va disproportionately enhances cleavage at Arg 320 , ultimately shifting the equilibrium toward the meizothrombin pathway.
FIG. 6. Schematic representation of the ping-pong-like mechanism. A, in this model, prothrombinase exists in two equilibrating forms, each of which is specific for a unique cleavage site in prothrombin. The E form of the enzyme recognizes Arg 320 in prothrombin (P), F1.2: Pre2 (P2), or rMZ-II (rMZ), whereas the EЈ form of the enzyme recognizes Arg 271 in prothrombin, meizothrombin (M), or rP2-II (rP2). After cleaving the recognized site, the enzyme converts to its alternate form. The binding constants (K) and the rate constants (k) shown correspond to those used in the model described under "Experimental Procedures." The constant K 1 refers to the equilibrium between E and EЈ (K 1 ϭ k Ϫ1 /k 1 ). B, this model suggests that, when rMZ-II or rP2-II is activated, only one of the two forms of prothrombinase can catalyze the reaction. Therefore, rMZ-II and rP2-II can each inhibit only one form of the enzyme when activated in the presence of WT-II-F*. T, thrombin; rP2a, rP2-IIa.