The Cobra Venom Factor-dependent C3 Convertase of Human Complement A KINETIC AND THERMODYNAMIC ANALYSIS OF A PROTEASE ACTING ON ITS NATURAL HIGH MOLECULAR WEIGHT SUBSTRATE*

Enzymes of the complement system exhibit, unlike most other proteases, a high substrate specificity, hy- drolyzing only a single peptide bond in their protein substrates. This property allowed the performance of a detailed analysis of the enzymatic activity of a protease acting on its natural high molecular weight sub- strate. The enzyme investigated was the cobra venom factor-dependent C3 convertase (EC 3.4.21.47) of hu- man complement. The enzyme constitutes a bimolecular complex of cobra venom factor and the catalytic site bearing fragment Bb of human Factor B. It hydrolyzes peptide bond 77 (Arg-Ser) of the a-chain of the human complement protein C3, thereby producing the fragments C3a and C3b. The enzyme was generated from isolated proteins. It exhibited spontaneous decay-dissociation into its subunits with a half-life of 7 h at 37 "C. The following kinetic parameters for C3 hydrolysis were determined: the Michaelis constant, K,, the catalytic constant, kc,,, the turnover number, the catalytic cycle time, the specific activity, the apparent second order rate constant, k,,,/K,, and the apparent first order rate constant for the low substrate concentration range. The encounter of enzyme and substrate pro-ceeded under rapid equilibrium conditions. For the for- mation of the enzyme-substrate complex, the equilibrium constant, K, the standard enthalpy, AH", standard entropy, AS", and standard Gibbs energy, AG", were determined. For the rate-limiting step of the overall reaction, the activation energy, E,, activation enthalpy, AH*, activation entropy, AS*, and Gibbs energy of activation, AG*, were derived. The results demonstrate that action of a protease of high molecular weight (Mr = 210,000) on its substrate of high molecular weight (Mr = 185,000) can be described in terms of Michaelis-Menten kinetics. The data are consistent with a double intermediate catalytic mechanism and a kinetic mechanism of a Tetra Uni Ping Pang Bi Bi reaction reduced to a Uni Bi reaction and therefore support the serine protease concept of Factor B-derived enzymes.

The enzymatic nature of many reactions occurring upon activation of complement' is well established (1)(2)(3)(4). Unlike most other proteases, complement enzymes exhibit a high substrate specificity, i.e. in most instances, they hydrolyze only a single peptide bond in their natural substrates. All of the well investigated proteases like trypsin or chymotrypsin lack this high substrate specificity and, therefore, the kinetic and thermodynamic parameters characterizing these enzymes have been derived from their reactions with synthetic low molecular weight substrates such as esters, amides, or oligopeptides (8). The present study was performed to determine the kinetic and thermodynamic parameters for the reaction of a complement enzyme with its natural high molecular weight protein substrate. The enzyme investigated is the cobra venom factor-dependent C3 convertase (EC 3.4.21.47)' of human complement.
The enzyme constitutes a bimolecular complex of cobra venom factor (M, = 147,000) and of the catalytic site-bearing fragment of human Factor B (10,11), designated Bb (MI = 63,000). The enzyme is formed when the proenzyme Factor B (M, = 93,000) binds to CVF3 in the presence of Mg2+ and is subsequently cleaved by its activating enzyme Factor D (EC 3.4.21.48) (12)(13)(14)(15). The CVF,Bb enzyme hydrolyzes bond 77 (Arg-Ser) (16,17) in the a-chain of C3 (Mr = 185,000) which results in the liberation of the activation peptide C3a (Mr = 9,000) and the formation of metastable C3b (M, = 176,000). The formation and action of the CVF-dependent C3 convertase are analogous to formation and action of the C3b-dependent C3 convertase (C3b,Bb). The latter enzyme is formed during activation of the alternative complement pathway (2). C3a constitutes one of the three complement-derived anaphylatoxins and C3b f d f i i s various functions in humoral and cellular mechanisms of host defense against infections. Metastable C3b contains a highly reactive carbonyl group through which it may form a covalent bond with surface constituents of biological particles. Through this mechanism, C3b becomes finny attached to targets of complement attack and may serve as ligand for specific complement receptors on the surface of phagocytic cells and as structural subunit of the C3 and C5 activating enzymes of complement (18)(19)(20). The CVF-'Terminology for the complement components conforms to the recommendations of the World Health Organization Committee on Complement Nomenclature (5,6). "xyC2 is C2 modified by oxidation The EC numbers for complement enzymes do not differentiate between the cobra venom factor-dependent and C3b-dependent C3 convertase of the alternative pathway of complement (9).
The abbreviations used are: CVF, cobra venom factor; B, Factor VBE, and GVBE, see "Experimental Procedures"; anti-CVF and anti-B; Ba and Bb, physiological cleavage fragments of Factor B; VBS, B, antiserum to CVF or Factor B. (7; 8292 dependent C3 convertase was selected for these investigations because it is characterized by a markedly greater stability than the C3b-dependent C3 convertase which is subject to rapid decay-dissociation (2, 21). A detailed kinetic and thermodynamic analysis wiU be presented below for this system in which enzyme and substrate are both macromolecular, each having M , -200,000.
Zsolation of Factor B, Factor 0, C3, and Cobra Venom Factor-Factor B ( E ) , Factor D (15), and C3 (22) were isolated from human serum or plasma as described. CVF was isolated from lyophilized cobra venom according to Ref. 23. All proteins were pure as judged by sodium dodecyl sulfate-polyacrylamide gel electrophoresis, immunoelectrophoresis, and analytical isoelectric focusing.
C3 Titration-Titration of C3 hemolytic activity was performed as described (24). The C5-C9 reagent was prepared from guinea pig serum by incubation with KSCN and hydrazine (25) and subsequent addition of functionally purified human C5 (22). Sheep erythrocytes bearing the complement proteins C1, C4, and OXyC2 were prepared according to published procedures (26,27).
Formation of the CVF-dependent C3 Conuertase-CVF (12 pg) was incubated at 37 "C with a 3-fold molar excess of Factor B and 0.2 pg of Factor D in a total volume of 100 pl of VBS containing 1 mM MgC12. After 60 min, the reaction was stopped by addition of 100 pl of VBS containing 20 m~ EDTA and the mixture was further diluted with VBE to the desired concentration.
Kinetic Analyses-Experiments were performed with five different C3 concentrations in GVBE (8.01 X M, 3.56 x M, 2.13 x M, 1.52 X 1O"j M, and 1.18 X M). At 0 "C, the C3 solutions were mixed with the CVF-dependent C3 convertase and the reaction was started by transferring the mixtures to a thermoconstant water bath of the desired temperature. Kinetic experiments were performed at 10, 20, 30, and 37 "C. At 1.5 or 2-min intervals, 30-pl aliquots were withdrawn and diluted with ice-cold GVBE to stop the reaction. The C3 concentration in these samples was adjusted to comparable values by addition of GVBE. The total dilution was between 150 and 5 0 0~. Dilution and temperature drop were found highly efficient in stopping further substrate hydrolysis, whereas addition of anti-CVF was without effect and anti-B was only partially inhibitory. Twenty p1 of these dilutions, in duplicate, were assayed for remaining C3 by hemolytic titration. Progress curves were obtained by plotting remaining C3 uersus time. The enzyme concentrations used at a given temperature were chosen to result in linear progress curves over a period of 8-10 37 " c , 2.86 X IO-' M). Initial velocities were calculated from the slopes of the progress curves by regression analysis using a Hewlett-Packard computer (Model 9815A) with plotter.
Since C3 titration requires incubation at 37 "C, a reactivation of the CVF-dependent C3 convertase present in the samples occurs. The presence of the enzyme has two effects on the C3 titration for which corrections were made by including the appropriate controls. First, reactivation of the enzyme caused C3 turnover which lowered the apparent amount of C3. Second, the CVF-dependent C3 convertase also hydrolyzes C5 and thereby causes C3-independent hemolysis. This effect resulted in an increase of the apparent amount of C3. Both effects were minor or negligible at low concentrations of the CVFdependent C3 convertase, but required correction in experiments where high concentrations of the enzyme were used.
The initial velocity, u, was plotted uersus the C3 concentration in the double reciprocal manner according to Lineweaver and Burk (28). CVF and Factor B were incubated at 37 "C in the presence of Factor D and Mg2+ in concentrations and molar ratios as described under "Experimental Procedures." After time intervals indicated, 10-p1 aliquots were transferred into 90 pl of VBE. Ten p1 of these enzyme solutions were incubated at 37 "C with 54 pg of isolated C3 in a total volume of 30 pl in the presence of 10 mM EDTA. The reaction was stopped after 10 min by adding 270 pl of ice-cold GVBE. The samples were assayed for remaining C3 by hemolytic titration. The difference between C3 input and remaining C3 was taken as a measure for the enzyme activity. lated from the Lineweaver-Burk plots by regression analysis. Turnover numbers and catalytic constants, kc.,, were calculated according to kc,, = Vm,,/[Et], where E , is the total enzyme concentration. The specific activities are reported in nkat. mg" following the recommendations of the International Union of Biochemistry (29). The apparent first order rate constants for the low substrate concentration range, ko, were determined (a) using the experimental values of substrate concentrations and initial velocities in the concentration range of apparent first order kinetics, ko = u / [ q and ( b ) according to ko = kcat'rEtl, a formula that is derived from the Michaelis-Menten equa-K, tion assuming low substrate concentrations.
The C3 concentration in the stock solution was determined by amino acid analysis. Molar concentrations were calculated using a protein M, = 182,000.
Thermodynamic Calculations4-Activation energy, E,, was calculated from the slope of a plot k,,, uersus 1/T using the Arrhenius equation. The integrated form of this equation was used to calculate the temperature coefficient 910. Standard enthalpy, A H " , was derived from the slope of a plot log K, uersus 1/T applying the van't Hoff law. Activation enthalpy, A H * , was calculated from the slope of a plot of log (kcat/T) versus 1/T according to the transition state theory of absolute reaction rates using the equation (31) where R is the molar gas constant, kg is the Boltzmann entropy constant, h is the Planck constant, and K is the transmission coefficient (assumed to be unity (8,31)). The standard Gibbs energy, AG", was calculated from AG" = -R . T.ln K and the Gibbs energy of activation, AG*, from AG* = -R . T. ln- (8,32). Entropies, ASo and A S * , were calculated using the Gibbs-Helmholtz equation. All slopes of linear graphs were determined by regression analysis.
Other Methods-Monospecific antisera to Factor B and CVF were obtained by immunization of rabbits and goats using complete Freund's adjuvant. Immunoelectrophoresis was performed in 1% (w/ v) agarose in 43.5 mM 5,5-diethylbarbituric acid, pH 8.6, for approximately 2 h at 5 V.cm" at 4 "C. Protein determination was performed by the Lowry method (33) and by amino acid analysis. Amino acid analysis was performed after hydrolysis in 6 N HCl with a Beckman amino acid analyzer (Model 121") (34). modified to the two-column system (35).

ks. T
The reported equilibrium constants and thermodynamic parameters are apparent ones for a given pH and are based on concentrations rather than activities. A prime and the subscript c as recommended by the Interunion Commission on Biothermodynamics to indicate these facts (30) have been omitted to simplify symbols. of Complement C3 Convertase FIG. 3. Decay-dissociation of the CVF-dependent C3 convertase. The enzyme was generated as described under "Experimental Procedures" and subsequently incubated at 37 "C in the presence of 10 mM EDTA. At time intervals indicated, aliquots were transferred into ice-cold GVBE and assayed for remaining convertase activity in a similar manner as described in Fig. 1.

Generation and Quantitation of the CVF-dependent C3
Conuertase-The formation of the CVF-dependent C3 convertase from Factor B and CVF in the presence of Factor D and Mgr+ proceeds according to the following expression: . 1 shows the generation of enzyme activity as a function of time. After approximately 10 min, the maximum activity is reached and remains constant because spontaneous decaydissociation of the enzyme is compensated by reformation of the enzyme from liberated CVF and excess Factor B. The amount of enzyme formed was calculated from CVF input, since in excess of Factor B, CVF is quantitatively incorporated into the enzyme as shown by immunoelectrophoresis (Fig. 2).  D generated a weak C3 convertase activity representing 1% of the activity generated in the presence of Factor D. A complex of CVF and native Factor B (CVF,B), in analogy' to the complex C3b,B (36), believed to be responsible for this activity, could not be detected by immunoelectrophoresis.
Stability of the CVF-dependent C3 Conuertase-The CVFdependent C3 convertase shows a spontaneous decay-dissociation into i t s subunits CVF and Bb. The decay was quantitated in order to determine whether it could influence the outcome of kinetic experiments. At 37 "C and physiological pH and ionic strength, the decrease of enzyme activity was first order with a half-life of approximately 7 h (Fig. 3), which corresponds to a decay rate constant of 2.75 X lo-$ s". Considering the duration of the kinetic experiments to be performed, the decay was negligible. The spontaneous dissociation of the enzyme into i t s subunits CVF and Bb could be shown by immunoelectrophoresis (Fig. 2). After incubation for 35 h a t 37 "C, the liberated CVF assumed the electrophoretic position Number of experiments performed: 37 "C, 6; 30 "C, 3; 20 "C, 2; 10 "C, 4.  of the free protein. At 6 "C, the half-life of the enzyme was 2 to 3 weeks, and at 0 "C it exceeded that time. Freezing at -70 "C and subsequent thawing resulted in a 30% loss of enzyme activity.
Dependence of the Initial Velocity on the Concentration of the CVF-dependent C3 Conuertase-CVF-dependent C3 convertase a t five different concentrations was incubated at 37 "C, ranging from 6 X lo-' to 6 X M with C3 a t a concentration of 1.1 X M. At 1.5-min intervals, aliquots were transferred to ice-cold GVBE and assayed for remaining C3. Initial velocities were determined and found to be a linear function of the enzyme concentration in the range tested. This result demonstrates that hydrolysis of C3 by the CVF-dependent C3 convertase exhibits the expected behavior of an enzymatic reaction.
Determination of Kinetic Parameters of the CVF-dependent C3 Conuertase-Kinetic experiments were performed as described under "Experimental Procedures." Progress curves were linear for 8-10 min, indicating that the reaction was pseudo-first order over that period. Fig. 4 shows the double reciprocal plots of the initial velocity, u, uersus the C3 concentration for four different temperatures. The results indicate that the rate of hydrolysis of C3 by the CVF-dependent C3 convertase depends on the C3 concentration in accordance with the Michaelis-Menten equation. were determined by serveral individual experiments. The other parameters were derived from these mean values. Since the CVF-dependent C3 convertase has only one catalytic subunit/molecule, the turnover number is identical with the catalytic center activity. Up to a C3 concentration of about 3 X M, the substrate turnover can be described as a fmt order reaction. The apparent first order rate constants, ko, were determined by two methods as described under "Experimental Procedures" and are also listed in Table I. Thermodynamic Parameters of the Rate-limiting Step-   (Fig. 5 ) . Linearity of the plot allowed the conclusion that the overall catalytic rate constant, k,,,, is the rate constant of the rate-limiting, unimolecular, or pseudounimolecular step rather than an apparent rate constant resulting from several individual elementary reaction steps. From the slope of the Arrhenius plot, the activation energy, E,, of the rate-limiting step was determined to be 10,000 cal. mol". This value corresponds t.o a temperature coefficient, Qlo, of 1.77 for the temperature range investigated. Since the Arrhenius plot was linear, it was concluded that no change in the rate-limiting step occurred within the temperature range studied. The absence of a sudden decline in the plot at higher temperatures indicates that the apparent temperature optimum of the reaction lies above 37 "C.
The transition state theory of absolute reaction rates allowed the determination of the activation enthalpy, AH*, of the rate-limiting step from the slope of a plot of log ( k c a t / T ) uersus 1/T (Fig. 6). A value of 9450 cal-mol" was found for the activation enthalpy. The relation of activation energy, E,, and activation enthalpy, AH+, is given by E , = AH* f R . T.
Using this expression, an activation energy of 10,000 cal. mol" was calculated which is consistent with the value derived from the Arrhenius plot. The Gibbs energy of activation, AG', of the rate-limiting step for the faur different temperatures investigated was calculated and the values are shown in Table 11. The activation entropy, AS*, of the rate-limiting step of Complement C3 Conuertase   Thermodynamic Parameters of the Formation of the Enzyme-Substrate Complex-A plot of the Michaelis constants according to the van't Hoff law showed a linear graph (Fig. 7 ) . Since the Michaelis constant is composed of at least three rate constants, a linear plot is usually expected only if k,, is much smaller than the rate constant of the dissociation of the enzyme-substrate complex into free enzyme and substrate, k-l. Therefore, it was possible to conclude that the encounter of C3 and enzyme proceeds under rapid equilibrium conditions. This is consistent with the value of the apparent second order rate constant, k,,,/K, (Table I), which is too low for a diffusion-controlled reaction, thereby excluding steady state conditions for the formation of the enzyme-substrate complex.
Since the encounter of C3 and enzyme proceeds under rapid equilibrium conditions, the Michaelis constant, K,, is identical with the substrate constant, K,, which is the reciprocal of the equilibrium constant K for the equilibrium between the enzyme-substrate complex and free enzyme and substrate. Therefore, it was possible to calculate the equilibrium constants K for the four temperatures studied ( Table 111). The standard enthalpy, AH", of the formation of the enzymesubstrate complex was calculated from the slope of the linear van't Hoff plot and a value of 5300 cal-mol" was obtained. The standard Gibbs energies, AGO, for formation of the complex are listed in Table IV, and the standard entropy, AS", was found to be 39.71 cal.mol" .K".
Temperature Dependence of the Apparent Second Order Rate Constant-k,,,/K, is a rather complex function of several rate constants (37) FIG . 7 (left). Temperature dependence of the Michaelis constant K , (van't Hoff plot). FIG. 8 (right). Temperature dependence of the apparent second order rate constant kcat/&.

-"
kcatkcat.rh+l K m kcat + k-I Therefore, the empirical Arrhenius law does not necessarily apply. But since the formation of the enzyme-substrate complex proceeds under rapid equilibrium conditions, kcat is much smaller than k-], and since k+,/k-] equals K , the function becomes k d K , = kc,,. K . Applying the Arrhenius law for kcat and the van't Hoff law for K results in katconstant.e"Eo + A t P 1 I R . T Therefore, the plot of log (kcat/Km) uersus 1/T should be linear. From the slope of the plot, the sum of the activation energy, E,, of the rate-limiting step and the standard enthalpy, AH", of the enzyme-substrate complex formation can be calculated. Fig. 8 shows the plot of log (kcak/Km) uersus 1/T. From the slope, a value for E , + AH" of 15,250 cal. mol" was determined which is consistent with the sum of E,, and AH" (15,300 cal. mol") as determined by Arrhenius (Fig. 5) and van't Hoff plots (Fig. 7 ) .

DISCUSSION
The CVF-dependent C3 convertase rather than the C3bdependent enzyme was chosen for these studies because of its greater stability. The C3b-dependent enzyme, C3b,Bb, exhibits a spontaneous decay-dissociation into its subunits, with a half-life of approximately 1.5 min at 37 "C (2l), whereas a half-life of 7 h was found for the CVF-dependent enzyme. At lower temperatures, the decay-dissociation was slower and freezing to -70 "C inactivated only 30% of the enzyme. A rather high stability of the CVF-dependent C3 convertase has also been reported by other investigators (38-40). The enzyme was also stable enough to perform ultrastructural studies by high resolution transmission electron microscopy (41).
Using the natural substrate C3, we determined the Michae-  (45) and for c l s acting on c 4 (9.6 X M) (49). Except for the recent report of Cls acting on C4 (49), kc,, values have not been determined for complement enzymes. None of the other kinetic parameters described here for the CVF-dependent C3 convertase has been reported for any of the other complement enzymes.
All well investigated proteases like trypsin or chymotrypsin show substrate specificity for a type of peptide bond rather than for a defined molecule and, consequently, hydrolyze substrate proteins at multiple sites into numerous split products. Therefore, all detailed kinetic analyses of these proteases have been performed with artificial substrates. Many kinetic parameters were reported for these substrates (8,(50)(51)(52)(53), but these are not comparable with the data presented here. Because of the high substrate specificity of the CVF-dependent C3 convertase, it was possible to determine many kinetic parameters for this protease acting on its natural high molecular weight protein substrate. The results demonstrate, in addition, that an enzyme-substrate system where enzyme and substrate are both proteins of high molecular weight (-200,000) can be described by Michaelis-Menten kinetics.
The turnover number, or k,,,, for C3 hydrolysis by the CVFdependent C3 convertase is rather low in comparison with many other enzymatic reactions. In order to evaluate the catalytic efficiency of an enzyme, the appropriate parameter is neither kc,, nor K,, but the apparent second order rate constant kCat/K,, which describes the reaction as a function of the concentration of substrate and free enzyme A high k,,,/K, at a K , that is greater than the physiological substrate concentration results in most efficient catalysis and is indicative of a well evolved enzyme (8). At 37 "C, the Kc,,/ K,,, for the CVF-dependent C3 convertase was found to be 4.05 X lo4 s-' M-'. This value excludes the diffusion-controlled encounter of enzyme and substrate as the rate-limiting step of the overall reaction as in the case of extremely fast acting enzymes like catalase (54) or carbonic anhydrase (55). But the kcat/K,,, for C3 hydrolysis by the CVF-dependent C3 convertase is higher than most kCat/Km values reported for proteases like trypsin (50), chymotrypsin (8), elastase (51), papain (52), and pepsin (53) acting on low molecular weight substrates. The rather high kCat/K,,, found for the CVF-dependent C3 convertase suggests a better complementarity between the substrate C3 and the enzyme in the transition state rather than in the enzyme-substrate complex. This conclusion implies that the maximum binding energy is present in the transition state, which is advantageous for the catalytic function of the enzyme (8). In addition, a high binding energy suggests multiple site interactions between enzyme and substrate and may explain the high specificity of the CVF-dependent C3 convertase for its natural substrate C3. The K , for C3, which is 1.16 x M at 37 "C, is approximately twice the physiological C3 concentration in human plasma, which is -6.5 X M (2). Consequently, when the C3 convertase is acting at physiological C3 concentration, the majority of the enzyme is present in free form, which contributes to a high velocity of C3 hydrolysis according to Equation 1.
This analysis of the kinetic data indicates that the C3 convertase is a rather highly evolved enzyme and well suited for its biological function. This conclusion is consistent with in vivo studies (56) which show that this enzyme introduced into the vasculature of an animal effectively hydrolyzes circulating C3.
The kinetic parameters have been determined for the CVFdependent C3 convertase at four different temperatures. Consequently, numerous thermodynamic parameters could be calculated. The Arrhenius plot of the kc,, values was linear and the activation energy could be determined. The linear Arrhenius plot suggests that kc,, depends only on a single rate constant, namely that of the rate-limiting elementary step of the overall reaction. Applying the transition state theory of absolute reaction rates, the activation enthalpy, activation entropy, and Gibbs energy of activation of this rate-limiting step were calculated. The Michaelis constants determined at different temperatures obeyed the van't Hoff law. The linear van't Hoff plot allowed the conclusion that kc,, is much smaller than k-l, the rate constant of the dissociation of the enzymesubstrate complex into free enzyme and substrate. Therefore, the encounter of enzyme and substrate proceeds under rapid equilibrium conditions. This finding is consistent with the order of magnitude of kCat/K,,, (see above) and its temperature dependence (see Fig. 8). It was possible to calculate the equilibrium constant of the equilibrium between the enzymesubstrate complex and free enzyme and substrate and the standard enthalpy, standard entropy, and standard Gibbs energy for the formation of the enzyme-substrate complex. Despite the positive standard enthalpy, AH", the formation of the enzyme-substrate complex is favored due to the increase in entropy. However, the equilibrium constant is not very high (K = 8.62 X lo4 M" at 37 "C), indicating a rather weak affinity of the substrate for the enzyme. The positive standard enthalpy and the rather low equilibrium constant suggest, in accordance with conclusions derived above from kinetic data, that in proceeding from the enzyme-substrate complex to the transition state, no major binding energy has to be overcome, but that the maximum binding energy occurs in the transition state.
The values of the standard entropy, AS", and the activation entropy, AS*, provide information on the nature of the changes in structure and solvation which accompany the formation of the enzyme-substrate complex and the transition state. Formation of the enzyme-substrate complex is accompanied by an increase in entropy. Since two molecules of about identical size form this complex, a decrease of total surface area must occur and therefore it is very likely that the increase in entropy is primarily due to solvation effects such as the release of water molecules. The subsequent conversion of the enzyme-substrate complex to the transition state should not be accompanied by major changes in solvation; and the decrease found in entropy is most likely due to tightening of the structure of the complex. This structural change suggests, in addition, a better complementarity between substrate and enzyme in the transition state than in the enzyme-substrate complex.
The CVF-dependent C3 convertase has been proposed to constitute a serine protease. This hypothesis was first advanced on the basis of inhibition of the proenzyme Factor B as well as the activated enzyme by diisopropylfluorophosphate (57). But the inhibition needed higher diisopropylfluorophosphate concentrations than are required for the inhibition of other serine proteases and other authors reported that Factor B-derived enzymes cannot be inactivated by diisopropylfluorophosphate (36,39,58). In addition, the molecular weight of the Bb polypeptide chain is approximately twice that of other serine proteases. And, no homology of the amino acid sequence in the NH2-terminal region between Bb and other serine proteases was found (59). While the present work was in progress, two reports (60,61) demonstrated an extensive sequence homology of Bb with other serine proteases in the COOH-terminal region of the molecule and showed the pres- differs from that of other serine proteases, but that the catalytic mechanism of Factor B-derived enzymes is a double intermediate mechanism characteristic for serine proteases. The kinetic and thermodynamic characteristics of the catalytic action of serine proteases are well established (8). The potentially rate-limiting elementary reactions are the nucleophilic attack of the active site serine hydroxyl group on the peptide bond carbon atom of the substrate (kt2) and the hydrolysis of the acylenzyme (k+s). The actual rate-limiting step depends on the nature of the substrate. If an amide bond is cleaved, as in the case of natural protein substrates, the fist reaction is the rate-limiting step (kt* << k+s) and K,, = K., = L l / k t z and kc,, = k+:! (8). Consequently, for a serine protease acting on a protein substrate, the encounter of enzyme and substrate proceeds under rapid equilibrium conditions, the van't Hoff plot is linear, kcat is identical with k+2, and the catalytic cycle time corresponds to the mean lifetime of the enzyme-substrate complex.
The results obtained on the action of the CVF-dependent C3 convertase on its natural substrate C3 are consistent with a double intermediate mechanism. Consequently, the thermodynamic parameters of the formation of the enzyme-substrate complex describe the bimolecular reaction k+ 1 k-1 CVF,Bb + C3 7") CVF,Bb. C3 and the thermodynamic parameters for the rate-limiting step describe the unimolecular conversion of the enzyme-substrate complex into the acylenzyme-product complex k+2 CVF,Bb. C3 "+ CVF,Bb-C3a. C3b Fig. 9 shows the changes of the thermodynamic parameters that occur during the initial phase of the overall reaction.
In order to support the concept that the CVF-dependent C 3 convertase is a serine protease, the results have to be consistent with the catalytic and the kinetic reaction mechanism. The overall reaction catalyzed by the CVF-dependent C3 convertase is bimolecular or a two-substrate reaction C3 + HzO CVFIBb+ C3a + C3b Assuming a double intermediate mechanism, the overall reaction is the result of the following sequence of elementary reactions 'Activation enthalpy, activation entropy, and Gibbs energy of activation for the formation of the enzyme-substrate complex have not been determined. Values shown are hypothetical, but obey the Gibbs-Helmholtz law. This reaction sequence is kinetically described as a Tetra Uni Ping Pong Bi Bi mechanism.6 Since Ping Pong mechanisms proceed under steady state conditions and the formation of the enzyme-substrate complex proceeds under rapid equilibrium conditions, the complete kinetic reaction mechanism of a serine protease is a steady state Tetra Uni Ping Pong Bi Bi mechanism with partial rapid equilibrium. The velocity equation for this reaction reduces to the Michaelis-Menten equation of a one-substrate reaction since the second substrate is water (see "Appendix"). Therefore, the kinetic reaction mechanism expected, if the enzyme constitutes a serine protease, is a Uni Bi mechanism. This kinetic characteristic has been observed for the CVF-dependent C3 convertase.
In conclusion, the kinetic and thermodynamic data for C 3 hydrolysis by the CVF-dependent C3 convertase are consistent with a double intermediate catalytic mechanism and a kinetic mechanism of a Tetra Uni Ping Pong Bi Bi reaction reduced to a Uni Bi reaction and support the serine protease concept of Factor B-derived enzymes. If the second substrate is water, as in hydrolytic reactions of serine proteases, it is present in saturating concentrations. Under these conditions, the velocity equation reduces to the normal Michaelis-Menten equation.
The velocity equations of two other common kinetic reaction mechanisms for two-substrate reactions (rapid equilibrium random sequential Bi Bi and steady state ordered sequential Bi Bi) reduce also to the Michaelis-Menten equation if one substrate is water. However, a rapid equilibrium ordered sequential Bi Bi mechanism, with the fiist substrate being C3 and the second substrate being water, can be excluded for the CVF-dependent C3 convertase because our results show a dependence of the initial velocity on the C3 concentration.