Kinetic Dissection of α1-Antitrypsin Inhibition Mechanism*

Serpins (serine protease inhibitors) inhibit target proteases by forming a stable covalent complex in which the cleaved reactive site loop of the serpin is inserted into β-sheet A of the serpin with concomitant translocation of the protease to the opposite of the initial binding site. Despite recent determination of the crystal structures of a Michaelis protease-serpin complex as well as a stable covalent complex, details on the kinetic mechanism remain unsolved mainly due to difficulties in measuring kinetic parameters of acylation, protease translocation, and deacylation steps. To address the problem, we applied a mathematical model developed on the basis of a suicide inhibition mechanism to the stopped-flow kinetics of fluorescence resonance energy transfer during complex formation between α1-antitrypsin, a prototype serpin, and proteases. Compared with the hydrolysis of a peptide substrate, acylation of the protease by α1-antitrypsin is facilitated, whereas deacylation of the acyl intermediate is strongly suppressed during the protease translocation. The results from nucleophile susceptibility of the acyl intermediate suggest strongly that the active site of the protease is already perturbed during translocation.

Serpins (serine protease inhibitors) inhibit target proteases by forming a stable covalent complex in which the cleaved reactive site loop of the serpin is inserted into ␤-sheet A of the serpin with concomitant translocation of the protease to the opposite of the initial binding site. Despite recent determination of the crystal structures of a Michaelis protease-serpin complex as well as a stable covalent complex, details on the kinetic mechanism remain unsolved mainly due to difficulties in measuring kinetic parameters of acylation, protease translocation, and deacylation steps. To address the problem, we applied a mathematical model developed on the basis of a suicide inhibition mechanism to the stoppedflow kinetics of fluorescence resonance energy transfer during complex formation between ␣ 1 -antitrypsin, a prototype serpin, and proteases. Compared with the hydrolysis of a peptide substrate, acylation of the protease by ␣ 1 -antitrypsin is facilitated, whereas deacylation of the acyl intermediate is strongly suppressed during the protease translocation. The results from nucleophile susceptibility of the acyl intermediate suggest strongly that the active site of the protease is already perturbed during translocation.
Serpins 1 (serine protease inhibitors) are responsible for the regulation of proteolysis in many physiological processes, such as blood coagulation, fibrinolysis, compartment activation, and inflammation (1)(2)(3). They share a highly ordered structural architecture consisting of three ␤-sheets, several ␣-helices, and the reactive site loop protruding at one pole of the molecule (4,5). Upon binding a target protease, the serpin acylates the protease, and the resulting cleavage at P 1 -P 1 Ј bond in the reactive site loop of the serpin triggers insertion of the loop into the major ␤-sheet, sheet A, of the serpin molecule, which accompanies translocation of the protease to the opposite pole (6 -10). Such translocation of the protease is the most striking structural change compared with the protease binding of small protease inhibitors like bovine pancreatic trypsin inhibitor (11). In the crystal structure of a serpin-protease complex the active site of the protease is distorted (10), which prevents deacylation and results in trapping the stabilized complex. One prominent feature of the serpins is that the native state is not in the most stable state but in a strained metastable state (2,4,5,12). The strain in the native conformation of the serpin appears to provide the driving force for the structural transition during the complex formation (1,10,(13)(14)(15).
Serpins inhibit target proteases by suicide substrate mechanism as depicted in Scheme 1 (6,16), where E denotes protease; I, serpin; EI, noncovalent Michaelis complex; E-I, the acyl complex prior to translocation of protease; I*, cleaved serpin formed by deacylation of acyl linkage in E-I; E-I*, the stable covalent complex in which protease is completely translocated to the opposite pole.
The stoichiometry of inhibition (SI, the number of moles of serpin inhibitor required to completely inhibit 1 mole of a target protease) is designated as 1 ϩ k deac /k tr and is determined by the competing rates of deacylation and the protease translocation. Various studies suggested that the rate of loop insertion is critical for the inhibitory function (6), and indeed retardation of the loop insertion by mutations showed a correlation with increased SI values (15,17). To elucidate the kinetic mechanism, kinetic analyses were carried out via fluorescent probing for the conformational change of serpins during complex formation (17)(18)(19)(20)(21)(22), measurement of post-complex fragments by high pressure liquid chromatography (22,23), and densitometry of the SDS-resistant complex (21,22,24). However, these kinetic analyses usually resulted in lumped kinetic parameters such as association rate constant (k a ) and SI (25)(26)(27)(28)(29), which did not allow precise understanding of the individual kinetic steps (i.e. acylation, translocation, and deacylation). We describe here a development of a mathematical model for the inhibition kinetics and an interpretation of a time-resolved fluorescence resonance energy transfer from protease to ␣ 1antitrypsin (␣ 1 AT), a prototype serpin, during complex formation with a target protease. This approach allowed us to measure the individual kinetic constants and to compare differences in the reaction of the protease with the serpin and that with a peptide substrate. In addition, steady state kinetic analyses of acyl-transfer efficiency of various nucleophiles provided evidence supporting that the active site of a protease is already perturbed during the translocation.
Determination of SI and Association Rate Constant-The SI was determined as described previously (16). The active concentration of * This research was supported by a National Creative Research Initiatives grant from the Korean Ministry of Science and Technology. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
‡ To whom correspondence should be addressed. Tel.: 82-2-958-6911; Fax: 82-2-958-6919; E-mail: mhyu@kist.re.kr. 1 The abbreviations used are: serpin, serine protease inhibitor; SI, stoichiometry of inhibition; ␣ 1 AT, ␣ 1 -antitrypsin; 1,5-IAEDANS, 5-((((2iodoacetyl)amino)ethyl)amino)naphthalene-1-sulfonic acid; RSL, reactive site loop. elastase was determined by measuring the initial rate of hydrolysis of 1 mM N-succinyl-(Ala) 3 -p-nitroanilide. The active concentration of trypsin was determined using p-nitrophenyl pЈ-guanidinobenzoate as an active site titrant (32). Purified ␣ 1 AT was incubated in 50 l of assay buffer (200 mM Tris, 160 mM NaCl, 0.1% polyethylene glycol 6000, 0.1% Triton X-100, pH 8.0) with 100 nM elastase or trypsin at predetermined molar ratios of ␣ 1 AT to protease. After incubation for 1 h at 25°C, the reaction mixture was diluted 10-fold with the assay buffer, and the residual activity of elastase or trypsin was determined using 1 mM N-succinyl-(Ala) 3 -p-nitroanilide or 0.1 mM D-Pro-Phe-Arg-p-nitroanilide as a substrate, respectively. The activity inhibition was extrapolated to yield the minimum molar ratio of ␣ 1 AT to the protease giving 100% inhibition. Measurements of the SI at pH values other than 8.0 were carried out using the same assay buffer (pH 7.5-8.5) or modified assay buffer (pH 6.5-7.0; Tris was replaced by potassium phosphate). Irrespective of pH values in the incubating solution, residual activity of protease was measured at pH 8.0. Determination of the SI toward elastase in the presence of nucleophiles was carried out in 50 l of the assay buffer (pH 8.0) containing 100 nM elastase and various concentrations of nucleophiles (0 -200 mM for L-Phe-NH 2 and L-Arg-NH 2 ; 0 -540 mM for Gly-NH 2 , L-Ala-NH 2 , L-Val-NH 2 , L-Met-NH 2 , L-Leu-NH 2 , and L-Lys-NH 2 ). After incubation for 1 h at 25°C, the reaction mixture was diluted 10-fold with the assay buffer and the residual activity of elastase was determined using 1 mM N-succinyl-(Ala) 3 -p-nitroanilide. The association rate constant between ␣ 1 AT and the protease was determined using a continuous assay procedure (25,33). Elastase or trypsin (10 nM) was incubated with various concentrations of ␣ 1 AT (100 -300 nM) in the assay buffer containing 1 mM N-succinyl-(Ala) 3 -pnitroanilide or 0.1 mM D-Pro-Phe-Arg-p-nitroanilide, respectively. The reaction was continuously monitored at 410 nm.
pH Dependence of Hydrolysis Kinetics of Elastase and Trypsin-Initial rates of hydrolysis of N-succinyl-(Ala) 3 -p-nitroanilide (0.1-1 mM) or D-Pro-Phe-Arg-p-nitroanilide (10 -100 M) by elastase or trypsin, respectively, were measured spectroscopically using molar extinction coefficient of p-nitroaniline of 8372 M Ϫ1 cm Ϫ1 (determined empirically) at 410 nm in the assay buffer described above. The concentrations of the proteases were 10 nM. At each pH value, K m and V m were obtained by non-linear fits of the kinetic data to Michaelis-Menten equation.
Preparation of Dansyl-labeled ␣ 1 AT-The 314-residue site of ␣ 1 AT was chosen for dansylation because of proximity to the protease (9, 10) and insensitivity to activity change by point mutations (14). The original cysteine at the 232 site was replaced with serine, and a unique cysteinyl residue was introduced at the 314 site by site-directed mutagenesis. Dansylation of the resulting Cys 314 /Ser 232 ␣ 1 AT variant was carried out with thiol-selective reagent, 1,5-IAEDANS, as described elsewhere (9) with a slight modification. The purified ␣ 1 AT mutant (10 -20 M) was reacted overnight with a 20-fold excess of 1,5-IAE-DANS in 50 mM Tris, 150 mM NaCl, pH 8.0, at 4°C in the dark. Dithiothreitol was added to the final concentration of 1 mM to quench the reaction. Residual reagents were removed by applying the solution on gel filtration chromatography (Sephacryl S-100). Labeling efficiency was determined spectrophotometrically using ⑀ 340 of 5700 M Ϫ1 cm Ϫ1 for the dansyl group (9) and the protein absorbance at 280 nm that was corrected for the contribution of dansyl at the wavelength (empirically determined to be 23.7% of the absorbance at 340 nm). The labeling ratios were above 0.95. Covalent complexes of protease-␣ 1 AT were prepared by reaction of 1:1 or 1:1.7 molar ratio of trypsin or elastase over dansyl-labeled ␣ 1 AT, respectively. The products, protease-␣ 1 AT complex and cleaved ␣ 1 AT, were separated by gel filtration chromatography on Sephacryl S-100. In all cases, SDS-polyacrylamide gel electrophoresis was used to characterize the reaction products. All fluorescence measurements were made on an LS-50B luminescence spectrometer (PerkinElmer Life Sciences) at 25°C using a thermostated cuvette. For measurement of fluorescence resonance energy transfer from tryptophan to dansyl, excitation was at 292 nm with emission recorded from 400 to 600 nm. Slits were 4 nm for both excitation and emission.
Stopped-flow Measurements of Inhibitory Complex Formation-Time-resolved fluorescence resonance energy transfer was measured using an SFM-4 stopped-flow apparatus (Bio-Logic, Claix, France).
Elastase-catalyzed Acyl-transfer and Hydrolysis Kinetics-The ratio between aminolysis and hydrolysis of acyl complex formed between elastase and the synthetic peptide spanning from P 4 to P 4 Ј of ␣ 1 AT (8-mer RSL: Ac-Ala-Ile-Pro-Met-Ser-Ile-Pro-Pro-NH 2 ) was determined by analyzing reaction products. Reactions were conducted for 1 h in 200 mM Tris, pH 8.0, containing 100 M synthetic peptide, 0 -40 mM nucleophiles (amide forms of amino acids) and 1 M elastase at 25°C. The reactions were quenched with 16% perchloric acid. After centrifugation of the reaction mixture, 100 l of supernatant was injected into a Vydac C8 column on an Ä cta explorer system (Amersham Biosciences Inc.). A gradient elution of water (A)/acetonitrile (B) (both contain 0.1% trifluoroacetic acid) was used (0 -7 min, isocratic elution of 95/5 (A/B), 7-32 min, linear gradient from 95/5 to 30/70, flow rate of 0.8 ml/min, and detection at 270 nm). Only one N-terminal fragment (Ac-Ala-Ile-Pro-Met) was identified on the reverse phase-high pressure liquid chromatography after hydrolyzing the 8-mer RSL, as reported previously (34). The aminolysis product was estimated from the decrease in the hydrolysis product because the presence of nucleophiles other than water decreased the concentration of the N-terminal fragment due to the formation of the aminolyzed product (Ac-Ala-Ile-Pro-Met-X-NH 2 ). In all cases, the reaction time of 1 h was sufficient to completely hydrolyze and/or aminolyze the 8-mer RSL in the reaction conditions. The ratio between aminolysis and hydrolysis rate constants were determined by linear regression of the product ratio against the concentration of nucleophile as described earlier (35,36). Initial rates of 8-mer RSL hydrolysis by elastase (100 nM) were measured in 200 mM Tris, pH 8.0, using the reverse phase-high pressure liquid chromatography described above. The concentration of the 8-mer RSL was varied between 50 and 500 M. The K m and V m values were obtained by non-linear fit.

Development of the Kinetic Model-
To develop a mathematical model for describing protease inhibition by serpin, mass balance equations for the six-reaction species in Scheme 1 were derived as follows in Equation 1.
Under pseudo-first order reaction conditions ([E] 0 Ͼ Ͼ[I] 0 ), the mass balance equations followed by Laplace transformation are given in matrix form in Equation 2, where ␣, ␤, and ␥ are given in Equations 4 through 6. .
indicates that the observed kinetic constants obtained by fitting the kinetic data to exponential growth function should approach k deac ϩ k tr or k ac as [E] 0 goes infinite.
Characterization of Dansyl-labeled ␣ 1 AT-Given the kinetic model above, kinetic measurement of E-I* production during the reaction was performed by monitoring fluorescence resonance energy transfer from tryptophans in the protease to the dansyl group labeled at Cys 314 of ␣ 1 AT. Fig. 1 shows that emission intensity of the dansyl group increased strongly by complex formation of ␣ 1 AT with elastase (dashed line) or trypsin (dot-dashed line) compared with dansyl-labeled free ␣ 1 AT (solid line) or cleaved ␣ 1 AT (dotted line). Contribution of elastase or trypsin to the emission spectra in the monitored region was negligible (data not shown). It was reported that formation of a Michaelis complex between dansyl-labeled ␣ 1 AT and anhydrotrypsin did not induce any increase in the emission spectra (9). Taken together, increase in the fluorescence intensity upon complex formation can be truly correlated with the actual increase in the concentration of the stable covalent complex (E-I*). To confirm that kinetic and inhibitory properties of ␣ 1 AT are not affected by dansyl labeling and the mutations (N314C/C232S) introduced for the labeling, the SI and association rate constants were measured. Dansyl-labeled ␣ 1 AT and the wild-type ␣ 1 AT exhibited nearly identical values toward both elastase and trypsin (Table I). Therefore, it is a reasonable assumption that the dansyl-labeling does not alter individual kinetic steps of the complex formation.
Stopped-flow Measurements of Inhibitory Complex Formation- Fig. 2A shows typical progress curves during the reaction between dansyl-labeled ␣ 1 AT and a target protease. The progress curve of the reaction between ␣ 1 AT and trypsin showed a double-exponential phase that extrapolated to the fluorescence of free ␣ 1 AT at zero time, whereas the progress curve of the elastase reaction showed a single-exponential phase of which the extrapolation greatly exceeded the fluorescence of free ␣ 1 AT. Fig. 2B shows the observed rate constants (k obs ) as a function of protease concentration (filled symbols, reaction with elastase; open symbols, reaction with trypsin), which follows a hyperbolic dependence. To identify steps corresponding to each phase, pH dependence of each phase was examined. The limiting value of k obs for the reaction between ␣ 1 AT and elastase (Fig. 3A, q) was relatively insensitive to the pH change. Similarly, the limiting value of k obs of the slow phase in the reaction between ␣ 1 AT and trypsin (Fig. 3B, ) was not sensitive to pH change. In contrast, the limiting value of k obs for the fast phase in the reaction between ␣ 1 AT and trypsin showed a bell-shaped pH profile (Fig. 3B, OE). The k cat value for the hydrolysis of N-succinyl-(Ala) 3 -p-nitroanilide or D-Pro-Phe-Arg-p-nitroanilide showed a typical bell-shaped pH profile for both proteases (Fig. 3, A and B, f). The SI values for both reactions were not sensitive to the pH change (data not shown).
Nucleophilic Susceptibility of Acyl Linkage during Complex Formation-Amide forms of amino acids often show high nucleophilicities for acyl transfer reactions catalyzed by proteases. We examined the susceptibility of the acyl linkage between ␣ 1 AT and elastase to nucleophilic attack during conformational change. The presence of the nucleophiles in reaction medium increased SI of ␣ 1 AT (Fig. 4). The nucleophiles added in reaction medium deacylate E-I and regenerate free enzyme as depicted in Scheme 2, where k N is the deacylation rate constant by the nucleophile and [Nu] is the concentration of the nucleophile. As shown in Equation 8, the SI value considering the deacylation by the nucleophiles can be derived as SI ϭ SI 0 ϩ ͑k N /k tr ͓͒Nu͔ (Eq. 8)  where SI 0 is the SI value in the absence of nucleophile. As predicted by Equation 8, irrespective of the nucleophiles employed, the SI values showed a linear correlation with nucleophile concentration (Fig. 4). The increase in SI was not from enhanced deacylation of stable covalent complex (E-I*) because regeneration of protease activity from the stable complex was negligible and was not affected by the nucleophiles under the experimental conditions (data not shown). Because the nucleophiles do not affect k tr , the slopes on the plot reflect relative nucleophilicities, L-Arg-NH 2 showing the strongest nucleophilicity, whereas Gly-NH 2 the weakest. The order of nucleophilicity in Fig. 4 was in accordance with the results from the previous report in which maleyl Ala-Leu-p-nitrobenzyl ester was used as an acyl donor (35). We compared the elastase-catalyzed acyl transfer efficiencies of the nucleophiles for ␣ 1 AT with that for 8-mer RSL (synthetic peptide spanning from P 4 to P 4 Ј of ␣ 1 AT). Relative nucleophilicity toward acyl intermediate between elastase and ␣ 1 AT with respect to water (i.e. k N /k deac ) was obtained by dividing the slopes (k N /k tr ) on Fig. 4 by k deac /k tr (SI Ϫ 1 ϭ 0.68, from Table  I). In case of the reaction with 8-mer RSL, k N /k deac was obtained by measuring the partitioning ratio of the resulting products. Fig. 5 shows the k N /k deac values for the acyl intermediates of elastase formed with ␣ 1 AT (gray bars, left coordinate in the y axis) or with 8-mer RSL (white bars, right coordinate in the y axis). The relative nucleophilicity showed similar propensity for both acyl intermediates, although the values for 8-mer RSL were 6-fold higher than the values for ␣ 1 AT. DISCUSSION Recent structural studies of the stable covalent complex between serpin and protease explain protease distortion as a molecular basis for the high kinetic barrier for the hydrolysis of the complex (10,37). However, details on the kinetic mechanism, such as kinetic parameters of acylation, protease translocation, and deacylation steps, remain unsolved. To date, no successful measurement of the individual kinetic constants has been reported due to absence of a suitable mathematical model enabling appropriate kinetic analysis. The kinetic model developed in the present study afforded measurements of individual kinetic constants in the inhibitory function of ␣ 1 AT and provided a more detailed understanding of serpin inhibition mechanism.
Acylation Is Facilitated, Whereas Deacylation Is Suppressed-It is a reasonable expectation that acylation step (k ac ) of serpin-protease reaction in Scheme 1 exhibits a similar pH profile to that of k cat for the hydrolysis of N-succinyl-(Ala) 3 -pnitroanilide because the active site of the protease is still intact and catalytically functional. On the other hand, the partition-

FIG. 2. Stopped-flow measurement of the complex formation between ␣ 1 AT and protease.
A, time-resolved fluorescence resonance energy transfer was measured using an SFM-4 stopped-flow apparatus (Bio-Logic, Claix, France). Excitation was at 292 nm, and emission was measured using a 435-nm cut-off filter. Reactions were carried out under the pseudo-first order reaction conditions (60 nM ␣ 1 AT, 2 M protease) in 200 mM Tris, pH 8.0, at 25°C. B, the observed rate constants plotted against the concentration of the protease (60 nM ␣ 1 AT, pH 8.0). Symbols are: q, k obs of the reaction between ␣ 1 AT and elastase; E, k obs of the slow phase of the reaction between ␣ 1 AT and trypsin; and Ⅺ, k obs of the fast phase of the reaction between ␣ 1 AT and trypsin. The y axis for the fast phase is shown in the right side. Solid lines represent curve-fitting of the data to a hyperbolic function from which the limiting values of the k obs were obtained.

FIG. 3. The pH dependence of limiting values of the observed rate constants.
Time-resolved fluorescence resonance energy transfer was carried out at 60 nM dansyl-␣ 1 AT (Cys 314 /Ser 232 ) and various concentrations of protease in 200 mM potassium phosphate, pH 6.5-7.0) or 200 mM Tris (pH 7.5-8.5) at 25°C. The limiting values of the k obs were obtained by fitting the data to a hyperbolic function. The k cat values of protease for hydrolysis of an amide substrate were measured to identify which step is associated with each phase. A, reaction between ␣ 1 AT and elastase. Symbols are: q, k obs, lim and f, k cat of elastase for hydrolysis of N-succinyl-(Ala) 3 -p-nitroanilide. B, reaction between ␣ 1 AT and trypsin. Symbols are: , k obs, lim of the slow phase; OE, k obs, lim of the fast phase; and f, k cat of trypsin for hydrolysis of D-Pro-Phe-Arg-p-nitroanilide.
ing step (i.e. k tr ϩ k deac ) is expected to show a similar pH dependence to that of SI (note that k tr ϩ k deac ϭ SI ⅐ k tr ) because the translocation rate (k tr ) does not vary significantly with pH change as reported previously (19). Fig. 3 shows that the pH profile of the fast phase of ␣ 1 AT-trypsin reaction is similar to that of the hydrolysis of D-Pro-Phe-Arg-p-nitroanilide, whereas the slow phase was insensitive to the pH change in both ␣ 1 ATelastase and ␣ 1 AT-trypsin reactions as also observed with SI. The pH profiles of the kinetic constants in Fig. 3 strongly argue that the fast and slow phases observed for the reaction between ␣ 1 AT and trypsin ( Fig. 2A) correspond to acylation and partitioning steps, respectively. The fast phase between ␣ 1 AT and elastase appears to be buried in dead time during stopped-flow measurements, leaving only the slow phase detected (Fig. 2A). From the limiting values of the observed rate constants for the slow phase (k tr ϩ k deac ) and SI (1 ϩ k deac /k tr ), it is possible to obtain individual rate constants (Table II). Some important features on the inhibitory mechanism of ␣ 1 AT can be elicited from the results. First, compared with acylation with 8-mer RSL, acylation by ␣ 1 AT is highly facilitated. The k ac values for elastase and trypsin are much higher with ␣ 1 AT than the corresponding k hyd values measured with the 8-mer RSL (note that acylation is the rate-determining step in the hydrolysis of amide substrate, Refs. 34,38,39). These results indicate that protease binding constrains the reactive site loop of ␣ 1 AT to be posed favorably for acylation. The structure of a proteaseserpin Michaelis complex has been reported recently (40). The structure clearly shows that the reactive site loop undergoes a substantial conformational change upon binding a protease although it is not apparent how the conformational change affects the acylation step. The facilitated acylation accounts for the relatively high association rates of ␣ 1 AT even toward a non-cognate protease like trypsin (Table I) despite a poor substrate specificity of the reactive site loop. Second, deacylation of acyl-linkage during conformational change is strongly suppressed. If the deacylation proceeds just like that of an acyl complex formed with normal amide substrate, k deac should be higher than k ac (34,38,39). However, the k ac /k deac values are much higher than unity (Table II). Third, both k ac and k deac values showed higher values for elastase than for trypsin, although translocation of trypsin is ϳ50% faster than that of elastase. These results indicate that the rate for the physical step of protease translocation is independent of catalytic efficiency of protease toward the reactive site loop. The higher rate constants of elastase for chemical steps such as acylation and deacylation appear to result from a greater substrate preference, as with much higher k hyd of elastase for 8-mer RSL (Table  II). It is worth noting that the translocation rates of the two proteases differ less than 2-fold but the deacylation rate of trypsin is over 16-fold slower than that of elastase. Although retardation of the translocation (e.g. retardation of the loop insertion by some mutations) may lower the inhibition outcome of a given serpin significantly (15,17), the inhibition outcome of a serpin for each target protease may be determined mainly by the difference in the deacylation rate rather than the translocation rate.
Suppression of the Deacylation Is Not from Water Inaccessibility-It is intriguing how the deacylation during the protease translocation is strongly suppressed. Given that k deac is a product of intrinsic deacylation constant and local concentration of water around the active site of protease, there would be two The gray and white bars represent k N /k deac for the reactions with ␣ 1 AT and 8-mer RSL, respectively. The inset shows the ratio of normalized values (each k N /k deac value was normalized by that of Gly-NH 2 ) for ␣ 1 AT over those for 8-mer RSL, which were plotted against the increase in the van der Waals volume of nucleophiles compared with Gly-NH 2 (44).  (39,45,46), k hyd of the 8-mer RSL would be a good indicator to compare with k ac .
b Because the fast phase of the reaction between ␣, AT and elastase is too fast to be observed, accurate measurement of k ac is not possible with our stopped-flow apparatus. options for the suppression: perturbation of active site and/or exclusion of water from the active site. X-ray crystallography and NMR studies on the stable E-I* complex showed that a substantial portion of the protease is deformed (10,37) and that the active site of protease is distorted (10,41,42). It was also reported that the active site of E-I* is completely noncatalytic and shows limited accessibility (43). However, it is not known if the active site of E-I is already distorted and has limited accessibility during the protease translocation. We compared the accessibility of nucleophile to acyl linkage in the acyl intermediate of elastase-␣ 1 AT and that of elastase-8-mer RSL. Fig. 5 shows a similar propensity of k N /k deac values for ␣ 1 AT to the values for 8-mer RSL. However, the k N /k deac values cannot be compared directly because k deac for the two acyl intermediates are different. To examine if the size of the nucleophiles affects the aminolysis of the acyl intermediates, the relative nucleophilicity (i.e. k N /k deac ) shown in Fig. 5 was normalized with that of Gly-NH 2 , the smallest one among the nucleophiles employed. The ratio of the normalized nucleophilicity for the acyl intermediate of ␣ 1 AT-elastase to that for 8-mer RSL (i.e. kЈ N for ␣ 1 AT divided by kЈ N for 8-mer RSL where kЈ N is k N of a nucleophile divided by that of Gly-NH 2 ) were determined. The inset of Fig. 5 shows that the ratios are near unity independent of the increase in the nucleophile size. If the suppression of deacylation in the E-I during translocation results from limited accessibility, the ratio should show negative correlation with the volume increase of the nucleophile. Therefore, the results showed that the acyl linkage of elastase-␣ 1 AT acyl intermediate and that of elastase-8-mer RSL have a similar accessibility to the nucleophiles. The suppression of deacylation during protease translocation thus appears to be not from water inaccessibility but from active site perturbation of protease during the translocation. The water inaccessibility is also counterintuitive because it should accompany close contact of the active site of the protease with the surface of the serpin molecule along the translocation path and thereby involve severe interfacial friction.
Implication for Inhibitory Mechanism-The mathematical model developed in the present study was based on the robustness of Scheme 1 in serpin inhibition mechanism. The branched pathway mechanism depicted in Scheme 1 is based on that the fate of E-I, the common acyl intermediate, is determined by the competing rates of deacylation and protease translocation (6,17). There is an alternative proposal, initial conformation pathway mechanism, in which SI depends on relative population between substrate and inhibitor conformations (28). The fact that SI is affected by nucleophiles (Fig. 4) cannot be explained by the initial conformation pathway mechanism because it is unlikely that the nucleophiles cause allosteric effects to switch a putative inhibitory conformation to a substrate form. Rather, it provides direct evidence supporting the branched pathway mechanism in that the nucleophiles added in medium deacylate the common acyl intermediate as depicted in Scheme 2.
Another issue that remains unresolved is the molecular mechanism for protection of the ester linkage of acyl intermediate from solvent hydrolysis during protease translocation. If the protease moves with its catalytic machinery fully active, the translocation rate should be high enough to override the extensive hydrolysis. However, such a fast translocation of protease requires a high energy cost because of severe friction with solvent. For instance, k tr of human leukocyte elastase (a cognate protease for ␣ 1 AT, SI Х 1) should be at least 1600 s Ϫ1 if an upper limit of SI is set to be 1.01 and k deac is higher than k cat for 8-mer RSL hydrolysis (34). This k tr value is two or three orders higher than the limiting values of the loop insertion rate published so far (15,(17)(18)(19)(20)(21)(22). Therefore, the highly efficient protease inhibition by serpin seems to result from suppressing the deacylation rather than from maximizing the rate of protease translocation, which is supported by our results. Our results also suggest that the protection of the ester linkage during protease translocation is achieved by a similar mechanism, i.e. perturbation of active site, as shown in stable covalent complex (10). Since regeneration of free protease from a stable covalent complex under the experimental conditions was negligible, the observed aminolysis by nucleophiles should occur from the acyl intermediate undergoing conformational change. This suggests that the catalytic function of the active site in E-I is not completely abolished during the translocation but is affected partially to suppress the deacylation. It may be that the protease during the translocation has a property intermediate between fully active EI and completely inactive E-I*. In conclusion, our results suggest that the inhibitory function of the serpin has evolved to suppress overwhelming deacylation even during protease translocation by perturbing the protease active site. The arguments so far open another question of what induces the perturbation.