Stopped Flow Fluorescence Energy Transfer Measurement of the Rate Constants Describing the Reversible Formation and the Irreversible Rearrangement of the Elastase-α1-Proteinase Inhibitor Complex*

Serpins are thought to inhibit proteinases by first forming a Michaelis-type complex that later converts into a stable inhibitory species. However, there is only circumstantial evidence for such a two-step reaction pathway. Here we directly observe the sequential appearance of two complexes by measuring the time-dependent change in fluorescence resonance energy transfer between fluorescein-elastase and rhodamine-α1-protease inhibitor. A moderately tight initial Michaelis-type complex EI 1(K i = 0.38–0.52 μm) forms and dissociates rapidly (k 1 = 1.5 × 106 m −1 s−1,k −1 = 0.58 s−1).EI 1 then slowly converts intoEI 2 (k 2 = 0.13 s−1), the fluorescence intensity of which is stable for at least 50 s. The two species differ by their donor-acceptor energy transfer efficiency (0.41 and 0.26, respectively).EI 2 might be the final product of the elastase + inhibitor association because its transfer efficiency is the same as that of a complex incubated for 30 min. The timedependent change in fluorescence resonance energy transfer between fluorescein-elastase and rhodamine-eglin c, a canonical inhibitor, again allows the fast formation of a complex to be observed. However, this complex does not undergo any fluorescently detectable transformation.

Proteolysis, a biologically important event, is regulated by protein proteinase inhibitors that belong to two major classes: the so-called "canonical" inhibitors and the serine proteinase inhibitors, called "serpins." The former are relatively small proteins (29 -190 amino acid residues) that belong to numerous structural families (1). The latter are larger proteins (400 -450 residues) that form a single family with highly conserved secondary structural elements (nine ␣-helices and three ␤-sheets) (2,3).
Canonical inhibitors form tight reversible complexes with their cognate enzymes. X-ray crystallography shows that they have an exposed peptidic sequence, the reactive site loop, that forms a "lock and key" complex with the substrate-binding crevice of the proteinase. This Michaelian-like complex is stabilized by a large number of noncovalent bonds which account for the high enzyme-inhibitor binding energy. Its hydrolysis is probably prevented by a small distortion of the P 1 -P 1 Ј linkage of the inhibitor (1).
Unlike canonical inhibitors, serpins form denaturant-stable complexes with their target proteinases and behave kinetically like irreversible inhibitors (3,4). Their mechanism of action is not well understood mainly because the tertiary structure of their complexes with proteinases has not yet been solved. A significant number of x-ray structures of active and inactive serpins are, however, available (5)(6)(7)(8)(9)(10)(11). These structures reveal that the reactive site loop of serpins is much longer and much more flexible than that of canonical inhibitors. It may easily insert into ␤-sheet A to form the central strand of this unusually malleable (12) sheet. Full insertion of the P 1 to P 14 sequence of the reactive site loop may occur spontaneously (9) or following cleavage of the P 1 -P 1 Ј bond (5). Serpins that have undergone such a ␤-sheet rearrangement are inactive. On the other hand, introduction into ␤-sheet A of a tetradecapeptide structurally related to P 1 -P 14 inactivates serpins because it renders them unable to insert their own P 1 -P 14 sequence (13). Thus, full loop-sheet insertion and lack of insertion both yield inactive serpins. This led to the suggestion that loop-sheet insertion modulates the inhibitory activity of serpins (14) and to the proposal of a number of models for the serpin-proteinase interaction (15)(16)(17)(18). All these models assume that the inhibition reaction takes place in at least two steps: an initial binding followed by a structural rearrangement that stabilizes the complex. However, these steps have not been observed directly and it is not known at which rate the proteinase moves from its initial to its final position.
Just as chemical kinetics helps elucidating reaction mechanisms (19), inhibition kinetics affords insight into inhibition mechanisms. For instance, several years before publication of the first three-dimensional structure of a canonical inhibitorproteinase complex, an inhibition mechanism for a canonical inhibitor has been proposed on the basis of a kinetic analysis (20). Most kinetic studies on serpins have reported measurements of k ass , the second-order inhibition rate constant, which is useful for delineating inhibitor efficiency and physiological function (21) but of poor mechanistic significance because it is a combination of rate constants for the individual reaction steps (22). On the other hand, two-step serpin-proteinase interactions have been demonstrated by a limited number of investigators. The measurements were based on competition experiments in which the serpins displaced a substrate or another ligand from the active center of the proteinase (23)(24)(25)(26). The time course of the reaction was thus followed indirectly. In addition, these experimental approaches did not provide access to k Ϫ1 and k 1 but only to K i , the ratio of these two constants.
We hypothesized that labeling of one reaction partner with a fluorescence donor and of the other with a fluorescence acceptor and measuring the time dependence of the fluorescence resonance energy transfer with a fast kinetic apparatus would allow us to directly observe the individual reaction species as well as the dynamics of their interconversion. The present work checks this hypothesis by investigating the interaction of elastase with ␣ 1 PI, a serpin, and comparing it with binding of elastase with eglin c, a canonical inhibitor.

MATERIALS AND METHODS
Porcine pancreatic elastase (elastase) 1 was isolated and active site titrated as described previously (27). Recombinant ␣ 1 PI and eglin c expressed in Escherichia coli were obtained from Novartis (Basel) and were titrated with human neutrophil elastase (27,28).
Fluorescent Labeling of ␣ 1 PI, Eglin c, and Elastase-␣ 1 PI was specifically labeled on Cys-232, its single free cysteinyl residue using tetramethylrhodamine-5-maleimide (Molecular Probes). A 140 M solution of ␣ 1 PI was made up in 50 mM TES, 150 mM NaCl, pH 7.0, and reacted with a 1.5 molar excess of the labeling reagent dissolved in dimethylsulfoxide. After 1 h at room temperature, excess reagent was removed by two gel filtrations on a PD-10 column (Amersham Pharmacia Biotech) equilibrated with 50 mM Hepes, 150 mM NaCl, pH 7.4. Active site titration with human neutrophil elastase showed that ␣ 1 PI was fully active after labeling. Yields varied from 0.7 to 0.9 label/ molecule of ␣ 1 PI as determined spectrophotometrically using ⑀ 555 nm ϭ 75,000 M Ϫ1 cm Ϫ1 for protein-bound label. Prior reaction of ␣ 1 PI with 4-N,N-dimethylaminoazobenzene-4Ј-iodoacetamido-2Ј-sulfonic acid (Protein Institute, Philadelphia, PA), a specific reagent of free thiols (29), yielded a protein that did not further bind tetramethylrhodamine-5-maleimide, indicating that the latter specifically labels Cys-232.
Eglin c (1.2 mM) was dissolved in the above TES buffer and reacted with a 3-fold molar excess of the succinimidyl derivative of tetramethylrhodamine dissolved in dimethylsulfoxide. After 1 h at room temperature, excess reagent was removed as described above. Active site titration with human neutrophil elastase showed that the labeled inhibitor retained full activity. There was 0.96 molecule of label/molecule of eglin c as determined spectrophotometrically using the above ⑀ 555 nm .
Elastase (0.8 mM) was dissolved in 0.1 M carbonate buffer, pH 9.0, and reacted with a 20-fold molar excess of FITC (Molecular Probes) dissolved in methanol. After 1 h at room temperature, excess reagent was removed by gel filtration on two PD-10 columns equilibrated and developed successively with the above carbonate buffer and with 1 mM HCl. Active site titration of FITC⅐elastase with nonlabeled ␣ 1 PI showed that the enzyme did not loose activity during labeling. There was 1.1 label/molecule of elastase as determined spectrophotometrically using ⑀ 495 nm ϭ 66,800 M Ϫ1 cm Ϫ1 for protein-bound FITC (30). A higher degree of labeling could not be achieved.
Absorption and Fluorescence Measurements-Absorption and emission spectra were recorded on a Cary 4 spectrophotometer and a SLM-8000 spectrofluorometer, respectively. Fluorescence quantum yields of free and ␣ 1 PI-bound FITC elastase were measured using acryflavin as a reference ( ϭ 0.45). Emission spectra were corrected for screening effects at both excitation and emission wavelengths (31).
Kinetics of interaction of FITC⅐elastase with TMR⅐␣ 1 PI or TMR⅐eglin c was monitored by fluorescence resonance energy transfer from FITC to TMR using a Bio-Logic SFM-3 stopped flow apparatus with a dead time of 1.7 ms (Bio-Logic, Claix, France). The reaction was done in 100 mM Hepes, 150 mM NaCl, pH 7.4, 25°C. The excitation and emission wavelengths were 450 and 514 nm (Melles-Griot interferential filter), respectively. Fig. 1 shows the fluorescence spectra of the free and bound species. It can be seen that reaction of FITC⅐elastase with TMR⅐␣ 1 PI significantly quenches the emission of FITC and enhances that of TMR, strongly suggesting fluorescence resonance energy transfer between the donor and the acceptor. To see whether part of the fluorescence intensity variation is due to a change in the environment of the label(s) following complex formation, we have recorded the spectrum of the complex formed of FITC⅐elastase and unlabeled ␣ 1 PI as well as that formed of TMR⅐␣ 1 PI and unlabeled elastase (Fig.  1). In both curves, the binding of the unlabeled protein only marginally affected the fluorescence of the labeled one. This clearly indicates that all of the fluorescence intensity variation is associated with a nonradiative energy transfer process between FITC and TMR.

Steady-state Fluorescence of Free and Bound FITC⅐Elastase and TMR⅐␣ 1 PI-
Kinetics of the Interaction of FITC⅐Elastase with TMR⅐␣ 1 PI- Fig. 2 shows a typical biphasic stopped flow trace observed upon mixing FITC⅐elastase with a 10-fold molar excess of TMR⅐␣ 1 PI. The fluorescence intensity rapidly decreases (t1 ⁄2 Ϸ 60 ms), falls to a minimum and then slowly recovers (t1 ⁄2 Ϸ 5 s) without reaching its initial value. We have tentatively assumed that the initial fluorescence quenching describes the formation of an initial complex EI 1 , which slowly converts into a second complex EI 2 (Fig. 2). The fluorescence intensity was stable for at least 50 s (i.e. 10 t1 ⁄2 of EI 2 formation) whether the reaction was run under pseudo-first-order conditions ( . This indicates that within this interval of time, EI 2 neither releases free FITC⅐elastase, which would enhance the fluorescence intensity, nor converts into a further complex with a different donor-acceptor transfer efficiency. The fluorescence intensity could not be recorded beyond 50 s because of photodecomposition of the label(s).
A control where FITC⅐elastase was mixed with unlabeled ␣ 1 PI showed a fluorescence decay of about 4% over the observation time of 50 s. This small decrease was considered to be negligible and was not taken into account for further calculations. Data analysis showed that the formation of the two complexes could be described by simple exponentials: the pseudo-first-order rate constant of EI 1 formation (k obs ) was 11.8 Ϯ To see whether the EI 1 complex is reversible or irreversible, we have recorded stopped flow traces using constant concentrations of FITC⅐elastase and variable concentrations of TMR⅐␣ 1 PI. We have found that the minimum fluorescence intensity (Fig. 2), a measure of the concentration of EI 1 , varies hyperbolically with the inhibitor concentration (Fig. 3). This rules out irreversible binding because reaction of constant concentrations of enzyme with increasing concentrations of inhibitor should lead to constant concentrations of complex if binding were irreversible. The data of Fig. 3 were thus analyzed assuming that FITC⅐elastase (E) and TMR⅐␣ 1 PI (I) form a reversible complex EI 1 whose equilibrium dissociation constant K i may be calculated by fitting the fluorescence data to Equation 1.
where ⌬F is the difference between the minimum fluorescence intensity of EI 1 and the fluorescence intensity at t ϭ 0 while ⌬F max is the asymptotic value of ⌬F for infinite concentrations of inhibitor. Nonlinear regression analysis yielded K i ϭ 0.52 Ϯ 0.08 M. The curve calculated using this value fairly well fits the experimental points (Fig. 3).
The above equilibrium may also be described by the rate constant of complex formation and dissociation by the following interaction.
which may also be written as E L | ; if pseudo-first-order conditions prevail. Hence, k obs , the pseudofirst-order rate constant for the EI 1 formation is given by To determine k 1 and k Ϫ1 we have measured k obs under pseudo-first-order conditions. Fig. 4 shows that k obs is linearly related to [I] o as predicted by Equation 2. The individual rate constants were calculated by linear regression analysis k 1 ϭ (1.5 Ϯ 0.02) ϫ 10 6 M Ϫ1 s Ϫ1 , k Ϫ1 ϭ 0.58 Ϯ 0.08 s Ϫ1 . The equilibrium dissociation constant K 1 of the EI 1 complex, calculated from k 1 and k Ϫ1 was 0.38 Ϯ 0.06 M. This value is in good agreement with that measured under equilibrium conditions and therefore provides good internal consistency to our data.
On the other hand, the fluorescence intensity corresponding to EI 2 did not change with the inhibitor concentration. In addition, k 2 , the first-order rate constant for the conversion of EI 1 into EI 2 was also inhibitor-independent (data not shown). These two observations are interpreted to mean that k 2 is a true first-order rate constant, i.e. that the transformation of EI 1 into EI 2 is an irreversible process. Our data therefore provide a complete kinetic description of the minimum steps of the interaction of elastase with ␣ 1 PI: Energy Transfer Efficiency within the FITC⅐Elastase-TMR⅐␣ 1 PI Complexes-The transfer efficiency, E D , within the complex prepared by manually mixing labeled elastase with labeled ␣ 1 PI (see legend to Fig. 1) was derived from steadystate fluorescence measurements and calculated as follows: where D,A and D are the quantum yields of the FITC⅐elastase-TMR⅐␣ 1 PI complex and the FITC⅐elastase-␣ 1 PI complex, respectively. D,A was corrected to take into account the degree of labeling, f, of ␣ 1 PI by TMR.
Following corrections for screening effects, E D was found to be 0.26 Ϯ 0.02.
The transfer efficiencies, E D , within the EI 1 and EI 2 complexes detected by stopped flow (Fig. 2) were also calculated from the fluorescence intensities at 515 nm, a wavelength at which FITC is the only fluorescent chromophore: where I D,A and I D are the fluorescence intensities of the FITC⅐elastase-TMR⅐␣ 1 PI complex and the FITC⅐elastase-␣ 1 PI complex, respectively. I D,A was again corrected for the degree of labeling. The screening effect was negligible in the stopped flow experiments. For the EI 2 complex, E D was 0.26 Ϯ 0.03, a value identical to that corresponding to the elastase-␣ 1 PI complex prepared by manual mixing. The value of I D,A used to calculate E D for the EI 1 complex was taken from the minimum fluorescence intensity (Fig. 2) of stopped flow mixtures containing 0.35 M FITC⅐elastase and 11.4 M TMR⅐␣ 1 PI, which yield 97% EI 1 complex, i.e. in which the fluorescence contribution of free FITC⅐elastase is negligible. After correcting for the degree of labeling, E D was found to be 0.41 Ϯ 0.04. Possible random labeling of the lysine residues of elastase precluded interchromophore distance calculations using the E D values.
Kinetics of the Interaction of FITC⅐Elastase with TMR⅐Eglin c-Eglin c is a reversible proteinase inhibitor that belongs to the class of canonical inhibitors (1). Mixing FITC⅐elastase with a 10-fold molar excess of TMR⅐eglin c yields an exponential fluorescence quenching whose amplitude does not change during the 50-s observation time (Fig. 5). This behavior sharply contrasts with that of ␣ 1 PI (Fig. 2). The reversible binding of elastase with eglin c (22) therefore takes place in only one fluorescently detectable step. We have measured the rate constant k obs of fluorescence energy transfer as a function of inhibitor concentration under pseudo-first-order conditions ([I] o ϭ 10 [E] o ). Fig. 6 shows that k obs increases linearly with the inhibitor concentration as already observed with ␣ 1 PI and described by Equation 2. The association rate constant k 1 calculated from this plot was found to be 1.8 ϫ 10 6 M Ϫ1 s Ϫ1 , in good agreement with the value of 10 6 M Ϫ1 s Ϫ1 , measured by enzymatic means (22). The k Ϫ1 value could not be determined accurately because the eglin c concentrations used in these experiments were at least 86-fold higher than the

DISCUSSION
Stopped flow recording of the changes in fluorescence resonance energy transfer observed upon mixing FITC⅐elastase with TMR⅐␣ 1 PI has enabled us to directly observe the sequential appearance of two enzyme-inhibitor complexes with significantly different donor-acceptor energy transfer efficiencies. It is commonly assumed but rarely demonstrated that the first step of the reaction of a proteinase with a serpin is the formation of a reversible Michaelis-type complex involving the substrate-binding site of the enzyme and the reactive site loop of the inhibitor. Serpin-induced displacement of ligands from the active center of proteinases (23)(24)(25)(26) or dissociation of serpinproteinase complexes by ␣ 2 -macroglobulin (32,33) have provided indirect evidence for such a reversible binding step. In the present work an initial complex referred to as EI 1 forms in less than 1 s after mixing. Rate and equilibrium measurements of the building up of this species clearly demonstrate that it is a fast equilibrating reversible complex. We believe this is the first direct evidence for a Michaelis-type complex between a proteinase and a serpin. On the other hand, the conversion of EI 1 into EI 2 is a true first-order process because its rate and amplitude do not depend upon the inhibitor concentration. This indicates that the formation of EI 2 and hence the overall elastase-␣ 1 PI interaction is an irreversible process, a view supported by enzymatic data showing that ␣ 1 PI and other serpins behave like irreversible proteinase inhibitors (4). The two-step model presented here is probably a minimal one because fluorescence detects only those species that significantly differ in energy transfer efficiency, whereas it is not unlikely that undetectable reaction intermediates also appear during the elastase ϩ ␣ 1 PI reaction.
Molecular modeling studies (15,16,18) and biochemical investigations (17,34) indicate that in the course of its reaction with a serpin, the proteinase moves more or less far away from its initial position, whereas the serpin's reactive site loop inserts more or less deeply into ␤-sheet A. It has also been demonstrated that proteinases cleave the P 1 -PЈ 1 bond of serpins and form acyl-enzyme intermediates between the serine residue of their catalytic site and the P 1 residue of the inhibitors. This cleavage is believed to trigger the above conformational changes and, as a consequence, to stabilize the final complex by preventing the hydrolysis of the acyl-enzyme (35,36). These findings may help discuss the nature of the EI 2 complex and the significance of k 2 , the rate constant of its formation. The stopped flow detected complex is probably structurally identical to the stable complex prepared by manual mixing and incubated for 30 min because the two species have identical donor-acceptor transfer efficiencies. As a consequence, EI 2 is likely to be identical with the elastase-␣ 1 PI complex, which Lawrence et al. (35) and Wilczynska et al. (36) have shown to be a translocated acyl-enzyme. Although k 2 describes the first-order fluorescence increase that accompanies the conversion of EI 1 into EI 2 , it is not necessarily the rate constant for the translocation of elastase. The enzyme's acylation and translocation are separate events characterized by two individual rate constants, k acylation and k translocation . Because the EI 1 to EI 2 conversion is a simple exponential process, k 2 might have either one of the following two meanings: (i) k 2 Ϸ k acylation , i.e. k acylation Ͻ Ͻ k translocation or (ii) k 2 Ϸ k translocation , i.e. k acylation Ͼ Ͼ k translocation . The second assumption implies that the acyl-enzyme would be exposed to water during the long lasting translocation process (t1 ⁄2 ϭ 5.3 s). Because enzyme translocation is required to prevent hydrolysis of the acylenzyme, active enzyme would be released during the translocation process. This is not the case because the 1:1 elastase⅐␣ 1 PI complex is enzymatically inactive (4). We may, therefore, tentatively conclude that k 2 is the rate constant for the acylation of elastase. We are not unaware that the above reasoning is somewhat speculative. For instance, despite its having an energy transfer efficiency identical to that of the stable complex prepared by manual mixing, EI 2 might not be the final inhibitory complex because it might still undergo fluorescently silent structural changes. On the other hand, the acylation and the translocation rates might not be as different from each other as we have hypothesized. Clearly, the only way to solve these uncertainties would be to directly measure the rate of acylation.
Like the serpin ␣ 1 PI, the canonical inhibitor eglin c (1) rapidly forms a Michaelis-type complex with elastase, but this complex does not undergo the characteristic conversion seen with the elastase-␣ 1 PI complex. This is in accord with crystallographic data showing that the P 1 -PЈ 1 bond of eglin c is not cleaved within the enzyme-inhibitor complex (37) and that there are no gross structural differences between free and proteinase-bound eglin c (38). Thus, kinetics of fluorescence resonance energy transfer unambiguously discriminates the serpin ␣ 1 PI from the canonical inhibitor eglin c.
Most extracellular serpins play a proteolysis-preventing function. The data collected using our new approach may help to better delineate this function. In vivo, a proteinase is usually released into a milieu containing both serpin and substrate. Knowledge of K i and [I] o , the in vivo inhibitor concentration, will allow prediction of whether the substrate may effectively compete with the serpin for the binding of the proteinase; competition is possible if [I] o /K i Ϸ [S] o /K m . Besides, the magnitude of k Ϫ1 will predict the rate at which a preformed EI 1 complex may be dissociated by substrate. Last, the magnitude of k 2 will predict the apparent reversible or irreversible nature of the inhibition in vivo. If k 2 is fast, for example say k 2 Ͼ 10 Ϫ2 s Ϫ1 (t1 ⁄2 Ͻ 1 min), the inhibition will be irreversible within a few minutes. However, if k 2 Ͻ 10 Ϫ2 s Ϫ1 , the inhibition may be reversible for a prolonged time, a view that is generally overlooked.