Short-lived protease–serpin complexes: Partial disruption of the rat trypsin active site

Abstract

Serpins inhibit serine proteases by mechanically disrupting the protease active site. The protease first reacts with the serpin's reactive center loop (RCL) to form an acylenzyme. Then the RCL inserts into a β-sheet in the body of the serpin, translocating the attached protease ∼70 Å and deforming the protease active site, thereby trapping the acylenzyme. Loop insertion (∼1 s⁻¹) is an order of magnitude slower than hydrolysis of a typical substrate acylenzyme (∼50 s⁻¹), indicating that the protease is inhibited during translocation. We have previously trapped a partially translocated covalent complex of rat trypsin and α₁-proteinase inhibitor (E_partI*) resulting from attractive interactions between cationic dyes and anionic rat trypsin. Here, using single pair Förster resonance energy transfer, we demonstrate that E_partI* is a metastable complex that can dissociate to free protease and cleaved serpin (I*) as well as convert to the canonical fully translocated complex E_fullI*. The partitioning between these two pathways is pH dependent, with conversion favored at low pH and dissociation favored at high pH. The short lifetime of E_partI* (∼3 h at pH 7.4) and the pH dependence of E_partI* dissociation suggest that, unlike in E_fullI*, the catalytic triad is intact in E_partI*. These results also demonstrate that interactions between target proteases and the body of the serpin can hinder protease translocation leading to short-lived covalent complexes.

Inhibitory serpins are ubiquitous regulators of serine and cysteine proteases involved in development, blood coagulation, fibrinolysis, inflammation, and many other physiological processes (Carrell and Travis 1985; Ray et al. 1992; Silverman et al. 2001; Hashimoto et al. 2003). Serpins use a unique, kinetically controlled mechanism in which remodeling of the serpin structure leads to mechanical disruption of the protease active site. As in the normal substrate reaction, the protease docks with the serpin's RCL to form the encounter complex, E•I (Scheme 1; Fig. 1; Ye et al. 2001^; Dementiev et al. 2003). The RCL is then cleaved resulting in the acylenzyme intermediate, E–I, where the C terminus of the cleaved RCL is attached to Ser195 of the protease. The catalytic His57 can then act as a general base to activate water, leading to hydrolysis of the acylenzyme and release of the protease and I*. Alternatively, the RCL can insert into a β-sheet in the body of the serpin translocating the attached protease ∼70 Å. Translocation disrupts the protease active site generating the covalent complex, E_fullI*, and trapping the acylenzyme intermediate (Huntington et al. 2000; Calugaru et al. 2001; Gettins 2002a; Dementiev et al. 2006).

Figure 1.

Protease inactivation by serpins. The protease, E, and serpin, I, dock to form the encounter complex, E•I, shown on the left (Dementiev et al. 2003) (loph.pdb). The RCL is then cleaved, resulting in the acylenzyme intermediate, E–I, which partitions between a substrate-like pathway yielding E and I*, and the inhibitory pathway where the RCL also inserts into β-sheet A and the attached protease is translocated, forming E_fullI*, shown on the right (Huntington et al. 2000) (1ezx.pdb). The protease, BTryp, is green with the catalytic triad in red. The Ile16–Asp194 salt bridge is purple, and the location of Alexa Fluor 555 is in green space fill. The serpin, α₁PI, is shown in blue with the RCL in yellow, β-sheet A in red, and Cys232, to which Atto 610 is attached, is in crimson space fill. Protein figures were made using PyMOL (DeLano Scientific). The generally accepted scheme for the protease–serpin reaction is shown at the bottom.

Structures of covalent complexes between bovine trypsin (BTryp) and the serpin α₁-proteinase inhibitor (α₁PI, also known as α₁-antitrypsin) as well as those between porcine pancreatic elastase and α₁PI show fairly extensive distortions of the protease structure relative to a substrate acylenzyme that can easily account for the stability of the acylenzyme in the serpin complex (Huntington et al. 2000; Dementiev et al. 2006). The oxyanion hole and the S1 site are disrupted, and Ser195 is located ∼6 Å from His57. The salt bridge between the N-terminal Ile16 and Asp194 is also missing, as is the 142–149 loop, and the 218–225 loop is displaced. These distortions appear to result from steric clashes between the protease and the distal portion of the serpin. These clashes would only occur upon full insertion of the RCL into β-sheet A, and therefore require full translocation of the protease (Huntington et al. 2000; Olson et al. 2001; Zhou et al. 2001; Gettins 2002b; Dementiev et al. 2006). The BTryp–α₁PI complex shows more extensive loss of secondary structure (Huntington et al. 2000), although the physiological relevance of this observation is disputed (Dementiev et al. 2006). The energy driving this structural remodeling arises from structural defects in I, which are resolved in I* (Im et al. 1999; Seo et al. 2000, 2002; Lee et al. 2001) as well as from favorable interactions that are unique to I* (Fulton et al. 2005). Thus, cleavage of the RCL allows the serpin to convert to the more stable I* conformation, inhibiting the protease like a molecular mousetrap (Huntington and Carrell 2001).

The partitioning between the substrate and inhibitor pathways (Scheme 1; Fig. 1) is determined by the rate of structural remodeling. However, while full disruption of the protease active site likely occurs late in translocation (Tew and Bottomley 2001; Zhou et al. 2001; Gettins 2002b; Cabrita et al. 2004), the rate constants for insertion of the RCL into β-sheet A are at least an order of magnitude slower than the rate constants of substrate deacylation (∼1 s⁻¹ vs. ∼50 s⁻¹) (Hedstrom 2002; Mellet et al. 2002; Shin and Yu 2006). Therefore, the active site must be perturbed early in the translocation process. Using single pair Förster resonance energy transfer (spFRET), we have previously observed a partially translocated complex E_partI* of rat anionic trypsin (RTryp) and α₁PI (Liu et al. 2006). The peak spFRET efficiency for E_partI* suggest that no more than the first two residues of the cleaved RCL may be inserted into β-sheet A. Partial translocation is not observed with BTryp, and is only found when α₁PI is labeled with cationic dyes at Cys232. Therefore, we proposed that an interaction between the cationic dye and anionic RTryp provides a restraining force that prevents full translocation. Since the protease is only partially translocated, the active site should not be completely disrupted; in fact, E_partI* has a lifetime of hundreds of minutes at pH 7.4 rather than days (Liu et al. 2006).

While our previous work shows that E_partI* can dissociate to E and I*, if E_partI* is trapped in a local energy minimum, it may also convert to E_fullI*. To investigate this possibility and to further characterize this intriguing, short-lived covalent complex, we have monitored the pH dependence of E_partI* decomposition. Here we report spFRET experiments which demonstrate that E_partI* decays to both I* and E_fullI*, and that the deacylation of E_partI* is mediated by His57, indicating that the protease is only partially disrupted. To the best of our knowledge, this work is the first characterization of a partially translocated, partially disrupted protease–serpin covalent complex.

Results

Dissociation of bovine trypsin (BTryp) covalent complexes

Covalent complexes were formed by preincubating BTryp and α₁PI at pH 7.4. After a 15-min incubation, these samples were diluted to 50–100 pM with the appropriate buffer. The apparent rate constants for complex dissociation, k _app, were determined by measuring the spFRET at times ranging from 15 min to 70 h after complex formation. Initially, the spFRET histograms show two distinct peaks (Fig. 2). The peak centers reflect the average distance between the donor and acceptor fluorophores while the half-widths are determined by the relative mobility of the two fluorophores as well as by photon shot noise and detector noise. The peak at 0% spFRET efficiency arises from complexes that only contain donor fluorophores and complexes in which the acceptor fluorophore has photobleached. At longer times, this zero peak also contains contributions from the BTryp released when BTryp-α₁PI covalent complexes dissociate. The wide peak centered at 27% spFRET efficiency arises from E_fullI* (Liu et al. 2006), and corresponds to the fully translocated conformation observed in X-ray crystal structures of α₁PI complexes (Huntington et al. 2000; Dementiev et al. 2006). The locations and half-widths of the spFRET peaks are independent of pH (Supplemental Table S1). At pH 7.4, the E_fullI* peak disappears over four days and the zero peak grows as the complex dissociates. The plot of the area under the E_fullI* peak versus time yields a reaction progress curve that is well described by a single-exponential equation (k _app = [6.1 ± 0.3] × 10⁻⁶ s⁻¹) (Fig. 2). The value of k _app is pH dependent, increasing at pH 8.5 and decreasing at pH 5.5 (Fig. 2). These values are ∼10-fold greater than those determined by monitoring the initial rates of BTryp–α₁PI dissociation in bulk experiments (Calugaru et al. 2001), which is reasonable given differences in experimental conditions and design.

Figure 2.

Monitoring dissociation of BTryp–α₁PI covalent complexes using spFRET. (A) Changes in BTryp spFRET histograms over time in 50 mM HEPES, pH 7.4, 100 mM NaCl with the Gaussian fits used to determine peak areas shown as lines. (B) Changes in BTryp spFRET histograms over time in 50 mM Bis-Tris, pH 5.5, 100 mM NaCl with the Gaussian fits used to determine peak areas shown as lines. (C) Area of the BTryp E_fullI* spFRET peak over time at pH 7.4. (D) Area of the BTryp E_fullI* spFRET peak over time at pH 5.5. For C and D, the line shows the fit to a single exponential used to determine k_app at pH 7.4 and pH 5.5, respectively.

Disappearance of rat trypsin (RTryp) complexes

RTryp–α₁PI complexes were formed as described above. Initially, RTryp–α₁PI spFRET histograms show three distinct peaks (Fig. 3A): the zero peak, a peak centered at 14% corresponding to E_fullI*, and a third peak centered at 58%. We have established previously that the 58% peak arises from covalent complexes in which RTryp is only partially translocated relative to α₁PI, E_partI* (Liu et al. 2006). E_partI* arises from interactions between anionic RTryp and cationic dyes (including Atto610, Texas Red, and tetramethylrhodamine) located at residue 232, and these interactions counteract the force exerted by the inserting RCL (Mellet et al. 2002; Liu et al. 2006).

Figure 3.

Monitoring dissociation of RTryp–α₁PI covalent complexes using spFRET. (A) Changes in RTryp spFRET histograms over time in 50 mM HEPES, pH 7.4, 100 mM NaCl with Gaussian fits used to determine peak areas shown as lines. (B) Changes in RTryp spFRET histograms over time in 50 mM Bis-Tris, pH 5.5, 100 mM NaCl with Gaussian fits shown as lines. Note the pronounced growth in the E_fullI* peak, 14% spFRET efficiency, at short times. (C) Area of the RTryp E_fullI* spFRET peak (filled squares) and the E_partI* peak (open circles) over time at pH 7.4. (D) Area of the RTryp E_fullI* spFRET peak (filled squares) and the E_partI* peak (open circles) over time at pH 5.5. For E_fullI* in C and D, the line shows the fit to a double-exponential that accounts for both the conversion of E_partI* to E_fullI* at short times and the dissociation of E_fullI* at long times. For E_partI* in C and D, the line is a single-exponential fit to determine k_app,part. The insets shows the E_partI* data at higher resolution. Differences in the Y-axis scale of C and D simply reflect the larger number of photons collected at pH 7.4.

As seen for the BTryp complexes, the locations and half-widths of the spFRET peaks are independent of pH (Supplemental Table S1). Fully translocated RTryp complexes consistently show narrower half-widths than BTryp complexes, independent of the location of the acceptor in α₁PI, reflecting the differences in mobility around trypsin residue 113 in the covalent complexes (Liu et al. 2006).

The distribution of RTryp complexes changes over time (Fig. 3). E_partI* disappears most rapidly under all conditions, and the data are well described by a single-exponential equation with rate constant k _app,part (Figs. 3, 4A). The value of k _app,part displays a bowl-shaped dependence on pH. At pH > 8, only the dissociation of E_partI* to free E and I* is observed. However, at pH < 8, the decrease in the 58% peak is accompanied by increases in both the 0% and 14% peaks, indicating that E_partI* both dissociates and converts to E_fullI* (Fig. 3). The conversion of E_partI* to E_fullI* is a single-exponential process described by the rate constant k_c. The value of k_c decreases with increasing pH, reaching an apparent minimum near pH 8 (Figs. 3, 4B). To determine the pK_a and identify the residue responsible for the decrease in k_c with increasing pH, the pH dependence of k_c was fit to Equation 4 (Fig. 4B) resulting in k _1c ≥ 0.02 s⁻¹, k _2c = (1.4 ± 1.2) × 10⁻⁵ s⁻¹, and pK_a ≤ 4, where k _1c and k _2c are the conversion rate constants for protonated and deprotonated E_partI* species, respectively (Scheme 3).

Figure 4.

(A) The pH dependence of k _app, derived from the dissociation of E_fullI*, with filled squares for RTryp and open squares for BTryp. The line shows the fit to Equation 1 for the RTryp data. Also shown is the pH dependence of k _app,part derived from the disappearance of the E_partI* for RTryp covalent complexes (open circles). As shown in Scheme 2, E_partI* can disappear by converting to E_fullI* with rate constant k_c or by dissociating to E and I* with rate constant k _dp. (B) The pH dependence of conversion, k_c. The line is the fit to Equation 4. (C) The pH dependence of dissociation, k _dp (k _app,part -k_c). The line is the fit to Equation 6. Compared to dissociation of E_fullI* (k _app), the pH-dependent dissociation of E_partI* is less steep indicating that the RTryp active site is not fully deformed.

Scheme 3.

The rate constant for the dissociation of E_partI* (k _dp) can be obtained from the difference between the rate constants for the disappearance of E_partI* (k _app,part) and that for the conversion to E_fullI* (k_c) (Equation 5), (Fig. 4C). The value of k _dp is relatively pH independent in the neutral pH region, but increases at higher pH. Equation 6 was used to model the pH dependence of k _dp resulting in: k ₁ = 0 s⁻¹, k ₂ = (1.16 ± 0.06) × 10⁻⁴ s⁻¹, k _OH = 46 ± 3 M⁻¹s⁻¹, and pK_a = 6.6 ± 0.1, where the uncertainties are based on the 95% confidence intervals. The reported pK_as for RTryp's His57 range from 6.8 for free RTryp (Hedstrom et al. 1996) to ∼8 for RTryp-α₁PI E_fullI* (Kaslik et al. 1997), suggesting that the active site in E_partI* is not disrupted enough to alter the pK_a of His57.

The dissociation of RTryp E_fullI* occurs on a much slower timescale than the disappearance of E_partI*, so the rate constant for this process could be obtained from single-exponential fits to data collected after the E_partI* reaction was complete. Remarkably, the kinetics of RTryp E_fullI* dissociation are indistinguishable from the dissociation of BTryp complexes (Figs. 2–4). The value of k _app is pH independent when pH <5, and increases linearly with pH from pH 6–9 (Fig. 4A), unlike previous experiments involving BTryp complexes where an inflection is observed (Calugaru et al. 2001). Above pH 9, the reaction becomes too fast to measure with diffusion-based spFRET, and the lack of high pH data may obscure this modest inflection point. The pH dependence of k _app is well described by the following equation (Calugaru et al. 2001; Plotnick et al. 2002):

with the water-mediated dissociation rate constant k_H2O = (3.8±0.5) × 10⁻⁷s⁻¹, and the hydroxide ion-mediated rate constant k _OH = 17 ± 1 M⁻¹s⁻¹ (Fig. 4A). The value of k_H2O is very similar to that determined for the dissociation of BTryp–α₁PI complexes in bulk experiments k_H2O = (3.2±0.7) × 10⁻⁷s⁻¹ (Calugaru et al. 2001). However, the value of k _OH determined from bulk experiments is slower (k_OH = 0.4 ± 0.6 M⁻¹s⁻¹) (Calugaru et al. 2001). This discrepancy may arise from differences in buffer conditions as well as differences in the techniques used to monitor complex dissociation. There are slight differences in the k _OH values for E_partI* (k _OH = 46 ± 3 M⁻¹s⁻¹) and E_fullI* suggesting that the acyl linkage may be more solvent accessible in E_partI*.

Discussion

Comparison of BTryp and RTryp E_fullI* complexes

As observed previously, the spFRET histogram E_fullI* peaks for BTryp complexes are much wider than those for RTryp complexes, indicating that the region around residue 113 is more mobile in BTryp complexes. These observations suggest that the structure of BTryp is more disrupted than that of RTryp, which might predict that RTryp E_fullI* complexes should hydrolyze faster than BTryp complexes. Instead, we observe that the values of k_H2O and k _OH are very similar for RTryp and BTryp complexes. These values are also are very similar to those for the hydrolysis of a simple alkylester (Calugaru et al. 2001; Plotnick et al. 2002), and therefore, most probably reflect the intrinsic reactivity of the acylester rather than a protease mediated process. Indeed, the rate of hydrolysis of porcine pancreatic elastase and BTryp covalent complexes with α₁PI are very similar despite the less extensive disruption seen in the elastase complexes (Huntington et al. 2000; Dementiev et al. 2006).

The coupling of translocation and disruption of the protease active site

The E_partI* complex of RTryp–α₁PI is the first example of a partially translocated complex with sufficient stability to permit detailed characterization. As shown in Scheme 2 (Fig. 4), E_partI* can either dissociate to E and I* or convert to E_fullI*. The rapid dissociation of E_partI* at neutral pH is readily explained by the presence of a relatively intact active site, and the pKa, ∼6.6, is most likely due to ionization of the catalytic His57. But, what accounts for the facile conversion of E_partI* to E_fullI*? One possible explanation is that low pH decreases the attractive force between the fluorophore and RTryp thus increasing k_c. Alternatively, lowering the pH may further destabilize the RTryp active site. In common with other serine proteases, RTryp has a stabilizing salt bridge between the N-terminal Ile16 and Asp194 (Hedstrom et al. 1996). We demonstrated previously that mutations which destabilize this salt bridge increase the initial population of E_fullI* at the expense of E_partI* (Liu et al. 2006). The pK_a ≤ 4 determined from the pH dependence of conversion suggests that protonation of an Asp or Glu residue is involved in conversion. Perhaps the protonation of Asp194 facilitates conversion by increasing the compliance of the acylenzyme linkage between RTryp's Ser195 and α₁PI's RCL.

The specificity of the interactions required to trap E_partI* are reminiscent of exosite interactions between positively charged residues in variable region 1 of tissue type plasminogen activator (tPA) and negatively charged residues in the RCL of plasminogen activator inhibitor-1 (PAI-1) C-terminal to the cleavage site (Madison et al. 1989, 1990a,b; Tachias and Madison 1997; Ibarra et al. 2004). In both cases, electrostatic interactions target specific proteases (RTryp but not BTryp for E_partI*) (Liu et al. 2006) (and tPA but not urokinase-type plasminogen activator or trypsin for exosite interactions) (Madison et al. 1990a; Olson et al. 2001; Ibarra et al. 2004) and make loop insertion rate limiting (Kvassman et al. 1998; Olson et al. 2001). Exosite interactions lead to a rapid equilibrium between the tPA–PAI-1 encounter complex and the initial acylenzyme, indicating that the protease active site is intact (Kvassman et al. 1998; Olson et al. 2001). In contrast, in E_partI* the acylenzyme is likely displaced from its location in the encounter complex and the protease active site is partially disrupted.

Shorter-lived α₁PI covalent complexes also occur when one or two Ala residues are added to the RCL N-terminal to the cleavage site (Zhou et al. 2001). Lengthening the RCL increases the distance between the body of α₁PI and the protease in E_fullI*, altering the strain on the acyl linkage and/or its solvent accessibility. Changing the interactions between the serpin and the protease in E_fullI* reduces the half-life of covalent complexes containing the α₁PI Pittsburgh variant of (Met358Arg, P1) from weeks to hours for thrombin and from weeks to minutes for factor Xa (Zhou et al. 2001). The short half-lives observed for RCL extensions and E_partI* illustrate the importance of specific protease–serpin interactions in determining the extent of protease active-site disruption, and thus the lifetime of covalent complexes. These and the exosite interactions provide a way for a single serpin to modulate its interactions with different proteases.

Partial disruption of the RTryp active site in E_partI* supports models of serpin inhibition in which full inhibition requires full translocation (Gettins 2002b; Shin and Yu 2006), and reflects the fact that partial translocation does not allow α₁PI to fully exploit the free energy difference between I and I*. Trypsin experiences two opposing forces during translocation: the force exerted by the serpin pulling on the protease and the opposing force of viscous drag from the solvent. Decreasing the energy stored in the initial, metastable serpin structure or increasing the drag decreases the rate of translocation (Shin and Yu 2006). The cationic dye label augments the opposing drag force (Liu et al. 2006). Unlike viscous drag, which affects the entire protein surface, the force from the dye arises from a stationary position. In effect, RTryp serves as the rope in a tug of war, with the RCL pulling in one direction and the fluorophore in another, trapping E_partI* before the RCL fully inserts and while the protease active site retains some structure and catalytic power. However, due to unrelieved strain in the α₁PI structure and the lower energy of the fully remodeled α₁PI structure, E_partI* is only metastable and it must either dissociate or convert to E_fullI*.

This work adds to the growing chain of evidence demonstrating that the stability of protease–serpin complexes is modulated by specific interactions that determine the extent of loop insertion, which in turn, determines the extent of deformation of the active site. While long inhibition requires full insertion of the RCL, short-lived covalent complexes can be generated by adding one or two residues to the RCL (Zhou et al. 2001) or by attractive interactions between the body of the serpin and the protease that counteract full insertion. These interactions can be quite specific, as demonstrated by our ability to trap E_partI* for RTryp but not BTryp complexes, and the fate of the short-lived complexes can be manipulated by changing the solution conditions. This ability to trap partially translocated complexes may allow us to follow serpin conformational changes along the insertion pathway and to engineer short-lived serpin complexes for different proteases.

Materials and Methods

Trypsin preparation

Chymotrypsinogen amino acid numbering is used for all trypsin variants. The Ser113Cys (S113C) bovine trypsinogen variant was expressed as inclusion bodies in Escherichia coli strain SG13009, refolded, purified, and activated to bovine trypsin (BTryp) as described previously (Peterson et al. 2001). The Lys113Cys (K113C) Rat anionic trypsinogen II variant was expressed in Saccharomyces cerevisiae strain DM101α, purified, and activated to RTryp as described previously (Hedstrom et al. 1992; Pasternak et al. 1998).

α₁PI preparation

The wild-type α₁PI gene in the plasmid pEAT8–137 (Kwon et al. 1994; Laska 2001) contains two natural sequence variations, a His101Arg mutation and a Glu376Asp mutation, which do not affect function (Huber and Carrell 1989). All α₁PI variants were expressed as inclusion bodies in E. coli BL21(DE3) cells, refolded, and purified using a combination of methods previously published (Kwon et al. 1994, 1995; Griffiths and Cooney 2002) as described previously (Liu et al. 2006).

Stoichiometry of inhibition (SI)

Trypsin variants were titrated with p-nitrophenyl-p′-guanidinobenzoate HCl to determine the concentration of the active enzyme (Chase and Shaw 1967). Active enzymes comprised >90% of all trypsin samples both before and after fluorescent labeling. The SI, the ratio of moles of serpin needed to inactivate 1 mol of active trypsin, was determined by titrating trypsin with α₁PI as described previously (Rubin et al. 1990). The values of SI are 1 for unlabeled and labeled trypsins and α₁PIs.

Protein labeling

Trypsin variants were labeled at residue 113 with Alexa Fluor 555 maleimide (Invitrogen) according to the manufacturer's instructions. Free dye was separated from trypsin using a soybean trypsin inhibitor column (Sigma Chemical) that binds trypsin. Wild-type α₁PI was labeled with Atto 610 maleimide (Atto-tec) according to the manufacturer's instructions. A PD-10 gel filtration column (GE Healthcare) was used to separate α₁PI from the free dye. The labeling efficiencies were 0.1–0.3 for trypsin and 0.5–0.8 for α₁PI. The value of R_o, the dye separation at which there is 50% energy transfer, is 59 Å for the Alexa Fluor 555-Atto 610 dye pair (Liu et al. 2006).

spFRET data collection and analysis

Donor-labeled trypsin variants (0.5–2 μM) were mixed at a ratio of 1:2 with acceptor-labeled α₁PI in 50 mM HEPES, 100 mM NaCl, pH 7.4 at room temperature. After a 15-min incubation, the samples were diluted to 50–100 pM in 50 mM buffer containing 100 mM NaCl and 10 mM of the trypsin inhibitor benzamidine. The following buffers were used: sodium acetate, pH 4.5 and 5.5; Bis-Tris, pH 6.3; HEPES, pH 7.4 and 8.0; and TAPS, pH 8.5 and 9.1. Samples (300 μL) were applied to coverglass-mounted wells (Nalgene) coated with 1 mg/mL bovine serum albumin (Sigma Chemical) to prevent protein adsorption unto the sides of the wells. The wells were sealed using a coverslip and vacuum grease to prevent evaporation over the course of the experiment. The fluorescence of single complexes diffusing in solution was collected using a one photon single molecule confocal setup with a 100-μm pinhole based on an IX-70 inverted microscope (Olympus) as previously described (Dahan et al. 1999; Liu et al. 2006). Data from the avalanche photodiode detectors were collected at 24 MHz using a two-channel data acquisition card and associated software (ISS).

Data from the donor and acceptor channels were binned at 1 kHz, and a threshold of 40 total, acceptor plus donor, photon counts was used to identify photon bursts arising from complexes diffusing through the illuminated volume. The photon counts were corrected for background fluorescence and for leakage of donor fluorescence in to the acceptor channel. The spFRET efficiency, E, was calculated using (Dahan et al. 1999):

where I is the corrected photon counts and D and A denote the donor and acceptor channels, respectively. The γ factor corrects for differences in the probability of detecting a photon from the donor or acceptor due to differences in the quantum yield, φ, or the detection efficiency of the APDs in different regions of the spectrum, η. For singly labeled samples with identical optical densities at the excitation wavelength, 520 nm, γ is the ratio of the fluorescence intensity of the acceptor-only samples to that of the donor-only samples measured on the single molecule fluorescence setup (Schuler et al. 2002). Values of the γ factor were measured using labeled free trypsin and labeled free α₁PI as well as singly labeled trypsin-α₁PI covalent complexes. The γ factor for BTryp-α₁PI covalent complexes is 1, while that for RTryp-α₁PI covalent complexes is 2 (Liu et al. 2006). The change in γ arises from an increase in Atto-610 fluorescence intensity in the RTryp–α₁PI covalent complexes. SpFRET histograms for RTryp-α₁PI show the same number of peaks and the same peak areas when calculated using γ values of 1 or 2, although the value of γ alters the location of the peaks.

Histograms of the spFRET data were generated and analyzed using Matlab (Mathworks) and Origin (Originlab). The spFRET histogram peak areas, half-widths, and maxima were determined using Gaussian fits to the data.

Determining the pK_a for conversion of E_partI* to E_fullI*

If the protonation of E_partI* affects the rate of conversion from E_partI* to E_fullI*, then conversion may be modeled as:

where k _1c and k _2c are the conversion rate constants for the protonated and deprotonated E_partI* species, respectively, and conversion is irreversible. Based on this Scheme and the apparent conversion rate constant, k_c, experimentally determined from the rate of increase in the E_fullI* population at a variety of pH, the pKa for deprotonation can be determined according to:

where k _1c, k _2c and K_a are fitting parameters. Fits were performed in Origin.

Determining the pK_a for E_partI* dissociation

E_partI* can either convert to E_fullI* or dissociate to form reactivated trypsin, E, and loop inserted α₁PI, I*. Thus, the apparent rate constant for disappearance of E_partI*, k _app,part, is dependent on k_c and the E_partI* dissociation rate constant, k _dp, where both k _app,part and k_c are experimentally determined. At neutral and higher pH, the dissociation rate constant mediated by water molecules, k _H2O, is negligible, and the possible pathways for dissociation are mediated either by hydroxide ions, k _OH, or, if the protonation of E_partI* affects the dissociation rate, by a deprotonated base in the protease or serpin with rate constant k_B:

Similar to Scheme 3 for conversion, the pH dependence of k _dp, and thus the pK_a for B can be derived from Equation 5 and the following scheme:

where k ₁ and k ₂, the base-mediated dissociation rate constants for protonated and deprotonated E_partI*, respectively, are fitting parameters along with K_a and k _OH.

Scheme 4.

Electronic supplemental material

A table of peak centers and half-widths for BTryp and RTryp covalent complexes from pH 4.5–9.1.