Linear competitive inhibition of human tissue kallikrein by 4-aminobenzamidine and benzamidine and linear mixed inhibition by 4-nitroaniline and aniline

Hydrolysis of D-valyl-L-leucyl-L-arginine p-nitroanilide (7.5-90.0 μM) by human tissue kallikrein (hK1) (4.58-5.27 nM) at pH 9.0 and 37oC was studied in the absence and in the presence of increasing concentrations of 4-aminobenzamidine (96-576 μM), benzamidine (1.27-7.62 mM), 4-nitroaniline (16.5-66 μM) and aniline (20-50 mM). The kinetic parameters determined in the absence of inhibitors were: Km = 12.0 ± 0.8 μM and kcat = 48.4 ± 1.0 min-1. The data indicate that the inhibition of hK1 by 4-aminobenzamidine and benzamidine is linear competitive, while the inhibition by 4-nitroaniline and aniline is linear mixed, with the inhibitor being able to bind both to the free enzyme with a dissociation constant Ki yielding an EI complex, and to the ES complex with a dissociation constant Ki, yielding an ESI complex. The calculated Ki values for 4-aminobenzamidine, benzamidine, 4-nitroaniline and aniline were 146 ± 10, 1,098 ± 91, 38.6 ± 5.2 and 37,340 ± 5,400 μM, respectively. The calculated Ki values for 4nitroaniline and aniline were 289.3 ± 92.8 and 310,500 ± 38,600 μM, respectively. The fact that Ki>Ki indicates that 4-nitroaniline and aniline bind to a second binding site in the enzyme with lower affinity than they bind to the active site. The data about the inhibition of hK1 by 4-aminobenzamidine and benzamidine help to explain previous observations that esters, anilides or chloromethyl ketone derivatives of Na-substituted arginine are more sensitive substrates or inhibitors of hK1 than the corresponding lysine compounds. Correspondence

The inhibition of hK1 by BPTI is not a simple competitive inhibition as first reported (6,10), but is competitive inhibition of the parabolic type, with two inhibitor molecules binding to one enzyme molecule, forming a ternary enzymatic complex (12).It is noteworthy that the second BPTI molecule binds to the enzyme with higher affinity, suggesting that this second binding site was probably created or positively modulated as a consequence of the binding of the first BPTI molecule (12).However, the nature of the second binding site for this inhibitor in hK1 is still unknown (12).
There are controversial reports in the literature about the inhibition of hK1 esterase activity by benzamidine (BzA).BzA has been reported to be a competitive inhibitor of the hK1-catalyzed hydrolysis of Tos-Arg-OMe with a K i value of 6.42 mM, but does not inhibit the hK1-catalyzed hydrolysis of Cbz-Tyr-OpNP even at a level of 2 mM (9).On the other hand, BzA has been reported to be a competitive inhibitor of the hK1-catalyzed hydrolysis of Cbz-Tyr-OpNP with a K i value of 0.2 mM (10).However, there are no reports concerning the inhibition of the amidase activity of hK1 by 4aminobenzamidine (4-ABzA), BzA, aniline (An) and 4-nitroaniline (4-NAn).
The purpose of the present study was to examine in depth the kinetics of the inhibition of hK1 amidase activity by 4-ABzA, BzA, 4-NAn and An in order to identify the precise mechanism of inhibition and to determine the number of binding sites and their accurate inhibition constants (K i ).
Our results clearly demonstrate that inhibition of hK1 amidase activity by 4-ABzA and BzA is a linear competitive inhibition with only one inhibitor molecule binding to one enzyme molecule, forming a binary enzymatic complex EI.On the other hand, our results also demonstrate that inhibition of hK1 amidase activity by An and 4-NAn is of the linear mixed type, with the inhibitors being able to bind both to the free enzyme to yield a binary enzymatic complex EI, and to the ES complex to yield a non-reactive ternary enzymatic complex ESI.All other reagents were of reagent grade from Sigma.

Enzyme
Homogeneous hK1 was purified in our laboratory from healthy male urine (12).BPTI-titrated hK1 was used in the enzymatic assays (12).
Bovine ß-trypsin (Bß-TR) (2.91 nM) was also assayed spectrophotometrically at 410 nm with the substrate D-Val-Leu-Arg-Nan (200-600 µM) in 100 mM Tris-HCl buffer, pH 8.1, containing 20 mM CaCl 2 and 0.05% (w/v) NaN 3 , in the absence and in the presence of An (10-40 mM) in order to check for inhibition.Total substrate concentration was determined from the amount of 4-NAn released after complete hydrolysis by excess Bß-TR.In the inhibition assays with 4-NAn the reference cuvette contained the same amount of 4-NAn as the sample cuvette.

Treatment of kinetic data
The kinetic data of the inhibition of hK1 by 4-ABzA and BzA and the kinetic data of Bß-TR inhibition by An can be described, according to Plowman (14), as competitive inhibition.
On the other hand, the kinetic data of the inhibition of hK1 by 4-NAn and An can be described by the following scheme: which, according to Cornish-Bowden (15), is the simplest formal mechanism for mixed inhibition.According to the author, the inhibitor (I) can bind both to the free enzyme (E) to give a complex EI with dissociation constant K i , and to the ES complex to give an unreactive ESI complex with dissociation constant K i .As shown in this scheme, both inhibitor-binding reactions are dead-end reactions and are therefore equilibria.As both EI and ESI exist, however, it is difficult to see why S should not bind directly to EI to give ESI.If this reaction is included in the mechanism the rate equation becomes much more complicated, because terms in S 2 and I 2 appear in it.These terms cancel only if all of the binding reactions are equilibria, i.e., if the substrate-and product-release steps are all fast compared with the reaction that converts ES into products.In practice, however, the predicted deviations from simple kinetics are difficult to detect experimentally, and one cannot use adherence to simple kinetics as evidence that K m , K i and K i are true dissociation constants.
The normalized initial rate (v) will be given by the following equation: According to Cornish-Bowden (15), when linear mixed inhibition occurs, both k cat app , and k cat app /K m app vary with the inhibitor concentration according to the following equations: which can be rearranged to Eq. 6 The kinetic parameters (K m , K m app , k cat , k cat app and K i for 4-ABzA, BzA, 4-NAn and An) were calculated based on unweighted non-linear regression analysis of the data fit to the appropriate Michaelis-Menten equations, while the K i values for 4-NAn and An were determined by fitting the experimental data to Equation 1. Whenever used, the linear replots (Equations 3 and 6) were shown only for diagnostic purposes; they were not used to calculate the K i and K i values.

Results
The hK1-catalyzed hydrolysis of D-Val-Leu-Arg-Nan followed Michaelis-Menten kinetics under the assayed substrate concentration range (7.5-90.0µM). Figure 1 shows the 1/v vs 1/[S] plot for the hydrolysis of D-Val-Leu-Arg-Nan (7.5-90.0µM) catalyzed by hK1 (4.58 nM) in the absence and in the presence of 4-ABzA (1.27-7.62 mM).The inset shows the replot of the slopes of the lines from Figure 1 (K m app /k cat app vs 4-ABzA concentration) according to Plowman (14).Each point is the mean of 4 determinations.Similar results were obtained with BzA.
Figure 2 shows the 1/v vs 1/[S] plot for the hydrolysis of D-Val-Leu-Arg-Nan (7.5-90.0µM) catalyzed by hK1 (5.27 nM) in the absence and in the presence of 4-NAn (16.5-66 µM).Each point is the mean of 4 determinations.Similar results were obtained with An.
Figure 3 shows the replots of K m app /k cat app (panel A) and 1/k cat app (panel B) vs 4-NAn concentration according to Cornish-Bowden (15) (Equations 6 and 3, respectively).The straight lines obtained are consistent with linear mixed inhibition.Statistical analysis of these data using the GraphPad program at the 95% confidence level showed that both lines have slopes that are significantly different from zero, and the statistical test for departure from linearity gave a negative (nonsignificant) result.Similar results were obtained with An.The kinetic parameters for hK1-catalyzed hydrolysis of D-Val-Leu-Arg-Nan in the absence and in the presence of 4-ABzA, BzA, 4-NAn and An are shown in Table 1.

Discussion
During the characterization of our hK1 preparation, we decided to check the inhibition of its amidase activity by 4-ABzA (pK a2 = pK a of the amidinium group = 12.39), BzA (pK a = 11.41),4-NAn (pK a = 1.0) (16) and An (pK a = 4.60) (16).At pH 9.0, the optimum pH for the hK1-catalyzed hydrolysis of D-Val-Leu-Arg-Nan, 4-ABzA and BzA showed a positive charge, while 4-NAn and An had no apparent electric charge, but dipole moments (µ) of 6.10 D and 1.53 D (16), respectively.4-ABzA and BzA were chosen because they are good models of the side chains of arginine and lysine (17) in the usual human tissue kallikrein substrates (6,7).Aniline was also chosen because of its struc- tural relationship to the side chain of the tyrosine constituent of the synthetic substrate CBz-Tyr-OpNP, which was demonstrated to be the hK1 substrate (9,10).On the other hand, 4-NAn was chosen not only because of its structural relationship to An, but also because it shows a larger dipole moment than the dipole moment of An (16); it is also one of the products of the hydrolysis of the chosen substrate.

hK1 inhibition by 4-ABzA and BzA
The double-reciprocal plot indicated that The data in  the hK1-catalyzed hydrolysis of D-Val-Leu-Arg-Nan is competitively inhibited by 4-ABzA (Figure 1).According to Plowman (14), competitive inhibition can be linear, hyperbolic, or parabolic.Thus, in order to distinguish the various types of competitive inhibition, it is necessary to replot the slopes of the lines obtained from the double-reciprocal plot vs inhibitor concentration.The result will be linear, hyperbolic or parabolic curves, distinguishing the various types of inhibition referred to as linear, hyperbolic or parabolic competitive inhibition, respectively.In order to clarify the type of inhibition of hK1 by 4-ABzA, it was decided to replot the slopes of the lines obtained from the double-reciprocal plot (Figure 1) vs 4-ABzA concentration.The results obtained showed a linear curve (Figure 1, inset), indicating that 4-ABzA is a linear competitive inhibitor ( 14) of hK1 amidase activity in the concentration range tested.Similar results were obtained with BzA (data not shown).
The present results can explain previous observations regarding the hK1 substrate specificity, which indicate that arginine ester or anilide derivatives are more sensitive substrates for the enzyme than the corresponding lysine compounds (19).Similarly, our data explain previous observations about the reactivity of arginine and lysine chloromethyl ketones in inactivating hK1 which revealed that the enzyme was 10-fold more reactive with the Arg chloromethyl ketones than with the Lys ones (11).Thus, since the pK a value of the guanidinium group localized on the side chain of Arg is 12.5 and the pK a value of the amino group localized on the side chain of Lys is 10.0, it is easy to explain why hK1 has a significant preference for Arg over Lys residues at the P 1 position (20) of their substrates (21).As previously reported, the stability of ion pairs increases with the difference in pK a of the groups involved (22).In this way, ion pairs formed by a given anion (for instance, carboxylate) with Arg will be more stable than those formed by Lys (22).There is evidence that this is true in many circumstances of biological interests (23,24).The interactions between hK1 and 4-ABzA and BzA seem to follow the same rule.
Comparison of the 4-ABzA and BzA inhibition of the amidase activities of human tissue kallikrein (this work) and trypsin (17) reveals that with these small molecules the inhibition mechanism of these two serine proteinases is similar -both enzymes are inhibited by a linear competitive mechanism.

hK1 inhibition by 4-NAn and An
The Michaelis-Menten plot for the hydrolysis of D-Val-Leu-Arg-Nan (7.5-90 µM) catalyzed by hK1 (4.58-5.27nM) in the absence and in the presence of 4-NAn (pK a = 1.00) (16.5-66 µM) and An (pK a = 4.60) (20-50 mM) showed enzyme inhibition (data not shown).The double-reciprocal plot for the 4-NAn data (Figure 2) showed convergent lines crossing approximately at the same point in the second quadrant, indicating linear mixed inhibition (15).Similar results were obtained with An.The data for 4-NAn and An were also analyzed by the Dixon plot (1/v vs [I]) and by the Cornish-Bowden plot ([S]/v vs [I]) (15), respectively.The straight lines obtained from the Dixon plots intersected approximately at the same point in the second quadrant, while the straight lines obtained from the Cornish-Bowden plots intersected approximately at the same point in the third quadrant (data not shown).These results also indicate linear mixed inhibition (15).According to Segel (25), the Dixon plots for partial and most mixed-type inhibition systems are curved.However, when the ESI complex is not catalytically active, the plot is linear.The data for 4-NAn and An in Table 1 are also not consistent with competitive inhibition.As both K m app and k cat app vary with inhibitor concentration, linear mixed inhibition is suggested (15).
Thus, in order to further clarify the inhibition type, we decided to replot the values of K m app /k cat app and 1/k cat app vs [I], respectively, according to Equations 6 and 3, respectively (Figure 3, panels A and B, shows the results obtained with 4-NAn).Similar results were obtained with An.As both K m app and k cat app vary with [I], linear mixed inhibition was indicated (15).The K i values for 4-NAn (38.6 ± 5.2 µM) and for An (37,340 ± 5,400 µM) and the K i values for 4-NAn (289.3 ± 92.8 µM) and for An (310,500 ± 38,600 µM), respectively, were calculated according to the fit of Equation 1 into the corresponding data in a Michaelis-Menten plot.
Comparison of the K i values for hK1 inhibition by 4-NAn (pK a = 1.00) (38.6 ± 5.2 µM) and 4-ABzA (pK a2 = 12.39) (146 ± 10 µM), respectively, reveals that 4-NAn binds 3.8-fold more strongly to the active center of hK1 than 4-ABzA.Since at pH 9.0 the amidinium group of 4-ABzA is bearing a full positive charge, while the amino group of 4-NAn shows a positive charge induced by intramolecular transfer of electrons from the amino group to the nitro group by isovalent resonance (16,26), it would be reasonable to expect that 4-ABzA would interact better with the S 1 subsite of the active center of hK1 (20) than 4-NAn.However, the data obtained do not concur with this reasoning.As a speculation, we may assume that 4-NAn, after binding to the S 1 subsite of the active center of hK1 (20), possibly could participate in an additional enzyme-inhibitor interaction of the dipole-dipole type, involving the negative charge of the oxygen atom of the nitro group at the C-4 position of the aromatic ring, induced by resonance (16), with some group in the neighborhood of the active center region of hK1, while 4-ABzA, which shows an uncharged-NH 2 group, also at the C-4 position of the aromatic ring, would not participate.The additional dipoledipole interaction would reinforce the binding of 4-NAn to the active center of hK1.
A similar interaction was suggested by Mares-Guia et al. (26) to explain their results about the electronic effects in the interaction of para-substituted benzamidines with trypsin.According to these authors, their data can be interpreted in terms of an enzymeinhibitor interaction of the dipole-dipole type.A dipole will appear in the inhibitor as a consequence of an intramolecular charge transfer from the substituent to the ring or vice-versa.Their data concur with the model in which intramolecular charge transfer renders positive the electron-donating substituent, thereby giving origin to a dipole that is able to interact with a site in the enzyme.According to the authors, the hydroxyl group of the reactive Ser 183 is the most probable candidate for the dipole of the enzyme that interacts with the dipole at the para position in substituted benzamidines.On the other hand, electron-withdrawing groups generate a dipole of opposite polarity that decreases binding by a dipole-dipole repulsion.
We do not know which group is a possible candidate for the dipole of the enzyme that interacts with the dipole in 4-NAn.
Comparison of the K i values for 4-NAn (38.6 ± 5.2 µM) and for An (37,340 ± 5,400 µM) reveals that 4-NAn binds 967-fold more strongly to the active center of hK1 than An.This result is partially consistent with the larger dipole moment of 4-NAn (6.10 D) over An (1.53 D) (16).However, the larger dipole moment of 4-NAn over An is not sufficient to explain the data obtained.As a speculation, we may state that, after binding to the S 1 subsite of the active center of hK1 (20) through its =NH 2 + group, An could not participate in an additional dipole-dipole interaction as 4-NAn can.
Comparison of the K i values for 4-NAn (289.3 ± 92.8 µM) and for An (310,500 ± 38,600 µM) reveals that 4-NAn binds 1073fold more strongly to a second binding site on hK1 than An.The second binding site for these molecules is not known, but it is quite probable that the negative charge of the oxygen atom of the nitro group of the 4-NAn molecule is more available for an additional dipole-dipole interaction with it than the negative charge at the C-4 position of the An molecule.
The fact that K i >K i indicates that both 4-NAn and An bind to a second binding site in the hK1 molecule with lower affinity than they bind to the S 1 subsite of the hK1 active center.
The presence of a second BPTI binding site in hK1 has been already demonstrated (12).We do not know the location of this second binding site for 4-NAn or An in hK1, and also whether it is different from the second binding site for BPTI.
4-NAn is a special case since it is present in the substrate molecule D-Val-Leu-Arg-Nan where it shows neither a positive nor a negative charge.In the ES complex, the Nan (4-NAn) group is accommodated at the S 1 position (20) of the hK1 active center.After substrate hydrolysis the released 4-NAn becomes a dipolar molecule.As a dipolar molecule 4-NAn is able to bind to the anionic site of hK1 as a competitive inhibitor through the positive charge on the amino group, and is also able to bind to a second binding site in hK1, possibly through the negative charge of the oxygen atom of the nitro group.Thus, 4-NAn is a product of the reaction that is able to inhibit hK1 as a mixed inhibitor.
The presence of a second inhibitor binding site in hK1 seems to be clear and may have important implications in the physiological activity of this enzyme.

Bß-TR inhibition by An
Comparison of the k cat /K m values for the hK1-and Bß-TR-catalyzed hydrolysis of D-Val-Leu-Arg-Nan (4.03 ± 0.43 and 8.4 ± 1.8 min -1 µM -1 , respectively) reveals that D-Val-Leu-Arg-Nan is a slightly better substrate for Bß-TR than for hK1.
Additionally, comparison of the K i values for An inhibition of hK1 (37,340 ± 5,400 µM) and of Bß-TR (10,800 ± 1,000 µM) reveals that An interacts better with the S 1 subsite of the active center of Bß-TR than with the S 1 subsite of the active center of hK1.

Figure 1 -
Figure 1 -Lineweaver-Burk plot for the hydrolysis of D-Val-Leu-Arg-Nan by hK1 in the absence and in the presence of 4-ABzA.Inset, K m app /k cat app vs [4-ABzA].Experimental conditions: 200 mM glycine/NaOH, pH 9.0, 37 o C, 5-min incubation.hK1 concentration: 4.58 nM.4-ABzA concentrations: closed circles, 0 mM; open circles, 0.096 mM; closed triangles, 0.192 mM; open triangles, 0.384 mM, and closed squares, 0.576 mM.Each point in the plot is the mean of quadruplicate determinations.More details are described in Material and Methods.

Table 1 -
Kinetic parameters of human tissue kallikrein.