1 Introduction

Enzyme kinetics are usually characterized by a sequential process, represented by (at least) two steps: (i) the formation of the enzyme–substrate complex (ES; reaction 1 in Scheme 1), and (ii) the formation of products (P; reaction 2 in Scheme 1). Reaction 2 is commonly represented as irreversible because the reverse reaction rate is very slow. A specific feature of enzyme kinetics is the fact that at the end of the catalytic cycle, the free enzyme E is able to restart the enzymatic reaction. This minimum reaction mechanism is depicted in Scheme 1.

Scheme 1
scheme 1

Minimum reaction mechanism for enzyme catalysis

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The rate of P production allows the empirical resolution of the overall rate (i.e., v) describing enzyme catalysis (see Scheme 1), according to Eq. (1a):

$$ \nu = \frac{{\partial \left[ {{P}} \right]}}{\partial t} = k_{{1{{\text{f}}}}} \cdot \left[ {{E}} \right] \cdot \left[ {{S}} \right] \cdot \frac{{k_{2} \cdot \left[ {{ES}} \right]}}{{\left( {k_{{1{\text{b}}}} \cdot \left[ {{ES}} \right] + k_{2} \cdot \left[ {{ES}} \right]} \right)}} $$
(1a)

where k 1f and k 1b are the forward and backward rate constants for the reaction 1 and k 2 is the rate constant for the reaction 2; the second term in Eq. (1a) represents the probability for the complex ES to either lead to the formation of the product P or to dissociate to E and S. Therefore, two possibilities can be envisaged: (i) when k 2 ≫ k 1b, Eq. (1a) becomes Eq. (1b):

$$ \nu = \frac{{\partial \left[ {{P}} \right]}}{\partial t} = k_{{1{{\text{f}}}}} \cdot \left[ {{E}} \right] \cdot \left[ {{S}} \right] $$
(1b)

and (ii) when k 1b ≫ k 2, Eq. (1a) becomes Eq. (1c):

$$ \nu = \frac{{\partial \left[ {{P}} \right]}}{\partial t} = k_{{1{{\text{f}}}}} \cdot \left[ {{E}} \right] \cdot \left[ {{S}} \right] \cdot \frac{{k_{2} }}{{k_{{1{\text{b}}}} }} = k_{2} \cdot \left[ {{ES}} \right]. $$
(1c)

Since the dissociation equilibrium constant for the formation of the ES complex is described by Eq. (2a):

$$ K_{1} = \frac{{\left[ {{E}} \right] \cdot \left[ {{S}} \right]}}{{\left[ {{ES}} \right]}} = \frac{{k_{{1{\text{b}}}} }}{{k_{{1{\text{f}}}} }} $$
(2a)

the concentration of the ES complex is defined from Eq. (2b):

$$ \left[ {{ES}} \right] = \frac{{k_{{1{\text{f}}}} \cdot \left[ {{E}} \right] \cdot \left[ {{S}} \right]}}{{k_{{1{\text{b}}}} }}. $$
(2b)

Equation (1c) describes enzymes catalysis obeying the so-called Michaelis–Menten approximation, wherefore the overall rate v is normalized for the total enzyme concentration (i.e., [E tot] = [E] + [ES]). Therefore, Eq. (1c) becomes Eq. (3a):

$$ \frac{\nu }{{\left[ {E_{\text{tot}} } \right]}} = k_{\text{cat}} \cdot \frac{{\left[ {{ES}} \right]}}{{\left( {\left[ {{E}} \right] + \left[ {{ES}} \right]} \right)}} $$
(3a)

where k cat = k 2 is defined as the catalytic rate constant.

If we then substitute [ES] with the expression reported in Eq. (2b) the canonical Michaelis–Menten equation is obtained (Eq. 3b):

$$ \frac{\nu }{{\left[ {E_{\text{tot}} } \right]}} = \frac{{k_{\text{cat}} \cdot \left[ {{S}} \right]}}{{K_{m} + \left[ {{S}} \right]}} $$
(3b)

where K m  = K 1 is defined as the Michaelis–Menten constant.

1.1 The catalytic mechanism of proteolytic enzymes

Proteolytic enzymes, or proteinases, lower dramatically the activation free energy barrier for the cleavage of the very stable peptide bond. The proteolytic process takes place through the formation of an acyl-enzyme intermediate (associated with the release of the newly formed amino-terminal group) and the activation of an H2O molecule (which acts as a nucleophile, leading to the release of the newly formed carboxylic terminal group) (Fig. 1). This enzymatic process can be achieved, employing several strategies, which indeed characterize different classes of proteinases, such as (i) serine proteinases, (ii) cysteine proteinases, (iii) aspartate proteinases, (iv) threonine proteinases, and (v) metallo-proteinases. Such a classification essentially reflects the chemical groups polarizing the carbonyl element of the peptide (or of the ester) bond and to initiate the cleavage process. The minimum reaction mechanism for proteinases actions is depicted in Scheme 2.

Fig. 1
figure 1

Schematic sketch of the different steps of the interaction and enzymatic processing of a substrate (i.e., a polypeptide) by a proteolytic enzyme, in this case a serine proteinase (residues numbering corresponds to chymotrypsin). Ground state (1) refers to the species E in Scheme 2, the Michaelis–Menten complex (2) refers to the species ES in Scheme 2, acyl-enzyme (4) refers to the species EP, with k 2 being the rate constant for the passage through the transition state 1 (3), and product (6) refers to the species P 2, with k 3 representing the rate constant for the passage through the transition state 2 (5)

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Scheme 2
scheme 2

Minimum reaction mechanism of proteinases

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The symbols E, S, and ES, already reported in Scheme 1, have the same meaning, EP refers to the acyl-enzyme intermediate, P 1 is the newly formed amino-terminal product, P 2 is the newly formed carboxy-terminal product, k 1f and k 1b are the association and dissociation rate constants for the ES complex formation, respectively, k 2 is the acylation rate constant and k 3 is the deacylation rate constant.

Under the Michaelis–Menten assumption (i.e., k 1b ≫ k 2, see above), parameters reported in Eq. (3b) take into account the two step-mechanisms shown by Scheme 1, thus:

$$ k_{\text{cat}} = \frac{{k_{2} \cdot k_{3} }}{{k_{2} + k_{3} }}. $$
(4a)

and

$$ K_{m} = \frac{{K_{1} \cdot k_{3} }}{{k_{2} + k_{3} }}. $$
(4b)

Consequently, Eq. (3b) becomes Eq. (4c):

$$ \frac{\nu }{{\left[ {E_{\text{tot}} } \right]}} = \frac{{k_{2} \cdot k_{3} \cdot \left[ {{S}} \right]}}{{K_{1} \cdot k_{3} + \left[ {{S}} \right] \cdot (k_{2} + k_{3} )}}. $$
(4c)

Equation (4c) accounts for the acylation and deacylation steps, and turns back to Eq. (3b) when k 3 ≫ k 2. Whenever the deacylation step is much faster than the acylation process, k 2 represents the rate-limiting step of catalysis. On the other hand, if the deacylation is the rate-limiting step (i.e., k 2 ≫ k 3), Eq. (4c) becomes Eq. (4d):

$$ \frac{\nu }{{\left[ {E_{\text{tot}} } \right]}} = \frac{{k_{2} \cdot k_{3} \cdot \left[ {{S}} \right]}}{{K_{1} \cdot k_{3} + \left[ {{S}} \right] \cdot k_{2} }}.$$
(4d)

This different behavior (i.e., k 3 ≫ k 2 or k 2 ≫ k 3) is exemplified in Fig. 2, where the simulation of the time dependence of the concentration of the reaction products (i.e., P 1 and P 2, see Scheme 2) and of the intermediate species (i.e., ES and EP, see Scheme 2) is shown. Under conditions where the acylation process (i.e., k 2) is the rate-limiting step, a steady-state kinetic behavior is present since the onset of the progress curve (see the dashed line in Fig. 2a). On the other hand, if the rate-limiting step is represented by the deacylation process (i.e., k 3) an initial “pre-steady-state” burst phase is observed (see the continuous line in Fig. 2a). This reflects the time evolution of the intermediate species (see Fig. 2b). Therefore, when k 3 ≫ k 2, the ES concentration remains essentially unchanged after the initial formation and only a small amount of EP is detected (see dashed lines in Fig. 2b). On the other hand, when k 2 ≫ k 3, a large amount of EP is built up at the expenses of ES (continuous lines in Fig. 2b) before the instauration of the steady-state process (represented by the flat portion of the simulated time course in Fig. 2).

Fig. 2
figure 2

a Time evolution of the formation of the P 1 and P 2 products (in Scheme 2) with two different rate-limiting steps, namely k 3 (i.e., k 2 = 1 s−1 and k 3 = 0.1 s−1, continuous line) or k 2 (i.e., k 2 = 0.1 s−1 and k 3 = 1 s−1, dashed line). Common parameters: [E tot] = 1 × 10−8 M, [S] = 1 × 10−5 M, K 1 = 1 × 10−5 M, k 1f = 1 × 106 M−1 s−1, k 1b  = 10 s−1. b Time evolution of the populations of ES and EP under the same conditions as in a with two different rate-limiting steps, namely k 3 (i.e., k 2 = 1 s−1 and k 3 = 0.1 s−1, continuous line) or k 2 (i.e., k 2 = 0.1 s−1 and k 3 = 1 s−1, dashed line)

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According to Scheme 2, the initial burst phase can be analyzed in terms of the time-dependent formation of the P 1 species according to Eqs. (5), (6a), and (6b) (Antonini and Ascenzi 1981):

$$ \left[ {{{P}}_{1} } \right] \, = \pi_{0} \cdot \left( {1{-}{{e}}^{{{-}k \cdot t}} } \right) + v \cdot t $$
(5)

where

$$ \pi_{0} = \left[ {{E}} \right] \cdot \left\{ {\frac{{k_{2} \cdot \left[ {{S}} \right]}}{{\left( {k_{2} + k_{3} } \right) \cdot \left( {K_{m} + \left[ {{S}} \right]} \right)}}} \right\}^{2} $$
(6a)

is the amplitude of the initial fast pre-steady-state phase (i.e., the “burst”),

$$ k = \frac{{k_{2} \cdot \left[ {{S}} \right]}}{{K_{1} + \left[ {{S}} \right]}} + k_{3} $$
(6b)

is the apparent rate constant of the initial fast pre-steady-state phase, ν indicates the rate of the subsequent slow steady-state process, and t is the time.

1.2 The case of the prostate-specific antigen (PSA)

The prostate-specific antigen, also known as kallikrein-related peptidase 3 (PSA and KLK3, respectively), is a serine proteinase of 30 kDa belonging to the kallikrein family (Lilja 1985). PSA is synthesized by prostate epithelial cells and its plasma level increases in the course of several diseases, including cancer and prostatitis, even though PSA is kept inactive. Therefore, it represents an invaluable biomarker currently used for early diagnosis of prostate cancer. Moreover, monitoring the serum level of PSA is also useful to predict recurrent cancer forms and to follow up the treatment response in not operable and metastatic tumors (Ilic et al. 2013).

In plasma, PSA is present in two main forms: (i) free PSA, which includes all the unbound zymogen derivatives, and (ii) complexed PSA, which embraces the active forms that are kept latent through the binding of serum protease inhibitors. Notably, extracellular fluid PSA surrounding prostate epithelial cells has been reported to be enzymatically active, suggesting that its proteolytic activity plays a role in the physiopathology of prostate cancer (Denmeade et al. 2001).

PSA is synthesized in the inactive form. The N-terminal region of the zymogen is characterized by (i) the pre-peptide (also known as signal peptide), which is pivotal for the intracellular trafficking, activation, and secretion and (ii) the pro-peptide, which maintains the enzyme in the inactive form. Inside the epithelial cell, the N-terminal 17 amino acid residues of the pre-sequence are first cleaved off by signal peptidases; afterwards, in the extracellular environment, the 7 amino acid pro-sequence is cleaved by human kallikrein 2 (hK2) (Williams et al. 2007).

PSA shows the catalytic triad Asp102/His57/Ser195 present in all serine proteinases (see Fig. 3; Watt et al. 1986); however, unlike most of kallikreins, which display a trypsin-like proteolytic specificity (i.e., they cleave on the carboxyl side of a positively charged amino acid residue, namely Arg and Lys, at the P 1 position), PSA shows instead a chymotrypsin-like substrate specificity (i.e., it cleaves on the carboxyl side of a hydrophobic amino acid residue, namely Tyr, Phe, Trp, and Leu). In addition, PSA is the only member of the kallikrein family that catalyzes the cleavage of substrates displaying the Gln residue at the P 1 position (LeBeau et al. 2009).

Fig. 3
figure 3

The three-dimensional structure of PSA (also named kallikrein 3; NCBI entry number CAD30845.1, PBD file: 3QUM). The image has been drawn using the Swiss-Pdb-Viewer 4.1.0. package. The amino acids of the protein are rendered in solid 3D and they are orange. The three amino acids of the catalytic triad (i.e., Asp 102/His 57/Ser 195) are reported in green. The S1 loop, formed by the 11 residues (all characterized by the serial number 95 followed by the letter according their position, i.e., 95ABCDEFGHIJK), is represented in white. In the case of this loop, the side chains are not shown, except for Lys95E, Arg 95G and Phe95H (color figure online)

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Figure 4 shows a typical time course of the PSA-catalyzed hydrolysis of the fluorogenic substrate Mu-His-Ser-Ser-Lys-Leu-Gln-AMC (wherein Mu is the morpholinocarbonyl protecting group and AMC is the 7-amino-4-methylcoumarin chromophoric group). Over the whole pH range explored (i.e., between pH 6.5 and 9.0), the time course of AMC release is characterized by the initial “burst” phase, which precedes the insurgence of the steady-state phase. This is a typical feature of enzymes characterized by the deacylation step slower than the acylation step (i.e., k 3 ≪ k 2; see Scheme 2).

Fig. 4
figure 4

Time course of the PSA-catalyzed hydrolysis of Mu-His-Ser-Ser-Lys-Leu-Gln-AMC, at pH 7.5 and 37.0 °C. Observation wavelength = 460 nm The concentration of PSA was 50 nM. The concentration of Mu-HSSKLQ-AMC was 5 μM

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Values of the catalytic parameters k cat, K m , k 2, k 3, and K 1 for the PSA-catalyzed hydrolysis of Mu-His-Ser-Ser-Lys-Leu-Gln-AMC were determined according to Eqs. (3b), (4a), (4b), and (6b) (see Fig. 5).

Fig. 5
figure 5

Dependence of k (a) and v (b) on the substrate concentration for the PSA-catalyzed hydrolysis of Mu-His-Ser-Ser-Lys-Leu-Gln-AMC, at 37.0 °C. The continuous lines fitting the data reported in a and b were obtained according to Eqs. (6b) and (3b), respectively, with values of k 2, k 3, and K 1 (a), and of k cat and K m (b) reported in Table 1. Values of pre-steady-state and steady-state parameters were obtained at pH 6.5 (open circle), pH 7.0 (times symbol), pH 7.5 (plus sign), pH 8.0 (asterisk), pH 8.5 (circled times), and pH 9.0 (circled plus)

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The pH dependence of the pre-steady-state and steady-state parameters for the PSA-catalyzed hydrolysis of Mu-His-Ser-Ser-Lys-Leu-Gln-AMC (Fig. 6) can be accounted for by the reaction scheme reported in Table 2 (Gioia et al. 2010), according to Eqs. (7)–(15):

$$ {}^{\text{obs}}k_{\text{cat}} = {}^{0}k_{\text{cat}} \cdot \frac{1}{{P_{L} }} + {}^{1}k_{\text{cat}} \cdot \frac{{K_{L1} \cdot \left[ {{{H}}^{ + } } \right]}}{{P_{L} }} + {}^{2}k_{\text{cat}} \cdot \frac{{K_{L1} \cdot K_{L2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }}{{P_{L} }} $$
(7)
$$ {}^{\text{obs}}k_{2} = {}^{0}k_{2} \cdot \frac{1}{{P_{{ES}} }} + {}^{1}k_{2} \cdot \frac{{K_{{{{ES}}1}} \cdot \left[ {{{H}}^{ + } } \right]}}{{P_{{ES}} }} + {}^{2}k_{2} \cdot \frac{{K_{{{{ES}}1}} \cdot K_{{{{ES}}2}} \cdot \left[ { {{H}} ^{ + } } \right]^{2} }}{{P_{{ES}} }} $$
(8)
$$ {}^{\text{obs}}k_{3} = {}^{0}k_{3} \cdot \frac{1}{{P_{L} }} + {}^{1}k_{3} \cdot \frac{{K_{L1} \cdot \left[ {{{H}}^{ + } } \right]}}{{P_{L} }} + {}^{2}k_{3} \cdot \frac{{K_{L1} \cdot K_{L2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }}{{P_{L} }} $$
(9)
$$ {}^{\text{obs}}K_{m} = {}^{0}K_{m} \cdot \frac{{1 + K_{U1} \cdot \left[ {{{H}}^{ + } } \right] + K_{U1} \cdot K_{U2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }}{{1 + K_{L1} \cdot \left[ {{{H}}^{ + } } \right] + K_{L1} \cdot K_{L2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }} $$
(10)
$$ {}^{\text{obs}}K_{1} = {}^{0}K_{1} \cdot \frac{{1 + K_{U1} \cdot \left[ {{{H}}^{ + } } \right] + K_{U1} \cdot K_{U2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }}{{1 + K_{{{{ES}}1}} \cdot \left[ {{{H}}^{ + } } \right] + K_{{{{ES}}1}} \cdot K_{{{{ES}}2}} \cdot \left[ {{{H}}^{ + } } \right]^{2} }} $$
(11)
$$ {}^{\text{obs}}\left( {k_{\text{cat}} /K_{m} } \right) = {}^{0}\left( {k_{\text{cat}} /K_{m} } \right) \cdot \frac{1}{{P_{U} }} + {}^{1}\left( {k_{\text{cat}} /K_{m} } \right) \cdot \frac{{K_{U1} \cdot \left[ {{{H}}^{ + } } \right]}}{{P_{U} }} + {}^{2}\left( {k_{\text{cat}} /K_{m} } \right) \cdot \frac{{K_{U1} \cdot K_{U2} \cdot \left[ {{{H}}^{ + } } \right]^{2} }}{{P_{U} }} $$
(12)

where

$$ P_{U} = 1 + K_{U1} \cdot \left[ {{{H}}^{ + } } \right] + K_{U1} \cdot K_{U2} \cdot \left[ {{{H}}^{ + } } \right]^{2} $$
(13)
$$ P_{{ES}} = 1 + K_{{{{ES}}1}} \cdot \left[ {{{H}}^{ + } } \right] + K_{{{{ES}}1}} \cdot K_{{{{ES}}2}} \cdot \left[ {{{H}}^{ + } } \right]^{2} $$
(14)
$$ P_{L} = 1 + K_{L1} \cdot \left[ {{{H}}^{ + } } \right] + K_{L1} \cdot K_{L2} \cdot \left[ {{{H}}^{ + } } \right]^{2} $$
(15)

where obs R refers to the observed parameter at a given pH value, 0 R refers to the parameter value of the un-protonated species, 1 R refers to the single-protonated species, and 2 R refers to the double-protonated species; K U1 and K U2 refer to the pK a values (i.e., \( pK_{U1} = 10^{{K_{U1} }} \) and \( pK_{U2} = 10^{{K_{U2} }} \)) of the protonating residues in the free enzyme, K ES1 and K ES2 refer to the pK a values (i.e., \( pK_{{{{ES}}1}} = 10^{{K_{{{{ES}}1}} }} \) and \( pK_{{{{ES}}2}} = 10^{{K_{{{{ES}}2}} }} \)) of protonating residues in the ES complex, and K L1 and K L2 refer to the pK a values (i.e., \( pK_{L1} = 10^{{K_{L1} }} \) and \( pK_{L2} = 10^{{K_{L2} }} \)) of protonating residues in the EP form (see Scheme 2). The resulting proton-linked parameters are reported in Table 2.

Fig. 6
figure 6

pH dependence of k cat (open circle), k 2 (times symbol), and k 3 (asterisk) (a), of K m (open circle) and K 1 (times symbol) (b), and of k cat/K m (open circle) and k 2/K 1 (times symbol) (c) for the PSA-catalyzed hydrolysis of Mu-His-Ser-Ser-Lys-Leu-Gln-AMC, at 37.0 °C. The continuous lines have been obtained by non-linear least-squares fitting of data according to Eqs. (7)–(12) with parameters reported in Table 2

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Table 1 Different parameters at various pH values, as obtained from the analysis of steady-state kinetics according to Eq. (3b) and of pre-steady-state kinetics according to Eq. (6b)
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Table 2 Proton-linked equilibria for the enzymatic activity of PSA at 37 °C
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The inspection of parameters reported in Table 2 envisages a complex network of interactions, such that protonation and/or deprotonation brings about the modification of different catalytic parameters. In particular, the substrate affinity for the un-protonated enzyme (i.e., E, expressed by K 1 = 8.8 × 10−5 M; see Table 2) shows a fourfold increase upon protonation of one ionizing group (i.e., EH, characterized by K 1H1 = 2.4 × 10−5 M; see Table 2), displaying a pK a  = 8.0 in the free enzyme (i.e., E, characterized by K U1 = 1.1 × 108 M−1; see Table 2), which shifts to pK a  = 8.6 after substrate binding (i.e., ES, characterized by K ES1 = 3.9 × 108 M−1; see Table 2). On the other hand, this protonation process brings about a drastic fivefold reduction of the acylation rate constant k 2 (from 0.15 to 0.036 s−1; see Table 2), which counterbalances the increase of the substrate affinity, ending up with a similar value of k 2/K 1 (or k cat/K m ) between pH 8.0 and 9.0 (see Fig. 6c). Because of the slowing down of the acylation rate constant (i.e., k 2), the difference with the deacylation rate is drastically reduced (thus k 2 ≈ k 3; see Table 2). Further pH lowering brings about the protonation of a second functionally relevant residue, displaying a pK a  = 7.6 in the free enzyme (i.e., E, characterized by K U2 = 4.1 × 107 M−1; see Table 2), which shifts to a pK a  = 5.1 upon substrate binding (i.e., K ES2 = 1.3 × 105 M−1; see Table 2). The protonation of this residue induces a drastic 250-fold decrease of the substrate affinity for the doubly protonated enzyme (i.e., EH2, characterized by K 1H2 = 7.5 × 10−3 M; see Table 2), even though it is accompanied by a 70-fold increase of the acylation rate constant k 2 (= 2.3 s−1; see Table 2).

The pK a value of the first protonating residue returns in the acylated intermediate EP similar to that observed in the free enzyme (= 8.0, see Table 2), indeed suggesting that this ionizing group is interacting with the fluorogenic portion of the substrate (i.e., AMC) which is released after the acylation step (i.e., P 1 in Scheme 2), concomitantly with the formation of the EP complex; therefore, this ionizing group does not seem to be involved anymore in the interaction with the N-terminal portion of the substrate, coming back to a situation similar to that of the free enzyme. On the other hand, the pK a value of the second protonating residue (= 5.1) remains unchanged after the release of AMC (i.e., the formation of the EP complex), indicating that this group is instead involved in the recognition of the substrate N-terminus portion that is transiently covalently bound to the enzyme. Of note, the dissociation (or deacylation) of the EP adduct represents the rate-limiting step in catalysis. Therefore, since this residue (which ionizes around neutrality) is unaffected by the conversion of ES to EP, this indicates that this ionizing residue does not modulate the enzyme/substrate recognition.

As a whole, from the mechanism depicted in Table 2 (Tomao et al. 2014) it comes out that the enzymatic activity of PSA is mainly regulated by the proton-linked behavior of two residues, characterized in the free enzyme by pK U1 = 8.0 and pK U2 = 7.6, which change their protonation state upon substrate binding and product(s) release. Moreover, these two ionizing residues interact selectively with the N- and C-terminal regions of the substrate. The group characterized by pK U1, which interacts with the portion released after the acylation process (probably corresponding to the original C-terminus of the substrate), displays a pK a increase after substrate binding (likely reflecting the fact that protonation favors the formation of the ES complex). On the other hand, the group characterized by pK U2, which interacts with the portion released after the deacylation process, displays a pK a decrease, clearly indicating that the ionizing residue tends to be deprotonated after substrate binding.

The identification of these two residues characterized by substrate-linked pK a shifts is not obvious, even though they are likely located in the kallikrein loop (Menez et al. 2008), which is known to restrict the access of the substrate to the active site and to undergo structural readjustment(s) upon substrate binding (Fig. 3). In particular, a possible candidate for the first protonating residue ionizing at alkaline pH is either Lys95E or Arg95G (see Fig. 3; Menez et al. 2008), which might be involved in the interaction with a carbonyl oxygen, orienting the substrate; this interaction could then distort the cleavage site, slowing down the acylation rate of the ESH (see Table 2). The second protonating residue ionizing around neutrality may be a histidine residue (possibly the catalytic His57 residue), whose protonation dramatically lowers the substrate affinity, though facilitating the acylation step and the cleavage process. However, this identification cannot be considered unequivocal, since additional residues might be involved in the proton-linked modulation of substrate recognition and enzymatic catalysis, as envisaged in a structural modeling study (Singh et al. 2009) suggesting that, beside the His57 catalytic residue, a possible role might be played by His172 (according to the PSA numbering in Menez et al. 2008).

The catalytic behavior of PSA is reminiscent to that of human urinary kallikrein and porcine pancreatic β-kallikrein (Ascenzi et al. 1982, 1984, 1989) representing a specific functional feature of kallikrein-like enzymes, even though it has been observed also in other proteolytic enzymes recognizing cationic substrates, such as trypsin, urokinase, and thrombin, at low pH (Antonini and Ascenzi 1981; Ascenzi et al. 1982, 1986).

2 Concluding remarks

The modulatory role of ionizing residues, which sense in a distinct fashion the acylating and deacylating steps, represents (i) an important mechanism in proteolytic enzymes to regulate macromolecular substrate recognition and product(s) release, and (ii) a relevant aspect to design selective proteolytic enzyme inhibitors.

In view of the very important physio-pathological role of proteolytic enzymes (Sotiropoulou et al. 2009; Mancek-Keber 2014), the investigation of mechanistic details indeed is important for the design of efficient inhibitors for pharmaceutical applications (Aureli et al. 2008; Cereda et al. 2015; Avgeris and Scorilas 2016). Therefore, the detailed mechanistic approach to the enzymatic action of PSA with the characterization of intermediate rate constants along the proteolytic cleavage process opens new scenarios for the design of inhibitory molecules that might influence the “in vivo” activity of this enzyme (Webber et al. 1995; Williams et al. 2007; Ilic et al. 2013) representing the most important marker for the evaluation of the prostate cancer severity (Denmeade et al. 1997, 2001).