Kinetic analysis of zymogen autoactivation in the presence of a reversible inhibitor Wei-Ning Wang, Xian-Ming Pan and Zhi-Xin Wang National Laboratory of Biomacromolecules, Institute of Biophysics, Academia Sinica Beijing, P.R. China Limited p roteolysis is a highly specific irreversible process, which can serve to initiate physiological function by con- verting a precursor protein into a b iologically active form. When the activating e nzyme and the ac tivated enzyme coincide, t he process i s an a utocatalytic zymogen activation (i.e. r eactions in which t he zymogens serves as a substrate f or the c orresponding active enzyme). The a ctivity of p roteases is frequently regulated by the binding of specific protease inhibitors. Thus, to understand the biological regulation of proteo lysis, one must understand the role of protease inhibitors. In the present study, a detailed kinetic analysis of autocatalytic reaction modulated by a reversible inhibitor is represented. On the basis of the kinetic equation, a novel procedure is developed to evaluate the kinetic parameters of the reaction. As an example of the application of this method, effects of acetamidine, p-amidinobenzamidine a nd benzamidine o n t he autoactivation of trypsinogen by trypsin were studied. Keywords: limited proteolysis; reversible inhibition; trypsin; trypsinogen; z ymogen activation. Proteolysis is required for a multitude of developmental a nd physiologic events including digestion, metabolism, differ- entiation, immunity, blood coagulation, fibrinolysis, apop- tosis and response to injury [ 1–9]. The e n zymes responsible for the catalysis o f proteolysis are p roteases. During the last century, the number of known enzymes that demonstrate proteolytic a ctivity has increases exponentially an d we h ave an increased understanding of the mechanisms and c ritical roles that proteases play in physiological and pathological processes. Proteases are normally biosynthesized as some- what larger inactive precursors. These precursors are known as zymogens (enzyme precursors, in general, are known a s proenzymes). T he zymogens must undergo an activation process, usually a limited proteolysis, to attain their catalytic activity at a physiologically appropriate time and p lace. Small peptides are cleaved from zymogens to form the active proteases. T he active forms of zymogens usually have powerful physiological effects, an d their synthesis in an inactive form permits them to be safely stored until they are required [1]. When the activating enzyme and the activated enzyme coincide, the process is an autocatalytic zymogen activation. Physiological examples of these processes are the activation of trypsinogen, prekallikrein, pepsinogen, procathepsin B and human blood coagulation factor XII by their active forms of enzymes, respectively [1,10–13]. Limited proteolysis is a highly specific irreversible process, which can serve to initiate physiological function by converting a precursor protein into a biologically active form. The conversion of a zymogen into a protease by cleavage of a single peptide bond is a p recise means of switching on enz yme activity. As this type of activation is irreversible, different mechanisms are needed to prevent proteolysis. Specific protease inhibitors accomplish th is task. T he activity of proteases can be inhibited by the binding of specific protease inhibitors. Both proteolytic enzymes and protease inhibitors are prevalent in all biological tissues and fluids. N early every protease is faced with an antagonist limiting its proteolytic a ctivity locally and in a timely fashion to prevent pathologies. Therefore, the activity of a proteolytic enzyme in a living organism is regulated by synthesis and secretion of the enzyme, by zymogen a ctivation and f requently by inhibit ion [14–16]. In addition, major reasons for proteolysis-induced pathologies are either excessive production of liberation (e.g. from cells and microbes) of proteases o r extensive consumption o f protease inhibitors or both, leading to an imbalance of the physiological protease/inhibitor equilibrium. Therefore, protease inhibitors are promising candidates for new therapeutic approaches based on the basic pathomecha- nisms of these diseases. Thus, t o understand t he biological regulation of proteolysis, one must understand the role o f endogenous and exogenous protease inhibitors [17–20]. Recently, detailed kinetic studies of the autoactivation o f protein kinase and zymogen h ave been reported [21–23]. I n the present communication, a global kinetic analysis of zymogen autoactivation regulated by a reversible inhibitor is represented. As an example of the application of this method, effec ts of acetamidine, p-amidinobenzamidine and benzamidine o n t he autoactivation of t rypsinogen by trypsin were analyzed. Correspondence to Z X. Wang, National Laboratory of Biomacro- molecules, Institute of Biophysics, Academia Sinica Beijing 1 00101, P.R. China. Fax: +86 10 64872026, E-mail: zx wang@sun5.ibp.ac.cn Abbreviations: DFP, diisopropylfluorophosphate; TAME, N-a-p-tosyl- L -arginine methyl ester. (Received 7 September 2004, acc epted 5 Oc tober 2004) Eur. J. Biochem. 271, 4638–4645 (2004) Ó FEBS 2004 doi:10.1111/j.1432-1033.2004.04416.x Theoretical analysis In the case of the autocatalytic reactions, the zymogen serves as a substrate in reactions. The general mechanism of the autocatalytic reaction o f an enzyme in the presence of a reversible inhibitor can be written as shown in Scheme 1: where W is the p eptid e which is e liminated from Z,andI, E and Z represent inhibitor, enzyme and zymogen, respect- ively. In this mech anism, both enzyme E and enzyme– zymogen complex EZ combine with i nhibitor I,butthe enzyme–inhibitor–substrate c omplex does not proceed to form product. As the concentrations of zymo gen and enzyme are of the same order of magnitude, the steady-state assumption is not satisfactory in this case [24]. W hen t here is rapid equilibrium as far a s EI, EZ and EIZ are concerned, i.e. when k 2 is sufficiently small as not to disturb equilib- rium, we then have K S ¼ ½E½Z ½EZ ; K 0 S ¼ ½E½EI ½EIZ K I ¼ ½E½I ½EI ; K 0 I ¼ ½EZ½I ½EIZ ð1Þ The total concentration of enzyme is ½T 0 ¼½E 0 þ½Z 0 ¼½Eþ½Zþ½EIþ2½EZþ2½EIZ ð2Þ where [E] 0 and [Z] 0 are the initial concentrations of the enzyme and zymogen, respectively. Let ½E T ¼½Eþ½EZþ½EIþ½EIZð3Þ when [I] 0 >> [T] 0 , the free inhibitor concentration can be considered to be essentially constant during the period of zymogen activation and, hence, set equal to its total concentration in the derivation of integrated rate expression describing the time dependence of e nzyme formation. Therefore, from Eqns (1–3), w e have K 0 I þ½I 0 K 0 I  ½EZ 2 Àð½T 0 þ K à m Þ½EZ þ ð½T 0 À½E T Þ½E T K 0 I K 0 I þ½I 0 ¼ 0 ð4Þ where, K à m ¼ ðK I þ½I 0 ÞK 0 I K S ðK 0 I þ½I 0 ÞK I ¼ ðK I þ½I 0 ÞK 0 S K 0 I þ½I 0 ð5Þ is the a pparent Michealis–Menten constant for the auto- catalytic reaction. The solution of E qn (4) for [ EZ]isgiven by the quadratic formula as ½EZ¼ K 0 I 2ðK 0 I þ½I 0 Þ Â½T 0 þK à m À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð½T 0 þK à m Þ 2 À4ð½T 0 À½E T Þ½E T  q  Therateoftheenzymeformationisgivenby d½E T  dt ¼k 2 ½EZ¼ k à cat 2 ½T 0 þK à m À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð½T 0 þK à m Þ 2 À4ð½T 0 À½E T Þ½E T  q  ð6Þ where, k à cat ¼ k 2 K 0 I K 0 I þ½I 0 ð7Þ is the apparent turnover number for the autocatalytic reaction. Eqn ( 6) can be rewritten as 2d½E T  ½T 0 þ K à m À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð½T 0 þ K à m Þ 2 À 4ð½T 0 À½E T Þ½E T  q ¼ k à cat dt ð8Þ To integrate this equation, put x ¼ 2½E T À½T 0 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð½T 0 þ K à m Þ 2 À 4ð½T 0 À½E T Þ½E T  q ; so that ½E T ¼ ðx þ½T 0 Þ 2 ÀðK à m þ½T 0 Þ 2 4x ð9Þ and ½T 0 þ K à m À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð½T 0 þ K à m Þ 2 À 4ð½T 0 À½E T Þ½E T  q ¼À ðx À K à m Þðx À K à m À 2½T 0 Þ 2x ð10Þ Differentiation of Eqn (9) with respect to x giv es d½E T ¼ x 2 þ 2K à m ½T 0 þ K Ã2 m 4x 2 dx ð11Þ Substitution of Eqns (10) and (11) into Eqn (8) yields x 2 þ 2K à m ½T 0 þ K Ã2 m xðx À K à m Þðx À K à m À 2½T 0 Þ dx ¼Àk à cat dt: With the boundary condition t ¼ 0, [E T ] ¼ [E] 0 ,this integrates to Àk à cat t ¼ ln x x 0 þ K à m þ½T 0 ½T 0 ln ðx À K à m À 2½T 0 Þðx 0 À K à m Þ ðx 0 À K à m À 2½T 0 Þðx À K à m Þ ð12Þ where, Ó FEBS 2004 Inhibition of zymogen autoactivation (Eur. J. Biochem. 271) 4639 x 0 ¼ 2½E 0 À½T 0 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðK à m þ½T 0 Þ 2 À 4½E 0 ½Z 0 q : In practice, the zymogen preparation a lways contains a trace amount of contaminating active enzyme. Therefore, the initial concentrations of enzyme specie s can be written as [E] 0 ¼ a[T] 0 and [Z] 0 ¼ (1 ) a)[T] 0 where a is a constant. In this case, x 0 in Eqn (12) can be written as x 0 ¼ð2a À 1Þ½T 0 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðK à m þ½T 0 Þ 2 À 4að1 À aÞ½T 2 0 q ; and a can be treated as an unknown parameter to be determined. It can b e s een from Eqns (5) a nd (7) t hat both k à cat and K à m are the functions of inhibitor concentration. Figure 1A,B shows the effects of varying [I] 0 on the k à cat and K à m value. As [I] 0 increases from z ero t o i nfinity, k à cat decreases from k 2 to zero. A plot of 1=k à cat against [I] 0 will give a straight line w ith the slope of 1=k 2 K 0 I and intercept of 1 / k 2 (inset of Fig. 1A). The shape of the p lot o f K à m against [I] 0 will depend on the relative magnitudes o f the two dissociation constants (Fig. 1 B). Curve 1 shows the behaviour when the value of K 0 I is larger than that of K I (i.e. the affinity of the inhibitor I for free enzyme E is lower than for enzyme–zymogen complex, EZ); a s [I] 0 increases f rom zero to infinity, K à m increases f rom K S to a limit of value, K 0 S . O pposite r esults are obtained if K 0 I < K I . Curve 2 corresponds to a h igher value of K I . Note that the expressions of k à cat and K à m are exactly t he same as the case of mixed inhibition for the classical Michealis–Menten k inetics. Three d ifferent types of special cases can be distinguished. In competitive i nhibition, theinhibitorcompeteswiththesubstratefortheactivesite of enzyme (K 0 I !1). The expressions of k à cat and K à m are given by k à cat ¼ k 2 ð13Þ K à m ¼ K S þ K S K I ½I 0 ð14Þ It can be seen from Eqns (13) and ( 14) t hat the apparent turnover number k à cat is independent o f [I] 0 (Fig. 1C), and the apparent Michealis–Menten c onstant K à m increases linearly with [I] 0 . F rom the slope and intercept of this straight line, K I and K S can be determined ( Fig. 1D). In uncompetitive inhibition, the inhibitor b inds directly to the enzyme–zymogen complex but not the free enzyme (K I fi 1), the expressions of k à cat and K à m are k à cat ¼ k 2 K 0 I K 0 I þ½I 0 K à m ¼ K 0 I K S K 0 I þ½I 0 In this case, both k à cat and K à m decrease as [I] 0 increases (Fig. 1 E,F). A straight line will be obtained if 1=K à m is plotted against [I] 0 as shown in the inset of Fig. 1F. According to this plot, uncompetitive inhibition can be easily distinguished from m ixed inhibition. In pure non- competitive inhibition, both enzyme and enzyme–zymogen complex bind inhibitor with equ al affinity (K I ¼ K 0 I ). The expressions of k à cat and K à m are given by k à cat ¼ k 2 K 0 I K 0 I þ½I 0 K à m ¼ K S which is t he special case of mixed inhibition, and as expected, the apparent turnover number k à cat shows a similar behaviour with [I] 0 increases ( Fig. 1G), but the apparent Michaelis constant K à m is independent of [I] 0 (Fig. 1H). In summary, the dependence o f k à cat and K à m upon [I] 0 in the different cases would suggest criteria for discriminating between them and provide estimates o f their kinetic parameters. The equations derived in the p revious section a ssume that there is no depletion of the inhibitor b y t he enzym e. I f, however, the enzyme has v ery high affinity for t he inhibitor, it will be necessary to use v ery low inhibitor concentration i n kinetic studies. A quantitative description of tight binding inhibition cannot be based on Eqn (12), as the assumpton that the free inhibitor c oncentration is equal to t he total inhibitor is not valid. Tight binding inhibitors cause inhibition at concentrations comparable to those at which enzymes are used for k inetic experiments. Consequently, t he formation of an enzyme–inhibitor co mplex can result in a considerable reduction in the concentration of added inhibitor, and a llowance m ust be m ade for this reduction. In the presence of a competitive inhibitor, autocatalytic processing can be represented b y Scheme 2: Fig. 1. Schematic representation of t he plots of k cat * and K m *vs.inhib- itor concentration for the case of m ixed inhibition (A,B); c ompetitive inhibition (C,D); uncompetitive inhibition (E,F); and noncompetitive inhibition (G, H). 4640 W N. Wang et al.(Eur. J. Biochem. 271) Ó FEBS 2004 Assuming that the formation of EZ and EI are fast reactions relative to the cleavage step of the peptide bond, for the three-component system described in Scheme 2, we then have K S ¼ ½E½Z ½EZ ; K I ¼ ½E½I ½EI ð15Þ Let ½Z T ¼½Zþ½EZð16Þ ½E T ¼½Eþ½EZþ½EIð17Þ where [Z T ]and[E T ] represent the total concentrations of zymogen a nd enzyme at any time t during t he reaction. Conservation of mass requires that ½I 0 ¼½Iþ½EIð18Þ ½T 0 ¼½E 0 þ½Z 0 ¼½E T þ½Z T ð19Þ From Eqns ( 15–19), we have [25] ½E 3 þ a½E 2 þ b½Eþc ¼ 0 ð20Þ where, a ¼ K S þ K I þ½T 0 þ½I 0 À 2½E T ; b ¼ K I ð½T 0 À 2½E T Þ þ K S ð½I 0 À½E T Þ þ K S K I and c ¼ÀK S K I ½E T  The solution of Eqn (20) for [E]is ½E¼À a 3 þ 2 3 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ q cos h 3 where, h ¼ arccos À2a 3 þ 9ab À 27c 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ 3 q Therefore, the expression for [EZ]isgivenby ½EZ¼ ð½T 0 À½E T Þ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ p cosðh=3ÞÀa no 3K S þ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ p cosðh=3ÞÀa no The rate of product formation is thus d½E T  dt ¼ k 2 ½EZ ¼ k 2 ð½T 0 À½E T Þ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ p cosðh=3ÞÀa no 3K S þ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða 2 À 3bÞ p cosðh=3ÞÀa no ð21Þ Unfortunately, Eqn (21) has no analytical solution. Therefore, the evaluation of kinetic parameters in this equation must be carried out by fitting of the numerically solved system to experimental data. Materials and methods Bovine pancreatic trypsinogen (catalog number T-1143), N-a-p-tosyl- L -arginine methyl ester (TAME), acetamidine, p-amidinobenzamidine and benzamidine hydrochloride were purchased from Sigma Ch emical Co. Trypsinogen preparations were dissolved in 1 m M HCl stock solution, and found to contain about 2% trypsin when enzyme activity was checked using T AME as a substrate. Traces of chymotrypsin activity would not be expected to interfere with the activation of trypsinogen, as the specificity does not fit the activation sites. The concentration of trypsi- nogen was determined by measuring the absorbance at 280 n m and using the absorption coefficient 33 600 M )1 Æ cm )1 [26]. All other chemicals were local products of analytical grade. In kinetic studies of the autocatalytic conversion of trypsinogen into trypsin, aliquots of the incubation mixture of trypsinogen and trypsin were periodically removed and the ac tivity of trypsin was determined. All experiments were performed at 37 °C using plastic tubes to avoid the effect of glass surfaces on the autoprocessing rate of trpsinogen in 40 m M Tris/HCl buffer (pH 8.1, 100 m M CaCl 2 ). Trypsin activity w as routinely assayed by monit- oring the increase in absorbance at 245 nm due to hydrolysis of TAME using a PerkinElmer lambda 45 spectrophotometer at 37 °C [27]. The assay system con- tained 40 m M Tris/HCl (pH 8.1), 1 m M TAME, and 100 m M CaCl 2 . I nitial r ates o f the reaction s w ere determined from the linear slope of the p rogress c urves obtained with an extinction coefficient e 245 ¼ 595 M )1 Æcm )1 . As there are many sets of constants that give essentially the same curve, the individual fit for each set of experimental data to Eqn (12) cannot give reliable estimates for the kinetic parameters of autocatalytic reaction. The problem of non-uniqueness of the estimated parameters can b e solved by a global analysis approach when a series of e xperiments are carried out at different initial concentrations of enzyme [22]. I n this c ase, Eqn (12) can then be considered as a function with two independ- ent variables, [E T ]and[T] 0 , and three parameters, a, K à m , and k à cat . In the present study, we use a commercially available computer programme for t he nonlinear regres- sion data analysis, SIGMAPLOT 2000. SIGMAPLOT ’s nonlinear curve fitter uses a least square procedure (Marquardt–Levenberg algorithm) to determine the parameters that minimize the sum of the squares of differences between the dependent variable in the equa- tions and the observations. Ó FEBS 2004 Inhibition of zymogen autoactivation (Eur. J. Biochem. 271) 4641 Results Trypsinogen, the zymogen form of t rypsin, is secreted into the duodenum by pancreatic cells. Trypsin catalyzes the activation o f trypsinogen in an intermolecular autocatalytic process. The conversion of trypsinogen to trypsin involves the removal of the N-terminal hexapeptide H 2 N-Val-Asp- Asp-Asp-Asp-Lys [28]. This process is strongly stimulated by calcium ions [23,29,30]. There are t wo binding sites for calcium to trypsinogen. One of these s ites has a high affinity for calcium ions, the binding of which causes a conform- ational change which protects the molecule from forming inert protein. The second site has a lower affinity for acceleration o f t he activation process [31]. Desnuelle & Gabeloteau showed that in the presence of c alcium ions the autocatalytic activation of trypsinogen is quantitative and therefore c alcium ions almost totally s u ppress h ydrolysis o f certain other linkages, which i n the absence of calcium are responsible for conversion of the precursor to i nert proteins [32]. I n 1965, Mares-Guia & Shaw reported t hat benzami- dine is a c ompetitive antitrypsin agent [33]. A large number of synthetic serine proteinase i nhibitors are d erived from benzamidine, which is, together with p-amindinobenzami- dine, probably the most potent small-molecule inhibitor ever reported [34]. However, up until now, m ost inhibitory studies on trypsin have been conducted with a rtificial chromogenic substrates. F urther understand ing of the specific functional role of trypsin inhibitors in cellular processes requires detailed i nvestigation w ith physiological protein substrates. To characterize the effect of inhibitor on the trypsin- catalyzed zymogen activation, the kinetic parameters of trypsin-catalyzed zymogen hydrolysis in the absence of inhibitor were determined first. The trypsinogen was incubated with t rypsin in 100 lL of reaction mixture containing 40 m M Tris/HCl (pH 8.1) and 100 m M Ca 2+ at 37 °C. At defined time i ntervals, an aliquot (5 lL) was taken from the reaction mixture and assayed for enzyme activity (1 mL). Enzyme activity assays were carried out under kinetically valid conditions with TAME as a substrate. Figure 2A shows t he activation of varying amounts of e nzyme and zymogen. The time course of the appearance of trypsin activity showed a typical sigmoidal curve. After an i nitial lag period, a rapid increase in trypsin activity was observed. The lag phase of the S-shaped activation curve is shortened by an increase in the trypsi- nogen concentration, and the maximal trypsin activity is proportional to the total concentration of trypsin plus trypsinogen, indicating that the reaction w ent to completion in each case. A s the autoc atalytic activation o f trypsinogen is q uantitative, t he increase in trypsin activity shows the appearance of newly p rocessed trypsin during t he reaction, and t he y scale ( ordinate) in Fig. 2 can then be expressed as the amount of active enzyme. When t he two d ata s ets s hown in Fig. 2A were analyzed simultaneously by a global fi tting procedure using the computer program, SIGMAPLOT 2000, the kinetic parameters were determined to be k 2 ¼ 0.046 ± 0.007 m in )1 , K S ¼ 6.4 3 ± 1.96 l M ,anda ¼ 0.018 ± 0.002, respectively. T he value of K S determined at 100 m M Ca 2+ is about seven times lower than that obtained i n the presence of 10 m M Ca 2+ [23,35], indicating that the dominant effect of the C a 2+ concentration appears to be on K S . In o rder to study the i nhibition mech anism o f p-amindinobenzamidine for the autoactivation o f trypsino- gen, the activation kinetics of trypsinogen were monitored at several fi xed c oncentrations of p-amindinobenzamidine. Figure 2B shows time courses for trypsinogen autoactiva- tion in the prese nce o f 100 l M p-amindinobenzamidine. As seen in this figure, the presence of p-amindinobenzamidine lengthened the lag time considerably. Similarly, the v alue s o f K à m , k à cat and a can be determined for each fixed concentra- tion of inhibitor by the global fitting procedure according to Eqn ( 12). F igure 3 shows the effect of increasing inhibitor concentration on the kinetic parameters of trypsinogen autoactivation. The dominant effect of the inhibitor concentration appears t o be on K à m , but it has no significant effect on k à cat . A plot of K à m against inhibitor concentration Fig. 2. Autocatalytic activation o f try psinoge n by tr ypsin in the absence or presence of p-amindinobenzamidine. (A) Effect of trypsinogen con- centration on the time c ourse for autoac tivation at 37 °C. The symbols represent the experimental data. The total concentrations of trypsi- nogen p lus trypsin are (s)7l M and (d)10l M , res pectively. The lin es are the best fitting cu rves generated by u sing Eqn (12) with k 2 ¼ 0.046 min )1 , K S ¼ 6.43 l M ,anda ¼ 0.018. (B) Effect of trypsinogen concentration on the time course for autoactivation in the presence of 100 l M p-amindinobenzamidine at 3 7 °C. The symbols represent the experimental data. T he total c on centrations of trypsinogen plus t ryp- sin are ( s)10.1 l M and (d) 15.1 l M , respectively. Th e lines a re the be st fitting curves generated by u sing Eqn (12) with k à cat ¼ 0.039 min )1 , K à m ¼ 20.64 l M ,anda ¼ 0.021. 4642 W N. Wang et al.(Eur. J. Biochem. 271) Ó FEBS 2004 gives a straight line, indicating that p-amindinobenzamidine is a c ompetitive inhibitor for the t rypsinogen autoactivation reaction. From the slope and intercept of the straight line, the kinetic parameters were determined to be K S ¼ 7.45 ± 0.93 l M and K I ¼ 61.1 ± 3.1 l M , respectively. Many protease inhibitors bind strongly to the active s ites of enzymes so that the assumption that the free concentra- tion of inhibitor i s equal t o its total c oncentration may not be valid in autoactivation experiments. In the case of competitive inhibition, the rate of enzyme f ormation is given by Eqn (21). Note that this equation is applicable to both tight and loose binding inhibitor. As an example, Eqn (21) was u sed to a nalyze the effects of acetamidine, p-amidino- benzamidine and benzamidine on the autoactivation of trypsinogen by trypsin. Figure 4 shows time courses of trypsinogen autoactivation in the presence of different inhibitors. When the kinetic parameters for zymogen autoactivation are known, the inhibition constant can t hen be determined by simultaneous fitting of the numerically solved system to all experimental data using a non linear least square analysis [36]. It can be seen from Fig. 4 that acetamidine is a very poor inhibitor. Using the fixed values of k 2 ¼ 0.0 46 min )1 , K S ¼ 6.4 3 l M ,anda ¼ 0.01 8, the inhibition constant of acetam idine was determined to be 9.63 ± 0.96 m M . Similarly, by fitting the expe rimental data to Eqn (21) with t he fixed parameters given above, the inhibition constants for binding o f p-amindinobenzamidine and benzamidine were determined to be 59.7 ± 7 .5 l M and 16.4 ± 1.16 l M , respectively. The K I values of these inhibitors d etermined by the present method are quite close to those obtained by direct binding experiments [ 37]. Discussion The activation m echanism of zymogens has been carefully studied fr om a structural point of view [38]. Havsteen et al. elaborated on a complete k inetic analysis for t hese processes [39]. However, these contributions did not include the autoactivation of zymogens, which is a particular case of the activation of zymogens. As the autocatalytic activation of zymogens plays a key role in the regulation of many integrated metabolic systems in living organisms, a detailed kinetic analysis for the autocatalytic zymogen activation reaction is desired. The a utocatalytic activation of zymogens in the presence of a competitive inhibitor has usually been described by t he simple second-order mechanism [ 12] given in Scheme 3: The reaction rate is given by d½Z dt ¼À k app K I K I þ½I 0 ð½T 0 À½ZÞ½Z which can be solved to give Fig. 4. Effects of different inhibitors on the autocatalytic activation of trypsinogen b y trypsin at 37 °C. The total concentrations of trypsinogen plus trypsin are fixed at 8 l M . T he symbols represent the experimen- tal data: d, without inhibitor; s,4m M acetamidine; .,25l M p-amindin obenzamidin e a nd ,,12l M benzamidine. Curve 1 i s gener- ated by using Eqn (12) with k 2 ¼ 0.046 m in )1 , K S ¼ 6.4 3 l M , a ¼ 0.018. The lines are the best fitting c urves generated by u sing Eqn ( 21) with k 2 ¼ 0.046 m in )1 , K S ¼ 6.43 l M , a ¼ 0.01 8, and K I ¼ 9.6 3 m M (curve 2), 59.7 l M (curve 3) and 16.4 l M (curve 4), respectively. Fig. 3. Plot of k* cat and K* m against [I] 0 . (A) Effect of p-amindino- benzamidine concen tratio n on k à cat for autoactivation of trypsinogen by trypsin. (B) Effec t of p-amindinobenzamidine concentratio n on K à m for autoactivation o f trypsinogen by tryp sin. Ó FEBS 2004 Inhibition of zymogen autoactivation (Eur. J. Biochem. 271) 4643 ln ð½T 0 À½Z 0 Þ½Z ð½T 0 À½ZÞ½Z 0 ¼À k app K I ½T 0 K I þ½I 0 t: Experimental data may be plotted linearly by plotting the left side of the equation against t, and the apparent reaction rate constant, k app K I [T] 0 /(K I +[I] 0 ) c an then be determined from the slope of the straight line. Therefore, from the change in the s econd-order rate constant of autoactivation in the presence of inhib itor, the K I can be calculated. However, many of the zymogen-activating enzymes operate by a U ni-Bi mechanism. Hence, a m ore detailed and realistic mechanism is Scheme 4 [35]: As the s tep EZ fi EE + W requires the cleavage of a peptide bond, whereas the step EE fi 2E is a simple dissociation process, the relation k 2 << k 3 is generally satisfied [40]. T herefore, S cheme 4 can b e a pproximated by Scheme 5: It can be v erified that Scheme 3 is a special situation of Scheme 2 w hen [ E] 0 ,[Z] 0 << K S . Several years ago, b ased on Scheme 2, Manjabacas et al. presented a global kinetic analysis for the zymogen autoactivation process in the presence of an inhibitor [ 41]. In this method, they assumed that the initial concentrations of zymogen and enzyme satisfy the condition [Z] 0 >>[E], and therefore the con- centration of zymogen remains approximately constant during t he course of the r eactio n. This method is essentially an initial-r ate method and t he kinetic equations der ived a re only valid from the beginning of the reaction. Because both the zymogen and enzyme concentrations change continu- ously with reaction time, their method is only a pplicable to the slow autoactivation reactions, in which an accurate record of the initial part of the reaction progress can be determined. In a ddition, some zymogen preparations may contain more than 5% of a ctive contaminating enzyme. In these cases, the initial-rate assumption becomes impractical, and alternative methods are required. It should be noted that in practice, zymogen autoactiva- tion can b e a very complicated p rocess [42]. The mathe- matical treatment of these cases is difficult. No exact solution of the differential r ate e q uations can be given even for the simplest case where z ymogens have p artially formed active sites and observed e nzymatic activity. T herefore, for a particular system to be studied, it is necessary to justify the validity of t he proposed model. Trypsin, like chymotrypsin and o ther serine proteases, is alkylated b y d iisopropylfluor- ophosphate (DFP) at its reactive Ser183. The resulting enzyme is completely inactive, indicating this serine residue is essential for catalysis [ 43]. Morgan et al. have s hown that DFP reacts with both trypsinogen and chymotryp sinogen and inhibits the potential activity of both [ 44]. The reactions follow first-order kinetics a nd proceed at four orders of magnitude lower than reaction of the corresponding activated enzymes with DFP. They suggested that the reduced reactivity of the zymogen as compared wit h the enzyme reflects inefficient binding of substrates and i nhib- itors. This chemical evidence is in agreement with the results obtained from steady-state kinetic experiments. Antonini et al . found that trypsinogen displays very low inherent proteolytic activity for synthetic substrates and reduced binding affinity to benzamidine [45]. The dissociation constant for the interaction o f b enzamidine with trypsino- gen (0.046 M ) is about 1000-fold higher than that for trypsin. Therefore, both the inherent proteolytic activity of trypsinogen and t he binding of inhibitors to trypsinogen c an be neglected under the present e xperimental conditions. In this study, a n analytical expression for d escribing a minimal scheme of zymogen autoactivation including the enzyme–zymogen c omplex and assuming rapid e quilibrium of the reversible step is presented. On the basis of the kinetic equation, we have designed and demonstrated the use of a new method to acquire essential k inetic parameters. This method does not need any assumption about the relative values of the initial concentrations of the enzyme and zymogen. The u se of the entire p rogress curve can avoid the subjective nature o f estimating initial rate from a curved plot, which is the m ost difficult portion to measure accurately, particularly i n the case of fast autoact ivation reactions. In comparison to other methods developed previously, t he only weakness of the present method is that it may not be applicable to more complex s chemes of autoactivation zymogen. In these cases, the initial method developed by Manjabacas et al. should be used to analyze the experime ntal da ta. Acknowledgements This work was s upported in p art by g rants from the National Science Foundation of China (30270327) and the M inistry of Science and Technology of China (G1999075606). References 1. Cohen, P. (1976) Control of Enzyme Activity. John Wiley and Sons, New Yo rk . 2. Hadorn, B. (1974) Pancreatic proteinases; their activation a nd the disturbances of this mec han ism in m an. Med. Clin. N orth Am. 58 , 1319–1331. 3. Malcinski, G.M. & Bryant, S.W. (1984) Pattern Formation: A Primer in Devel opmental Biology. Macmillan, New York. 4. MacDonald, H.R. & Nabholz, M. (1986) T-cell activation. Annu. Rev. Cell Biol. 2, 231–253. 5. Mu ¨ ller-Eberhard, H.J. (1988) Molecular organization and func- tion of the c omplemen t system. An nu . Rev. B ioch em. 57, 321–347. 6. Neurath, H. & Walsh, K.A. ( 1976) The role of proteases in bio- logical regulation. In Proteolysis and Physiological Regulation (Ribbons, E.W. & Brew, K., eds), pp. 29–40. Academic Press, New York. 4644 W N. Wang et al.(Eur. J. Biochem. 271) Ó FEBS 2004 7. Lo ¨ ffler, G. & Petrides, P.E. (1988) Physiologische Chemie, pp. 832 –843. Springer, Berlin, Heidelberg a nd New Y ork. 8. Thornberry, N.A. & Lazebnik, Y. (1998) C aspases: Enemies within. Science 28 1 , 1312–1316. 9. Smith, W.L. & Borgeat, P. (1985) The eicosanoids: prosta- glandins, thromboxanes, leukotrienes, and hydroxy-eicosaenoic acids. In Bioc hemistry of Lipids a nd Membranes (Vance, D.E . & Vance, J.E., e ds), pp. 325–360. Benja m in-Cunnings, Menlo Park, CA. 10. Tans,G.,Rosing,J.,Berrettini,M.,Lammle,B.&Griffin,J.H. (1987) Autoactivation of human plasma prekallikrein. J. Biol. Chem. 262, 113 08–11314. 11. Karlson, P. (1988) Biochemie, 13th e dn, pp. 160–161. Georg Thieme Verlag, S tuttgart and New Y ork. 12. Tans, G., Rosing, J. & Griffin, J.H. (1983 ) Sulfatide-dependent autoactivation of human blood coagulation Factor XII ( Hageman Factor). J. Biol. Chem. 25 8, 8215–8222. 13. Rozman, J., Stojan, J., Kuhelj, R., Turk, V. & Turk, B. (1999) Autocatalytic p rocessing of recombinant human pro cathepsin B is a bimolecular process. FEBS Lett. 459, 3 58–362. 14. Ellerbroek, S.M., Wu, Y. & Stack, M.S. (2002) Regulatory mechanisms for proteinase a ctivity. In Proteinas e and Pe ptidase Inhibition: Recent Potential T argets for Drug D evelopment. (Sm i th, H.J. & Simons, C., eds), pp. 22–34. Taylor & Francis Inc., New York. 15. Barrett, A.J. (2001) Proteolytic enzymes: nomenclature and classification. In Proteolytic Enzymes, 2nd edn (Beynon, R. & Bond, J.S., e ds), pp. 1–21. Oxfo rd University Press, Oxford. 16. Von d er Helm, K., Korant, B.D. & Cheronis, J .C. (2000) Pro- teases as Targets f or Therapy. Springe r, Berlin. 17. Nagas, H. & Salvesen, G.S. (2001) Finding, purification and characterization of natural protease inhibitors. In Proteolytic Enzymes, 2nd edn (Beynon, R. & B ond, J .S., eds), pp. 1 31–147. Oxford Uni versity Press, Oxford. 18. Barrett, A.J. & Salvesen, G. (1986) Protei nase Inhibitors. Elsevier, Amsterdam . 19. Turk, V. (1999) Proteases New Perspectives.Birkha ¨ user-Verlag, Basel. 20. Katunuma, N., Fritz, H., Kido, H. & Travis, J. (1997) Medical Aspects of Proteases and Protease Inhibitors.IOSPress, Amsterdam . 21. Wu, J.W., Wu, Y. & Wang, Z.X. (2001) Kinetic analysis of a simplified scheme of autocatalytic zymogen activation. Eur. J. Biochem. 268, 1 547–1553. 22. Wang, Z .X. & Wu, J.W. ( 2002) Autophosphorylation k in etics of protein kinases. Bioch em. J. 36 8 , 947–952. 23. Liu, J. & Wang, Z.X. (2004) Kinetic a nalysis of ligand-induced autocatalytic reactions. Bioc hem. J. 379, 697–702. 24. Laidler, K.J. & Bunting, P.S. (1973) The Chemical Kinetics of Enzyme Action, 2nd edn, pp. 73–74. Oxford University Press, Oxford. 25. Wang, Z.X. (1995) An exact m athematical e xpression for descri- bing compe titive binding of two different ligands to a protein molecule. FEBS Lett. 360 , 111–114. 26. Walsh, K.A. (1970) Trypsinogens and trypsins of various species. Methods En zymol. 19, 41–63. 27. Wang,S.S.&Carpenter,H.(1968) Ki netic studies at high pH of the trypsin-catalyzed hy drolysis of N-a-benzoyl Derivatives of L -arginamide, L -lysinamide, and S-2-aminoethyl- L -cysteinamide and related compounds. J. Biol. Chem. 243, 3 702–3710. 28. Colomb, E. & Fig arella, C. ( 1979) Comparative studies on the mechanism o f a ctivation of the two human trypsinoge ns. Biochim. Biophys. A cta 571, 343 –351. 29. Delaage, M ., Desnuelle, P. & Lazdunski, M. (1967) On the a cti- vation of trypsinogen. A study of p eptide models related to the N-terminal se quence of the z ymogen. Biochem. Biophys. R es. Commun. 29 , 235–240. 30. Abita, J.P., Delaage, M. & Lazdunski, M. (1969) The mechanism of activation of trypsinogen. The r o le of the four N-terminal aspartyl r esidues. Eur. J. Biochem. 8, 3 14–324. 31. Delaage, M. & Lazdunski, M. (1967) The binding of Ca 2+ to trypsinogen and i ts relation to the mechanism o f activation. Bio- chem. B iophys. Res. Commun. 28, 3 90–394. 32. Desnuelle, P. & Gabeloteau, C. (1957) Role of calcium during the activation of trypsinogen by t rypsin. Arch. B iochem. B iophys. 69, 475–485. 33. Mares-Guia, M. & Shaw , E. ( 1965) Studies o n t he active center of trypsin; the b inding of amid in es and g u anidines as models of the substrate side chain. J. Biol. C hem. 240, 1579 –1585. 34. Ho ¨ m, H. & Heidland, A. (19 92) Protease s: pote ntial role in he alth and d iseases. Plenum Press, New York. 35. Garcı ´ a-Moreno, M., Havsteen, B.H ., Varo ´ n, R. & R ix-Matzen, H. (1991) Evaluation of the k inetic parameters of the activation of trypsinogen b y trypsin. Bioc him. Biophys. A cta 1080, 1 43–147. 36. Tojian, J. ( 1997) Analysis of progress curves in an acetylcholin- esterase reaction: a numerical integration treatment. J. Chem. Inf. Comput. Sci. 37, 1 025–1027. 37. Talhout, R . & Engberts, J .B.F.N. (2001) Thermodynamic a nalysis of bind ing o f p-substituted benz amidines t o t rypsin. Eur . J. Bio- chem. 268, 1 554–1560. 38. Huber, R., Kukla, D ., Bode, W., Schwager, P., Bartels, K., Dei- senhofer, J. & Steigemann, W . (1974) Struct ure of the complex formed by bovine t rypsin and b ovine p ancreatic trypsin inh ibitor. II. Crystallographic r efinement at 1.9 A ˚ Resolution. J. Mol. Biol. 89, 7 3–101. 39. Havsteen, B .H., Garcı ´ a-Moreno, M., Val ero, E., Manjabacas, M.C. & V aro ´ n, R. (1993) The k inetics o f enzyme systems i nvol- ving acti vation of z ymogens. Bull. Math. Biol. 55 , 561–583. 40. Havsteen, B.H. (1976) Kinetic studies of elementary steps in t he interaction o f chymotrypsin with inhibitors. Studia Biophys. 57, 117–122. 41. Manjabacas, M.C., Valero, E., Garcı ´ a-Moreno, M., Garcı ´ a- Canovas, F., Rodriguez, J.N. & Varo ´ n, R. (1 992) Kinetic a nalysis of the control through inhibition of autocatalytic zymogen acti- vation. Bioc hem. J. 282 , 583–587. 42. Donepudi, M. & Gru ¨ tter, M.G. (2002) Structure and zymogen activation of caspases. Bioph ys. Chem. 101 –102, 145–153. 43. Jansen, E.F. & Balls, A.K. (1952) The inhibition of beta- and gamma-chymotrypsin and trypsin b y diisopropyl fluorophos- phate. J. Biol. Chem. 194 , 721–727. 44. Morgan, P .H., Robinson, N .C., Walsh, K.A. & Neurath, N. (1972) Inactivation of bovine trypsinogen and chymotrypsinogen by diisopropylphosphorofluoridate. Proc. Natl Acad. Sci. USA 69, 3312–3316. 45. Antonini, E., Asce nz i, P., Bolognesi, M., Guarneri, M., Me negatti, E. & Amiconi, G. (1984) Catalytic a nd ligand binding properties of bovine trypsinogen and its complex with the effector dipeptide Ile-Val. Mol. Cell. Biochem. 60, 1 63–181. Ó FEBS 2004 Inhibition of zymogen autoactivation (Eur. J. Biochem. 271) 4645 . Kinetic analysis of zymogen autoactivation in the presence of a reversible inhibitor Wei-Ning Wang, Xian-Ming Pan and Zhi-Xin Wang National Laboratory. parameters of the reaction. As an example of the application of this method, effects of acetamidine, p-amidinobenzamidine a nd benzamidine o n t he autoactivation