Báo cáo khoa học: Kinetic analysis of zymogen autoactivation in the presence of a reversible inhibitor pptx

Keywords: limited proteolysis; reversible inhibition; trypsin; trypsinogen; zymogen activation.. The general mechanism of the autocatalytic reaction of an enzyme in the presence of a rev

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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 proteolysis is a highly speciﬁc irreversible process,

which can serve to initiate physiological function by

con-verting a precursor protein into a biologically active form

When the activating enzyme and the activated enzyme

coincide, the process is an autocatalytic zymogen activation

(i.e reactions in which the zymogens serves as a substrate for

the corresponding active enzyme) The activity of proteases

is frequently regulated by the binding of speciﬁc protease

inhibitors Thus, to understand the biological regulation

of proteolysis, 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 and benzamidine on the autoactivation of trypsinogen by trypsin were studied

Keywords: limited proteolysis; reversible inhibition; trypsin; trypsinogen; zymogen activation

Proteolysis is required for a multitude of developmental and

physiologic events including digestion, metabolism,

differ-entiation, immunity, blood coagulation, ﬁbrinolysis,

apop-tosis and response to injury [1–9] The enzymes responsible

for the catalysis of proteolysis are proteases During the last

century, the number of known enzymes that demonstrate

proteolytic activity has increases exponentially and we have

an increased understanding of the mechanisms and critical

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 as proenzymes) The zymogens must undergo an

activation process, usually a limited proteolysis, to attain

their catalytic activity at a physiologically appropriate time

and place Small peptides are cleaved from zymogens to

form the active proteases The active forms of zymogens

usually have powerful physiological effects, and 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 precise means of switching on enzyme activity As this type of activation is irreversible, different mechanisms are needed to prevent proteolysis Specific protease inhibitors accomplish this task The 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 Nearly every protease is faced with an antagonist limiting its proteolytic activity 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 activation and frequently by inhibition [14–16] In addition, major reasons for proteolysis-induced pathologies are either excessive production of liberation (e.g from cells and microbes) of proteases or extensive consumption of 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, to understand the biological regulation of proteolysis, one must understand the role of endogenous and exogenous protease inhibitors [17–20] Recently, detailed kinetic studies of the autoactivation of protein kinase and zymogen have been reported [21–23] In 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, effects of acetamidine, p-amidinobenzamidine and benzamidine on the autoactivation of trypsinogen by trypsin were analyzed

Correspondence to Z.-X Wang, National Laboratory of

Biomacro-molecules, Institute of Biophysics, Academia Sinica Beijing 100101,

P.R China Fax: +86 10 64872026, E-mail: zxwang@sun5.ibp.ac.cn

Abbreviations: DFP, diisopropylﬂuorophosphate; TAME,

N-a-p-tosyl- L -arginine methyl ester.

(Received 7 September 2004, accepted 5 October 2004)

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Theoretical analysis

In the case of the autocatalytic reactions, the zymogen

serves as a substrate in reactions The general mechanism

of the autocatalytic reaction of an enzyme in the presence

of a reversible inhibitor can be written as shown in

Scheme 1:

where W is the peptide which is eliminated from Z, and I, E

and Z represent inhibitor, enzyme and zymogen,

respect-ively In this mechanism, both enzyme E and enzymeỜ

zymogen complex EZ combine with inhibitor I, but the

enzymeỜinhibitorỜsubstrate complex does not proceed to

form product As the concentrations of zymogen and

enzyme are of the same order of magnitude, the steady-state

assumption is not satisfactory in this case [24] When there is

rapid equilibrium as far as EI, EZ and EIZ are concerned,

i.e when k2is sufﬁciently small as not to disturb

equilib-rium, we then have

KSỬơEơZ

ơEZ ; K

0

SỬơEơEI

ơEIZ

KIỬơEơI

ơEI ; K

0

IỬơEZơI

ơEIZ

đ1ỡ

The total concentration of enzyme is

ơT0Ử ơE0ợ ơZ0Ử ơE ợ ơZ ợ ơEI ợ 2ơEZ ợ 2ơEIZ

đ2ỡ where [E]0 and [Z]0 are the initial concentrations of the

enzyme and zymogen, respectively Let

ơET Ử ơE ợ ơEZ ợ ơEI ợ ơEIZ đ3ỡ

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 enzyme formation

Therefore, from Eqns (1Ờ3), we have

K0

Iợ ơI0

K0

I

ơEZ2 đơT0ợ KmỡơEZ

ợđơT0 ơETỡơETK0

I

where,

KmỬđKIợ ơI0ỡK0

IKS

đK0

Iợ ơI0ỡKI

ỬđKIợ ơI0ỡK0

S

K0

is the apparent MichealisỜMenten constant for the auto-catalytic reaction The solution of Eqn (4) for [EZ] is given

by the quadratic formula as

0 I

2đK0

IợơI0ỡ

ơT0ợKm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi đơT0ợK

mỡ24đơT0ơETỡơET q

The rate of the enzyme formation is given by dơET

dt Ửk2ơEZỬk

cat

2

ơT0ợKm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi đơT0ợK

mỡ24đơT0ơETỡơET q

đ6ỡ where,

kcatỬ k2K

0 I

is the apparent turnover number for the autocatalytic reaction Eqn (6) can be rewritten as

2dơET

ơT0ợ K

m

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi đơT0ợ K

mỡ2 4đơT0 ơETỡơET

đ8ỡ

To integrate this equation, put

xỬ 2ơET ơT0ợ

mỡ2 4đơT0 ơETỡơET

q

;

so that

ơET Ửđx ợ ơT0ỡ2 đK

mợ ơT0ỡ2

and

ơT0ợ K

m

mỡ2 4đơT0 ơETỡơET q

Ử đx K

mỡđx K

m 2ơT0ỡ

Diﬀerentiation of Eqn (9) with respect to x gives

dơET Ửx

2ợ 2K

mơT0ợ K2

m

Substitution of Eqns (10) and (11) into Eqn (8) yields

x2ợ 2K

mơT0ợ K2

m

xđx K

mỡđx K

m 2ơT0ỡdxỬ k

catdt: With the boundary condition tỬ 0, [ET]Ử [E]0, this integrates to

kcattỬ lnx

x0ợK

mợ ơT0

ơT0 ln

đx K

m 2ơT0ỡđx0 K

mỡ

đx0 K

m 2ơT0ỡđx K

mỡ đ12ỡ where,

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x0¼ 2½E0 ½T0þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðK

mþ ½T0Þ2 4½E0½Z0

q

:

In practice, the zymogen preparation always contains a

trace amount of contaminating active enzyme Therefore,

the initial concentrations of enzyme species can be written as

[E]0¼ a[T]0and [Z]0¼ (1) a)[T]0where a is a constant

In this case, x0in Eqn (12) can be written as

x0¼ ð2a 1Þ½T0þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ðK

mþ ½T0Þ2 4að1 aÞ½T20

q

; and a can be treated as an unknown parameter to be

determined

It can be seen from Eqns (5) and (7) that both k

catand K m

are the functions of inhibitor concentration Figure 1A,B

shows the effects of varying [I]0on the kcat and Km value As

[I]0increases from zero to inﬁnity, kcat decreases from k2to

zero A plot of 1=kcat against [I]0will give a straight line with

the slope of 1=k2KI0and intercept of 1/ k2(inset of Fig 1A)

The shape of the plot of Km against [I]0will depend on the

relative magnitudes of the two dissociation constants

(Fig 1B) Curve 1 shows the behaviour when the value of

K0

I is larger than that of KI(i.e the afﬁnity of the inhibitor I

for free enzyme E is lower than for enzyme–zymogen

complex, EZ); as [I]0 increases from zero to inﬁnity, K

m

increases from KSto a limit of value, K0

S Opposite results are obtained if K0

I < KI Curve 2 corresponds to a higher value of KI Note that the expressions of k

cat and K

m are exactly the same as the case of mixed inhibition for the

classical Michealis–Menten kinetics Three different types of

special cases can be distinguished In competitive inhibition,

the inhibitor competes with the substrate for the active site

of enzyme (KI0! 1) The expressions of k

cat and Km are given by

Km¼ KSþKS

KI

It can be seen from Eqns (13) and (14) that the apparent turnover number kcat is independent of [I]0(Fig 1C), and the apparent Michealis–Menten constant Km increases linearly with [I]0 From the slope and intercept of this straight line, KIand KS can be determined (Fig 1D) In uncompetitive inhibition, the inhibitor binds directly to the enzyme–zymogen complex but not the free enzyme (KIﬁ 1), the expressions of k

catand K

mare

kcat¼ k2K

0 I

KI0þ ½I0

Km¼ K

0

IKS

K0

Iþ ½I0

In this case, both k

cat and K

m decrease as [I]0 increases (Fig 1E,F) A straight line will be obtained if 1=K

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 mixed inhibition In pure non-competitive inhibition, both enzyme and enzyme–zymogen complex bind inhibitor with equal afﬁnity (KI¼ K0

I) The expressions of kcatand Km are given by

kcat¼ k2K

0 I

K0

Iþ ½I0

Km¼ KS

which is the special case of mixed inhibition, and as expected, the apparent turnover number k

catshows a similar behaviour with [I]0 increases (Fig 1G), but the apparent Michaelis constant K

mis independent of [I]0(Fig 1H) In summary, the dependence of k

catand K

m upon [I]0in the different cases would suggest criteria for discriminating between them and provide estimates of their kinetic parameters

The equations derived in the previous section assume that there is no depletion of the inhibitor by the enzyme If, however, the enzyme has very high afﬁnity for the inhibitor,

it will be necessary to use very low inhibitor concentration in kinetic studies A quantitative description of tight binding inhibition cannot be based on Eqn (12), as the assumpton that the free inhibitor concentration is equal to the total inhibitor is not valid Tight binding inhibitors cause inhibition at concentrations comparable to those at which enzymes are used for kinetic experiments Consequently, the formation of an enzyme–inhibitor complex can result in a considerable reduction in the concentration of added inhibitor, and allowance must be made for this reduction

In the presence of a competitive inhibitor, autocatalytic processing can be represented by Scheme 2:

Fig 1 Schematic representation of the plots of k * and K cat m * vs

inhib-itor concentration for the case of mixed inhibition (A,B); competitive

inhibition (C,D); uncompetitive inhibition (E,F); and noncompetitive

inhibition (G,H).

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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

KSỬơEơZ

ơEZ ; KIỬ

ơEơI

Let

ơET Ử ơE ợ ơEZ ợ ơEI đ17ỡ

where [ZT] and [ET] represent the total concentrations of

zymogen and enzyme at any time t during the reaction

Conservation of mass requires that

ơT0Ử ơE0ợ ơZ0Ử ơET ợ ơZT đ19ỡ

From Eqns (15Ờ19), we have [25]

ơE3ợ aơE2ợ bơE ợ c Ử 0 đ20ỡ

where,

aỬ KSợ KIợ ơT0ợ ơI0 2ơET;

bỬ KIđơT0 2ơETỡ ợ KSđơI0 ơETỡ ợ KSKI

and

cỬ KSKIơET The solution of Eqn (20) for [E] is

ơE Ử a

3ợ2 3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ

q

cosh 3 where,

hỬ arccos2a

3ợ 9ab 27c 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ3 q

Therefore, the expression for [EZ] is given by

ơEZ ỬđơT0 ơETỡ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ

p

cosđh=3ỡ a

3KSợ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ

p

cosđh=3ỡ a

The rate of product formation is thus

dơET

dt Ử k2ơEZ

Ử

k2đơT0 ơETỡ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ

p

cosđh=3ỡ a

3KSợ 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

đa2 3bỡ

p

cosđh=3ỡ a

đ21ỡ 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 Chemical Co Trypsinogen preparations were dissolved in 1 mM HCl stock solution, and found to contain about 2% trypsin when enzyme activity was checked using TAME 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 nm and using the absorption coefﬁcient 33 600M )1ẳ

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 activity of trypsin was determined All experiments were performed at 37C using plastic tubes to avoid the effect of glass surfaces on the autoprocessing rate of trpsinogen in 40 mM Tris/HCl buffer (pH 8.1, 100 mM

CaCl2) Trypsin activity was routinely assayed by monit-oring the increase in absorbance at 245 nm due to hydrolysis of TAME using a PerkinElmer lambda 45 spectrophotometer at 37C [27] The assay system con-tained 40 mM Tris/HCl (pH 8.1), 1 mM TAME, and

100 mMCaCl2 Initial rates of the reactions were determined from the linear slope of the progress curves obtained with an extinction coefﬁcient e245Ử 595M )1ẳcm)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 be solved by a global analysis approach when a series of experiments are carried out at different initial concentrations of enzyme [22] In this case, Eqn (12) can then be considered as a function with two independ-ent variables, [ET] and [T]0, and three parameters, a, K

m, and k

cat In the present study, we use a commercially available computer programme for the nonlinear regres-sion data analysis, SIGMAPLOT 2000 SIGMAPLOTỖs nonlinear curve ﬁtter uses a least square procedure (MarquardtỜLevenberg algorithm) to determine the parameters that minimize the sum of the squares of differences between the dependent variable in the equa-tions and the observaequa-tions

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Trypsinogen, the zymogen form of trypsin, is secreted into

the duodenum by pancreatic cells Trypsin catalyzes the

activation of trypsinogen in an intermolecular autocatalytic

process The conversion of trypsinogen to trypsin involves

the removal of the N-terminal hexapeptide H2

N-Val-Asp-Asp-Asp-Asp-Lys [28] This process is strongly stimulated

by calcium ions [23,29,30] There are two binding sites for

calcium to trypsinogen One of these sites 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 of the activation process [31] Desnuelle &

Gabeloteau showed that in the presence of calcium ions the

autocatalytic activation of trypsinogen is quantitative and

therefore calcium ions almost totally suppress hydrolysis of

certain other linkages, which in the absence of calcium are

responsible for conversion of the precursor to inert proteins

[32] In 1965, Mares-Guia & Shaw reported that

benzami-dine is a competitive antitrypsin agent [33] A large number

of synthetic serine proteinase inhibitors are derived from

benzamidine, which is, together with

p-amindinobenzami-dine, probably the most potent small-molecule inhibitor

ever reported [34] However, up until now, most inhibitory

studies on trypsin have been conducted with artiﬁcial

chromogenic substrates Further understanding of the

speciﬁc functional role of trypsin inhibitors in cellular

processes requires detailed investigation with 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 trypsin in 100 lL of reaction mixture

containing 40 mM Tris/HCl (pH 8.1) and 100 mM Ca2+

at 37C At deﬁned time intervals, 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 the activation of varying

amounts of enzyme and zymogen The time course of the

appearance of trypsin activity showed a typical sigmoidal

curve After an initial 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 went to completion

in each case As the autocatalytic activation of trypsinogen

is quantitative, the increase in trypsin activity shows the

appearance of newly processed trypsin during the reaction,

and the y scale (ordinate) in Fig 2 can then be expressed as

the amount of active enzyme When the two data sets shown

in Fig 2A were analyzed simultaneously by a global ﬁtting

procedure using the computer program, SIGMAPLOT2000,

the kinetic parameters were determined to be k2¼

0.046 ± 0.007 min)1, KS¼ 6.43 ± 1.96 lM, and a¼

0.018 ± 0.002, respectively The value of KS determined

at 100 mM Ca2+ is about seven times lower than that

obtained in the presence of 10 mMCa2+[23,35], indicating

that the dominant effect of the Ca2+concentration appears

to be on KS In order to study the inhibition mechanism of p-amindinobenzamidine for the autoactivation of trypsino-gen, the activation kinetics of trypsinogen were monitored

at several ﬁxed concentrations of p-amindinobenzamidine Figure 2B shows time courses for trypsinogen autoactiva-tion in the presence of 100 lMp-amindinobenzamidine As seen in this ﬁgure, the presence of p-amindinobenzamidine lengthened the lag time considerably Similarly, the values of

K

m, k catand a can be determined for each ﬁxed concentra-tion of inhibitor by the global ﬁtting procedure according to Eqn (12) Figure 3 shows the effect of increasing inhibitor concentration on the kinetic parameters of trypsinogen autoactivation The dominant effect of the inhibitor concentration appears to be on K

m, but it has no signiﬁcant effect on k A plot of K against inhibitor concentration

Fig 2 Autocatalytic activation of trypsinogen by trypsin in the absence

or presence of p-amindinobenzamidine (A) Effect of trypsinogen con-centration on the time course for autoactivation at 37 C The symbols represent the experimental data The total concentrations of trypsi-nogen plus trypsin are (s) 7 l M and (d) 10 l M , respectively The lines are the best fitting curves generated by using Eqn (12) with k 2 ¼ 0.046 min)1, K S ¼ 6.43 l M , and a ¼ 0.018 (B) Effect of trypsinogen concentration on the time course for autoactivation in the presence of

100 l M p-amindinobenzamidine at 37 C The symbols represent the experimental data The total concentrations of trypsinogen plus tryp-sin are (s) 10.1 l M and (d) 15.1 l M , respectively The lines are the best ﬁtting curves generated by using Eqn (12) with k

cat ¼ 0.039 min)1,

Km¼ 20.64 l M , and a ¼ 0.021.

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gives a straight line, indicating that p-amindinobenzamidine

is a competitive inhibitor for the trypsinogen autoactivation

reaction From the slope and intercept of the straight line,

the kinetic parameters were determined to be KSỬ

7.45 ổ 0.93 lMand KIỬ 61.1 ổ 3.1 lM, respectively

Many protease inhibitors bind strongly to the active sites

of enzymes so that the assumption that the free

concentra-tion of inhibitor is equal to its total concentraconcentra-tion may not

be valid in autoactivation experiments In the case of

competitive inhibition, the rate of enzyme formation is given

by Eqn (21) Note that this equation is applicable to both

tight and loose binding inhibitor As an example, Eqn (21)

was used to analyze the effects of acetamidine,

p-amidino-benzamidine and p-amidino-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 then

be determined by simultaneous ﬁtting of the numerically

solved system to all experimental data using a nonlinear

least square analysis [36] It can be seen from Fig 4 that

acetamidine is a very poor inhibitor Using the ﬁxed values

of k2Ử 0.046 min)1, KSỬ 6.43 lM, and aỬ 0.018, the

inhibition constant of acetamidine was determined to be

9.63 ổ 0.96 m Similarly, by ﬁtting the experimental data

to Eqn (21) with the ﬁxed parameters given above, the inhibition constants for binding of p-amindinobenzamidine and benzamidine were determined to be 59.7 ổ 7.5 lMand 16.4 ổ 1.16 lM, respectively The KI values of these inhibitors determined by the present method are quite close

to those obtained by direct binding experiments [37]

Discussion

The activation mechanism of zymogens has been carefully studied from a structural point of view [38] Havsteen et al elaborated on a complete kinetic analysis for these 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 autocatalytic activation of zymogens

in the presence of a competitive inhibitor has usually been described by the simple second-order mechanism [12] given

in Scheme 3:

The reaction rate is given by

dơZ

dt Ử kappKI

KIợ ơI0đơT0 ơZỡơZ

which can be solved to give

Fig 4 Eﬀects of diﬀerent inhibitors on the autocatalytic activation of

trypsinogen by trypsin at 37 ồC The total concentrations of trypsinogen

plus trypsin are ﬁxed at 8 l M The symbols represent the experimen-tal data: d, without inhibitor; s, 4 m M acetamidine; , 25 l M

p-amindinobenzamidine and ,, 12 l M benzamidine Curve 1 is gener-ated by using Eqn (12) with k 2 Ử 0.046 min)1, K S Ử 6.43 l M , a Ử 0.018 The lines are the best ﬁtting curves generated by using Eqn (21) with k 2 Ử 0.046 min)1, K S Ử 6.43 l M , a Ử 0.018, and K I Ử 9.63 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 concentration on k

cat for autoactivation of trypsinogen

by trypsin (B) Eﬀect of p-amindinobenzamidine concentration on K

m

for autoactivation of trypsinogen by trypsin.

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lnđơT0 ơZ0ỡơZ

đơT0 ơZỡơZ0Ử

kappKIơT0

KIợ ơI0 t:

Experimental data may be plotted linearly by plotting the

left side of the equation against t, and the apparent reaction

rate constant, kappKI[T]0/(KI+[I]0) can then be determined

from the slope of the straight line Therefore, from the

change in the second-order rate constant of autoactivation

in the presence of inhibitor, the KIcan be calculated

However, many of the zymogen-activating enzymes

operate by a Uni-Bi mechanism Hence, a more detailed

and realistic mechanism is Scheme 4 [35]:

As the step EZ ﬁ EE + W requires the cleavage of a

peptide bond, whereas the step EE ﬁ 2E is a simple

dissociation process, the relation k2<< k3 is generally

satisﬁed [40] Therefore, Scheme 4 can be approximated by

Scheme 5:

It can be veriﬁed that Scheme 3 is a special situation of

Scheme 2 when [E]0, [Z]0<< KS Several years ago, based

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 the course of the reaction This method is essentially

an initial-rate method and the kinetic equations derived are

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 applicable to

the slow autoactivation reactions, in which an accurate

record of the initial part of the reaction progress can be

determined In addition, some zymogen preparations may

contain more than 5% of active 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 be a very complicated process [42] The

mathe-matical treatment of these cases is difﬁcult No exact

solution of the differential rate equations can be given even

for the simplest case where zymogens have partially formed

active sites and observed enzymatic activity Therefore, for a

particular system to be studied, it is necessary to justify the

validity of the proposed model Trypsin, like chymotrypsin

and other serine proteases, is alkylated by diisopropylﬂuor-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 shown that DFP reacts with both trypsinogen and chymotrypsinogen and inhibits the potential activity of both [44] The reactions follow first-order kinetics and 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 with the enzyme reflects inefficient binding of substrates and inhib-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 of benzamidine with trypsino-gen (0.046M) is about 1000-fold higher than that for trypsin Therefore, both the inherent proteolytic activity of trypsinogen and the binding of inhibitors to trypsinogen can

be neglected under the present experimental conditions

In this study, an analytical expression for describing a minimal scheme of zymogen autoactivation including the enzymeỜzymogen complex and assuming rapid equilibrium

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 kinetic parameters This method does not need any assumption about the relative values of the initial concentrations of the enzyme and zymogen The use of the entire progress curve can avoid the subjective nature of estimating initial rate from a curved plot, which is the most difﬁcult portion to measure accurately, particularly in the case of fast autoactivation reactions In comparison to other methods developed previously, the only weakness of the present method is that

it may not be applicable to more complex schemes of autoactivation zymogen In these cases, the initial method developed by Manjabacas et al should be used to analyze the experimental data

Acknowledgements

This work was supported in part by grants from the National Science Foundation of China (30270327) and the Ministry of Science and Technology of China (G1999075606).

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