Biochem. J. (1974) 141, 365-381 365Printed in Great Britain

Kinetics of the Hydrolysis of N-Benzoyl-L-serine Methyl Ester Catalysedby Bromelain and by Papain

ANALYSIS OF MODIFIER MECHANISMS BY LATTICE NOMOGRAPHY,COMPUTATIONAL METHODS OF PARAMETER EVALUATION FOR

SUBSTRATE-ACTIVATED CATALYSES AND CONSEQUENCES OF POSTULATEDNON-PRODUCTIVE BINDING IN BROMELAIN- AND PAPAIN-CATALYSED

HYDROLYSES

By CHRISTOPHER W. WHARTON, *t1 ATHEL CORNISH-BOWDEN,tJIKEITH BROCKLEHURST*§ and ERIC M. CROOK*

*Department ofBiochemistry and Chemistry, St. Bartholomew's Hospital Medical College, University ofLondon,Charterhouse Square, London ECIM 6BQ, U.K.,

andtDepartment ofBiochemistry, University ofBirmingham, P.O. Box 363, Birmingham B15 2TT, U.K.

(Received 20 December 1973)

1. N-Benzoyl-L-serine methyl ester was synthesized and evaluated as a substrate forbromelain (EC 3.4.22.4) and for papain (EC 3.4.22.2). 2. For the bromelain-catalysedhydrolysis at pH 7.0, plots of [SO]/vi (initial substrate concn./initial velocity) versus [SO]are markedly curved, concave downwards. 3. Analysis by lattice nomography of amodifier kinetic mechanism in which the modifier is substrate reveals that concave-down[So]/vi versus [SO] plots can arise when the ratio of the rate constants that characterize thebreakdown of the binary (ES) and ternary (SES) complexes is either less than or greaterthan 1. In the latter case, there are severe restrictions on the values that may be taken bythe ratio of the dissociation constants of the productive and non-productive binary com-plexes. 4. Concave-down [So]/vl versus [SO] plots cannot arise from compulsory substrateactivation. 5. Computational methods, based on function minimization, for determinationof the apparent parameters that characterize a non-compulsory substrate-activatedcatalysis are described. 6. In an attempt to interpret the catalysis by bromelain of thehydrolysis of N-benzoyl-L-serine methyl ester in terms of substrate activation, the generalsubstrate-activation model was simplified to one in which only one binary ES complex(that which gives rise directly to products) can form. 7. In terms of this model, the bromel-ain-catalysed hydrolysis of N-benzoyl-L-serine methyl ester at pH 7.0, I= 0.1 and 25°Cis characterized by Kmj (the dissociation constant of ES)= 1.22±0.73mM, k (the rateconstant for the breakdown of ES to E+products, P) =1.57x 10-2+0.32x 10-2s-1,Ka2 (the dissociation constant that characterizes the breakdown of SES to ES and S)=0.38 ±0.06M, and k' (the rate constant for the breakdown of SES to E+P+S) = 0.45±0.04s-1. 8. These parameters are compared with those in the literature that characterize thebromelain-catalysed hydrolysis of a-N-benzoyl-L-arginine ethyl ester and of a-N-benzoyl-L-arginine amide; K,,,1 and k for the serine ester hydrolysis are somewhat similar to K,,,and kca,t. for the arginine amide hydrolysis and Ka, and k' for the serine ester hydrolysis aresomewhat similar to Km and kcat. for the arginine ester hydrolysis. 9. A previous interpre-tation of the inter-relationships of the values of kca,. and Km for the bromelain-catalysedhydrolysis of the arginine ester and amide substrates is discussed critically and an alterna-tive interpretation involving substantial non-productive binding of the arginine amidesubstrate to bromelain is suggested. 10. The parameters for the bromelain-catalysedhydrolysis oftheserine ester substrateare tentatively interpreted in terms ofnon-productivebinding in the binary complex and a decrease of this type of binding by ternary complex-formation. 11. The Michaelis parameters for the papain-catalysed hydrolysis of theserine ester substrate (Km = 52±4mM, kcat. = 2.80±0.1 s-' at pH7.0, I= 0.1, 25.0°C) aresimilar to those for the papain-catalysed hydrolysis of methyl hippurate. 12. Urea andguanidine hydrochloride at concentrations of 1 M have only small effects on the kineticparameters for the hydrolysis of the serine ester substrate catalysed by bromelain andby papain.

Present address: Department of Biochemistry, § To whom reprint requests should be addressed.University of Birmingham, P.O. Box 363, Birmingham II To whom requests for copies of the computerB15 2TT, U.K. program should be addressed.

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C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

In connexion with the study ofthe matrix-perturba-tion of bromelain-catalysed hydrolyses caused byfactors other than charge-charge interaction (seeWharton et al., 1968a,b) it was necessary to find asubstrate for bromelain which is (a) uncharged inapproximately neutral media, (b) at least as good asubstrate for bromelain as x-N-benzoyl-L-arginineethyl ester, i.e. kcat. ,approx. 0.5s-I and K,,<approx.0.1 M, and (c) sufficiently water-soluble to allowdetermination of the Michaelis parameters withoutinclusion of organic solvent in the assay medium,i.e. the solubility would probably have to be greaterthan 0.1 M. The latter requirement, desirable in anyenzyme study, is particularly important in compara-tive studies of free solution and matrix-supportedenzyme catalyses because ofthe possibility that addedorganic solvent might modify differentially theproperties of the two systems.

In our search for such a substrate for bromelain,we considered first a number of uncharged substratesthat have been used by other workers in the study ofhydrolytic enzymes other than bromelain. Methyland ethyl hippurate are not sufficiently water-soluble.Cohen & Petra (1967) and Williams & Whitaker(1967) have studied the papain-catalysed hydrolysisof ac-N-benzoyl-L-citrulline methyl ester and foundthis compound to be a very good substrate forpapain. When it was tested as a substrate for brome-lain, however, it was found that the initial velocityincreased in direct proportion to the substrateconcentration up to the solubility limit ofthe substrate(0.1M), i.e. Km>0.1M. The solubility of N-acetyl-glycine methyl ester in water is approx. 1 M, but thebromelain-catalysed hydrolysis of this compoundwas barely detectable even at [SO] 0.5M and[Er] (total enzyme concentration) - 0.1 mm. Murachi(1970) has reported that for the bromelain-catalysedhydrolysis of acetylglycine ethyl ester Km is 33M(kcat. =0.55 s-). Since the uncharged N-acylaminoacid esters that are commonly used as substrates forother hydrolytic enzymes such as a-chymotrypsin,papain and ficin proved to be unsuitable as substratesfor bromelain, we decided to synthesize N-benzoyl-L-serine methyl ester as a potential substrate forbromelain. This compound, which has been used asan intermediate in the synthesis of oxazolines (Fry,1950), has not previously been used as a substratefor hydrolytic enzymes. N-Benzoyl-L-serine methylester was synthesized and found to have a solubilityin water at room temperature of approx. 0.25M. Thebromelain-catalysed hydrolysis of this substrateproceeded at an easily measurable rate at substrateconcentrations of 0.5-150mM and a degree ofsaturation of the enzyme by the substrate wasapparent. The present paper describes a kinetic studyof the hydrolysis of N-benzoyl-L-serine methyl estercatalysed by bromelain and by papain.

TheoreticalOur finding that kinetic plots for the catalysis by

bromelain of the hydrolysis of N-benzoyl-L-serinemethyl ester are curved in a manner frequently takenas suggestive of substrate activation (see the Resultsand Discussion section) necessitated detailed con-sideration of the steady-state rate equation ofsubstrate-activated catalyses and of its graphicalrepresentation. There is continuing discussion ofwhich of the three linear plotting forms of theMichaelis-Menten equation is most useful in practice[see, e.g., Dowd & Riggs (1965) and referencestherein]. Our choice of the [SO]/vi (initial substrateconcentration/initial velocity) versus [SO] plot wasbased on the fact that it demonstrates any non-linearity that may exist much more effectively thandoes the l/vi versus 1/[SO] plot and also still allowsthe fitting of a line by the method of least squares.This procedure is not applicable in a simple mannerto the third linear plot, i.e. vj versus v/l[SO], since inthis case both plotted variables are subject to error.The objectives were (1) to define the type ofmodifier

kinetic mechanisms which can give rise to concave-down (SO]/vl versus [SO] plots, (2) to elucidate anysimple relationships that might be required to existbetween the characterizing parameters of a givenmodifier kinetic mechanism to permit curvature in theplot; and (3) to consider methods of determining thecharacterizing parameters.

Steady-state kinetics of substrate-activated enzymecatalyses: the effect ofsubstrate activation on the shapeof [So]/v1 versus [SO] plots

In order to simplify the algebraic representation,the kinetic models in this section are described interms of the conventional two-step mechanism, andreversible steps are regarded as unperturbed equilibriacharacterized by equilibrium constants rather thanmore complex assemblies of rate constants.Scheme 1 is a general form of kinetic mechanism

involving enzyme, substrate and modifier (M), in

M M+ +Km1 k

S+E < ES - E+P

Kaij, jKaIKm2 k'

S+ME MES - ME+P

Scheme 1. General kinetic mechanism involving enzyme,substrate and modifier (M) in which dead-end complexes

may notformA special case is that in which M _ S.

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which dead-end complexes may not formn and in whichthe characterizing constants are defined by eqns. (1)-(4). The interdependence of the four equilibriumconstants is expressed in eqn. (5). The initial rate offormation of products (P) is given in eqn. (6) and theconservation of enzyme is expressed in eqn. (7).

Km] = [E][S]/[ES]

Km2 = [ME][S]/[MES]Ka, = [M][E]/[ME]Ka2 = [ES][M]/[MES]

Ka /Ka2 = Kml/Km2d[P]/dt = v1 = k[ES] +k'[MES]

[ET] = [El+ [ES]+ [ME]+ [MES]

(1)(2)(3)

are given in eqns. (12) and (13). Eqn. (13) is obtainedby expanding the denominator in eqn. (11) anddividing numerator and denominator by [So]2.

Lt d([ET][SO]) m 'm

[SoL -t 0 d[T5O] k kKaj k2Ka2

Lt d [ET][SO])[Sol]÷cz =1/k'd[50]

(12)

(13)

(4) The condition that a plot of [So]/vl versus [SO] beconcave down is given in the inequality (14).

X-,f

(6)(7)

Steady-state analysis of Scheme 1 by eqns. (1)-(7)provides eqn. (8) and differentiation with respect to[SO] gives eqn. (9).

[ET][So]/Vi =

Ka2[So] + Ka2Kmj + [S0][M] + K,[MK(kKa2+ k'[M]) v(8

d([So][ET]/Vi) Ka2 +[M]d[So] kK2+k'[M]

If [M] is maintained constant, a plot of [ETI[SoI/VIversus [So] (or [So]/vl versus [SO] when [ET] is con-stant) will be linear with slope (Ka2+ [M])/(kK a2+k'[M]) and intercept

a +KmjKa2[M]Ka2Kml + KMK2M

kKa2 + k'[M]In the special case where the modifier is the

substrate, the rate eqn. (8) becomes eqn. (10), whichon differentiation with respect to [SO] gives eqn. (11).

[ET][SO]I/Vi =

[SO]2 + (Ka2+ K~a,) [SO] + Ka2KMj

kK2+k'[So] (10)d[ET][So]/Vi =

d[So]kKa2 + 2kKa2[SO] + kK 2- k'K K l + k'[SO]2(2Ka anK[2K

(kKa2 +k'[S0])2

The condition that a plot of [SO]/v1 versus [SO] be

concave down may be demonstrated by comparingthe limiting values of eqn. (II) when [SO] tends tozero and when [SO] tends to infinity. These limits

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1 Km, k'Kmj 1k kKal k2Ka2 k'

(14)

This may be rewritten as inequality (15) in whichx = k/k', a = KmI/Kaj and b = Km1/Ka2.

x2-(1+a)x+b<Ox2-(1 +a)x+b =0

(15)(16)

Some solutions of the equation obtained by settingthe left-hand side of inequality (15) equal to zero(eqn. 16) are presented in the lattice nomogram (seeOtto, 1963) (Fig. 1) as plots of log a versus log xfor various values ofb in the range 10-3_103.

It is useful to consider the various regions andfeatures of Fig. 1.

(I) Solid lines (contours). These represent solutionsto eqn. (16) and thus correspond to situations inwhich plots of [So]/vl versus [SO] will be linear.The common boundary line (A) provides the

essentially common upper root to eqn. (16). Theportion of line A below the abscissa relates only tovalues of b <1.(II) Region on the right ofcommon boundary line A.This region represents situations in which plots of[So]/vi versus [So] will always be concave up, and isnot considered further in the present paper.(III) and (IV) Regions between the common boundaryline A and a given contour defined by the value of b.These regions represent conditions (values of a, b andx) that give rise to plots of [So]/vi versus [SO] that areconcave down. Thus the system passes from a regionon the right of line A where plots are concave up,over line A into a region of downward concavitywhich ends when the appropriate contour defined bythe particular value of b is reached. On passing overthis contour the system is once more in a region ofupward concavity.The region of downward concavity corresponding

to values of b <1 (region III) has a 'funnel'-shapedappearance, whereas that corresponding to valuesof b> 1 (region IV) has an inverted conical shape. Itis apparent from Fig. 1 that region IV is more limitedin terms of the permitted variability of x and athan is region III.

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368 C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

Fig. 1. Lattice nomogram giving some solutions to eqn. (16),X2-(1+a)x+b=O, and defining situations in which

x2-(1+a)x+b<0x = k/k', a = K ../Kaj and b = Km.IKai; k, k', Km,, and Ka2are the parameters that define the kinetic model given inScheme I in which the modifier (M) is the substrate (S).The common boundary line (A) provides the essentiallycommon upper root to eqn. (16). Line B is the locus thatdefines the limits of the constituent constants of the aboveparameters that characterize the hydrolysis of N-benzoyl-L-serine methyl ester catalysed by bromelain at pH7.0,I= 0.1, 25.0°C; for the parameters see legend to Fig. 2.

It is noteworthy that the region contained withinthe ordinate axis and the common boundary line Acorresponds to situations in which there will bedownward concavity in a plot of [SO]/vj versus [SO]even though x> 1, i.e. even though k > k'. In thesecircumstances b has no upper limit but a is limited tovalues greater than 0.1, i.e. Kmj, must be greater than0.1K., This implies that downward concavity inplots of [So]/vl versus [SO] can result not only fromprovision of a ternary SES complex whose rateconstant for breakdown to products is greater thanthat for the breakdown of the binary ES complex,but also in another way. The alternative mechanismthat can operate even when k> k' involves relief athigh substrate concentrations from the accumulationofa significant fraction of the enzyme at low substrateconcentrations as the SE complex that cannot giverise directly to products. Thus this mechanism ofsubstrate activation might best be described asactivation by relief from non-productive binding.When this work had been completed, Dixon &

Tipton (1973) presented a discussion of substrateactivation as part of a more general considerationof negatively co-operative ligand binding and pointedout that it is not necessary for x to be less than I to

observe kinetic plots of the form commonly inter-preted as characteristic of substrate activation.

Determination of the values or limits on the values ofthe parameters that characterize Scheme 1

Eqn. (17), a transform of (10), is written in termsof the four parameters p, q, y and z, where p = kKa2,q = k', y = Ka2[1+(KmjIKal)] and z = KmjKa2.

(p+q[So])[ET][SO][Sol' +y[So]+z

(17)

Since the expressions used to define the fourparameters involve five constants, it is not possibleto isolate the constants (except for k' = q). Similarly,it is not possible to extract simple ratios of theseconstants from the parametric relationships. It ispossible, however, to relate the ratios a and b ofeqn. (16) to the parameters y and z. This is given ineqn. (18):

a = (y Vbb/A/z)-1 (18)Since a must be positive y Vlb/z> 1. If values of yand z are known, a series of values of b may be usedto calculate the corresponding values of a. Thesecorresponding values of a and b may then be used toconstruct a locus to define the limits that may beplaced on values of x, b and a in the particular situa-tion characterized by the known values of y and z.The determination of the parameters y, z, p and q isdiscussed in the following part of the Theoreticalsection and the locus that defines the limits of theirconstituent constants for the bromelain-catalysedhydrolysis of a-N-benzoyl-L-serine methyl ester atpH7.0, I= 0.1, 25.0°C, is presented as the dashedline (B) in Fig. 1.

Special cases ofthe model in Scheme 1(i) Compulsory substrate activation. If k = 0,

Scheme 1 represents compulsory substrate activation.In this case x =0 and the left-hand side of theinequality (15) (=b) cannot be less than 0. Thus plotsof downward concavity cannot be interpreted interms of compulsory substrate activation; thisphenomenon must always give rise to plots of [So]/v1versus [SO] of upward concavity.

(ii) Only one type of binary complex can form andthis gives rise to products. In this situation, Scheme 1simplifies to Scheme 2. The inequality that definesthe circumstances in which plots of [So]/v, versus[SO] will exhibit downward concavity on the basis ofthe model in Scheme 2 may be obtained frominequalities (14) and (15) by letting Ka1 , i.e.a -> 0. Inequality (15) then becomes inequality (19)or (20):

x2_-x+b<O(k)2 k+Km <0

(19)

(20)

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BROMELAIN- AND PAPAIN-CATALYSED HYDROLYSES

SK1 +

E+S ES k E+P

] [Ka2

SES k- E+P+S

Scheme 2. Special case of the kinetic mechanism ofScheme1 in which the modifier is the substrate and only one type ofbinary complex (that which gives rise toproducts) canform

For downward concavity the left-hand side ofinequality (20) must be negative. This implies thatfor this simplified model, k <k', and further that Km.must be sufficiently less than Ka2 to prevent com-pensation.

Computational methods for the determination of thecharacterizing parameters for an enzyme catalysissubject to non-compulsory substrate activation

The four parameters that characterize the non-compulsory substrate-activation rate equation, eqn.(17), may be determined graphically if initial velocitiesmay be determined in two ranges of substrate con-centration, (i) [SO] < K,n, and (ii) [SO] > Ka2 (seeTrowbridge et al., 1963). Preliminary plots of thedata for bromelain-catalysed hydrolyses of N-benzoyl-L-serine methyl ester as vi/[ET] versus log[SO] (see Fig. 2(a) and Trowbridge et al., 1963)suggested that for these catalyses the range ofsubstrate concentration in which the rate of catalysiswas readily measured is such that Km. <[SO] <Ka2,i.e. graphical determination of the parameters is notpossible. Accordingly, we explored the use ofcomputational techniques for evaluation of theparameters. It is necessary to be able to arrive at the'best' values of the parameters of eqn. (17) startingfrom initial 'estimated' values, which may differconsiderably from the 'best' values. Thus the objectof the optimization is to refine sequentially the valuesof the 'estimates' in such a way as to minimize theerror criterion. There are may ways of approachingthis problem (Rosenbrock & Storey, 1966, p. 48)Method 1. Eqn. (17) may bere written as eqn. (21).

(p+q[So])[ET][SO][SO]2+y[So]+z

In practice the left-hand side of eqn. (21) will besome non-zero value, X. It is assumed that the set ofX values for a given data set will be distributednormally about zero. The best-fit values of theparameters are obtained by application of the least-squares criterion. This condition is expressed ineqn. (22):Vol. 141

n X2 n lvA([So]P+y[So]+z)-(p+q[So])[ET][So]I1=0 s= o [So]2+y[So]+z

= a minimum (22)The partial differentials of eqn. (22) will be rathercomplicated unless the equation is simplified. Thismay be achieved by using an iterative technique andmaintaining the denominator as a constant withrespect to the dissociation constants during any oneiterative cycle. It is convenient to rewrite eqn. (22)as eqn. (23), in which w1 is defined by eqn. (24).n n

I = E w1i{v([So]2 +y[So]+ Z)i=O i=O

-(p +q[S0])[ET][SO]}2 (23)

Wj = 1/([So]2+y[So]+z)2 (24)

The value of wi is set to 1.00 for the first cycle and isreadjusted for each subsequent cycle by using thevalues of the dissociation constants determined inthe previous cycle.Eqn. (23) may be partially differentiated with

respect to p, z, q and y, a procedure facilitated bysubstitution of eqn. (25) and (26) into eqn. (23).

p[ETr] = m

q[ET] = k'E

(25)

(26)

The resulting expressions for the partial derivativeswith respect to z, m, y and k'E are set equal to zeroand the set of simultaneous equations is solved forthe above parameters by matrix inversion. The cal-culated values of z and y are used to calculate a newset of w1 values. The iteration procedure is thenrepeated until the parameters achieve constantvalues. It is not possible, in any simple manner, toobtain standard errors for the parameters, as w1 isdefined as being constant for any one iterative cycle.In addition, the method described above places noconstraints on the sign of the parameters and themethod frequently produces negative values for theparameters where the data are not of the highestquality. Thus although this method was used success-fully on some sets of data (see Table 3), it provedunable to produce values for the parameters in aninterpretable form in a number of cases. The lack ofestimates of the standard errors is also serious whenfitting experimentally determined data to a relativelyelaborate model of this type. A second method, cap-able of eliminating the above disadvantages, hasbeen developed and is described below.Method2. The considerable difficulties encountered

in fitting data to equations of the form of eqn. (17)arise because of extremely high correlation betweenthe parameters. These difficulties are aggravated when,as in this study, it is possible to use substrate concen-trations which cover only a small part of the rangefrom zero to saturation. In the fitting procedure it is

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C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

x1-

a 10

20

I0

0

x

(a)

log [So]+4

(c)

0.10

[So] (M)

LU-c

h..

x

C

1-%

1-1

0.15 0.20 o

(b)

0.5 1.0

10-3/[So] (M-1)

(d)

0.10[So] (M)

Fig. 2. Kinetic plots for the hydrolysis ofN-benzoyl-L-serine methyl ester catalysed by bromelain atpH7.0 in46.3 mM-potassium phosphate buffer, I= 0.1 at 25.00C

This data set, which is representative of a large number of such sets, was collected on a single day. The points are experi-mental and the lines were calculated from the various transforms of:

V -(p +q(SOI)[ET][So]/([So]2 +y[SO]+ Z)[i.e. eqn. (17) in the Theoretical section] in which the values of the parameters (p = 1.57 x 10-2 x 0.38 = 5.95 x 10-3M-S-1Iq = O.45s-1,y = 0.38Mand z = 1.22x 10-3x0.38 = 46.36 x 10-5M2)were computed by Method2describedin the Theoreti-cal section. (a) Plot of v,/(ET] versus log [SO]; (b) plot of [ET]/Vi versus 1/[So]; (c) plot of [SoI[ETI/Vi versus [SO]; (d) plot ofvl/[ET] versus [SO]. The dotted line in Fig. 2 (a) was calculated from vi/[ETI = k'[So]I(Ka2+ [Se]) in which k' = 0.45 s- andKa2 = 0.38M.

necessary that the parameters be constrained to bepositive.A non-linear regression procedure which was

originally suggested for use in fitting data to ligand-

binding equations (Cornish-Bowden & Koshland,1970) seemed appropriate to apply to this work. Inthis procedure, negative parameters are preventedby carrying out the calculations in terms of the

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logarithms of the parameters. The method dependsin essence on the assumption that the sum of squaresof residuals can be presented approximately by aquadratic function of the logarithms of theparameters. Starting at any values of the parameters,it is possible in principle to calculate the first andsecond partial derivatives of the sum of squares withrespect to each parameter, and use the quadraticassumption to calculate the location of the minimum.If the quadratic assumption has any validity thiscalculated minimum approximates to the trueminimum, and the calculation is repeated as manytimes as are necessary to find the trueminimum. Whenthis technique was applied to the fitting of kineticdata to eqn. (17) it worked well only in the immediatevicinity of the minimum; in other words, it wasnecessary to have very good starting guesses. Thisis because eqn. (17) is rather 'overdefined', in thatit contains more parameters than are actuallyrequired to produce a good fit to the data, and as aresult the parameters are very highly correlated,and the sum-of-squares contours are exceedinglyelongated. It was therefore necessary to complementthe procedure of Cornish-Bowden & Koshland(1970) with one which was capable of proceedingefficiently from poor starting guesses when thequadratic approximation was inadequate.

Various methods of proceeding in the earlyiterations were tried, including various modificationsof the method of steepest descent, mostly with ratherunsatisfactory results. Themethod thatwas eventuallyused, which gave excellent results in all cases tried,was the modified simplex method of Nelder & Mead(1965). In this method, a 'simplex' is set up, consistingof (n+1) sets of values for the n parameters, and thesum of squares is computed at each set of values, or'vertex'. The worst vertex is then replaced by oneobtained by reflecting the worst vertex through thecentroid of the other n vertices. The amount by whichthis vertex is changed is then increased if the newvertex is a new best, and decreased if it is a new worst.The calculation is then repeated until the differencesbetween the vertices become negligible. The mainadvantages of this method are its extreme simplicityand the fact that fewer assumptions are made aboutthe shape of the sum-of-squares surface than in anyother method. It is also particularly suitable for usein conjunction with the method described previously,because it is much more effective in the early partof the minimization, becoming very slow as theminimum is approached.

In summary, therefore, the results given wereanalysed by fitting to eqn. (17) by using the methodof Nelder & Mead (1965) to obtain rough estimatesof the kinetic parameters, which were subsequentlyrefinedby themethodofComish-Bowden&Koshland(1970). On completion of the minimization, standarderrors of the parameters were estimated as described

Vol. 141

by Cornish-Bowden & Koshland (1970). It shouldbe noted that since in almost all cases the calculatederrors were rather large, the linear assumptions usedin calculating them are unlikely to be accurate, sothat the actual value must be regarded only as anindex of precision.

Materials and MethodsBromelain preparationsThe starting material was food-grade bromelain

[Seravac Laboratories (Pty.) Ltd., Maidenhead,Berks., U.K. (now Miles Seravac Ltd.), batch no.E.V. 1 a]. This material was purified bya method whichis essentially that of Murachi et al. (1964) to yieldwhat in the present paper we shall call 'bromelain'.For some experiments a preparation of the enzymein which the chromatography on Sephadex G-100was omitted was used. This preparation we shall call'partially purified bromelain'. Both of these prepara-tions are essentially the same as that which in otherconnexions we have called T-bromelain (Brocklehurstet al., 1972).

Extraction. Crude bromelain powder (40g) wasadded to 0.05M-potassium phosphate buffer, pH6.10(200ml), and the resulting suspension stirred atroom temperature (approx. 26°C) for 30min. Theresulting cloudy solution was centrifuged at 100OOgfor 30min and the supernatant collected.

Chromatography on Amberlite CG-4B. This resin(a weakly basic anion exchanger) was chosen as asubstitute for the Duolite A-2 used by Murachi et al.(1964) which is not obtainable in this country. Inearly purifications the supematant from the extrac-tion was applied to a column (2.5cmx45cm) ofthis resin which had been fully acid-base cycled.Chromatography of crude bromelain on this resindid not result in resolution of the crude enzyme intodiscrete components (as monitored by E280 measure-ment), but resulted in a single main peak with a longtail. Murachi et al. (1964). reported that chromato-graphy on a resin very similar to Amberlite CG-4B(Duolite A-2) removes some of the yellow-colouredmaterial from the crude enzyme. This was not thecase with Amberlite CG-4B, which seems to havevery little effect. As a result of this finding, this stageof the preparation was omitted from preparations ofenzyme used in this work.

Chromatography on Amberlite CG-50. Murachiet al. (1964) applied 10g of crude bromelain in 100mlof the phosphate buffer, pH6.1, to a 500ml columnof Amberlite CG-50 resin (a weakly acidic cationexchanger).

In the present work, a column (2.5cm x 100cm) ofAmberlite CG-50 resin was acid-base cycled and thenequilibrated overnight with 0.2M-potassium phos-phate buffer, pH 6.05. A solution of crude bromelainextracted from lOg of crude powder in 100ml of

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C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

the same buffer was applied to the column. A furtherquantity (lOOml) of this buffer was pumped throughthe column in 1 h and then 5 litres of0.05M-potassiumphosphate buffer, pH 6.05, was pumped through ata rate of 2 litre/h. The breakthrough fraction thatresulted from this washing was discarded. Thecolumn was then eluted with 0.2M-K2HPO4 con-taining 1 M-KCl at a rate of 36ml/h and 5ml fractionswere collected and monitored by measurement ofE280. The fractions containing protein, whichemerged as a single symmetrical peak after thebreakthrough fraction, were pooled and thensubjected to (NH4)2SO4 fractionation. For everylOOml of collected ice cold eluate, 25.5 g of(NH4)2SO4was added slowly with gentle stirring. When all the(NH4)2S04 had been added, a moderate cloudinesswas apparent in the solution. The cloudy solutionwas left at 4°C for 1 h and centrifuged at lOOOOg and4°C for 30min. The precipitate was discarded and thesupematant was subjected to (NH4)2S04 precipita-tion as described above, by using 6g of (NH4)2SO4for each lOOml of original collected eluate. Theprecipitate, which was collected by centrifugation,was dissolved in the minimum volume of water atroom temperature and dialysed against 3 x 5 litres of0.01 M-KCl containing 1 mM-EDTA at 4°C. Thisenzyme, prepared by chromatography on AmberliteCG-50 and (NH4)2SO4 fractionation, is designated'partially purified bromelain'. This chromatographicstep is the one which separates extraneous proteinand most of the carbohydrate associated with thecrude enzyme; these components appear in thebreakthrough fraction. The composition of thebreakthrough fraction varied somewhat from run torun, as did the exact elution volume of the enzyme.This was shown to be due to the exceptional pH-sensitivity of bromelain chromatography on this typeofcolumn. Variation of± 0.1 pH unit can cause eitherthe superimposition of the breakthrough and enzymefractions or the emergence of the enzyme fraction ina very large volume of eluate. Crude bromelain wasassociated with 0.41 g of carbohydrate/g of totalmaterial, whereas after chromatography on Amber-lite CG-50 the carbohydrate content was decreasedto 0.025 g/g of total material.

Chromatography of 'partially purified bromelain'on Sephadex G-100. A column (2.5cm x 100cm) wasfilled with Sephadex G-100, which had been allowedto swell overnight in 0.05M-sodium acetate buffer,pH5.2. The column was then equilibrated at 4°Cby slowly passing the acetate buffer through it for24h. Partially purified bromelain was then appliedto the column and eluted with the above-mentionedacetate buffer at a flow rate of lOml/h. Fractions(1 or 5ml) were collected and protein was detectedby measurement of E280. The elution pattern wasindicative of only a single component absorbing at280nm. The protein solution emerging from this

column was subjected to (NH4)2S04 precipitationessentially as described above in the second step ofthe (NH4)2SO4 fractionation and dialysed asdescribed above. The enzyme so obtained is desig-nated 'bromelain.'Chromatography on Sephadex G-100 and sub-

sequent (NH4)2S04 precipitation decreases thecarbohydrate content from 0.025 g/g of total material(in partially purified bromelain) to 0.02g/g of totalmaterial (in bromelain). No circumstances have beenfound in which the enzyme that has been subjected toSephadex G-100 chromatography has shown be-haviour different from that of partially purifiedbromelain.

Other materials

Papain. This was the 2 x crystallized product ofBDH Chemicals Ltd., Poole, Dorset, U.K., and wasused without further purification.

Substrates. a-N-Benzoyl-L-arginine ethyl esterwas obtained from Koch-Light Laboratories Ltd.,Colnbrook, Bucks., U.K. a-N-Benzoyl-L-citrullinemethyl ester was obtained from BDH ChemicalsLtd. Acetylglycine methyl ester was prepared bythe acetylation ofglycine methyl ester (obtained as thehydrochloride from Koch-Light Laboratories Ltd.)with acetic anhydride by the method of Wolf &Niemann (1963).

N-Benzoyl-L-serine methyl ester. This was preparedby reaction of L-serine methyl ester with benzoylchloride.L-Serinemethylesterhydrochloride(Aldrich,Milwaukee, Wis., U.S.A.) (3.1 g) was dissolved inwater (20ml). Benzoyl chloride (2.08g) dissolvedin chloroform (40ml) was then added and the biphasicmixture was stirred vigorously with a magneticstirrer and NaHCO3 added in small portions tomaintain the pH at 8.5. After 2h the pH of theaqueous layer was adjusted to 7.0 after prior separa-tion from the chloroform layer. The aqueous layerwas extracted with chloroform (5 x 50ml). Thechloroform extracts and the original chloroformlayer were combined and dried over anhydrousMgSO4. The MgSO4 was then removed by filtrationand the chloroform removed from the filtrate byrotary evaporation in vacuo. The resulting oil solidifiedwhen cooled in solid C02-acetone and the solid wastwice recrystallized from benzene. The final producthad m.p. 85°C [Fry (1950) gives m.p. 84-860C] andwas shown to be a single component by t.l.c. inchloroform-acetone-acetic acid (79:20:1 by vol.)(Found: C, 59.0; H, 5.9; N, 6.3. Calc. for N-benzoyl-L-serine methyl ester, C11H13N04: C, 59.2; H, 5.8;N, 6.3 %). [a]4 = 17.9±0.20 (c = 1 in 95% ethanol)[Fry (1950) gives [a]"5 = 17.7 (c = 1 in 95 % ethanol)].Other chemicals. (NH4)2SO4 was the BDH product

'special for enzymology.' Buffers and other solutions

1974-

372

BROMELAIN- AND PAPAIN-CATALYSED HYDROLYSES

were made up with AnalaR-grade reagents whereverpossible. Water was distilled and subsequentlydeionized by passage through a Deminrolit MK.7mixed-bed ion exchanger. In experiments in whichthe enzymes were used without L-cysteine or dithio-threitol in the reaction mixture, the deionized waterwas deoxygenated by refluxing and cooling under02-free N2.

Preparation ofstock solutions ofactivated, activator-free bromelain and papain. These were prepared byincubating the enzyme (approx. 0.1 mM) withL-cysteine or dithiothreitol (5mm) at pH6.5 for 15minat room temperature, and then separating the enzymefrom low-molecular-weight species on a column(1.25cmx 30cm) of Sephadex G-25. The column hadpreviously been equilibrated with a deoxygenatedsolution of0.01 M-KCI and 1 mM-EDTA. The enzymewas eluted with this solution, and a stream of 02-freeN2 was passed through the eluent reservoir and overthe eluting solution.

Determination of thiol contents oJ bromelain andpapain

These were determined by using samples of activa-ted, activator-free enzyme by titration ofthe enzymes'essential thiol groups with 5,5'-dithiobis-(2-nitro-benzoic acid) at pH 8.0 [see Ellman (1959) andWharton et al. (1968a)]. The thiol content of brome-lain was generally 0.8mol of thiol/mol of protein,and of papain approx. 0.6mol of thiol/mol of proteinbased on the following optical and molecular-weightdata: bromelain, mol. wt. = 3.32 x 104, 6280 = 6.33 x104M-Icm' (Murachi et al., 1964); papain, mol.wt.2.07x 104 (Smith et al., 1955), 6280 = 5.1 x 104m-1 -

cm-' (Glazer & Smith, 1961). Spectrophotometricmeasurements were made on Cary 15 or Cary 16Kspectrophotometers. When measuring initial rates ofbromelain- and papain-catalysed hydrolyses (seebelow) the reactions were generally studied in thepresence of 5mM-L-cysteine.

In the calculation of catalytic rate constants, theenzyme concentration was calculated from measure-ments of E280.

Measurement of initial rates of hydrolysis of a-N-acylamino acid ester substrates catalysed by bromelainand bypapainThese measurements were made in a Radiometer

pH-stat. A total initial reaction volume of 5ml wasused. The reaction mixture was contained in ajacketed vessel through which water from a thermo-statically controlled bath set at 25.0°C was circulated.The titrant was 0.04 or 0.1 M-NaOH, which was madeup from standardized BDH concentrated volumetricreagent and 02-free and C02-free deionized water.The titrant was protected from atmospheric CO2Vol. 141

by guard tubes filled with self-indicating Carbosorb(BDH Chemicals Ltd.). 02-free N2 was passed overthe surface of the reaction mixture. A typical reactionmixture is as follows: 0.5M-KCI (1.Oml); 0.1 M-EDTA(0.05ml), 0.2M-L-cysteine hydrochloride neutralizedto pH7.0 (±0.1 ml); substrate solution (x ml); water[5.0-(x+y+1.15 or 1.05) ml]; enzyme solution(y ml). Any further additions to the reaction mixture(modifiers) were added in a volume which wassubtracted from the water volume. The reaction wasgenerally started by addition of the substrate. In theruns carried out in the presence of L-cysteine, theenzyme was incubated with L-cysteine-EDTA-KCIsolution for 10min before the reaction was started byaddition of the substrate.

Carbohydrate determinations

These were done by the method of Winzler (1955).

Data processing

Data pairs ([SO], v1) were processed on the Univer-sity of London Atlas computer by using programswritten in the EXCHLF language and on the Univer-sity of Birminghain English Electric KDS9 computerby using programs written in FORTRAN IV. Copiesof the FORTRAN program used to fit data to eqn.(17) may be obtained from Dr. A. Cornish-Bowden.

Results and Discussion

Kinetic plots of the datafrom the bromelain-catalysedhydrolysis ofN-benzoyl-L-serine methyl ester

Fig. 2(b) shows a Lineweaver-Burk plot of typicaldata obtained from the hydrolysis of N-benzoyl-L-serine methyl ester catalysed by bromelain at pH7.0,I= 0.1, and 25°C. This plot deviates somewhat fromlinearity giving rise to a curve ofdownward concavity.When the same data are plotted as [So]/vi versus[SO] (Fig. 2c) marked non-linearity becomes apparent,the curvature being concave down. Figs. 2(b) and2(c) show that the catalysis of the hydrolysis ofN-benzoyl-L-serinemethyl esterby bromelain does notfollow simple Michaelis-Menten kinetics. Downwardconcavity in the plot forms of Figs. 2(b) and 2(c) mayarise from a number of factors: (i) the enzyme maybe impure in that it may be composed of more thanone species able to catalyse the hydrolysis of thesubstrate in non-identical ways, (ii) the substratemay be impure in that in addition to the species whosehydrolysis is catalysed by the enzyme, there is anotherspecies which may bind to the enzyme to produce acomplex which catalyses the hydrolysis of thesubstrate more effectively than the enzyme; (iii) theenzyme may have more than one active site permolecule whose catalytic properties are non-identical

373

374 C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

or the sites may be interactive as a result of substratebinding; (iv) the enzyme may have a single catalyticsite per molecule, but be subject to non-compulsorysubstrate activation (see the Theoretical section).The possible reasons for curvature in plots of

enzyme kinetic data have been discussed byTrowbridge et al. (1963), who studied the trypsin-catalysed hydrolysis of a-N-tosyl-L- and -D-argininemethyl esters and found that these catalyses did notfollow simple Michaelis-Menten kinetics. Theyobtained concave-up Eadie plots, which are equiva-lent to concave-down Lineweaver-Burk and [So]/viversus [SO] plots, and interpreted their data in termsof substrate activation. It is demonstrated in theTheoretical section that concave-down [So]/vi versus[So] plots may be due to non-compulsory substrateactivation but may not arise from compulsorysubstrate activation.

Steady-state kinetic experiments do not allow thefactors (i)-(iv) to be distinguished as interpretationsfor curved kinetic plots. Other types of experiments,however, may sometimes suggest that certain of thesefactors are less likely than others to be responsible forthe curvature.

Factor (i). Factor (i) is very difficult to eliminate,since no absolute criteria for enzyme purity areavailable. The enzyme purified by the method ofMurachi et al. (1964) is homogeneous by ultracentri-fugal sedimentation, free-boundary electrophoresisand diffusion analysis (Murachi et al., 1964).Chromatography on Amberlite CG-50, CM-Sepha-dex, DEAE-Sephadex, or Sulphoethyl-Sephadexyields a single symmetrical peak (Ota et al., 1964;Murachi et al., 1964). No evidence for inhomogeneitywas found by disc electrophoresis on polyacrylamidegel in either the absence or the presence of 8M-urea(Chao & Liener, 1967; C. W. Wharton & I. Trayer,unpublished work). On the other hand, the chromato-graphically purified enzyme, which migrates as a

Table 1. Apparent first-order rate constants at constantsubstrate concentrations for the hydrolysis ofN-benzoyl-L-serine methyl ester catalysedby 'partiallypurifiedbromelain'

and bromelain at pH7.0, 25.0°C and I=0.1For details see the text.

vI/[ET] (s-i)

IS1(M)0.0250.0500.750.100.1250.150

Partiallypurified

bromelain0.0350.0570.0770.0970.1270.133

Bromelain0.0310.0560.0840.1080.1120.132

A(vi/[ETJ) (s')+0.004+0.001-0.007-0.011+0.01510.001

single band during electrophoresis on celluloseacetate (Ota et al., 1964), contains small amounts ofextraneous end groups in addition to the terminalvaline residue (Ota et al., 1964). This, together withthe finding of Whitaker and his co-workers (El-Gharbawi & Whitaker, 1963; Feinstein & Whitaker,1964) that stem bromelain can be fractionated intofive proteolytically active components, each havingdifferent amino acid compositions, pH optima forcasein hydrolysis and heat s.tabilities, casts doubt onthe strict homogeneity of bromelain obtained bysome methods of preparation. There is evidence,however, which, although not conclusive, suggeststhat such inhomogeneity as may exist in the purifiedbrornelain preparations used in the present work isprobably not responsible for the curvature in Fig.2(b) and 2(c). First, at pH approx. 7, kinetic plots(Lineweaver-Burk, Eadie and [SO]/vl versus [So])for the catalysis by bromelain and by O-carboxy-methylcellulose-bromelain of the hydrolysis ofa-N-benzoyl-L-arginine ethyl ester are linear (Inagami& Murachi, 1963; Wharton et al., 1968a). Secondly,the values of vi/[ET] at fixed substrate concentrationsfor the catalysis of the hydrolysis of N-benzoyl-L-serine methyl ester by 'partially purified bromelain'and 'bromelain' are closely similar and the differencesnot apparently systematically distributed about zero(see the Materials and Methods section and Table 1).Thirdly, the values of viI[ET] at fixed substrateconcentrations are closely similar when differentfractions from an [NH4)2SO4 fractionation of'partially purified bromelain' are used for the catalysis(see Table 2). The values of viI[ET] in Table 2 are ingood agreement with those obtained by using thenormal 'partially purified' and 'fully purified' enzymepreparations (Table 1). The results given in Tables 1

Table 2. Comparison of the apparent first-order rateconstants for the bromelain-catalysed hydrolysis of N-benzoyl-L-serine methyl ester catalysed by two (NH4)2SO4fractions of 'partially purified bromelain' at pH7.0, 25.0°C

and I= 0.1Fraction 1 was obtained from a solution of partiallypurified bromelain at 4°C by addition of solid (NH4)2SO4to 42% saturation, and centrifugation. Fraction 2 wasobtained by adding (NH4)2SO4 to 50% saturation to thesupematant remaining after removal of fraction 1,followed by centrifugation. In both cases the precipitatewas redissolved in water and extensively dialysed againstI .Omi-EDTA before assay.

[S](M)

0.01250.0500.100.15

vi/[ET] (S-i)__-

Fraction ... 10.0230.0580.0970.130

20.0180.0580.0970.140

A(vi/[ET] (S')

+0.0050.00.0

-0.01

1974

BROMELAIN, AND PAPAIN-CATALYSED HYDROLYSES

and 2 were obtained from experiments carried outwith an interval of 6 months between them and withdifferent enzyme preparations. The latter two piecesof evidence indicate that if bromelain contains akinetically significant impurity, the impurity isclosely associated with it and is not separable eitherby chromatography on Sephadex G-100 (the stepwhich converts 'partially purified bromelain' into'bromelain') or by (NH4)2SO4 fractionation. Thefirst piece of evidence shows that any impurity inbromelain kinetically significant in N-benzoyl-L-serine methyl ester hydrolysis must catalyse thehydrolysis of a-N-benzoyl-L-arginine ethyl estereither in a manner indistinguishable from thecatalysis by bromelain or not at all.Nakata & Ishii (1972) reported that the hydrolysis

of a-N-benzoyl-L-arginine p-nitroanilide is subject tosubstrate activation when catalysedeither by a-trypsinor by f8-trypsin. This finding greatly strengthens thesuggestion by Trowbridge et al. (1963) that thedeviation of the trypsin.,catalysed hydrolysis ofa-N-tosyl-L-and -D-arginine methyl esters fromsimple Michaelis-Menten kinetics might be due tosubstrate activation.Takahashi et al. (1973) have reported the resolution

of bromelain prepared by the method of Murachiet al. (1964) into two fractions designated SB1 andSB2. These fractions differ in amino acid compositionby only 2 or 3 residues of glycine, alanine and tyrosineand are essentially identical in molecular properties,active-centre sequences and catalytic properties.

In the absence of evidence to the contrary, it istentatively suggested that impurity in the bromelainpreparation is not responsible for the non-linearity ofthe plots in Figs. 2(b) and 2(c); fractions SBI andSB2 appear to be so similar that their co-existencewould seem unlikely to produce the 'substrate-activation' effect reported here.

Factor (ii). This factor involves the presence ofimpurity in the substrate. The N-benzoyl-L-serinemethyl ester prepared as described in the Materialsand Methods section provided good analytical andoptical-rotation data and was pure as assessed byt.l.c. Titration with NaOH showed that there wasless than 1 % of N-benzoyl-L-serine present, andninhydrin analysis of a stock solution of aqueoussubstrate that had been stored at 4°C for 2 weeksshowed that the maximum possible concentration ofL-serine methyl ester present was less than 0.1 %.Preliminary experiments with N-benzoyl-DL-serinemethyl ester have demonstrated that the 'substrate-activation' phenomenon characterized by the highbinding constant K,, (=0.38±0.06M, see below) is notdue to binding of low concentrations of N-benzoyl-D-serine methyl ester characterized by a much smallerbinding constant.

Factors (ii) and (Iv). These factors cannot bedistinguished by the available data. In the absence of

Vol. 141

independent evidence that bromelain catalysesexhibit co-operativity, we have chosen to interpretthe rate data in terms of parameters that characterizea catalysis subject to non-compulsory substrateactivation (Schemes 1 or 2). As a general view it seemsreasonable that many hydrolyses of low-molecular-weight substrates catalysed by proteolytic enzymesmight be found to be subject to non-compulsorysubstrate activation if examined over a sufficientlywide range of substrate concentration. Since thenatural substrates for these enzymes are proteins,and since binding sites in such enzymes are probablycomposed ofseveral sub-sites (see Berger& Schechter,1970), each binding one amino acid residue, it seemsplausible that with low-molecular-weight substratesthe 'second' substrate molecule might occupy oneof these sub-sites. This could result either in enhance-ment of the catalytic effectiveness of the enzymeacting on the substrate molecule bound at the catalyticsite, by conformational changes, or by decreasing thenumber of non-productive binding modes of thissubstrate molecule.

Kinetic parameters ofthe bromelain-catalysed hydroly-sis of N-benzoyl-L-serine methyl ester: comparisonwith those of the bromelain-catalysed hydrolyses ofc-N-benzoyl-L-arginine ethyl ester and ca-N-benzoyl-L-arginine amide

Figs. 2(a)-2(d) demonstrate the good fit of the datafor the bromelain-catalysed hydrolysis of N-benzoyl-L-serine methyl ester to eqn. (17).The parameters of eqn. (17) that characterize this

catalysis are given in the legend of Fig. 2. The locusthat defines the limits of the constituent constants ofthese parameters in terms of Scheme 1 is presentedas line B of Fig. 1. Certain limitations must be placedon the values that may be taken by x, b and alx. Thus,the minimum value ofx is 3.3 x 10-3 and the minimumvalue ofb is 3.21 x 10-. The ratio alx has a maximumlimit of 316 but has no minimum limit. Ifx>1, a andb must be greater than approx. 300, i.e Km1 > 300K,1and Kmj > 300K 2. Thus although it is possible to setcertain limits on the values of the ratios of theconstants that characterize Scheme 1, it is notpossible to define the value of any constant exceptthat of k'.As discussed in the Theoretical section, it is possible

to simplify Scheme I to Scheme 2 if it is assumed thatonly one type of binary ES complex can form (or thatall such complexes are equivalent). Scheme 2 could beinterpreted in a general way analogous to the treat-ment of dibasic acids in terms of stages of ionizationcharacterized by macroscopic dissociation constants(see Edsall & Wyman, 1958). There seems littleadvantage in this approach in the present context, asit merely hides complexity in simple parametric

375

C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

formulation. Scheme 2 could also be interpreted interms of a compulsory binding order in ternarycomplex-formation, i.e. the substrate molecule thatundergoes transformation to products binds beforethe substrate molecule that acts as modifier and doesnot undergo transformation to products. It isinteresting to adopt this interpretation of Scheme 2,because this allows a comparison of the parametersof Scheme 2 with the Michaelis parameters of otherbromelain-catalysed hydrolyses. Ordered binding ofligands to enzymes is well established for multi-substrate enzymes, e.g. many NAD-linked dehydro-genases. The possibility that the substrate activationobserved in the present study might involve anobligatory order of binding in what might constitutetwo of the sub-sites (see Berger & Schechter, 1970)for a protein or polypeptide substrate raises intriguingquestions about the mechanism of binding of theamino acid residues in such substrates.The kinetic parameters that characterize the

hydrolysis of this substrate catalysed by bromelainand, for comparison, by papain, in the presence (seebelow) and absence of urea and guanidine hydro-chloride are presented in Table 3, which also showsthe kinetic parameters that characterize the bromelain-catalysed hydrolysis of x-N-benzoyl-L-arginine ethylester and of a-N-benzoyl-L-arginine amide. The latterparameters are discussed first because they constituteone of the most important, hitherto unresolved,problems in the kinetics of bromelain-catalysedhydrolyses and provide a background for discussionof the N-benzoyl-L-serine methyl ester hydrolysis.

Bromelain-catalysed hydrolysis of a-N-benzoyl-L-arginine ethyl ester and a-N-benzoyl-L-arginine amide

The kinetic property that most dramaticallydistinguishes bromelain from the somewhat similarthiol proteinases papain and ficin is the large differ-ence in the value of kcat. for the hydrolyses ofa-N-benzoyl-L-arginine ethyl ester and a-N-benzoyl-L-arginine amide found only for the bromelaincatalyses (Inagami & Murachi, 1963). An associatedfeature that could be significant is that for each ofthese bromelain catalyses the values of the ratiokcat . Km are closely similar (see Table 3). Inagami &Murachi (1963) have interpreted the large differencein these kcat. values in terms of the usual commonacyl-enzyme model (eqn. 27) by assuming thatdeacylation is rate-limiting for the ester hydrolysis(i.e. kcat. = k+3), whereas acylation is rate-limitingfor the amide hydrolysis, i.e. (kcat. = k+2 for the amidesystem)

E+S3 ES + ES' -3 E+P2 (27)k_,

+Pi

The constants of eqn. (27) are related to those of thesimple Michaelis-Menten eqn. (28) by the well-known relationships (29-31)

Km E k cat EE+S Izz ES - - E+P

kcat. = k+2k+3/(k+2 + k+3)

Km = (k , + k+2)k+31k+l(k+2 + k+3)

kcat.lKtn = k+,k+2/(k-, +k-+ 2)

(28)

(29)(30)

(31)

To explain the similarity in the values of kcat.IKmfor the bromelain-catalysed hydrolyses of the esterand amide substrates, Inagami & Murachi (1963)suggested that k-1 < k+2, in which case kcat.IKm(eqn. 31) reduces to k+1, the second-order rateconstant for the formation of the adsorptive complex.Consideration ofthe value (Inagami & Murachi, 1963)of kcal. KKm (2.9M-1 - s-1) for the bromelain-catalysedreactions, however, suggests that this ratio cannotrepresent k+1, since the formation of an adsorptivecomplex is usually considered to be diffusion-con-trolled with a rate constant of approx. 1 x 108M-1 .S-1(see Gutfreund, 1965). It is unlikely therefore thatk_1 k+2. It could be suggested that the similarity inthe values of kcat./Km for the amide and ester hydro-lyses might be due to fortuitous compensation of thesmaller value of k+2 for the amide hydrolysis by aproportionately larger value of k+1/(kL +k+2)(or k+1/k-1 i.e. 1/K, if k-, >k+2) than obtains forthe ester hydrolysis. Such compensation, althoughnot impossible, seems unlikely, and this casts doubton the interpretation suggested by Inagami &Murachi (1963) of their finding that kca,. (ester)/kcat. (amide) = 140. We would like to propose analternative interpretation of the relationships thatexist between the kinetic parameters of these brome-lain-catalysed hydrolyses. We have shown previously,in another connexion (Brocklehurst et al., 1968),that one phenomenon which is characterized by adecrease in the magnitude of kcat. without change inthe magnitude of kcat./Km is non-productive bindingof the substrate. When the acyl-enzyme model(eqn. 27) is extended to include binding of thesubstrate by the enzyme in modes that will not permitacylation (SE), it becomes eqn. (32).

E+S k ES- ES' k+ E+P2 (32)k_- +Pi

SE

The parameters that characterize eqn. (32) arerelated to those of the simple Michaelis-Mentenmodel (eqn. 28) by eqn. (33) and (34) in which Km*and K.' are defined by eqns. (35) and (36).

1974

376

377BROMELAIN- AND PAPAIN-CATALYSED HYDROLYSES

4a)-C)

o1 en*.

*

_ _1+ --

o 4 0 X.

a) a-) oo o o o I I I I I I

0o -Wo0 C =

0 _~ W el 0} cyb 'I C O~ +1= C14 ,0 en0o

* ._ -4oe 2

cn~~~~~~~~~~~~~~~~~e

t- ;4 M e;> m n +1 +l +l +1 +1

CSE~ eic

0 ei r- 00E 8 2

.,. en_

ti TI~~ en N + +I +I +I +I

0

C~~~~~~~~~I~~~

A a), e# or _- 0 --o-

C>sz) Qo 0 6 6a EA)

0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

00 00

U44

;~ -4 E - 0; , 000dg i

0 F a) ma 'm4

~~~~~ ~~~04-4 4) 0 0 0 0 0 0C)

~~~~~~~~~ U)~~~~~~~~~~~~~~~~~~~~~

0 0

4)a)) )a-4- co U) C) 0

Cdd cr co

$-4 0 0~~ -Cd 1-4 S-4 $ 4)4)Ca

a).'-, 4 m 0

Vol. 141

C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

kcat .=,- k+2k+3

k+3 m*+ k+2 + k+3Ks'Km-= k+3Km*kk3KKm

Kmk+3Kn* + k+2 + k+3K,'

Km* = (k_ + k+2)/k+IK,' = k-,'Ik+

Comparison ofeqns. (33) and (34) with the analogouseqns. (29) and (30) that result from the steady-statetreatment of eqn. (27) demonstrates that if twocatalyses are characterized by similar parametersfor the formation of the productive adsorptivecomplexes, and for the subsequent acylation anddeacylation steps, but one catalysis is moresubject to non-productive binding than is the other,the former catalysis will be characterized by botha lower kcat. and a lower Km but the ratio kcat.IKmwill be unaffected. Thus if bromelain catalyses thehydrolyses of a-N-benzoyl-L-arginine ethyl ester anda-N-benzoyl-arginine amide by similar mechanismscharacterized by similar values of Km* (see eqn. 35)and similar values of k+2k+3/(k+2+k+3), the observedvalues of the Michaelis parameters for the twocatalyses could result from a much larger non-productive component in the binding of the amidethan in the binding of the ester.One way in which this could arise would be if the

susceptible primary-amide group (R3) of the amidewere bound to an appreciable extent at a site on theenzyme (Pi) which is occupied by the N-acylaminogroup (R1) of the substrate when it is bound pro-

P2

(a)

(33) ductively (see Scheme 3). Since for N-acylamino(33) acid amide substrates both R1 and R3 are amide

groups, this type of non-productive binding might beexpected to exist in most, if not all, catalyses by

(34) proteolytic enzymes of the hydrolysis of this class ofsubstrate. Similarly, R3 could bind non-productivelyin P2, the site which may exist in bromelain for thebinding of the amino acid side chain, in this case

(35) the arginine side chain.(36)

Bromelain-catalysed hydrolysis of N-benzoyl-L-serinemethyl ester

The four kinetic parameters for the apparentsubstrate-activated bromelain-catalysed hydrolysis ofN-benzoyl-L-serine methyl ester bear a remarkableresemblance to the two sets of kinetic parameters forthe bromelain-catalysed hydrolysis of a-N-benzoyl-L-arginine amide and a-N-benzoyl-L-arginine ethyl ester(see Table 3); k and Kn,1 for the N-benzoylserinemethyl ester hydrolysis are somewhat similar to kca,.and Km for the x-N-benzoyl-i.-arginine amide hydro-lysis and k' and Ka2 are somewhat similar to kcat. andK. for the oc-N-benzoyl-L-arginine ethyl ester hydro-lysis. We tentatively propose the following inter-pretation of this similarity. For the N-benzoyl-L-serine methyl ester hydrolysis Km. and k are the para-meters which, in terms of the model given in Scheme2, characterize the binding of a substrate molecule togive the binary enzyme-substrate complex and thesubsequent chemistry which results in its hydro-lysis. The relatively low values of both Km1 andk could result as suggested for the a-N-benzoyl-L-arginine amide hydrolysis from a large non-produc-tive component in the binding of N-benzoyl-L-serine

(b)

Scheme 3. Schematic representations of the productive binding ofan N-acylamino acid amide by a proteolytic enzyme suchas bromelain

It is considered that binding of the N-acylamino group [RI in (a) and RCO-NH in (b)] to a site in the enzyme, Pi, and of theside chain (R2) to a site P2 presents the group in the substrate that contains the susceptible linkage [R3 in (a) and CO-NH2in (b)] to the catalytic site of the enzyme, p3.

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BROMELAIN. AND PAPAIN,CATALYSED HYDROLYSES

methyl ester to give the binary complex. Since thesusceptible linkage in N-benzoyl-L-serine methyl esteris not an amide group, the reason for strongnon-productive binding cannot be the same as thatproposed for x-N-benzoyl-L-arginine amide. It couldoccur, however, for another reason. Whereas a-N-benzoyl-L-arginine amideand a-N-benzoyl-L-arginineethyl ester may be trifunctional substrates, inwhich the orientation of the susceptible linkage atthe catalytic site of bromelain results from bindingof the N-benzoylamino group (R1) at a particularsite (p1) on the enzyme and of the arginine side chain(R2) at another site (P) (see Scheme 3), N-ben-zoyl-L-serine methyl ester might serve only as abifunctional substrate. This would be the case if thehydroxymethyl side chain is not bound to any signi-ficant extent in the P2 site. If this is so, non-produc-tive binding could result from binding of RI of N-benzoyl-L-serine ethyl ester in site P2. Alternative-ly, there may be other sub-sites in the bromelain-binding site at which N-benzoyl-L-serine methylester binds relatively strongly but non-productively.

In terms of our chosen model, the parameters K.2and k' characterize the binding ofa second N-benzoyl-L-serine methyl ester molecule to give a ternarycomplex, SES (see Scheme 2), and the subsequentchemistry which results in the hydrolysis of oneN-benzoyl-L-serine methyl ester molecule. It isnoteworthy that the value of k' is similar to that ofkc.t. for the x-N-benzoyl-L-arginine ethyl esterhydrolysis. In the N-benzoyl-L-serine methyl esterhydrolysis the function of the substrate molecule thatis causing the 'activation', and is not itself undergoinghydrolysis, is envisaged as a blocking ofone ormoreofthe binding sites which it is suggested may be involvedin non-productive binding of N-benzoyl-L-serinemethyl ester in the binary complex.

It has been common practice to use low-molecular-weight substrates to study proteolytic enzymes.Evidence is accumulating, however, that there are alarge number of possible interactions between theamino acid residues in the active sites of someproteinases, notably papain (Berger & Schechter,1970; Wolthers et al., 1970), and the arnino acidresidues of large polypeptide substrates, and thatlow-molecular-weight substrates may bind in non-productive modes in such active sites. We have shownpreviously (Brocklehurst et al., 1968) that postulatednon-productive binding modes could satisfactorilyresolve the contradictory conclusions reached byWhitaker & Bender (1965) and by Sluyterman (1968)concerning the rate-limiting step in papain-catalysedhydrolysis of a-N-benzoyl-L-arginine ethyl ester, ifthis ester could bind to papain in a mode which doesnot permit acylation of the enzyme but which mayincrease the reactivity of the thiol group ofcysteine-25towards alkylating agents. This suggestion sub-sequently received strong support from the demon-

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stration by Whitaker (1969) that the rate of alkylationof the thiol group of cysteine-25 is enhanced by thebinding of the inhibitor a-N-benzoyl-D-arginine ethylester. Hinkle & Kirsch (1971) have produced evidencethat the principle mode by which both papain andficin bindp-nitrophenyl esters ofN-acylamino acids isnon-productive. They point out that the eliminationof a non-productive binding mode for a reagent bysubstrate binding can produce enhancement of thereactivity ofa functional group in the enzyme towardsthe reagent. This is analogous to our present interpre-tation of the substrate-activated bromelain-catalysedhydrolysis of N-benzoyl-L-serine methyl ester and isan altemative type ofinterpretation to that commonlyoffered for rate enhancements occasioned by sub-strate binding, i.e. substrate-induced conformationalchanges in theenzyme (Koshland, 1958). It is probablethat, at least insome cases, blocking ofnon-productivebinding modes by substrate binding will be accom-panied by conformational changes in the enzyme.It remains to be discovered whether in a given casethese factors support or oppose each other and towhat extent.Some of the points discussed in this section have

been reported in a preliminary communication(Brocklehurst et al., 1967).

Effect of urea and guanidine hydrochloride on thekinetics of the bromelain-catalysed hydrolysis ofN-benzoyl-L-serine methyl ester and of oc-N-benzoyl-L-arginine ethyl ester

The kinetic parameters that characterize thesecatalyses in the presence and absence of the potentialmodifiers urea and guanidine hydrochloride are givenin Table 3.The effect of these potential modifiers on the

N-benzoyl-L-serine methyl ester hydrolysis wasstudied to ascertain their effectiveness in com-pensating this substrate for its lack of an arginine orcitrulline side chain. The observed activation of thetrypsin-catalysed hydrolysis of acetylglycine methylester by alkylguanidines and alkylamines has beeninterpreted in terms of pseudo-specific substrateformation in the adsorptive complex (Inagami &Murachi, 1964; Inagami, 1965; Mares-Guia & Shaw,1965).The effect of urea and guanidine hydrochloride at

concentrations of 1M on the bromelain-catalysedhydrolysis of N-benzoyl-L-serine methyl ester isunremarkable. Further, the effect of these potentialmodifiers at concentrations of 1 M on the initial ratesof hydrolysis of a-N-benzoyl-L-arginine ethyl esterat substrate concentrations of 0.01M and 0.1M isnegligible. That a measure of competive inhibitionis not observed in the latter system is perhapssurprising. This indicates that the binding constantscharacterizing binding of urea and guanidine at the

379

380 C. W. WHARTON, A. CORNISH-BOWDEN, K. BROCKLEHURST AND E. M. CROOK

30

lol

0 0.05 0.10 0.15

[So] (M)Fig. 3. [Sol/v1 versus [S0] plots for the hydrolysis of N-benzoyl-L-serine methyl ester catalysed by papain atpH7.0in 46.3 mM-potassium phosphate buffer, I= 0.1, at 25.0°C

in thepresence and absence ofguanidine hydrochloride

o, and , 0.1M-KCI; * and --- -, 1.Om-KC1; A and---, 1.0M-guanidine hydrochloride.

P2 site must be greater than 0.1 M. This high apparentvalue of these binding constants suggests that thealkane portion of the arginine side chain may play animportant part in determining the binding constantof the R2-p2 interaction for arginine substrates ofbromelain. A similar effect has been reported intrypsin-catalysed hydrolyses (Inagami & Murachi,1964; Mares-Guia & Shaw, 1965).

Kinetics ofthe hydrolysis ofN-benzoyl-L-serine methylester catalysed by papain

These were studied to provide a comparison withthe analogous bromelain-catalysed hydrolyses. Thekinetic parameters are given in Table 3. Fig. 3 showsthat at I= 0.1 a plot of [So]/v1 versus [SO] appears todeviate slightly from linearity at low substrateconcentrations. It was considered that this deviationdid not necessitate interpretation of this system interms of substrate activation, although it is possiblethat the deviation may be more marked at lowersubstrate concentrations. The slight deviation fromlinearity apparent at I= 0.1 is even less apparent atI= 1.0 in either the presence or the absence ofguanidine hydrochloride. Urea and guanidinehydrochloride at concentrations of 1.OM have littleeffect on the Michaelis parameters for the papain-catalysed hydrolysis of N-benzoyl-L-serine methylester, which are similar to those for the papain-catalysed hydrolysis ofmethyl hippurate (see Table 3),as would be expected from the similarity in structureof the substrates.

We thank the Whitehall Foundation for a grant.

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