Kinetic study of α-chymotrypsin-catalyzed synthesis of kyotorphin

Biochimica et Biophysica Acta 953 (1988) 157-163

157

Elsevier BBA 33088

Kinetic study of a-chymotrypsin-catalyzed synthesis of kyotorphin Pere Clap6s a Gregorio Valencia a, Josep Lluis Torres a, Francesca Reig a, Jos&Maria Garcla-Ant6n a and Juan Mata-Alvarez b a Laboratory of Peptides, Biological Organic Chemistry Department, Centro de lnvestigacion y Desarrollo, CS1C, and t, Chemical Engineering Department, Faculty of Chemistry, University of Barcelona, Barcelona (Spain)

(Received 7 September 1987)

Key words: Alpha chymotrypsin; Enzyme kinetics; Model fitting; (Bovine)

A kinetic analysis of reaction-rate data obtained during a series of optimization experiments of the a-chymotrypsin-catalyzed synthesis of kyotorphin has been performed. The kinetic data have been fitted to a model equation derived from a proposed sequential mechanism, which has been further simplified to a first-order equation as a function of the substrate consumption. Statistical tests performed validate the model, since the fitted constants were statistically significant. In addition, the activation energy of the process has been calculated and resulted to be 32.5 + 2.3 k J / m o l which is within the range of other enzymatic reactions.

Introduction Our current interest on opioid peptides and enzymatic synthesis has led us to study the proteinase-catalyzed coupling reaction between Z-Tyr and Arg-NH 2 to yield the analgesic dipeptide Z-kyotorphin. Such derivative is a synthetic precursor of the naturally occurring peptide kyotorphin [1] which can be obtained by deamidation with carboxypeptidase Y ~ d further hydrogenolysis of the benzyloxycarbonyl-group (Zgroup). On the basis of a controlled kinetic approach, the choice for a catalyst was a-chymotrypsin and for an organic cosolvent, dimethylformamide

Abbreviations: Z, benzyloxycarbonyl; DMF, dimethylformamide. Correspondence: P. Clap6s, Laboratory of Peptides, Biological Organic Chemistry Department, Jorge Girona Salgado, 18-26, 08034 Barcelona, Spain.

(DMF). The donor ester was the benzyloxycarbonyl (Z) derivative, and the nucleophile the amide. For practical purposes, this reaction can be summarized as two reaction processes occurring simultaneously at different rates. Z-Tyr-OMe+ Arg-NH2 a-chymotrypsin)Z_Tyr_Arg.NH2+ MeOH Z-Tyr-OMe+ H20 -* Z-Tyr-OH+ MeOH The reaction primarily yields the water-soluble dipeptide Z-Tyr-Arg-NH 2 and the byproduct ZT y r - O H resulting from substrate hydrolysis. In this work we will mostly deal with the reaction yielding the peptide product. With the final aim to develop and scale up such a system, in a previous paper, we have conducted an optimization study. The influence on the reaction yield of the following experimental factors: D M F / b u f f e r proportion, reaction temperature, and donor/nucleophile ratio have been examined.

0167-4838/88/$03.50 © 1988 Elsevier Science Publishers B.V. (Biomedical Division)

158 The experimental design showed that relatively better yields are obtained by increasing the reaction temperature and lowering the cosolvent proportion while maintaining a slight excess of nucleophile [2]. A step further on this scaling up attempt implies a better understanding of the performance of this particular reaction. In this way knowledge of the appropriate reaction kinetics will be a key aid. In this sense we have undertaken a kinetic analysis of reaction-rate data obtained during the optimization study, with the aim to fit the experimental data to a proper rate equation. Taking into account the considerable importance of the decay characteristics of the enzyme in large scale processes, such as the one we are trying to set up, in the present work a study of the time-course of the reaction was conducted. Observations of initial rates of reaction have been avoided, since problems associated with product inhibition and changes in reaction media are not taken into account by this approach [3]. Moreover, the kinetic parameters have been fitted by numerical rather than graphical procedures to a rate equation. In addition, the reliability of the fitted constants have been statistically analyzed. For parameter estimation, although single linear regression analysis of the data in one of the linear plotting forms can give satisfactory results, non-linear regression is often better [4,5]. Thus, since a precise estimation of the parameters and of the goodness-of-fit of the experimental data to the mathematical model was required, the kinetic parameters have been estimated by numerical techniques involving iterate fitting procedures of non-linear regression, using the principle of least-squares [6]. Model Different kinetic models have been proposed for kinetically controlled enzymatic peptide synthesis using an amino acid or peptide ester as a carboxyl component. Among them, the most common feature is the proposal of the competitive partitioning of the rapidly formed acyl-enzyme intermediate between water and the amino-acidor peptide-derived nucleophile [7,8]. Such a mechanism as outlined in Scheme I, is

kl

RCO-X+ EH ~--~ [RCO-X] •EH k- 1

[RCO-X]. E H ~ [RCOI-E+ HX [RCO]-E+ H2N-R'~2~RCO-NH-R' + EH [RCO]-E + H 20~RCOOH + EH Scheme I

characterized by the binding of the first substrate, RCO-X, to the proteinase, EH, forming a binary enzyme-acyl donor complex [RCO-X]. EH. The first reaction product, H-X, is then released, leaving a covalent acyl-enzyme complex, [RCO]-E, which could transfer the acyl group either to the second substrate, the amine, NH2-R' , to yield the second product, the peptide, RCO-NHR', or to water to give the alternative second product or byproduct, RCOOH. Accordingly, the terms, RCO-X, NH2-R', H-X, RCO-NHR' and RCOOH, given in the proposed reaction pathway (Scheme I) can be replaced by Z-Tyr-OMe, Arg-NH2, MeOH, Z-Tyr-Arg-NH 2 and Z-Tyr, respectively. More elaborated mechanism involving enzymebound covalent intermediates where both substrates add to the enzyme before the release of either product have been postulated. For instance, the one presented in scheme II, represents a ping-pong mechanism modified by a hydrolytic branch [9] which is analogous to serine and cysteine proteinases [10], phosphatase [11], and transglutamiaase [12] catalyzed transformations. Although this modified ping-pong mechanism is better able to explain some features of the enzymatic catalysis, we have preferred to use in this study a much-simplified sequential-ordered reaction mechanism (Scheme I). For this choice, practical consideration in order to facilitate further developments can be argued. In fact, in any kinetic modelling, two factors are always involved. The model must be complex enough to be realistic, but simple enough for its fitted parameters to be easily interpreted and thus useful for design purposes. Furthermore, considering simple and re-

159 RCOX

~

[RCO-X].EH~

H-X

o

EH

f [RCOI-E

k'-s

k23

RCO_NH.R,

[RCOI_E.[NH2R,] / ~

NH2R

SchemeII

alistic assumptions, the ping-pong mechanism (Scheme II) can be reduced to the sequential one (Scheme I). In this way, a four-statement hypothesis has been taken into account: (1) Choosing the proper reaction conditions, a proteinase-catalytic action producing increasing amounts of peptide bond will make k~>> k'_ 4 (Scheme II). (2) The aminolysis of the complex [RCO]-E[NH2R' ] being very fast when compared with its own formation, this partial process can be summarized as the interaction between [RCO]-E and NH2R' yielding RCO-HNR' and EH. (3) Choosing the proper reaction conditions, it is possible to favor a fast formation rate for the complex [RCO]-E (k 2 >> k'_2). (4) The [RCO]-E formation rate from [R-COOH] and enzyme is extremely slow, because it implies a thermodynamic approach. In accordance with this hypothesis, and considering the formation of [RCOO-X]. EH as the limiting step, we have based our rate expressions for the synthesis of kyotorphin on a sequential mechanism analogous to Scheme I. Moreover, considering a steady-state approximation hypothesis for the intermediate species, Eqns. 1 and 2 have been deduced.

d[RCO-NHR'] _ dt

k3[RCO-X][H2NR'] k 3 [ H 2 N - R ' ] / k 1 + k 4 / k 1 + [RCO-X]

(1)

d[RCOOH]

k4[RCO-X]

dt

k 3 [ H 2 N - R ' ] / k I + k 4 / k I + [RCO-X]

(2)

By application of mass balance, the consumption rate of substrate Z-Tyr-OMe can be deduced from the differential Eqn. 3:

- d[RCO-X] d[R-CO-NH-R'] d[RCOOH] dt dt + dt

(3)

Materials and Methods

Both the donor ester, Z-Tyr-OMe, and the nucleophile, Arg-NH 2, were prepared in our laboratory by standard procedures [2]. Bovine achymotrypsin was obtained from Merck. Other chemicals were of the purest commercial grade available. Enzymatic reactions were performed in carbonate buffer, 0.004 M sodium carbonate/ 0.046 M sodium bicarbonate (pH 9) - dimethylformamide mixtures containing 450, 500, 550 or 650 ml/1 of DMF, 30 mmol/1 Z-Tyr-OMe with various donor ester/nucleophile ratios (1:0.7, 1:1.5, 1:2, 1:3.3, mmol/mmol) and 10 /~mol/1 [E0] a-chymotrypsin. Four sets of reaction temperatures (10, 15, 20 and 30°C) were assayed. A second series of experiments were conducted at a substrate ratio of 1 : 1.5 mmol/mmol, DMF con-

160

centration of 450 ml/1, and at five reaction temperatures (5, 10, 15, 20 and 25 o C). The reaction progress was followed by analysis of 100/xl frozen samples taken at 0.5, 1, 1.5, 2, 3, 4, 5, 6, 7 and 10 rain on a Perkin-Elmer series 2 HPLC system fitted with a 250 × 4 mm Spherisorb ODS2 0Off) column eluted isocratically with acetonitrile/phosphate buffer (0.02 M, pH 7) (50:50, v / v ) at a flow rate of 0.8 ml/min. The eluted substances were monitored spectrophotometrically at 230 nm. Ester substrate, product acid and peptide were baseline separated in all cases. The capacity factors, k', varied between 1.56 for peptide product and 2.13 for methyl ester substrate. As an example, an HPLC chromatogram of a typical reaction is reported in Fig. 1. The

O~

t~ >.

amounts of ester substrate and products were calculated from peak areas by the external standard method on a D-2000 Hitachi-Merck chromatointegrator. Results and Discussion

The kinetic patterns of two experiments, for quite different reaction conditions, are given in Figs. 2 and 3. Both concentration profiles of products (Z-Tyr-Arg-NH 2 and Z-Tyr) and substrate (Z-Tyr-OMe) are presented. Similar kinetic data have been obtained for the whole set of experimental conditions. A computer program have been written in F O R T R A N 77 to fit the raw data to the model described by Eqn. 3. This program uses two subroutines from the N A G file library [13]. The first subroutine performs numerical integration following a fourth-order Runge-Kutta-Merson algorithm. The second subroutine based on a corrected Gauss-Newton method [6] is used to find an unconstrained minimum of a sum of squares obtained by difference between experimental and calculated values (residuals). As a result of the calculations, a list of the generated constants (kl, k 3 and k 4 ) is presented in Table I. For every particular condition assayed, the values of k 3 and k 4 far outweighed kl, and this makes k 3 [ N H z R ' ] / k 1 + k 4 / k t >> [RCO-X]. For practical purposes this, in turn, allows a re34

:

30 28 26

o

c,4

\ I 0

I

I

I

I

8 [ 5

I

I

I

I

I

I

I

I0

Fig. 1. HPLC analysis of a typical reaction mixture. The sample was taken after 4 rain of reaction time, and analyzed on a Perkin-Elmer series 2 fitted with a 2 5 0 × 4 m m Spherisorb ODS2 (10#) column eluted isocratically with acetonitrile/ phosphate buffer (0.02 M, p H 7) (50 : 50, v / v ) at a flow rate of 0.8 ml per min. Elution was monitored spectrophotometrically at 230 nm.

2

4

6

8

10

TIME ( M I N )

Fig. 2. Kinetically controlled synthesis of kyotorphin using a-chymotrypsin as biocatalyst. Computed - solid line - and experimental values of Z-Tyr-OMe (n), kyotorphin ( ~ ) and Z-Tyr, ( × ) obtained with 50% of dimethylformamide at 15 ° C.

161 54 32

as:

0

30

d[RCO-NHR'] dt

28 26 ~" 24

~22 z~ 20

d[COOH] dt

QI8

k][RCO-X][H2NR'] [H2N-R'] + p

k I p [RCO-X] [HzN-R'] + p

(6)

(7)

z14 z°12

Therefore, the resulting rate of substrate consumption derived from them, follows the first-order Eqn. 8:

4

2

4

6

8

10

TIME (MIN)

Fig. 3. Kinetically controlled synthesis of kyotorphin using a-chymotrypsin as biocatalyst. Computed - solid lines - and experimental values of Z-Tyr-OMe (O), kyotorphin ( ~ ) and Z-Tyr ( × ), obtained with 55% dimethylformamide at 10 o C.

duction of Eqns. 1 and 2, which become: d[RCO-NHR' ] dt d[RCOOH]

dt

k3[RCO-X][H2NR' ] k 3 [ H z N - R ' ] / k 1+ k 4 / k ]

k 4 [RCO-X] k3[H2N-R']/k ] + k4/k I

(4)

(5)

- d[RCOX] dt

k~ [RCOX]

(8)

Since kl(k[E0] ) is the kinetic constant of the limiting step of the sequential model initially proposed, Eqn. 8 clearly reveals the importance of such a step in substrate conversion. A second data fitting to the reduced model expressed by Eqns. 6 and 7 was performed by means of the same computer program. The calculated kinetic constants, kl, p and a residual sum of squares given by Eqn. 9, are summarized in Table II. SQ = ~ ([RCOX]exp - [RCOX]c~¢) 2

Moreover, defining the partition constant, p, as k a / k 3 , the foregoing equations can be expressed

+ ~([RCOOH]exp - [RCOOH]calc) 2

(9)

TABLE I K I N E T I C DATA F I T T I N G FOR THE OPTIMIZATION OF SUBSTRATE RATIO, TEMPERATURE A N D COSOLVENT PROPORTIONS ON THE ENZYMATIC SYNTHESIS OF Z-TYR-ARG-NH 2 Experimental design presenting the reaction conditions and the fitted kinetic constants calculated for the first proposed model as expressed by Eqns. 1 and 2. The standard errors have been calculated on the basis of variance and covariance matrix. For each experiments 9 degrees of freedom are considered. Substrate ratio (M : M)

Temp. ( o C)

DMF (ml/l)

k] (rain 1)

k3 ( m m o l - 1.1. min - 1)

k4 ( m i n - 1)

1 : 3.3 1 : 3.3 1 : 3.3 1 : 3.3 1 : 0.7 1 : 0.7 1 : 0.7 1 : 0.7 1 :2 1 :2 1 :2 1 :2

20 20 10 10 20 20 10 10 15 15 15 15

450 550 450 550 450 550 450 550 500 500 500 500

0.971 +0.049 0.400 + 0.020 0.771 + 0.035 0.210 + 0.007 1.321 _+0.029 0.270+0.020 0.401 + 0.036 0.105 _+0.006 0.321 + 0.014 0.590+0.016 0.405 + 0.009 0.381 + 0.010

10.55 +0.53 12.66 + 0.64 5.75 + 0.35 58.64 + 4.69 11.52 + 0.58 2.34+0.07 6.36 + 0.44 1.93 ___0.10 15.83 + 0.95 16.57+ 1.12 17.82 + 1.21 15.53 + 0.99

68.84+ 5.50 81.45 + 6.15 34.85 + 3.11 525.55 + 10.15 21.66 + 2.10 7.23 + 0.44 32.03 + 5.20 6.82 + 0.95 80.78 ___ 6.15 77.14+ 5.24 71.66 + 4.95 65.41 _ 5.50

162 TABLE II SECOND KINETIC DATA FITTING TO A MORE REDUCED MODEL FOR THE WHOLE SERIES OF OPTIMIZATION EXPERIMENTS A combination of two experimental designs showing the reaction conditions and the fitted kinetic constants obtained by the simplified model as expressed by Eqns. 6 and 7 are presented. The residual sum of squares (SQ) is also given as calculated from Eqn. 9. The standard errors have been calculated on the basis of variance and covariance matrix (degrees of freedom, 9). Substrate ratio (M:M)

Temp. ( ° C)

DMF (%)

kI (min -1)

p (mmol-1-1)

SQ

1 : 3.3 1 : 3.3 1 : 3.3 1 : 3.3 1 : 0.7 1 : 0.7 1 : 0.7 1 : 0.7 1:2 1:2 1 :2 1 :2 1 : 1.5 1 : 1.5 1 : 1.5 1 : 1.5 1 : 1.5

20 20 10 10 20 20 10 10 15 15 15 15 30 10 10 20 20

450 550 450 550 450 550 450 550 500 500 500 500 450 650 450 550 550

0.949 -+0.035 0.399_+0.035 0.757 _+0.016 0.214 -+ 0.007 1.027 _+0.034 0.239 _+0.020 0.355 _+0.027 0.098 _+0.007 0.325_+0.014 0.580 + 0.030 0.397 _+0.006 0.375 _+0.008 1.104 _+0.039 0.063 _+0.003 0.599 _+0.022 0.329 -+0.026 0.320 _+0.023

7.46 -+ 0.32 6.54_+0.54 6.20 ___0.29 8.97 _+0.89 3.97 _+0.07 3.07 _+0.22 5.13 _+0.10 3.52 _+0.39 5.13_+0.20 4.47 + 0.17 3.94 _+0.13 4.23 -+0.16 2.79 _+0.06 4.26 -+0.06 2.79 _+0.08 3.42 _+0.31 2.93 _+0.35

3.85 19.06 1.49 1.67 8.29 12.34 16.11 1.75 3.91 8.84 0.94 1.31 3.34 6.97 8.06 12.43 9.92

T h e r e s i d u a l s u m o f s q u a r e s is p r e s e n t e d as m e a s u r e o f t h e l a c k o f fit; h o w e v e r , it w a s u s e d to c a r r y o u t t h e F - t e s t to s t a t i s t i c a l l y v a l i d a t e t h e m o d e l . I n all cases, t h e f i t t e d c o n s t a n t s w e r e s t a t istically significant. Examining the data of Table II, it is c l e a r t h a t c o s o l v e n t c o n c e n t r a t i o n e x e r t s a more decisive effect on k l than temperature. This is i n g o o d a g r e e m e n t w i t h t h e f a c t t h a t a h i g h proportion of organic cosolvent inhibits the enz y m a t i c a c t i v i t y [14]. O n t h e c o n t r a r y , b e t w e e n a r a n g e o f s u b s t r a t e r a t i o o f 1 : 0.7 t o 1 : 2 , t h e p a r t i t i o n c o n s t a n t is n e i t h e r a f f e c t e d b y r e a c t i o n t e m perature nor by DMF concentrations. Although most authors report that p mainly depends on the structural features of the substrates, and thus either different nucleophiles or donor esters show differe n t p a r t i t i o n c o n s t a n t s [15], s e v e r a l o t h e r s h a v e f o u n d a l i n e a r v a r i a t i o n as a f u n c t i o n o f t h e n u c l e o p h i l e c o n c e n t r a t i o n [16]. I n o u r h a n d s , p is constant, except when a large excess of nucleophile is u s e d . T h i s c o u l d b e e x p l a i n e d as a c a l c u l a t i o n artifact based on the definition of p. A series o f five a d d i t i o n a l e x p e r i m e n t s h a s b e e n

conducted to examine the quantitative influence o f t h e r e a c t i o n t e m p e r a t u r e u p o n k 1. A D M F c o n c e n t r a t i o n o f 45%, a s u b s t r a t e r a t i o o f 1 : 1.5, and a temperature range of 5-25 °C were chosen. The experimental kinetic data obtained have been fitted to the reduced model by the computer program. The resulting kinetic parameters, k I and p, a r e r e p o r t e d i n T a b l e III. A s e x p e c t e d , b y r i s i n g

TABLE II1 INFLUENCE OF REACTION TEMPERATURE UPON k 1 Variation of k I with temperature is presented. Kinetic constants have been calculated according to the simplified model expressed by Eqn. 9. Substrate ratio(M:M)

Temp. (°C)

DMF (%)

kI (min- b

p (mmol.l - l )

1:1.5 1:1.5 1:1.5 1 : 1.5

5 10 15 20 25

450 450 450 450 450

0.399+0.015 0.509+0.012 0.736_+0.016 0.848-+0.017 1.129_+0.015

3.08_+0.09 3.85_+0.13 4.25+0.09 3.78-+0.08 4.19_+0.09

1:1.5

163

the reaction temperature, k t increased, while p was nearly constant and within the values previously obtained. Using a simple Arrhenius approach and from the data presented in Table III, the activation energy (EA) has been calculated applying the following equation:

concentrations assayed if a moderate excess of nucleophile is used. By explaining these important features of the reaction under study, this quite simplified kinetic model reveals its applicabihty on the scaling up to a pilot plant step which is due to follow.

Acknowledgements In k 1 = l n A - E A / R T

Although plots of In k 1 vs. 1/T allow the determination of EA, a numerical solution was again preferred. The equation fitting was done by a weighted linear regression standard program which rended Eqn. 10: In k I = 14.31 - 4230.1/T

(10)

The fitting was rather good, since the regression coefficient is 0.9937. The calculated activation energy value is E A = 35.2 + 2.3 kJ/mol, which falls within the range of 20-80 kJ/mol reported for enzymatic reactions, cellular- and life-related reactions that occur at around room temperature [17,18].

Conclusions In order to facilitate further scaring-up operations, the basic objective of this work was to fit the experimental kinetic observations of a previous optimization study to a simple mechanism. In a first attempt, our aim was partly fulfilled as the experimental data were consistent with the proposed mechanism described by Eqn. 3. Among the generated constants, k 3 and k 4 do not show a logical variation with changes in reaction temperature and cosolvent percentage. However, some characteristic features of the system allowed the proposal of a more reduced model which resulted in the first-order Eqn. 8 for substrate consumption. The kinetic constant, k x, of this model decreased by increasing concentrations of organic cosolvent due to loss of enzymatic activity. Moreover, the partition constant, p, remains practically unchanged at the various temperatures and DMF

These investigations were supported by the Spanish Comisi6n Asesora de Investigaci6n Cientifica y Trcnica (CAICYT).

References 1 Takagi, H., Shioni, H., Ueda, H. and Amano, H. (1979) Nature 82, 410-412. 2 Claprs, P., Valencia, G., Reig, F., Garcia Anton, J.M. and Mata J. Appl. Biochem. Biotech., in press. 3 Atkinson, B. (1974) in Biochemical Reactors (Lagnado, J.R., ed.), pp. 180-181, Pion, London. 4 Cleland, W.W. (1979) Methods Enzymol. 63A, 103-138. 5 Sagnela, G.A. (1985) Trends Biochem. Sci. 10, 100-103. 6 Gill, P.E. and Murray, W. (1978) SIAM J. Numer. Anal. 11,977-992. 7 Fastrez, J. and Fersht, A.R. (1973) Biochemistry 12, 2025-2035. 8 Bender, M.L., Clement, G.E., Gunter, C.R. and Kezdy, F.J., (1964) J. Am. Chem. Soc. 86, 3697-3714. 9 Kullmann, W. (1984) Biochem. J. 220, 405-416. 10 Walsh, C. (1979) in Enzymatic Reaction Mechanisms, pp. 53-107, W.H. Freeman, San Francisco. 11 Arion, W.J. and Nordlie, R.C. (1964) J. Biol. Chem. 239, 2752-2757. 12 Folk, J.E. (1969) J. Biol. Chem. 244, 3707-3713. 13 Numerical Algorithms Group Ltd. (1984) NAG Central Office Myfield House, 256, Bambury Road, Oxford, U.K. 14 Schellenberger, V. and Jakubke, H.D. (1987) Peptides 1986 (Theodoropoulos, D., ed.), pp. 195-199, Walter de Gruyter, Berlin. 15 Koennecke, A., Schellenberger, V., Hofmann, H.-J. and Jakubke, H.-D. (1984) Pharmazie 39, 11, 785-786. 16 ScheUenberger, V. and Jakubke, H.-D. (1986) Biochim. Biophys. Acta 869, 54-60. 17 Buchholz, K. and Ruth, W. (1976) Biotech. Bioeng. 18, 95-104. 18 Wang, D.I.C., Cooney, C.L., Demain, A.L., Dunnill, P., Humphrey, A.E. and Lilly, M.D. (1979) in Fermentation and Enzyme Technology, pp. 316-318, John Wiley & Sons, New York.