Reaction kinetics and mechanisms of penicillin amidase: a comparative study by computer simulation S. B. Lee and D e w e y D. Y. R y u

The Korea Advanced Inst i tute o f Science, POB 150, Chung-Ryang-Ri, Seoul, Korea

(Received 16 December 1980; revised 27 March 1981)

Based on experimental results, two different kinetic models and reaction mechanisms o f penicillin amidase (penicillin amidohydrolase EC 3.5.1.11) have been studied and analysed. The enzyme from Escherichia coil shows an ordered uni-bi reaction mechanism while the enzyme from Bacillus megaterium shows kinetics o f double inhibition by the reaction products. The difference in the reaction mechanism is elucidated by two possible mechanistic models on a theoretical basis. Also suggested is the analytical method by which two different reaction mechanisms can be tested and confirmed.

Keywords: Chemical kinetics; penicillin amidohydrolase; EC 3.5.1.11; computer simulation

Introduction

Penicillin amidase (penicillin amidohydrolase, EC 3.5.1.11) hydrolyses benzyl penicillin to yield 6-aminopenicillanic acid (6-APA or P) and phenylacetic acid (PAA or A). This enzyme is of considerable commercial interest, because many semisynthetic penicillins are prepared from 6-APA.

Several species of microorganisms, as well as some plant and animal tissues, are good sources of penicillin amidase. Among these, the enzyme obtained from Bacillus mega- terium (ATCC-14945) was used by Ryu 1 and Chiang2and the enzyme from Escherichia coli (NC1 B-8743A) was used by Balashingham 3 and Warburton. 4

Ryu I and Chiang 2 studied the reaction kinetics of enzymatic hydrolysis of benzylpenicillin to determine the kinetic constants. They found that both products of hydro- lysis, 6-APA and PAA, were inhibitors of the reaction, 6-APA non-competitively and PAA competitively and this is consistent with other workers. 3,4 An interesting finding by Balashingham et al. 3 for the enzyme produced from E. coli was that the enzyme was inhibited also by the sub- strate, whereas Ryu et al. 1 did not observe the inhibition effect by substrate within the range of substrate concen- tration <0.5 mol with the enzyme from B. megaterium.

From their experimental results of enzymatic reaction and the reaction mechanisms postulated, Ryu et al. 1 pro- posed a kinetic model. The performance of the continuous penicillin amidase reactor system was simulated on a com- puter using their kinetic model. Reasonably good agree- ment between the experimental results and the results of computer simulation based on the kinetic model was found. Warburton 4 also proposed a kinetic model for the hydrolysis of benzylpenicillin assuming that an 'ordered uni-bi reaction mechanism' can be applied to the enzyme reaction. In view of those differences and similarities observed by the authors, a comparative study on the reac- tion kinetics of penicillin amidase was carried out using the kinetic data obtained by Ryu et al., 1 Balashingham et al. 3 and computer simulation. The objectives were to: (1) find

possible reasons for the differences between those kinetic models, (2) find the significance of those differences in terms of reaction mechanisms, and (3) illustrate an analytical method by which the differences may be resolved.

Kinetic models

The enzymatic hydrolysis of benzylpenicillin can be expressed as:

BenzylpeniciUin Penicillin amidase -, 6-APA + PAA (1) (S) (P) (g)

For the reaction, the following three kinetic models are all very reasonable when the double product inhibition mech- anism is taken into account. These models are shown schematically in Figure 1.

M o d e l I

Since two products of hydrolysis, 6-APA and PAA, are non-competitive and competitive inhibitors of the enzyme,

Figure 1 Schematic diagram of reaction mechanism and kinetic models

1 E + S ~ E S ~ E + P + A [ ~ [ - - - - P + A 2 E + A ~ - E A

Model 3 E + P ~ E P E A s E ~ E S I 4 ES + P ~- EPS IL lit

5 EP+S~-EPS EP~EPS

1 E + S ~ E S - - ~ E + P + A 2 E + A ~ E A ~ P + A

Model 3 E + P ~ - E P h I II 4 E S + P ~ E P S EA ~ E ~ E

5 EP + S ~ EPS 1[ I[, IL. 6 E A + P - ~ E P A EPA~-EP~EPS 7 EP + A ~ EPA

Model 1 E + S ~ E S ( ~ E P A ) E ~ E S ( ~ E P A ) III ~ E A + P k~ 7/

2 E A ~ E + A EA

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respectively, Ryu et al. a derived a kinetic model for the enzyme reaction that takes the double product inhibition effect into consideration. In their formulation of the rate expression, step 2 describes the competitive inhibition by PAA, and steps 3, 4 and 5 represent the non-competitive inhibition by 6-APA (Model I in Figure 1). If the rapid equilibrium assumption is used, the rate expression for this model can be easily derived as shown in Equation (2): 5

Vmax v = (2)

+Km + A + P K m

S Kip

where, o is the reaction rate; Vmax, maximum reaction rate; S, P, and A represent the concentrations of substrate, 6-APA, and PAA, respectively;Kin, Michaelis-Menten constant; and Kip and Kia, the inhibition constant for 6-APA and PAA respectively.

Ryu et al. 1 assumed that the enzyme can be inhibited by either product, PAA or 6-APA, whichever hits the respec- tive inhibitor site first (Model I in Figure 1). Further complex formation with the other product (i.e., (EAP) or (EPA)) does not change the fraction of active enzyme substrate complex (ES). Furthermore, the formation of an inactive complex (EPA) or (EAP) (not shown in Model I in Figure 1) by a simultaneous and concerted association of both (A) and (P) with the enzyme was considered unlikely by Ryu since Kia and Kip have different values.

Model H If we consider (EPA) as one of the intermediates, the

reaction mechanism has to be modified (Model II in Figure 1). In this Model II mechanism, the first five reaction steps are identical with those of Model I, and the reaction steps 6 and 7 represent the formation of (EPA) complex. For this Model II reaction mechanism, the rate equation becomes:

Vmax O = (3)

+Km( I+K@a)+P(1 Kin_ ) AP K m 1 s Kip +--S/+s'KiaKip

It should be noted that Equation (3) has an additional term:

AP K m

S KiaKip

in its denominator as compared with Equation (2) due to (EPA) complex formation.

Model III

Warburton et al. 4 suggested that the ordered uni-bi reaction mechanism (Model III in Figure 1) is applicable. In this case, a substrate inhibition term S/Kis is added to the denominator of Equation (3).

Resul ts and discussion

Since the substrate concentration used in industrial opera- tion is low enough (far below the level of substrate concen- tration) to cause a significant degree of inhibition and the inhibition constant for substrate Kis is far greater than Km, Kia o r Kip (Table 1), the substrate inhibition effect can be ignored for the purpose of comparing these models on the

Table 1 Kinetic constants of penicillin amidase in soluble and insoluble forms f rom B. mega te r i um and E. c o i l (Vma x value was chosen to be 0.082 mM min -1 based on the data f rom ref. 1)

B. m e g a t e r i u m I E. co i l 3

Soluble Insoluble Soluble Insoluble

K m 4.5 mM 6.0 mM 0.67 mM 0.63 mM Kia 450 620 4.8 4.6 K ip 26 250 7.1 9.0 Kis -- - - 270 250

same basis. When the substrate inhibition effect is neglected, the rate equation of Warburton et al. 4 reduces to Equation (3).

The kinetic models I and II and corresponding reaction mechanisms are compared using the kinetic data obtained by Ryu et al. 1 and Balashingham et al. 3 and computer simulation.

Comparison o f kinetic models I and H Computer simulation studies were carried out in order

to find the difference in performance of CSTR type (con- tinuous stirred tank reactor) enzyme reactor system when two different sets of kinetic constants determined experi- mentally and the kinetic models I and II are used. The results of simulation of two models were then compared.

The steady-state equation for CSTR of model I (as shown in Equation (2)) may be expressed as:

S2 Kia X3 - (gmgipS 0 + KmgiaS 0 + S2 Kia

-- SoKiagip)X 2 - (SoKiaKip + KmKiaKip

+ VmaxKiaKip7-)X + VmaxKiaKip 7" = 0 (4)

where 7" is the space time of the reactor, and X is the frac- tional conversion of substrate. For derivation of Equation (4), v = SoX/7", S = So (1 - X), A = SoX, and P = So X are substituted into Equation (2).

By using the same procedure, the steady-state equation of model II (as shown in Equation (3)) can be written as"

S~(Kia - Km)X 3 - (KmKipS 0 + S~Kia - SoKiaKip

+ KmKiaSo) X 2 - (SoKiaKip + KmKiaKip

+ VmaxKiaKipT")X + VmaxKiaKip 7" = 0 (5)

These two steady-state equations are the same except for the coefficients of the first terms in Equations (4) and (5). These coefficients are SoK ~ and So(Kia -Kin) for Equations (4) and (5) respectively. Using the kinetic con- stants shown in Table 1, the fractional conversion X was calculated as a function of space time and feed substrate concentration. The roots of Equations (4) and (5) were found by using the Newton-Raphson method. There is only one physically meaningful steady-state solution of X which should lie between zero and one.

When the kinetic contants of Ryu et al. 1 were used for the simulation of enzyme reactor performance, the differ- ence between the two models in terms of the fractional conversion or productivity was found to be negligible. For the penicillin amidase from B. megaterium, the value of Kia is about 100 times greater than that of Kin, thus the first coefficient (Kia -Km) in Equation (5) is practically the same as the first coefficient Kia in Equation (4). For this enzyme, there are two possible reaction mechanisms: (1) the inactive complex (EPA) is not formed, and (2) the

36 Enzyme Microb. Technol., 1982, Vol. 4, January

Computer simulation of reaction kinetics." S. B. Lee and Dewey D. Y. Ryu

formation of inactive complex (EPA) does not influence the reaction rate. Based on these results, it may be con- cluded that Model I is satisfactory for the penicillin amidase from B. megaterium.

When the kinetic constants of Warburton et al. 4 were used for the simulation of enzyme reactor performance, the deviation between the two models in terms of the fractional conversion and productivity was found to be significant. Figure 2 shows the fractional conversion as a function of reactor space time and feed substrata concentration. Although the deviation between the two models is signifi- cant for 0.01 M < S 0 < 0 . 5 ~ , it is negligible for So < 0.01 M and So > 0.5 M.

The productivity of 6-APA, SoX/z, is plotted against reactor space time, r, in Figure 3. The simulation results in

E

c 8

L I / / I I I / / I l l / / rl/// _

1.0

0.8

0.6

0.4

0.2

00 I0 20 30

Reactor space time, ~ min Figure 2 Fractional conversion in a continuous stirred tank reactor as a funct ion of reactor space t ime at varying substrate feed concen- trations. The kinetic data of Warburton etaL for soluble enzyme were used. Results of computer simulation of Models I {Ryu) - - and II (Werburton) . . . . . A, S0= 0.01 M; B, 0.05M; C, 0.1 M; D, 0 . 2 M ; E , 0.5M

0.7

0.6

i ._¢ E 0.5

T

E "~ 0.4

f ~ 0.3

13,_

0.2

0.1

" \ ~ -~"-~--...

I t I 0 20 40 60

Reactor space time, % rnin Figure 3 Product iv i ty of 6-APA as a funct ion of reactor space t ime at varying substrate feed concentrations. The kinetic data of Warburton et aL for insoluble enzyme were used. Results of com- puter simulation of Models I (Ryu) - - . , and II (Warburton) . . . . . A, So = 0.3 M; B, 0.1 M; C, 0.05M; D, 0 .01M

a Increasing [ A]

Intercept

b Increasing [A]

~-Intercept

I

IS ]

Figure 4 Lineweaver--Burk plot of (a) Model I (Ryu) or Equation (2) at constant [P].

Slope I = ~ m 1 + Kia-- + -~ipJ" Intercept -~mm- 1 + ~'t'~tpT"

(b) Model II (Warbur ton)or Equation (3) at constant [P].

S lope l l Km (1 [ A ] I ( + [ P ] ~ ' l n t e r c e p t 1 ( + [ P ] ~ = -V"mm + K--~"a / 1 K'~'~pi' =V--ram 1 K-~pi

terms of productivity also show significant deviation between the models. These results suggest that the penicillin amidase obtained from E. coli may in fact have a reaction mechanism by which the inactive complex (EPA) is formed and this complex somehow influences the rate to a certain extent.

We can determine experimentally whether or not this enzyme from E. coli indeed has such a reaction mechanism. A method by which this problem can be analysed is illus- trated next. 6

Comparative study of reaction mechanism Equations (2) and (3) for Model I and II may be re-

arranged as Equations (6) and (7).

1 _Kin( A+~ip) l + 1 ( 1 1 + - + P-if--. (6) ) 0 V m Kia S ~ Kip,

and

1 K m + A

The Lineweaver-Burk plots of Equations (6) and (7) at constant P with varying value of A are shown in Figures 4a

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Slope I

Slope II

Increasing [A]

]

ntercept

[P3

Figure 5 Replotting of a set of slopes obtained from Figure 4 vs. [P]. (a) Model I or Equation (2) (Ryu)

Slope I' Km 1 , intercept = ~_.~.(1 + [A].__~. Vm Kip Kia]'

(b) Model II or Equation (3) (Warburton)

Slopel l ' Km 1 ( l+ [A~ ]~ . l n te rcep t=Km ~ + [A]~ Vm Kip \ ~m ~ia]

and 4b respectively. These plots show the same intercepts but different slopes.

The values of slope I and slope II obtained from Models I and II respectively are then plotted against P for different values of A as shown in Figures 5a and 5b. We can now deter. mine the difference between the two models: Model I shows the slope of constant value, while Model II shows the slope of varying value with A. These results indicate that the slope of Model I in Figure 5a is independent of A, and the slope of Model II in Figure 5b increases with increasing value of A.

By using simulation analysis of the kinetic models as described in this paper, it is possible to determine the reac- tion mechanisms that agree better with the experimental results. It still remains to be seen whether or not the enzymes obtained from two different sources, namely, B. megaterium and E. coli have truly different reaction mechanisms or only slight variations of certain reaction mechanisms. Further biochemical studies on active sites and inhibitor sites of penicillin amidase and positive identifi- cation of the inactive complex (EPA) will be required prior to drawing any definite conclusions concerning the reaction mechanism.

R e f e r e n c e s

1 Ryu, D. Y., Bruno, C. F., Lee, B. K. and Venkatasubramanian, K. Proc. 4th Intl. Ferment. Symp., 1972, p. 307

2 Chiang, C. and Bennett, R. E. J. Bacteriol. 1967, 93,302 3 Balashingham, K., Warburton, D., Dunnill, P. and Lilly, M. D.

Biochim. Biophys. Acta 1972, 276, 250 4 Warburton, D., Dunnill, P. and Lilly, M. D. Biotechnol. Bioeng.

1973, 15, 13 5 Lee, S. B. and Ryu, D. Y. Biotechnol. Bioeng. 1979, 21,2329 6 Segal, I. H. in Enzyme Kinetics Wiley Interscience, N. Y., 1975,

p. 161

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