Kinetic and mechanistic studies with bovine testicular hyaluronidase

ELSEVIER

Biochimica et Biophysica Acta 1200 (1994) 315-321

etBiochi~ic~a BiophysicaA~ta

Kinetic and mechanistic studies with bovine testicular hyaluronidase Jeffrey A. Cramer ,,1, Leonard C. Bailey, Carole A. Bailey 2, Robert T. Miller 3 Department of Pharmaceutical Chemistry, College of Pharmacy, Rutgers, The State University, Piscataway, NJ 08855-0789, USA Received 5 November 1993

Abstract

Bovine testicular hyaluronidase exhibits hydrolase and transglycosylase activity. To assess the magnitude of each type of reaction, the time-course of hyaluronidase catalysed hyaluronic acid degradation was followed using a sensitive and specific HPLC method. The kinetic parameters K m and Vm~, were calculated for purified short chain hyaluronic acid oligomers and native hyaluronic acid based on the appearance of unreactive hyaluronic acid tetrasaccharide. For hyaluronic acid oligomers, as substrate size increased K m decreased from 2.06 to 1.09 mM while Vm~, remained about the same, indicating a 5-fold increase in the enzyme-substrate association constant, kl(kcat/Km). The values of k 2 (kcat), the enzyme-substrate disassociation constant, for native hyaluronic acid and hyaluronic acid decasaccharide were similar. The value of k I for native hyaluronic acid, however, was larger by 70-fold. Kinetic degradation mechanisms for each hyaluronic acid oligomer, using chemical-reaction kinetics, were proposed and evaluated by computer curve fitting analysis of the experimental time vs. concentration data. The derived rate constants, together with mass balance calculations, revealed that transglycosylation plays a significant role in the degradation of all hyaluronic acid oligomers studied.

Key words: Testicular hyaluronidase; Transglycosylation; Enzyme kinetics; Computer modeling; Carbohydrate

1. Introduction

Bovine testicular hyaluronidase (BTH) 1 (EC 3.2.1.35) is used pharmaceutically as an aid in the diffusion of subcutaneously administered drugs. An endoglycanhydrolase that cleaves the 1 ~ 4 bond of hyaluronic acid (HA) 1 [(1 ~ 3)0-(2-acetamido-2-deoxy-8-o-glucopyranosyl)-(1 ~ 4)-0-13D-glucopyranuronosyl]n, BTH leaves saturated oligosaccharides with reducing N-acetylglucosamine (GIcNAc) 1 endgroups. BTH has also been reported to degrade chondroitin sulfate (CS) 1, another component of the extracellular matrix structurally related to HA [1]. Studies on the kinetics of BTH catalyzed HA degradation are complicated

Abbreviations: BTH, bovine testicular hyaluronidase; HA, hyaluronic acid; GlcNAc, N-acetylglucosamine; CS, chondroitin sulfate; C-6, HA hexasaccharide; C-4, HA tetrasaccharide; TBA-OH, tetrabutylammonium hydroxide; 2-CA, 2-cyanoacetamide; C-8, HA octasaccharide; C-10, HA decasaccharide; C-2, HA disaccharide; E0, amount of BTH * Corresponding author. Fax: + 1 (201) 5036076. 1 Present address: Sandoz Pharmaceuticals Corp., East Hanover, NJ 07936, USA. 2 Present address: Hoffmann-La Roche, Inc. Nutley, NJ 07110, USA. 3 Present address: Warner Lambert Pharmaceuticals, Morris Plains, NJ, 07950, USA. 0304-4165/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved

SSDI 0 3 0 4 - 4 1 6 5 ( 9 3 ) E 0 1 5 2 - 9

by the fact that the enzyme also exhibits transglycosylase activity [2,3]. The smallest BTH substrate is HA hexasaccharide (C-6) 1, an oligomer that may react only via transglycosylation to give oligomers of lower and higher molecular weight. Commonly used assay procedures for studying BTH kinetics include the colorimetric measurement of liberated reducing GlcNAc endgroups [4] or the reduction in turbidity of high molecular weight polydisperse substrates [5]. The time consuming colorimetric method measures unreacted substrate and all reaction products while the indirect turbidimetric method assumes that each enzymatic cleavage yields a product below the 8000 molecular weight necessary to cause turbidity [6]. Using a recently developed reversed-phase ion-pair HPLC method with postcolumn derivatization [7], we have calculated the kinetic parameters for purified short chain HA oligomers and native HA based on the end product of enzymatic degradation, an unreactive HA tetrasaccharide (C-4) 1. Kinetic degradation mechanisms for each oligomer have been proposed and evaluated by computer curve fitting analysis of the experimental time vs. concentration data to establish, in conjunction with mass balance calculations, which elementary transglycosylation and or hydrolysis reactions predominate in the degradation of each respective HA oligomer.

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J~A. Crameret al. / Biochimica et Biophysica Acta 1200 (1994) 315-321

2. Materials and methods 2.1. Materials

HA, grade III-P potassium salt from human umbilical cord, CS grade 111 from shark cartilage, alcian blue 8GX, carbazole and p-dimethylaminobenzaldehyde were obtained from Sigma (St. Louis, MO). Purified BTH (mol wt. 61,000) with an activity of 2723 turbidity reducing U / m g was purchased from Calbiochem (LaJolla, CA). A 40 weight % solution of tetrabutylammonium hydroxide (TBA-OH) 1 in water and 2-cyanoacetamide (2-CA) 1 were products of Aldrich Chemical Co. (Milwaukee, Wl). Methanol, pyridine and HPLC-grade acetonitrile were from Fisher (Fairlawn, NJ). BioGel-P-6 size exclusion resin, 200-400 mesh, was a product of BioRad (Richmond, CA). Sodium boro [3H]hydride in 0.1 N NaOH (specific activity 517.4 mCi/mg) was obtained from Amersham (Arlington Heights, IL). All other chemicals were analytical grade and used as received. 2.2. Purification of HA and generation of oligomers

CS contaminants were removed from the supplied HA using cetylpyridinium chloride precipitation procedures previously described [8,9]. The amount of CS remaining was determined via an alcian blue glycosaminoglycan staining assay [10]. The purified HA was degraded by adding 6000 U of BTH to 60 mg of HA dissolved in 7.5 ml of reaction buffer. The buffer for this and all kinetics experiments was 0.1 M sodium acetate, 0.15 M sodium chloride, with the pH set at 5.2 using glacial acetic acid. The 37°C enzymatic reaction was terminated after 1 h by placing the mixture in a boiling water bath for 5 min. The cooled mixture was filtered (0.45 /zm Gelman Acrodisc) and the oligomers separated by size exclusion chromatography [11]. Aliquots were tested for carbohydrate content using a colorimetric assay for total glucuronic acid [12]. Fractions containing the respective oligosaccharide peaks were pooled and lyophilized. Oligomer peaks with similar retention times from repetitive enzymatic degradations were pooled and reapplied to the size exclusion column as a further purification step. A portion of each lyophilized oligomer was dissolved in water and assayed in duplicate for total uronic acid and reducing GIcNAc content [4]. The mol wt. of each oligomer was determined by taking the ratio of total uronic acid to reducing GlcNAc endgroups, so as to obtain the number of disaccharide units per oligomer, and then multiplying this number by 397 to arrive at the oligosaccharide mol wt. The mol wt. of purified native HA was obtained by determining the intrinsic viscosity [n] of HA using capillary viscometry [13,14]. The mol wt. was calculated from the empirical Mark-Howink relationship: [n] = K M a , where M is the mol wt., and K and a are empirical

constants equalling 2.28 × [151.

10 - 4

and 0.816, respectively

2.3. HPLC chromatography

An isocratic reversed-phase ion-pair HPLC method with postcolumn derivatization was used to quantitate oligomer degradation products from enzyme kinetic experiments. Optimization of this method has been described in detail [7]. Briefly, 20 /zl of the diluted reaction mixture was injected onto a polymeric C18 column using a mobile phase of 0.03 or 0.04 M TBA-OH, pH 9.0/acetonitrile 4:1. A solution of 2-CA in pH 9.0 borate buffer was added post-column and the reaction proceeded at 100°C in a 10 m reaction coil. Reaction products were quantitated at 276 nm. The lower limit of detection for C-4 was 20 ng (25 pmol). 2.4. Reduction of HA octasaccharide

A 1.0 m g / m l solution of HA octasaccharide (C-8) 1 in 0.1 N NaOH was reacted with 3.87 /xg of boro [3H] hydride solution for 2.5 h at 25°C. 10 mg of solid sodium borohydride was added and the mixture stirred overnight to complete the reaction. The solution pH was adjusted to 6.5 with 1 N acetic acid and stirred for 30 min to convert any unreacted borohydride into tritium, hydrogen gas, and borate. The solution was then lyophilized to remove any residual tritiated water. The residue was reconstituted in 4 ml of 0.5 M pyridinium acetate buffer, pH 6.5, and desalted on a 1.5 × 45 cm column of BioGel-P-6 [11]. Fractions positive for carbohydrate (total glucuronic acid assay) and radioactivity were pooled and lyophilized. The resulting 2.5 mg sample was 95% reduced based on HPLC analysis and had a specific activity of 0.467/xCi/mg. 2.5. Kinetics experiments

Duplicate 800 /zl solutions of C-6 in reaction buffer were prepared at the following concentrations: 0.79, 1.58, and 3.15 mM. The solutions were equilibrated in a 37°C water bath and the reaction started by adding 2000 U of BTH dissolved in 200 /xl of reaction buffer to give final C-6 concentrations of 0.63, 1.26 and 2.52 mM. 50 /zl was removed from each sample at preset times over a 180 minute time course and diluted with 3 to 15 volumes of HPLC mobile phase to stop the reaction. The samples were mixed and stored at 0°C until analysis. The concentration of the reaction substrate and products for each sample was determined in duplicate, using the external standard method, and plotted as a function of time. The slopes of the initial linear portions of the curves (based on regression analysis) were used to determine initial reaction velocities, v, for the appearance of C-4 and the disappearance of C-6. Initial reaction velocites were calculated using the rate of C-4 formation because it is common to all degradation pathways and it does not react further. The disappear-

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J.A. Cramer et al. / B iochimica et B iophysica A cta 1200 (1994) 315-321

ance of C-6 from C-6 degradation experiments was used to calculate the kinetic parameters in an effort to obtain the true C-6 transglycosylation rate constant. Initial velocities were subsequently used to obtain K m and Vmax [16], k 1 (kcat//Km) the enzyme-substrate association constant, and k 2 (kcat) , the slowest of several possible rate constants. For C-8, 500 /xl solutions were prepared in duplicate at the following concentrations: 0.28, 0.63, 1.12 and 1.96 mM. The solutions were equilibrated at 37°C and the reaction started by adding 400 U of BTH dissolved in 200 /xl of reaction buffer. Aliquots (50/xl) were removed over a 3 h period and diluted with 3 to 32 volumes of HPLC mobile phase to stop the reaction. For the 3H C-8 experiment, a 1.12 mM solution was prepared and treated as above. All C-8 samples were processed in the same manner as C-6. Duplicate solutions of decasaccharide ( C - 1 0 ) 1 w e r e prepared at the following concentrations: 0.14, 0.28, 0.63, 1.12, and 1.96 mM. The 500 /xl solutions were reacted with BTH and treated in the same way as C-8 except 3 to 15 vol of HPLC mobile phase was used to stop the enzymatic reaction. For purified HA, 1.3 ml solutions in reaction buffer were prepared at the following concentrations: 0.00244, 0.00488 and 0.00976 mM. The solutions were equilibrated and the reaction started by adding 4000 U of BTH dissolved in 200/zl of reaction buffer. Aliquots were removed over time and processed in the same way as C-10. 2.6. C o m p u t e r c u r v e f i t t i n g

The rate constants for each elementary reaction of the proposed C-6, C-8 and C-10 degradation schemes were determined using the IBM PC compatible computer programs PRGEAR, GEAR and GIT (Project SERAPHIM, Univ. of Wisconsin, Madison, Wl). The program PRGEAR was used to construct a kinetic scheme of elementary hydrolysis and transglycosylation reactions. The schemes were made as simple as possible while still including the most likely reactions for substrate degradation to C-4. Transglycosylation, for the purpose of this work, is defined as the transfer of one disaccharide residue (C-2) 1 from the reducing end of a donor oligomer to the non-reducing end of an acceptor oligomer. It is conceivable that the transfer of larger residues could occur, but this would greatly complicate the kinetic schemes. The program GEAR integrated the proposed rate equations using initial oligomer concentrations and estimates of the rate constants. A time vs. concentration profile for each species was generated and compared to the experimental data. The process was repeated until the derived profile was similar to the experimental profile. The equations, initial concentrations, derived rate constants and experimental data were then processed by the iterative program GIT. This algorithm finds the optimum rate constants to fit the experimental data within the scope of the proposed model by minimizing the

1.0

1

C-4

'~ 0.6 E

C-6

i ~. 0.4 c;3

8.2 ¸ C-0

C-tO

_

0.8~ 40

oo

,io

,;o

289

TIME [min)

Fig. 1. Time vs. concentration profile for 0.800 mM decasaccharide degradation. C-4, tetrasaccharide; C-6, hexasaccharide;C-8 octasaccharide; C-10, decasaccharide.

deviation between the model lines and the observed data points.

3. Results and discussion

The purity of HA is important when studying BTH kinetics as the enzyme also reacts with CS [1]. The reaction rate of BTH towards CS, however, has been reported to be about one-fifteenth that of HA [17]. To eliminate the possibility of CS interfering with the HA oligomer kinetics experiments, CS was removed from the high molecular weight HA by precipitation. Based on the results of the alcian blue glycosaminoglycan complexation assay, the purified HA contained less than 0.5% CS compared to the 10.2% found in the starting material. The identities of the HA oligomers, baseline resolved by a second size exclusion chromatography step, were determined by the ratios of results obtained from uronic acid and reducing GlcNAc assays. Ratios of 2.02, 2.91, 3.99, and 5.05 were obtained and assigned to C-4 through C-10, respectively. The mol wt. of purified native HA, determined by viscometry, was calculated to be 6.72 × 105 Da. The BTH preparation used was equivalent in enzyme activity to the United States Pharmacopeia Reference Standard [18]. A representative time vs. concentration profile for the 0.800 mM C-10 degradation experiment is shown in Fig. 1. An abrupt drop in substrate concentration is seen at the

318

J~A. Cramer et al. /Biochimica et Biophysica Acta 1200 (1994) 315-321

"°t

IO0

i

~

5 []

L

=

4

w m

3'

99'

•

88"

mM

z 2"

? iii

7B

1

•

,

.

4 60

ZO

40

5'0

SO

100

TIME (min)

Fig. 2. Plot of time vs. mass balance for octasaccharide degradation at four different substrate concentrations.

earliest experimental time point followed by a slow decrease in C-10 concentration out to 180 min. The appearance of C-4 is linear for 30 min with appreciable amounts of C-6 and C-8 also being produced. If C-10 degradation were described simply by hydrolysis, equimolar amounts of C-4 and C-6 would be expected. Instead, C-6 concentration was found to be greater than C-4 concentration for almost 80 min. This phenomenon suggests that C-10 transglycosylation to yield C-8 and higher molecular weight products that degrade to give various oligomers, among them C-6, is an important reaction in C-10 degradation. A similar profile, where C-6 concentration exceeds C-4 concentration, was also seen for C-8 (see Fig. 4b.). If C-8 underwent hydrolysis only, 2 mol of C-4 should be produced from each mole of C-8 with no C-6 being seen. Transglycosylation, therefore, must be an important process in C-8 degradation as well. The results from C-6 degradation experiments have been reported [7] and an experimental profile is shown in Fig. 4a. A significant finding from the C-6 and C-8 kinetics experiments is that HPLC quantifiable oligomer mass balance is lowest at the first experimental time point and increases gradually to almost complete recovery in 90 min. A plot of mass balance as a function of time for C-8, shown in Fig. 2, reveals that mass balance is between 68 and 76% at 10 min. For C-6, oligomer mass balance at the first experimental time point was between 81 and 87% with decreasing substrate concentration, respectively, and

,

.

5

,

.

6

,

.

7

INIT. VELOCITY/[C-IS] [(nmoles/min)/mM] Fig. 3. Eadie Plot for decasaccharide degradation based on the appearance of tetrasaccharide.

approached 100% at 150 min. A similar mass balance trend was seen for C-10 with HPLC quantifiable oligomer content ranging from 40-50% at 10 min and increasing to 70-80% at 2 h. All of these results strongly suggest that C-6, C-8 and C10 transglycosylation to give lower and higher molecular weight products (not quantifiable by the analytical method) that ultimately degrade to C-4 is an important reaction. Initial reaction velocities for each substrate concentration were plotted using the Eadie-Hofstee equation. A plot of v vs. v/[S] for C-10, shown in Fig. 3, gives a straight line ( r = -0.992) based on the appearance of C-4. The kinetic parameters and related rate constants from the kinetics experiments are summarized in Table 1. It is evident that as substrate size increases K m decreases while Table 1 Kinetic parameters for bovine testicular hyaluronidase. Starting oligomer

gm (mM)

Vmax (nmol/min)

E0 (nmol)

k2 (min -1)

k 1 * ** (mM-lmin -1)

C-6 * C-6 C-8 C-10 HA

2.06 1.44 1.38 1.09 0.0172

25.6 28.0 15.7 ** 8.30 132

10.03 10.03 2.41 2.41 34.6

1.28 2.79 3.26 3.44 3.82

0.62 1.94 2.36 3.15 222

Initial reaction velocities for the appearance of the tetrasaccharide terminal reaction product, resulting from the bovine testicular hyaluronidase catalysed degradation of purified oligomers and native hyaluronic acid, were determined and used to obtain g m and VmaX via Eadie analysis. C-6, hexasaccharide; C-8, octasaccharide; C-10, decasaccharide; HA native hyaluronic acid. * Measured as the rate of C-6 disappearance (k 1 units = nmol mM "1 min -1. * * V m a x = 2k2E 0. ***k I = kcat / K m.

J.A. Cramer et al. / Biochimica et Biophysica Acta 1200 (1994) 315-321

Vmax remains essentially unchanged. The value of Vm~x for C-10, however, is one-half that seen for C-8 using the same total amount of BTH (E0) 1. This is because Vmax for C-8 is defined as 2k2E 0 since 2 moles of C-4 are produced from 1 mol of C-8 whereas C-10 degradation yields 1 mol each of C-4 and C-6. The values for k 2 also increase with substrate size but the differences become small for C-8, C-10 and HA. The values for kl, on the other hand, increase over 5-fold when going from C-6 degradation based on the disappearance of C-6 to the degradation of C-10 based on the appearance of C-4. In fact, k 1 for C-6 based on the disappearance of C-6 is 3 times less than kl for C-6 degradation based on the appearance of C-4. One explanation for the fact that the results differ, could be that the disappearance of C-4. One explanation for the fact that the results differ could be that the disappearance of C-6 data reflects only the transglycosylation of two C-6 oligomers to give C-4 and C-8 while the appearance of C-4 data includes C-4 produced by the degradation of C-8. The value of k I for HA, however, is increased over 70 fold compared to C-10. These results support earlier work suggesting that reaction rate is greatly dependant on substrate size and that the active site of BTH is able to accommodate C-10 [19]. The overall mechanism for enzyme catalyzed reactions, involving several possible substrates and reaction products, can be viewed within the context of chemical-reaction kinetics where the series of elementary reactions constitute

319

a kinetic scheme. The time vs. concentration experimental data for BTH catalyzed C-6 degradation was modeled with the following kinetic scheme: ka

C-6+C-6

~ C-12

(1)

kb

C-12

~ C-8+C-4

(2)

k¢

C-8

~ C-4+C-4

C-8+C-6

(3)

kd

~ C-10+C-4

(4)

kc

C-IO

~ C-6+C-4

(5)

where the rate constants represent some combination of the enzymatic rate constants discussed earlier. A plot of the 1.26 mM C-6 degradation experiment modeled to this scheme (Fig. 4a) shows good agreement between the simulated plot and the experimental data. The rate constant estimates for the 1.26 and 2.52 mM C-6 degradation experiments are listed in Table 2. The model was executed at two different substrate concentrations to ensure that the derived rate constants are characteristic of the scheme and are not unique to one particular substrate concentration. The agreement among the rate constants for the two different substrate concentrations strongly supports the reaction scheme constructed for C-6 degradation. The results in Table 2 indicate that the second order transglycosylation D.5

2.e.

a

L

b c-4

8.4 1.5 -

c-4

-5 w

~ 1.0

~

Z

0.2

O.S' 0.1

0 0.0 t O

•

•

•

C-8

C-8

•

. . . .

50

180

TIHE |rain|

0.0 ,SO

208

.___

0

50

100 TiHE

1;0

200

[min)

Fig. 4. Time vs. concentration profile comparing experimental data and the computer simulated kinetic reaction scheme. (a) 1.26 mM hexasaccharide degradation; (b) 0.800 mM octasaccharide degradation. Experimental data represented by symbols, computer model represented by lines. C-4, tetrasaccharide; C-6, hexasaccharide; C-8, octasaccharide.

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J.A. Cramer et al. / Biochimica et Biophysica Acta 1200 (1994) 315-321

Table 2 Estimated rate constants for hexa- and octasaccharide degradation. Reaction

Hexasaccharide

Octasaccharide

1.26 mM

0.450 mM

2.52 mM

Transglycosylation ka C-6+C-6~C-12

6.2*

3.4

ka C-6+C-8~C-10+C-4

9.1

6.1

kf C-8+C-8~C-10+C-6

nd**

Hydrolysis kb C-12~C-8+C-4

110"**

k~ C-10~C-6+C-4

130

kc C-8~C-4+C-4 HC-8

a

~ C-4+C-4

51 nd

3.6

0.800 mM

1.7

15

14

nd

100

89

160

nd

nd

99

61

40 nd

3.8 nd

77 1.7 1.1

Chemical-reaction kinetics degradation schemes for hexa- and octasaccharide were proposed and evaluated by computer curve fitting analysis of the experimental time vs. concentration data at two different substrate concentrations. * Units are m M l m i n -1 × 1 0 -3. ** not determined. • ** Units are min -1 × 10 "3.

stants are substituted into GEAR and the simulated C-10 and C-12 concentrations plotted, the concentration lines for these species rapidly increase and then decrease to undetectable levels in the first 20 minutes. This may be why no C-10 (lower limit 200 ng) or C-12 (lower limit 400 ng) was observed by HPLC, since the first experimental time point for C-6 degradation was 20 minutes. The transglycosylation reaction between C-8 and C-6, shown in eq. 4, was added to the C-6 reaction scheme for two reasons. First, it is a mechanistically correct equation and given the large concentration of C-6 present, would seem likely to occur. Second, it has been speculated that this reaction is more predominant in the degradation of C-6 than Eq. 3, the hydrolysis of C-8 [19]. The results from this work reflect just the opposite trend as k c is at least five times larger than k a (Table 2). The time vs. concentration experimental data for C-8 degradation was modeled using Eqs. 1, 4, 5, and 6. In addition, Eq. 7, the transglycosylation of two C-8 oligomers to give one C-10 and one C-6 residue has been added in order to account for the large concentrations of C-6 that were observed experimentally. kf

C-8+C-8 reactions for Eqs. 1 and 4 are much slower than the first order hydrolysis reactions for Eqs. 2, 3 and 5. Statistical considerations lend support to this observation, as the binding of two substrates is required before a transglycosylation reaction can occur. In addition, one of the transglycosylation substrates in Eqs. 1 and 4 is C-6, the oligomer with the lowest k I value in Table 1. For the C-6 hydrolysis reactions in Table 2, as substrate size increases from C-8 to C-10 the reaction rate constant doubles. A marginal increase in reaction rate is seen when going from C-10 to C-12. This is consistent with the idea that k e increases from C-6 to C-10, but does not increase appreciably for substrates larger than C-10. Initially, the kinetic scheme for C-6 degradation included the reaction: C-6+C-6-*C-8+C-4

(6)

instead of Eqs. 1 and 2 in order to make the reaction scheme as straightforward as possible. However, when rate constant estimates were obtained using Eqs. 3 - 6 with GEAR, a satisfactory fit containing the observed lag period for C-4 appearance was not obtained. The addition of Eqs. 1 and 2 to the reaction scheme allowed for a better fit of the experimental data. By making the rate of Eq. 1 (ka) very small and setting the rate of Eq. 2 (k b) very large, and then decreasing the value of k b during repetitive GEAR simulations, the observed lag period was approximated. An added advantage to this exercise is that an estimate of the C-12 hydrolysis rate constant, k e (Table 2), can be obtained without the benefit of C-10 or C-12 experimental data. If the C-6 kinetic scheme and the optimized rate con-

~ C-10+C-6

(7)

The intermediate reaction for C-8 transglycosylation, giving one C-16 residue, was not included in this scheme because no perceptible lag is seen in C-4 appearance in the experimental data. No other elementary reaction in the scheme, modeled at several different values of k, was able to contribute the large quantities of C-6 required to reconcile the experimental data. A single additional equation was necessary to describe the C-8 degradation profile compared to the C-6 data. Given the decrease in mass balance to approximately 85% for C-6 and 75% for C-8 at the early experimental time points, it is feasible that more reactions involving higher molecular weight oligomers could be written for which there is no experimental data. This would result in a much more complicated kinetic reaction scheme, whereas the proposed reaction scheme for C-8 adequately fits the observed concentrations for C-4, C-6 and C-8 (Fig. 4b). There are two major reactions for the C-8 degradation kinetic scheme evident from the constants listed in Table 2. One of the predominant reactions is homogeneous C-8 transglycosylation to give a C-10 and C-6 residue, while the second major rate constant is for the C-10 hydrolysis reaction. The data also indicate that transglycosylation rate constants for (C-6 + C-6) and (C-8 + C-8) reactions are similar for both the C-6 and C-8 degradation schemes. The rate constant, kc, for C-8 hydrolysis when C-8 is the substrate, however, is at least 10 fold less then when C-6 is the substrate. In order to confirm the C-8 hydrolysis rate constant, an experiment with reduced 3H C-8 was performed in which the reduction of the aldehyde to the corresponding alcohol prevents transglycosylation from oc-

.I.A. Cramer et al. / Biochimica et Biophysica Acta 1200 (1994) 315-321

curring [2]. In this experiment the reduced C-8 substrate can yield only two C-4 residues, one of which is quantifiable by the HPLC method. The experimental ~H C-8 hydrolysis rate constant thus obtained (Table 2) is in good agreement with the 0.800 mM unreduced C-8 hydrolysis rate constant previously described, thus further confirming the kinetic scheme. For both the C-6 and C-8 degradation schemes modeled here, the predominant first reaction is transglycosylation, with the rate constant for C-6 transglycosylation being about 30 times less than the rate constant involving C-8. Efforts to propose a C-10 degradation mechanism were less successful. Employing Eqs. 1 - 7 and the associated rate constants, at least 5 additional equations are necessary to adequately fit the observed concentrations of C-4 and C-10. Further, the modeled concentrations of the intermediate species C-6 and C-8 did not agree with the observed profiles. In addition, a limitation of the computer modelling software which was used is that only 5 rate constants may be varied independently during the optimization procedure. Calculations for C-10 mass balance were also low at initial time points and did not reach 100% after 2 h. In a separate experiment, complete recovery of C-10 related degradation products was obtained after an overnight incubation with BTH. These results strongly suggest that BTH catalyzed transglycosylation, to give lower and higher mol wt. products not detectable by the analytical method, must be an important process in the C-10 degradation scheme. In summary, the catalytic rate constant k 2 (kca t) for BTH catalysed H A degradation approaches a limiting value with increasing substrate size. The enzyme-substrate association constant k 1 (k2//kcat), on the other hand, continuously increases when going from the smallest to largest BTH substrate. The derived rate constants for each elemen-

321

tary hydrolysis and transglycosylation reaction, and mass balance calculations indicate that transglycosylation plays a significant role in the degradation of all H A oligomers studied.

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