Vladimir Stefuca,* Peter Gemeiner, Lubica Kurillova, Bengt Danielssont and. Vladimir B~ile~ ... Such methods would be of great interest since they would allow ...
Application of the enzyme thermistor to the direct estimation of intrinsic kinetics using the saccharose-immobilized invertase system Vladimir Stefuca,* Peter Gemeiner, Lubica Kurillova, Bengt Danielssont and Vladimir B~ile~ Institute o f Chemistry, Slovak A c a d e m y o f Sciences, Brat&lava, Czechoslovakia t Pure and A p p l i e d Biochemistry, Chemical Center, University o f L u n d , Lund, S w e d e n $ D e p a r t m e n t o f Chemical and Biochemical Engineering, SIovak Technical University, Brat&lava, Czechoslovakia
The possibility of using the enzyme thermistor (ET) for the direct determination of kinetic parameters
(Km, Ki, Vrn) of immobilized enzyme (IME) was evaluated using different preparations of invertase conjugated to bead celluloses. Two different ET columns packed with IME were operated in the mode of a differential enzyme reactor (short length, low substrate conversion). Kinetic parameters of the above IME reactor were computed by a nonlinear curve-fitting procedure. The obtained kinetic parameters were superverified by means of an independent differential reactor (DR) system. This system utilized an indirect postcolumn analytical method based on determination of glucose concentration in the stirred reservoir. Best agreement between the data acquired by direct (ET) and indirect (DR) methods was obtained if the ET column was operated at flow rates within the range of l.O-1.5 ml min -1 using invertase-cellulose chlorotriazine conjugate. Influence of heat loss and flow nonideality is discussed. The proposed ET method offers a rapid, convenient, and general approach to determination of kinetic constants of lME preparations by omitting postcolumn analytical methods.
Keywords:Enzyme thermistor;
intrinsic kinetics; differential reactor: immobilized invertase; bead cellulose
Introduction T h e r e is a lack of rapid and direct methods for the determination of kinetic constants of immobilized enz y m e (IME). Such m e t h o d s would be of great interest since they would allow one to obtain numerical characteristics o f I M E preparations and facilitate comparisons b e t w e e n different materials and p r o c e d u r e s for e n z y m e immobilization. The e n z y m e thermistor (ET) is a simple flow calorimeter primarily designed for metabolite determina-
This work was carried out at the Institute of Chemistry, Slovak Academy of Sciences, Bratislava, Czechoslovakia * Permanent address: Department of Chemical and Biochemical Engineering, Slovak Technical University, J~nska 1, CS-812 37 Bratislavia, Czechoslovakia Address reprint requests to Dr. Gemeiner at the Institute of Chemistry, Slovak Academy of Sciences, Dtlbravsk~i cesta 9, CS-842 38 Bratislava, Czechoslovakia Received 31 March 1989; revised 7 September 1989
830
tion.~,2 The fact that m o s t enzymic reactions are acc o m p a n i e d by considerable heat evolution m a k e s e n z y m e calorimetry a highly versatile technique. The lack of specificity due to the general detection principle is adequately c o m p e n s a t e d for by the use of specific, immobilized biocatalysts, such as enzymes. Packing of I M E inside an E T column should allow simultaneous evaluation of both substrate concentration and e n z y m e kinetics. To date, calorimetric studies on e n z y m e kinetics have mostly b e e n p e r f o r m e d with conventional flow microcalorimeters using soluble e n z y m e s ) ,4 As the E T e m p l o y s a small column of I M E , it presents an opportunity to carry out analogous kinetic m e a s u r e m e n t s on I M E s . Such a study has been p u b l i s h e d ? H o w e v e r , verification o f the obtained kinetic constants by alternate methods has not b e e n done. We h a v e previously studied the kinetic properties of invertase bound to bead cellulose by various immobilization techniques. 6 B e c a u s e of the localization of invertase on the external surface of the beads, internal
Enzyme Microb. Technol., 1990, vol. 12, November
© 1990
Butterworth-Heinemann
Kinetics of immobilized invertase in an enzyme thermistor: V. Stefuca et al.
diffusion did not exert a serious influence on the reaction kinetics. Generally, immobilization procedures on bead cellulose are simple, exhibiting both high yield and high operational stability. 7 Moreover, bead celluloses are often cheap and, thus, they are good alternatives to other enzyme carriei's for ET analyses, such as controlled pore glass (CPG), Sepharose, Eupergit, etc. 1.2,s The aim of the present study was to ascertain whether the ET is a suitable instrument for the estimation of IME steady-state kinetics. For that reason, the kinetic behavior of invertase immobilized in the ET was compared to that in a differential reactor where the reaction course was followed by the enzymatic estimation of glucose concentration. Invertase was immobilized covalently using methods previously described for bead cellulose 6,7,9and other carriers. 10,1JAll procedures were adapted for bead cellulose. A procedure similar to the common method of invertase immobilization on CPG, 8 i.e., condensation with CPG aldehyde beads, was also used.
Materials and methods
Invertase Invertase (EC 3.2.1.26, fl-fructofuranosidase) grade V: practical (Sigma, St. Louis, MO) from baker's yeast, after removal of water-insoluble material, exhibited an activity of 46.6 U mg -~ (776.4 nkat mg ~) at 25°C. All steps in the purification of invertase were carried out at 0-5°C unless otherwise specified. In a typical run, the powdery invertase (3.0 g) was suspended in 10 mM phosphate buffer, pH 6.5 (120 mi), adjusted to pH 5.0 with 30% v/v acetic acid and stored overnight. The suspension was then heated, ~2 and after cooling, centrifuged (10,000 g for 10 min), and the precipitate discarded. Addition of ammonium sulfate to 80% saturation and storage overnight was required to precipitate an extracellular invertase. The supernatant obtained by centrifugation (30,000 g for 30 min) j2 was desalted by dialysis and, finally, lyophilized. An invertase preparation, exhibiting an approximate catalytic activity of 175 U mg -1 (2.92 mkat mg -I) at 25°C was used throughout the present work.
Bead celluloses Bead cellulose chlorotriazine (cellulose I, particle diameter 120-315/zm, dry weight 12.9%, DS 0.178) was prepared by reaction of bead cellulose (120-315/xm, 14.85%) with cyanuric chloride. 6 Bead 2-(4aminophenylsulphonyl)ethyl cellulose (cellulose II, 40-320/xm, 20.4%, 1.26 mmol NH2 g-J) marketed under the trade name Ostsorb AV, was kindly provided by O. Tokar from the United Chemical and Metallurgical Works (l~lstf nad Labem). Bead cellulose aldehyde (cellulose III, 40-320/.~m, 23.4%) was prepared from cellulose II after activation with glutardialdehyde j° and bead formylmethyl cellulose (cellulose IV, 60-240 /zm, 20.5%, DS 0.065) by reaction of bead cellulose
with bromoacetaldehyde diethylacetal and subsequent hydrolysis. ~3
Immobilization of invertase A freshly prepared solution of invertase (9.2-23.0 mg ml -=, 2500-5000 units) and 2.5-7.5 g of the suction dried (0.5-1.0 g of dry weight) bead cellulose derivative were used for covalent immobilization whereby the liquid/solid phase volume ratio was kept within the range of 10-25. Invertase was coupled (i) by direct substitution 6 of the triazine chlorine of cellulose I: (ii) by coupling 11 with a diazonium salt prepared from the cellulose II; (iii) by condensation 1° with cellulose III; and, finally, (iv) by condensation 9 with cellulose IV. Using these procedures, INV-cel I, II, III, and IV conjugates were prepared following both reaction time and pH as described in the above-mentioned references. The condensation reaction (iii) proceeded for 3 h at ambient temperature. 11 INV-cel conjugates were thoroughly washed with water, 0.1 M acetic acid, 1 M KC1, and, finally, with water following blocking of residual cellulose triazine chlorine and aldehyde groups with glycine (150 mM) and the diazonium salt with tryptophan (saturated), both in 50 mM acetate buffer, pH 4.65. The amount of bound invertase and/or bound protein was obtained by measuring the difference between the activity and/or the amount of protein added to the reaction mixture and that recovered in the solution. Conjugates were stored in 50 mM acetate buffer, pH 4.65, either at 4°C or at ambient temperature.
Apparatus The enzyme thermistor (ET) was the aluminum-blocktype thermostat. 1,2 Resistance measurements were made using a precision Wheatstone bridge. 8 Both of these were constructed at the University of Lund (Lund, Sweden). This instrument is now marketed by ThermoMetric Co. (J~trf~illa, Sweden) under the name Thermal Assay Probe (TAP). The mobile phase was continuously pumped via the injection valve (Rheodyne, Type 5020; Cotati, CA) through the system by a peristaltic pump (Microperpex; LKB; Bromma, Sweden) with negligible or little pulsation. Temperature signals were recorded on a Line Recorder TZ 4100 (Laboratornf P~fstroje, Prague) and the highest sensitivity was limited to 10 -2 °C full scale. The instrument was equipped either with a 0.8-ml standard column (0.7 cm i.d. × 2 cm) or with a 3.85-ml socalled long column (0.7 cm i.d. × 10 cm). Both columns were packed with approximately equal amounts of IME conjugate, i.e., 470 -+ 30 mg of wet weight corresponding to 100 mg -+ l0 mg of dry weight INV-cel I. The bed of | M E (height, h = 2 cm) located in the long column (h = I0 cm) was placed between two layers (input, h = 7 cm; output, h = 1 cm) of glass beads (particle diameter, d = 0.03 cm). The beds were separated from each other by stainless-steel sieves. The output and input of the column were sealed by Teflon filters (thickness 1 mm).
Enzyme Microb. Technol., 1990, vol. 12, November
831
Papers Estimation of kinetic constants
All measurements were performed at 25 and 30°C. Saccharose solutions were buffered with 50 mM acetate buffer, pH 4.65. Free invertase. The hydrolysis of saccharose, catalysed by free invertase, was performed within the concentration range 0.028-1.54 M saccharose (concentration step 0.05-0.1 M). The liberation of reducing saccharides in the reaction media was determined using the Bio-Lachema-Test "Glucose enzymatically" (Lachema, Brno). The procedure differed from that described by Trinder 14 in the chromogen used (4chloro-3-cresol) and the monitoring wavelength (490 nm). The reaction rate was estimated within the first 5-10 min. Km, Ki, and Vm were calculated by nonlinear regression analysis of the Michaelis-Menten equation expanded to include a substrate inhibition term, as described by Bowski et al.15 Invertase immobilized in a differential reactor. For the measurement of the initial reaction rate of saccharose hydrolysis, the differential reactor (DR) system with infinite recirculation of substrate solution was used. Modus operandi of this DR system was described by Vallat et al. 16 The reactor column (5 cm i.d. × 12 cm) was packed with a 0.5-cm layer of immobilized invertase beads, and to secure good fluid distribution, the layer consisting of the IME beads was sandwiched by layers of inert glass beads of the same size. Initial saccharose concentrations varied within the range of 23-815 mM. The substrate solution was recirculated with high superficial velocities (1.5-3.2 cm min -1) to preclude the limitation of external mass transfer. The glucose concentration in the stirred reservoir was measured during the first 15 min by the same method as was described for free invertase. Initial reaction rates were calculated from the time-concentration dependence by linear regression analysis.
Temperature response curves were weekly over a period of 2 months.
remeasured
Mathematical treatment ~['experimental data from the enzyme thermistor and differential reactor Assuming that the IME column placed in the ET can be considered as a packed-bed reactor (PBR) conditioned in such a way that both the external mass transfer limitation and axial and radial dispersion effects may be neglected, the steady-state mass balance equation for the substrate would be: - w ( d S / d z ) + (1 - e)r = 0
(1)
where S, z, w, e, and r are, respectively, the substrate concentration, the axial coordinate, the superficial velocity, the void fraction, and the reaction rate. The heat balance is defined by the following equation: -WpCp(dT/dz) + (1 - e)rAHr = 0
(2)
where AHr, p, Cp, and T represent, respectively, the molar reaction enthalpy, the fluid density, the heat capacity, and the temperature. To calculate the initial reaction rate of saccharose hydrolysis catalyzed by invertase, the substrate inhibition plus total water concentration model developed by Bowski et al. 15 was appliedl8: r = {VmS/[Km + S + (S2/Ki)]}(W/Wo)
(3)
where Ki is the substrate inhibition constant, W0 is equal to 55.33, and the total water concentration is calculated from: W = 55.33 - 0.01186 S
(4)
where substrate concentration is expressed in mM. Substituting r from equation 2, equation 3 can be rewritten as follows: wpcp(dT/dz) = {VmSAHr(1 - ~)/[Km + S
Invertase immobilized in the e n z y m e thermistor. A buffer solution was pumped through the system at a flow rate within the range 0.5-2.0 ml min -1. After thermal equilibration, the buffered saccharose solution (0.05-1.0 M) was introduced and continuously pumped through the ET column until steady-state heat production was obtained. 17 The temperature change due to the hydrolytic reaction was measured manually from the height of the peak on the thermogram.
+ (S2/Ki)]}(W/Wo)
from which a valid equation for a differential bed may be derived: dT/dz = AT/Az = {VmAHr(1 - s)S/wpcp[Km + S
+ (S2/Ki)]}(W/Wo)
832
(6)
After introducing the following parameter = VmAHr(1 - e)Az/wpCp
Storage stability of immobilized invertase
The stabilities of invertase-bead cellulose conjugates stored at ambient temperature were examined in a standard column at 30°C. A saccharose solution (25500 mM) was injected into a continuous buffer stream at flow rates of 1.45, 2.30, and 3.20 ml min -1 through the injection value using a 0.5-ml sample loop. The height of the temperature peak recorded was used for manual measurement 2 of the temperature change.
(5)
(7)
equation 6 can be simplified to: AT = {~xS/[Km + S + (S2/Ki)]}(W/Wo)
(8)
For the calculation of parameters c~, Km, and Ki according to equation 8, temperature changes were measured in terms of varying substrate concentrations. The required parameters of equations 3 and 8 were obtained by a nonlinear Marquard's regression proce-
Enzyme Microb. Technol., 1990, vol. 12, November
Kinetics of immobilized invertase in an enzyme thermistor: V. Stefuca et al.
dure using experimental data obtained from both the differential reactor system and the enzyme thermistor. Assuming that the parameters Km and Ki are intrinsic and invariable kinetic constants, it is useful to rewrite equation 8 in the form: AT = orS'
'C
(9) < O"
where the transformed substrate concentration S' is represented by the term S' = {S/[Km + S + (S2/Ki)]}(W/Wo)
1.2
o
0.8
Z
_o
(10)
0.4
The intrinsic kinetic constants K,, and Ki were determined in the DR system. Then, results obtained in the ET were tested using equation 10 after inclusion of the remaining parameter, a. SACCHAROSE CONC.(raN1)
Results and discussion Structure-activity relations In Figure 1 the temperature changes due to the hydrolytic reactions catalysed by the same amount of INVcel conjugates were compared. Differences between the three catalytically active conjugates, INV-cel I, II, and III, were considerable and varied by almost two orders of magnitude. Catalytic activity of the fourth conjugate, INV-cel IV, was thermometrically nondetectable. The mass balance method used for the estimation of the amount of protein bound onto the cellulose derivatives (celluloses I-IV) proved not to be sufficiently accurate because some interference was observed. Therefore, specific activities of IME were not used. Alkylation by triazine chlorine of cellulose I proved to be the optimal immobilization procedure from the standpoint of immobilized invertase activity. Moreover, in agreement with previously published data, 6
60
.L)
Figure 2 Effect of saccharose concentration on the rate of reaction catalysed by INV-cel I in the differential reactor (DR) system. Line represents least squares parameter fits of equation 3 to experimental data
this procedure had little influence on the kinetic behavior of invertase. Although the storage stability of conjugate INV-cel I was less when compared to conjugates INV-cel II and III, it was still sufficiently high (Figure 1) for kinetic measurements to be performed in both the ET and DR systems. Intrinsic kinetics in the e n z y m e thermistor As it is evident from the data presented in Table 1, the flow rate influenced the apparent kinetics. To facilitate analysis of this phenomenon, intrinsic kinetic parameters were determined using the DR system coupled with postcolumn analysis of the glucose concentration. Packing INV-cel I inside the differential reactor, the values Km = 48.5 mM and K/ = 1752 mM were calculated from the experimental results plotted as shown in Figure 2. These values were similar to those obtained for free invertase: K,, -- 36.4 mM and Ki = 1783 mM, and corresponded satisfactorily with values published by Geankoplis et al. 18 The influence of flow rate on the kinetics was then studied from 1.0 to 2.0 ml min -1. These flow rates were
I,--
