`VOL. XVIII, PAGES 669-684 (1976)
`
`Effects of Immobilization on the Kinetics of
`Enzyme-Catalyzed Reactions. I. Glucose
`Oxidase in a Recirculation Reactor System
`
`K. B. RAMACHANDRAN and D. D. PERLMUTTER, Department
`of Chemical and Biochemical Engineering, University of Pennsylvania,
`Philadelphia, Pennsylvania 191 74
`
`Summary
`Glucose oxidase from Aspergillus niger was immobilized on nonporous glass
`beads by covalent bonding and its kinetics were studied in a packed-column
`recycle reactor. The optimum pH of the immobilized enzyme was the same as
`that of soluble enzyme; however, immobilized glucose oxidase showed a sharper
`pH-activity profile than that of the soluble enzyme. The kinetic behavior of
`immobilized glucose oxidase at optimum pH and 25'C was similar to that of the
`soluble enzyme, but the immobilized material showed increased temperature
`sensitivity.
`Immobilized glucose oxidase showed no loss in activity on storage
`a t 4°C for nearly ten weeks. On continuous use for 60 hr, the immobilized enzyme
`showed about a 40% loss in activity but no change in the kinetic constant.
`
`INTRODUCTION
`With the recent development of immobilization techniques, in-
`teresting potential applications of enzymes as catalysts have been
`proposed in fields as diverse as medicine, sewage treatment, and
`industrial processing. Since enzymes depend upon specific three-
`dimensional conformation of their molecules for activity, any physical
`influence of the matrix or chemical modification of the enzyme might
`Indeed, a number of recent
`have
`alter its properties.
`reported altered properties of enzymes after immobilization. How-
`ever, it has not always been taken into consideration that the ap-
`parent change in the chemical properties are not entirely due to the
`physical influence of the matrix or chemical modification of the
`enzyme. External and internal diffusion effects can considerably
`alter the Michaelis-Menten constant, the activity, and the thermal
`sensitivity. For engineering purposes, better understanding is
`needed of immobilized enzyme kinetics and the factors that influence
`669
`
`@ 1976 by John Wiley & Sons, Inc.
`
`Page 1 of 16
`
`HOLOGIC EXHIBIT 1028
`Hologic v. Enzo
`
`
`
`670
`
`RAMACHANDRAN AND PERLMUTTER
`
`the rate of the reaction. In this study glucose oxidase was im-
`mobilized on nonporous glass beads by covalent bonding and its
`kinetics studied under well-defined reactor geometry and flow con-
`ditions. Glass was chosen as the support material because of its
`strength and incompressibility.
`
`BACKGROUND
`The kinetics of the homogeneous glucose oxidase reaction have
`been widely studied'-l2 with 8-D glucose, at 25"C, and pH = 5.5.
`The mechanism is generally given as
`
`'-'E~ - G & E , + P
`E o + G e
`E, + 0 2 A EO + H202
`(2)
`where Eo, E,, and Eo - G stand for the oxidized and reduced forms
`of the enzyme and the enzyme complex, respectively. Based upon
`this mechanism the reaction rate at steady state can be expressed as
`
`(1)
`
`(3)
`
`where ET is the enzyme concentration, kcat = kz, k,, = kl and
`k r e d = (kIk2/k-1 + kz) or (klk2/k-J, if the assumption is made of
`
`rapid equilibrium.
`For a given amount of enzyme and at fixed glucose concentration
`eq. (3) can be reduced to
`
`where
`
`and
`
`Previous kinetic studies of glucose oxidase, immobilized by various
`techniques, have indicated that immobilization can affect the proper-
`ties of the enzyme. For example, Weibel and BrighP immobilized
`
`Page 2 of 16
`
`
`
`IMMOBILIZEI) GLUCOSE OXIIIASE
`
`671
`
`Catalyst
`
`L
`
`R
`Recycb stream
`
`t
`
`Fig. 1 . Flowsheet for a recycle reactor system.
`
`glucose oxidase on porous glass beads by covalent bonding and found
`that the apparent bimolecular constant was increased by a factor of
`14. For gel entrapped glucose oxidase, Hinberg et al.14 observed an
`increase in the value of the bimolecular constant by a factor of 2,
`but Miyamura and Suzukils found that the values of the kinetic
`constants approached those of soluble enzyme as the particle size
`was decreased. Glucose oxidase crosslinked on a cellophane mem-
`brane16 and covalently coupled on a nickel oxide screen17 showed no
`change in the value of kinetic constants.
`In the same studies the
`optimum pH of the enzyme also did not change, however, in both
`cases the sensitivity of the enzyme to changes in pH was increased.
`Immobilized glucose oxidase showed decreased temperature sensi-
`tivity” and increased storage stability.’*
`The chemical engineering literaturelg describes the advantages of
`a packed-bed reactor linked to an external recirculation system.
`In such a continuous flow recirculation reactor system part of the
`effluent stream is returned and mixed with the feed stream, as
`schematically shown in Figure 1. A mass balance on the substrate
`at the mixing point gives:
`
`As the ( R / F ) ratio is increased sufficiently, the concentration changes
`within the reactor decrease to the point where the reactor is called
`“differential,” i.e., the reaction may be considered to occur at a
`constant average concentration level. The overall conversion must
`however be significant enough to be detectable by the available
`measurement techniques. Under these circumstances the reaction
`rate can be calculated from
`
`Page 3 of 16
`
`
`
`672
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`RAMACHANDRAN AND PERLMUTTER
`
`where W is the catalyst weight.
`in the modified form
`
`Equation (8) can also be written
`
`where [OZ]S is the saturated oxygen concentration. Values for
`different temperatures are reported in the literature.*O
`Since the glucose concentrations used in this study were very much
`higher than those of oxygen, they can be assumed to be constant
`throughout the reactor and equal to the inlet value. From eq. (7)
`the inlet oxygen concentration to the reactor can be written as
`
`and the average oxygen concentration is given by
`
`Equations (9)-(11) provide the numerical values needed in the
`evaluation of the rate expression eq. (3). Kinetic constants in this
`rate expression were calculated by using Rosenbrock’s search tech-
`nique.2l
`
`EXPERIMENTAL
`
`Materials
`Nonporous glass beads (40-60 mesh) used for covalent coupling
`of glucose oxidase were obtained from Ana Laboratories Incorporated,
`New Haven, Connecticut. The enzyme preparation (analytical
`grade from Aspergillus niger) used for immobilization was obtained
`from Sigma Chemical Company, St. Louis, Missouri and further
`purified. D- Glucose solutions of different concentrations were pre-
`pared by using “Baker analyzed” reagents purchased from J. J.
`Baker Chemical Company, Phillipsburg, N. J. The buffer solution
`used was 0.1M sodium acetate and the pH was adjusted to the
`desired level by adding acetic acid. Since the enzyme preparation
`contained trace amounts of catalase, O.lmM KCN was added to
`suppress its activity. EDTA in the amount of 0.5mM was also
`added to the glucose solution to protect the enzyme from metal ions
`which may deactivate it. Sodium acetate, KCN and EDTA used
`were analytical grade materials (J. J. Baker). Compressed air used
`
`Page 4 of 16
`
`
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`IMMOBILIZED GLUCOSE OXIDASE
`
`673
`
`for saturating the glucose solution was obtained from Linde Gas
`Company. All solutions were prepared from distilled-deionized
`water.
`
`Methods
`The nonporous glass beads were prepared by first adding 100 ml
`of water to 50 g of beads and then slowly adding 100 ml of 50%
`hydrofluoric acid, allowing the contents of the beaker to cool between
`additions. The mixture was allowed to react for 1 hr and then 10N
`NaOH was added, enough to cover the beads. The slurry was heated
`to 80°C for 1 hr, washed with distilled water, and dried overnight
`in an oven a t 80°C. The dry beads were immersed in a 2% solution
`of 3-aminopropyltriethoxy silane in acetone. Excess liquid was
`decanted and the beads were allowed to stand in an oven at 45°C
`for 24 hr. The alkylamine glass was refluxed for 24 hr in 200 ml of
`chloroform containing 10 ml of triethylamine and 20 g of nitro-
`benzoyl chloride. The beads were washed with chloroform and
`ethyl alcohol and dried in an oven at 60°C for 12 hr. The arylamine
`glass was reduced by refluxing in 200 ml of 5% (w/v) sodium
`dithionite in water for 1 hr. The beads were washed with water
`and benzene and dried a t 60°C.
`For diazotization and coupling the glass was slurried in 50 ml of
`2N HC1 and placed in an ice bath in a dessicator connected to a
`vacuum source. When cool, 2.5 g of sodium nitrate was added to
`the slurry ; the reaction was allowed to proceed under vacuum for
`20 min. The beads were then quickly but thoroughly washed with
`ice-cold 1% (w/v) sulfamic acid, until no more bubbling was seen.
`A 0.1M Tris-C1 solution (pH = 8.7) was used for a last rinse. Excess
`liquid from the top of the beads was removed by decantation to
`prevent dilution of the enzyme solution. Glucose oxidase that had
`been column purified and concentrated was diluted by 1:lO and
`10 ml was added to the glass beads. The reaction was allowed to
`proceed for 1 hr. The beads were then washed with Tris-C1 buffer
`thoroughly to remove the loosely bound enzyme and the supernatant
`containing unreacted enzyme was saved. Glucose oxidase beads
`were stored at pH=6.5 in the cold.
`Recycle Reactor
`The essential features of the recycle system consist of the reactor,
`the feed preparation and product analysis parts, and the measure-
`ment and control devices. Glucose feed solution is maintained
`within f0.2"C by a Blue M Electric Co. Model MR-3240A-1 con-
`
`Page 5 of 16
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`
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`674
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`RAMACHANDRAN AND PERLMUTTER
`
`stant temperature bath. It is saturated with air by bubbling through
`four gas dispersion rods. A positive pressure Micro Pump, model
`12-00-316 supplies the feed to the reactor, at rates measured by
`rotameters. The heat added to the solution by the agitation of the
`pump is removed by passing the reactants through stainless steel
`coils maintained inside the constant temperature bath.
`The reactor consists of a glass tube of 2.5 cm diameter and 30 cm
`length, surrounded by a Plexiglas water jacket. Spacers on both
`sides are used to adjust the bed height to any desirable level. The
`glass beads are supported inside the column by nylon screens, one of
`which also serves as a fluid distributor. Water from the constant
`temperature bath is circulated through the water jacket to maintain
`uniform reactor temperature.
`A part of the reactor effluent stream is metered and recycled.
`The rest of the stream is passed through a specially built holder for
`the dissolved oxygen electrode. The holder is provided with magnet-
`driven agitation to maintain a minimal velocity past the faces of the
`electrodes and the oxygen level in the reactor product is measured
`by using a polarographic electrode Model YSI 5331 Yellow Spring
`oxygen analyzer. The oxygen probe is connected to a Model YSI 53
`biological oxygen monitor, which measures the dissolved oxygen level
`as a percentage of saturation value and supplies a signal for a con-
`tinuous record. The reactor is also equipped with a bypass line for
`calibrating the oxygen probe.
`The temperatures in the water bath, and at the entrance and exit
`of the reactor are monitored by thermocouplbs. All tubings and
`tube fittings are made of either stainless steel or polyethylene.
`Further details of equipment and procedure are recorded elsewhere.22
`
`RESULTS AND DISCUSSION
`
`Two different preliminary experiments were run to evaluate the
`effects of external mass transfer on the chemical reaction rate to be
`In the first
`studied on the nonporous 50-60 mesh glass beads.
`experiment, conversions from a plug flow reactor were compared at
`given space time (W/F) but at three different catalyst weights.
`Figure 2 shows the results obtained. Since the data for all three
`catalyst weights overlap, conversion is evidently not affected by
`flow velocity and it can be concluded that external film resistance
`is negligible.
`In the second experiment, reaction rates from a differential recycle
`reactor were compared at a given feed rate ( F ) but at different total
`
`Page 6 of 16
`
`
`
`IMMOBILIZED GLUCOSE OXIDASE
`
`675
`
`V
`
`I
`0.2
`
`,
`1
`I
`I
`0.8
`0.4
`0-6
`1.0
`Spoco tlnr , ma min/ml
`Fig. 2. Dependence of oxygen conversion on space time.
`
`1
`1.2
`
`I
`1.4
`
`I
`1.8
`
`flow rates (F + R). Data obtained at four different feed rates from
`8.4 to 41.1 cc/min and over a range of recycle rates from 360 to 1640
`cc/min showed that the reaction rate is independent of total flow.
`It can therefore be concluded as before that the external mass transfer
`resistance is negligible above a total flow rate of 360 cc/min, cor-
`In all subsequent experi-
`responding to a linear velocity of 1 cm/sec.
`ments the reactor was operated well above this flow velocity.
`Using the correlation of Wilson and Geankoplis23 for mass transfer
`in packed beds, surface concentrations of oxygen and gluconic acid
`were calculated, corresponding to each of the experimental condi-
`tions.
`In all the cases, surface concentration of oxygen was found
`to be only slightly different from that of the bulk concentration
`(<<l%), confirming that external mass transfer effects are negligible
`for this system. The surface concentration of gluconic acid was
`similarly found to be nearly the same as that of the bulk, indicating
`that the microenvironment near the glass was not different from
`that of the bulk.
`Experiments were conducted with different amounts of immobilized
`enzyme to test whether axial dispersion effects and end effects are
`significant. Reaction rates were measured at 25°C and lOmM
`glucose concentration a t different oxygen concentrations and over a
`threefold range of bed weight. The data were fitted to eq. (4) and
`the parameters V,,, and K,M were estimated. The kinetic constants
`
`Page 7 of 16
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`
`
`676
`
`I
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`RAMACHANDRAN AND PERLMUTTER
`
`T = 25OC. pH = 5.5
`
`Calalysl weight, gmr
`Fig. 3. Effect of bed weight on the reaction rate.
`
`are independent of bed weight, indicating that dispersive effects are
`not significant. Figure 3 shows the same data, but plotted in a form
`that would produce a straight line passing through the origin, iftaxial
`dispersion and end effects were negligible. The results clearly
`support such a conclusion.
`
`pH Projiles
`The effect of pH upon the activities of the enzyme in solution and
`in the immobilized form was studied at a glucose concentration of
`100mM. At this concentration level, the values of V,,,
`estimated
`by applying eq. (4) are essentially the true maximum velocities when
`oxygen and glucose are in great excess. The results for both soluble
`and immobilized enzymes are compared in Figure 4 for pH between
`3 and 8 on normalized scales.
`It can be seen from Figure 4 that the optimum pH = 5.5 of the
`immobilized enzyme is the same as that of the enzyme in solution,
`however, the immobilized enzyme seems to be more susceptible to
`the changes in pH of the bulk solution. Below a pH of 3 the im-
`mobolized glucose oxidase completely and irreversibly lost activity.
`The results of this work are consistent with the findings of Broun
`et a1.16 for glucose oxidase crosslinked on cellophane and also with the
`findings of Weetall and Hersh” for glucose oxidase covalently linked
`on nickel oxide screens. These effects have been attributed to
`charges on the water insoluble carrier or unidentified chemical
`modification, but there exists no experimental verification for these
`speculations.
`
`Page 8 of 16
`
`
`
`IMMOBILIZED GLUCOSE OXIDASE
`
`677
`
`I
`
`T = ~ ! ~ ~ , I = o . I M
`
`b
`
`PH
`Fig. 4. pH-Activity profiles of soluble and immobilized glucose oxidase.
`
`E$ect of Substrate Concentrations
`At 25OC and at pH = 5.5 a series of runs were made to evaluate
`the effects of glucose and oxygen concentrations on the kinetics of
`immobilized glucose oxidase. Reaction rates were measured at
`different oxygen concentrations for each of seven glucose levels
`between 5 and 100mM. The experimental results are shown in
`Figure 5 together with curves computed from eq. (3) by inserting
`best estimates of the various parameters. The estimated parameter
`values and their respective 95% confidence interval values are given
`in Table I along with the comparable literature results for the free
`enzyme and for glucose oxidase immobilized on porous glass.
`Applying the standard statistical t-test for significant differences
`between means, a comparison of the kinetic constants for soluble and
`immobilized glucose oxidase shows no evidence that the former was
`affected by immobilization. It can be concluded that there is very
`
`TABLE I
`Comparison of Kinetic Parameters for Glucose Oxidase
`
`System
`
`Soluble enzyme
`Bound to porous glass
`Bound to nonporous
`glass
`
`k,,t/kox X lo3
`(mol/liter)
`
`0.51
`0.50
`0.59 f 0.177
`
` red
`k
`k d
`(mol/liter)
`
`Ref.
`
`0.071
`0.005
`0.08 f 0.020
`
`12
`13
`This work
`
`Page 9 of 16
`
`
`
`678
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`RAMACHANDRAN AND PERLMUTTER
`
`T = W'C, pH'5.5
`
`- Model (Equalion 3 )
`
`v
`
`0
`
`I
`OC6
`
`1
`01
`141 XI^ maerr/liter
`Fig. 5. Effect of substrate concentration on the reaction rate at 25°C.
`
`I
`015
`
`I
`0.2
`
`little or no interaction between the carrier and the active enzyme
`sites at this optimum pH = 5.5. However, it should be noted that
`the kinetic constant could be significantly different at other pHs,
`as suggested by the trends shown in Figure 4. The results obtained
`from this study are not in agreement with the results obtained by
`Weibel and Bright,13 who observed a 14-fold increase in the value
`
`Page 10 of 16
`
`
`
`IMMOBILIZED GLUCOSE OXIDASE
`
`679
`
`of the apparent bimolecular constant, k r e d . However, when the
`data of Weibel and Bright were corrected for external and internal
`diffusion effects,24 the resulting constant was reduced by an order
`of magnitude. Moreover, when the data of the present work were
`analyzed by the inverse-plot method used by Weibel and Bright,
`it was found that the results could differ from the nonlinear parameter
`estimates by another factor of two.22
`An order of magnitude estimate of the surface concentration of the
`enzyme can be calculated from the value of kcatET for the immobilized
`enzyme. The value of kcat for the enzyme is readily available since
`it did not change upon immobilization, but an estimate is needed
`of surface area per gram of glass beads. Assuming the average
`diameter to be 0.2 mm for 40-60 mesh beads and the glass density
`to be 2.2 g/cc, the surface concentration was calculated to be
`7.2 X 10-13 mol/cm2. In actual preparation the surface concentra-
`tion will be smaller than this, because the surface area of textured
`glass beads is higher than that of uniform spheres. To evaluate this
`result it is of interest to compare it to the surface concentration level
`that corresponds to monolayer coverage. Using a molecular di-
`ameter for the enzyme of lo-' cm, monolayer coverage on 0.2 mm
`uniform spheres corresponds to a surface concentration of 13 X
`mol/cm2, a figure which is twice as high as the surface concentration
`estimated for the enzyme preparation used in this study. It may be
`concluded, therefore, that approximately 50y0 (or less) of the glass
`surface is involved in the enzyme catalysis.
`
`E$ect of Temperature
`Reaction rates were measured at four different temperatures and
`the data for each temperature were fitted to eq. (3) to obtain the
`parameter estimates (with 95% confidence interval) shown in Table
`11. Since kcatET is the maximum velocity at excess concentration
`of glucose and oxygen, the rates are normalized for presentation as
`the temperature-activity profile in Figure 6 . The corresponding
`profiles for soluble glucose oxidase and glucose oxidase immobilized
`on nickel oxide screen'7 are also shown. It can be seen from the
`figure that glucose oxidase immobilized on nonporous glass beads
`shows a sharper temperatureactivity profile than those of glucose
`oxidase in solution or immobilized on a nickel oxide screen.
`The decreased temperature sensitivity reported by Weetall and
`Hersh'? may also be attributed to external diffusion effects. When
`such effects are significant, the enzyme molecules are not all effici-
`ently used. As a result, denaturation due to increase in temperature
`
`Page 11 of 16
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`
`
`680
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`RAMACHANDRAN AND PERLMUTTER
`-- WUcow oaldar solution
`--- Immobll\z~d on NIO 1 R.1.
`IT
`-0- ImmoMlimd on non-porous gbrs
`In this work.
`
`loo -
`
`ZI 8 0 -
`c .- .-
`c
`0 60-
`s
`E .-
`P
`z
`
`40-
`
`20 -
`
`Fig. 6. Effect of temperature on the activity of immobilized glucose oxidase.
`
`Temroture , 'C
`
`TABLE I1
`Kinetic Constants for Immobilized Glucose Oxidase a t Various Temperatures
`(kEBt/kOX) x 103
`x 106
`k,.&
`(mol/g/min)
`(mol/liter)
`0.41 f 0.024
`1.6 f 0.43
`0.27 f 0.015
`2.3 f 0.36
`0.59 f 0.177
`5.9 f 2.47
`1.0 f 0.12
`0.11 f 0.003
`
`kcat/kred
`(mol/liter)
`0.051 f 0.0026
`0.036 f 0.0017
`0.080 f 0.0199
`0.006 f 0.0002
`
`~~
`
`"C
`15
`20
`25
`30
`
`will not affect the overall reaction rate since the latter is in any case
`mass transfer limited. One may therefore, in agreement with
`
`O l l i ~ , ~ ~ anticipate a flatter temperature-activity profile and an
`increased optimum temperature when diffusional restrictions are
`present. A similar increase in the sensitivity of the temperature-
`activity profile upon immobilization was also observed for glucose
`oxidase crosslinked on cellophane membranes16 and invertase co-
`valently coupled to porous glass.26
`Stability
`Two runs which were made ten weeks apart with lOmM glucose
`solution at 25°C gave the following values for V,,,
`(with 95%
`confidence interval) :
`Run no.
`1
`42
`
`V,,, x lo6 (mol/min g)
`0.59 f 0.036
`0.63f0.067
`
`Page 12 of 16
`
`
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`IMMOBILIZED GLUCOSE OXIDASE
`
`681
`
`It can be concluded that the immobilized enzyme lost no activity
`upon storage for nearly ten weeks at 4°C.
`The same batch of immobilized enzymes was used continuously
`for 60 hr with lOmM glucose at 25°C to obtain information on
`operational stability. At the end of each 15 hr, the oxygen level
`was varied inside the reactor to determine the kinetic constants
`KM and V,,,
`in eq. (4). The results, in Figure 7, show that K M
`does not substantially change from run to run, indicating that the
`three-dimensional structure of the enzyme was not altered due to
`fluid motion near the glass surface. It can be seen from Figure 8,
`however, that the immobilized enzyme lost 40% of its original activity
`after 60 hr. Since K M did not change upon continuous use for
`60 hr, the change in V,,, must be due to a change in ET, the con-
`centration of active enzyme. The loss in activity is due to de-
`naturation rather than physical leaching, for if physical leaching had
`been responsible, the enzyme would have lost activity on storage.
`When the deactivation data were fitted to a first order model, the
`magnitude of
`the deactivation constant (with 95% confidence
`interval) was found to be (7.6 f 3.09) X 10-3hr-1, corresponding to
`a half-life of 91.0 hr.
`
`Efects of Diferent Preparations
`Glucose oxidase was immobilized in two different batches to test
`whether both batches would give the same kinetic constants. Re-
`sults obtained for 6.5mM glucose at 25°C and pH=5.5 buffer are
`
`0
`
`15
`
`I
`
`Jo
`
`I
`45
`
`60
`
`Time, Hrs
`Fig. 7. Continuous operation of immobilized glucose oxidase, effect of K M .
`
`Page 13 of 16
`
`
`
`682
`
`RAMACHANDRAN AND PERLMUTTER
`
`Time, Hrs
`Fig. 8. Continuous operation of immobilized glucose oxidase, effect on V-=.
`
`given in Table 111. The K M values for both batches are the same to
`within their 95% confidence intervals, however, the VmaX for batch I
`is three times greater than that for batch 11. That K M did not
`change from batch to batch indicates that the binding mechanism
`for immobilization did not change. The difference in V,,,
`is due to
`different amounts of enzyme immobilized on the glass surface.
`
`TABLE I11
`Kinetic Constants for Different Immobilized Enzyme Preparations
`vmsx x 107
`(mol/min/g)
`
`K M X 106
`(mol/liter)
`
`Batch no.
`
`I
`I1
`
`5.2 f 2.87
`5.7 f 2.41
`
`5.3 f 1.04
`1.8 f 0.25
`
`Nomenclature
`total immobilized enzyme concentration, mol/g
`feed rate, cc/min
`average concentration of glucose, mol/liter
`ionic strength of buffer, mol/liter
`-1, k2 rate constants defined by eq (1)
`rate constant defined by eq. (2)
`rate constant for the dissociation of enzyme glucose complex, min-1
`rate constant for the reaction between oxygen and reduced form of
`enzyme, liter/mol/min
`
`Page 14 of 16
`
`
`
`IMMOBILIZED GLUCOSE OXIDASE
`
`683
`
`apparent bimolecular rate constant for the interaction of substrate
`and the oxidized form of enzyme, liter/mol/min
`Michaelis-Menten constant, mol/liter
`average oxygen concentration, mol/liter
`oxygen concentration at the inlet of the reactor, mol/liter
`saturated oxygen concentration, mol/liter
`recycle rate, cc/min
`substrate concentration a t the reactor inlet, mol/liter
`substrate concentration in the make-up feed, mol/liter
`substrate concentration at the outlet stream, mol/liter
`temperature, "C
`reaction rate, mol/min/g
`maximum velocity a t a fixed concentration of glucose and excess
`concentration of oxygen, mol/min/g
`catalyst weight, g
`conversion
`
`This research was supported by a grant from the NSF-RANN program.
`
`References
`1. A. K. Sharp, G. Kay, and M. D. Lilly, Biotechnol. Bioeng., 11, 363 (1969).
`2. L. Goldstein, M. Pecht, S. Blumberg, D. Atlas, and Y. Levin, Biochemistry,
`9, 2322 (1970).
`3. L. Goldstein, Y. Levin, and E. Katchalski, Biochemistry, 3, 1913 (1964).
`4. W. F. Line, A. Kwong, and H. H. Weetall, Biochim. Biophys. Acta, 242,
`194 (1971).
`5. H. H. Weetall and G. Baum, Biotechnol. Bioeng., 12, 399 (1970).
`6. P. J. Robinson, P. Dunnill, and M. D. Lilly, Biochim. Biophys. Acta, 242,
`659 (1971).
`7. Q. H. Gibson, B. E. P. Swoboda, and V. Massey, J . Biol. Chem., 239,3927
`(1964).
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`RAMACHANDRAN AND PERLMUTTER
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`Accepted for Publication January 23, 1976
`
`Page 16 of 16