Reactor-Separator Membrane Combining Immobilized Urease and an Anion Exchange Membrane W. J. Blaedel’ and T. R. Kisse12 Department of Chemistry, University of Wisconsin, Madison, Wis. 53706
The reactor-separator membrane was prepared by molding a urease gel layer directly onto a commercial anion exchange membrane. When this two-layer membrane was used as a barrier between donor urea and acceptor buffer solutions, product ammonium ion was enriched in the acceptor solution up to a hundredfold over donor ammonium ion levels during a thirty-minute reaction period. The rate of product ammonium ion buildup was linear with time and was found to be proportional to initial donor substrate concenlration over several orders of magnitude. A quantitative theoretical model of the transport behavior of this membrane was derived. The model predicted that under conditions of high enzyme concentratlon the overall reaction would be substrate diffusion-limited by the anion exchange layer. Experimental support for the model was obtained by comparing measurements of the urea diffusion coefficient in the reactor-separator membrane with the value obtained independently in the anion exchange membrane itself.
The application of immobilized enzymes in chemical analysis systems has greatly increased during the past decade. As analytical reagents, they possess excellent specificity, and their high stability and insolubility permit ready reuse in multiple analyses. Vieth and Venkatasubramanian have recently reviewed a number of immobilized enzyme methodologies ( I 1. In many of the present applications, the enzyme of interest is bound in or onto an inert support material such as a polymeric membrane or porous glass beads. The supports are often chosen merely on the basis of their physical characteristics rather than for any chemical advantage. That is, their main function is to provide a strong or non-deformable matrix for the attached enzyme which is easily prepared and which can be easily manipulated during usage. Such enzyme supports usually provide only for the reactive or transformation steps in a total analysis scheme. Generally, this is not enough and, where needed, separation and measurement capabilities must be added independently, especially if the total scheme deals with complex media such as waste waters or human fluids. One approach to the integration of several components into a single complete analytical device is to allow the enzyme support material itself to perform a separative function. Rather than being viewed only as an inert matrix, the support is chosen also because of its ability to separate the reaction components on the basis of charge, molecular size, or gas permeability. Barker has outlined a number of membrane systems in which an enzyme is immobilized onto supports of varying separative characteristics, and he has introduced the term “reactor-separator’’ to describe them (2).
Despite their analytical potential, very few experimental immobilized enzyme systems employing the reactor-sepaTo whom correspondence should be addressed.
* Present address, Eastman Kodak
Company, Rochester, N.Y.
14650 1602
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
rator concept have been described to date. Gregor has reported work on an enzyme-coupled hollow fiber reactor in which chymotrypsin was bonded to a cellulose acetate reverse osmosis membrane ( 3 ) .Separation of high molecular weight protein substrate from membrane-diffusable low molecular weight product was achieved when the reaction was allowed to proceed under an ultrafiltration pressure. Urease has been immobilized onto the surface of a gas-permeable ammonia probe to prepare a novel urea electrode that is insensitive to those cations in human serum that would normally interfere with a glass electrode sensor ( 4 ) . The use of ion exchange membranes as logical extensions of the reactor-separator concept has been limited, despite the demonstration of their combined separative and concentrative powers ( 5 , 6). Several workers have immobilized enzymes upon ion exchange supports (7, 8 ) , but the charged groups were used chiefly to provide reactive enzyme binding sites after chemical conversion. Broun has employed an ion exchange reactor-separator system using a multilayer sandwich consisting of two charged dialysis membranes enclosing a gel containing hexokinase and glucose phosphatase (9). The principal objective of the work was to model the active transport of substrate glucose across the multilayer. In our work, the behavior of a reactor-separator for urea is described that combines an immobilized urease gel and a commercial anion exchange membrane. A quantitative theoretical model of the two-layer membrane system is presented, and the model is tested experimentally using several different anion exchange membranes. The analytical utility of the reactor-separator membrane is also discussed.
THEORY Description of the General Reactor-Separator Membrane System. In order to characterize the experimental behavior of the reactor-separator membrane, a theoretical model of the steady state membrane transport properties was derived. A schematic of the general reactorseparator system used in the model is shown in Figure 1A. The membrane is shown as a barrier between a donor and an acceptor solution, each of which may contain substrate S and product P. In the most common configuration, the anion exchange layer of the two-layer membrane faces the donor solution (Solution 1) which initially contains only substrate. Barred quantities represent membrane concentrations or other characteristics, while unbarred quantities indicate solution concentrations or other characteristics. Subscripts 1 and 2 represent concentrations in donor or acceptor solutions. The additional subscript rn indicates a membrane-solution interfacial concentration, while i indicates an internal membrane-membrane interface. Concentrations in the anion exchange or enzyme layers are further characterized by subscripts a and e, respectively. Layer thicknesses are shown as a (anion exchange membrane layer) or X (enzyme membrane layer). At steady state in the general system, there exist measurable fluxes of substrate and product into and out of both the donor and acceptor solutions. Although equilibrium
can be postulated a t all interfaces, there will be undefined gradients of both S and P in the anion exchange and enzyme layers. These gradients, together with the numerous unmeasurable interfacial concentrations make a rigorous solution of the transport behavior difficult and unsuitable for experimental confirmation. In order to obtain a more workable solution for the transport model, a number of simplifying assumptions and boundary conditions were applied to the general membrane system. These constraints were based in part upon known characteristics of the individual membrane components, and in part upon exploratory work with early prototype reactor-separator membrane systems. The Simplified Reactor-Separator Membrane System. The following assumptions and approximations were used to describe a simplified system whose transport behavior could be quantitatively described in terms of fundamental membrane and solution properties. 1) The surface film concentrations Slm,Szm,PI,,and P e m are equal to the bulk concentrations SI, SZ, PI,and Pz. In all the experiments performed, the stirring rates were made high enough so that the measured rates of product buildup were independent of stirring rate. This indicated negligible liquid film resistance in both donor and acceptor solutions. 2) Michaelis-Menten kinetics are followed within the enzyme membrane under substrate-limited conditions.
SI
S I 'I,,,~
PI
Plm Plrn,a
-
-
-
Si,a Si,e
-
-
SOLUTION 2 (ACCEPTOR)
ENZYME MEMBRANE
ANION MEMBRANE
SOLUTION I (DONOR)
Pi,a ?,e
~ 2 m , o~ 2 r n
'2
P2m,o p2rn
p2
-
-
X
d
c
(e) SIMPLIFIEDSYSTEM ENZYME
Figure 1. Schematic of the reactor-separator membrane system at steady state
to begin with, PI= plm,a = pi,, = 0. The approximation was supported by the relatively low levels of product observed in the donor solution after each run. Although some ammonium ion leakage does actually occur, the amount is small over the time of each experiment. With these assumptions and approximations, the general vs L' = -== (1) membrane system of Figure 1A can be reduced to the simK plified system shown in Figure 1B. Here no product exists Here 0 is the local enzyme reaction rate, P is the maximum except in the enzyme membrane or in the acceptor solurate constant, and K is the Michaelis constant. Direct sup- tion, and the solution interfacial concentrations have been port for Michaelis-Menten kinetics was obtained using en- replaced by the bulk solution values. Under these condizyme membrane disks in a substrate solution (10). Because tions, it is possible to obtain a workable mathematical deof the high membrane enzyme concentrations, and because scription of the two-layer membrane system that yields exthe anion exchange membrane resistance to diffusion plicitly the rate of product buildup in the acceptor solution would limit the amount of substrate reaching the enzyme in terms of the fundamental system parameters. layer, substrate-limited conditions would exist in the enMathematical Description of the Simplified Model zyme membrane, perhaps even a t very high substrate conof the Reactor-Separator Membrane. The enzyme comcentrations in the donor solution. Under such conditions, ponent of the reactor-separator membrane is described as there would be a large gradient of substrate in the mema special case of the two-solution immobilized enzyme brane layer and Slm,a >> Si,a; membrane system outlined in a previous publication (12). 3) The donor substrate level (SI)is effectively constant The anion exchange membrane is treated as an additional over the short times involved in the experiments. This asfilm diffusional resistance on one side of the enzyme memsumption was supported by direct experimental measurebrane. Within the enzyme membrane, a material balance ment, and by the relatively small amount of product buildon the diffusional flux and on the enzyme reaction yields up observed in all experiments. solvable differential equations from which the steady state 4) The substrate (urea) flux across the anion exchange fluxes of substrate and product are derived. Unmeasurable layer follows the common linear nonelectrolyte flux relasubstrate and product surface concentrations are eliminattionship (11): ed using the established boundary constraints so that, in the final solution, the measurable substrate and product solution concentrations can be related to steady state reaction time, enzyme kinetic constants, and diffusional transIn this equation, Ds,, is the diffusion coefficient of the subport characteristics of the membranes. strate in the anion exchange membrane. Because of the When substrate S within the enzyme membrane is limithigh substrate concentration gradient through the anion ing, the material balances within the enzyme layer yield exchange membrane layer (outlined in the second approxisolvable differential equations a t steady state (13): mation above), the term is small, and the flux Equation (4) 2 becomes:
si,e.
si,a
-
In Equation 3, is defined as the partition coefficient of substrate between the donor solution and the anion exchange membrane. 5 ) The anion exchange membrane is assumed to be perfectly permselective. In this case, no leakage of charged ammonium cation occurs through the anion membrane, Le., J P ~=, 0.~ As a result, if the donor solution is product-free
-
s=
S i , e sinh z(2 -
s;) + S2m,esinh
sinh 2
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
(6)
1603
La is acceptor solution volume and A is the reactor-separaIn these equations, n is the stoichiometric coefficient of the enzyme reaction, and &,e are the diffusion coefficients of the substrate and product in the enzyme layer, and P are local substrate and product concentrations within this layer, and f is a distance through the enzyme layer, varying from zero a t the anion exchange layer interface to a t the acceptor solution boundary. is the thickness of the enzyme membrane layer. Enzyme kinetic parameters are found in the quantity 8 , defined as
s
x
x
IT
?=-
\
(8)
KDs, e T o find the fluxes S S ,and ~ Jp,e within the enzyme layer, the gradients of 3 and P formed by differentiation of Equations 6 and 7 with respect to 2 can be evaluated a t the enzyme membrane interfaces:
tor membrane area. In a similar fashion, Equations 11, 12, 13, and the assumption 5 of zero product flux into the donor solution can be used to derive the product flux into the acceptor solution: JP2m,e =
dP L Z 2dt
A
=
( n z scosh ,,6s, ,Linh aX aX
)s2
+
Given the assumption of constant SIin the donor solution, Equation 15 may be solved to give the variation in acceptor substrate concentration (Sz) with time:
In this equation, is the acceptor substrate concentration a t the initiation of steady state and the constants are given by:
By combination of Equations 16 and 17, one can find the product buildup rate in the acceptor solution, and thereby obtain the final expression for P:! in terms of fundamental constants and steady state time:
(11)
The existence of interfacial equilibrium a t steady state permits expression of the nonmeasurable qembrane concentrations in terms of the measurable solution concentrations:
From Equation 3 and the fact that no reaction of S occurs in the anion exchange layer,
Equation 14 may be used along with Equations 9, 10, and 13 to eliminate the unmeasurable and and to obtain the substrate flux into the acceptor solution in terms of the measurable SIand S:! concentrations:
si,e
cosh 1604
aX
)SZ
(15)
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
Here P:!orepresents product concentration in the acceptor solution a t the initiation of steady state time. The relationship between acceptor product concentration (P2) and steady state time in Equation 20 is complex, but if the conditions are such that the second term dominates the behavior, the acceptor P:! should build up linearly with time. The rate of buildup of P:! should also be proportional to initial donor concentration SI, which gives promise of analytical utility to the reactor-separator system. Simulation of the Simplified Reactor-Separator Membrane Model. In order to delineate the behavior of the reactor-separator as given by Equation 20, a program was written for its simulation on a Tektronix 31 programmable calculator (Tektronix Corporation, Beaverton, Ore.). The relation between Pz and steady state time was obtained as a function of the variables 8 and SI, all other parameters being held constant. Estimates for 6 and the other parameters were taken from independent experimental measurements whenever feasible. Exact values for several of the parameters were not available, but order of magnitude estimates permitted the analysis of the limiting behavior predicted by the model. Figure 2 shows that the simulation of Equation 20 produced linear increases in acceptor product with time in all cases. When enzyme concentration was relatively high (as reflected in a high 8 value), the P2 buildup became constant for a given substrate level and independent of 8 . The data output of the simulation revealed that with high u, the l/sinh functionality in the third term of Equation 20
I
/
J
7
m/
I
A
SLOPES,
1
MIN-~
-1 520
31 3
d
15-
a
a 4 10-
2
/
I
/
nN TIME AFTER STEADY STATE (MIN)
5-
Figure 2. Simulation of P2 vs. time according to Equation 20 A e u r v e s , a 2 250; Bcurves, a = 50; Ceurves, B I5. For each B value chosen, the product curves for substrate concentrations of 0.001, 0.0003, and 0.0001M are shown. Other parameters are assumed constant, as described in text
sI
became vanishingly small. Since S20 is also small if enzyme reaction is efficient, the second term of the equation became dominant regardless of the value of the exponent. Under these high 6 conditions, the reaction rate is effectively diffusion-limited by the presence of the anion exchange membrane, As enzyme concentration decreased, the model predicted that the acceptor product buildup became a function of a. As 6 (or enzyme activity) decreased to very low levels, the amount of Pz produced became negligible, as would logically be expected. The simulated data output revealed that the exponential term of Equation 20 approached unity as d was decreased, but the third term multiplier containing S20 and SI became quite significant. As a net reslilt, the third term began t o cancel the value of the linear second term. Effectively, the system would be enzyme-limited under the low u conditions. The plots of P2 buildup rate (slopes of Figure 2) against donor SIconcentration are shown in Figure 3. Linear correlations of the buildup rates with donor concentration are seen in each case, indicating promise for the reactor-separator as an analytical device. In the condition of high enzyme activity, the slope of this plot becomes constant and independent of the d value. The magnitude of the slope is then determined by the multiplier of S,t in the second term of Equation 20. This high enzyme activity case is analytically desirable since day-to-day variations in enzyme activity would have little effect on a calibration curve such as Figure 3A. As enzyme activity decreased into the region of enzyme-limited conditions, the slope of the rate vs. SI plots was no longer constant but varied with d (approximately according to the function (1-(l/cosh a x ) ) .For these conditions, the analytical usefulness of the reactor-separator configuration would be limited by the necessity of frequent calibration checks.
EXPERIMENTAL The experimental work involved testing of the reactor-separator membrane in a transport cell configuration. Comparisons with the behavior predicted in the model were then sought. Apparatus. Ammonium ion product measurements were made with the use of Beckman Instruments 39047 and 39137 cation electrodes, a Beckman 39167 p H glass microelectrode, and a differential amplifier constructed as outlined by Brand and Rechnitz (14). T h e amplifier output was monitored with a Leeds and Northrup Model 7415 p H meter in the millivolt mode or with a strip chart recorder (Omniscribe No. 5141-106, Houston Instruments, Bellaire, Texas). All transport measurements on the reactor-separator were performed with the Lucite cell pictured in Figure 4. In this cell, the membrane serves as a barrier between the internal acceptor solution and an external donor solution (usually placed in a glass bea-
C
- ,2 . . 4
1
. 1
6
0.0003
4
1
J
8
10
(~~104)
Flgure 3. Simulation of P2 buildup rate vs. SI according to the model Points show; are slopes of curves in Figure 2 piotted vs. the donor concentration (SI). For t h e point at S, = 0.0007M,the curve is not shown in Figure 2 in order to preserve clarity
-E
fs?3-G -H
Figure 4. Transport cell used in reactor-separator membrane characterization Cylindrical Lucite cell body (cutaway view). (6)Acceptor volume cavity (0.5 to 2.0 ml). (C)Stainless steel k e y pegs. (D) Teflon washers. (E) Reactor(A)
separator membrane, Enzyme layer faces internal acceptor solution. (F) Tefion membrane holder. (G) Lucite cell cap. (H) Lucite paddle which is fastened to cell cap for increased turbulence at membrane surface ker). The acceptor sensing electrodes are positioned with the aid of a Lucite holder arm so that they sense the small volume (0.5-2.0 ml) held in B. The assembled cell can then be dipped into the beaker containing the external donor situation. Stirring and turbulence were achieved on both sides of the membrane (inside and outside) by oscillating the cell in a back and forth motion with a motor (Model GT21 with GT21 Controller, G. K. Heller Co., Bellerose, N.Y.). All work was done in a constant temperature bath (Model MR 3210A-1, Blue M Electric Company, Blue Island, Ill.) at 25.0 f 0.05 "C. Reagents. A powdered urease (URC 8C, 73 Units/mg, Worthington Biochemical Corp., Freehold, N.J.) was used for preparation of the enzyme layer. Other enzyme membrane reagents were bovine serum albumin (A-4378, crystallized and lyophilized, Sigma Chemicals, St. Louis, Mo.) and glutaraldehyde (25% aq. solution, Aldrich Chemicals, Milwaukee, Wis.). Tris(hydroxymethy1)aminomethane was obtained from either Aldrich Chemicals (Tris U1trapure) or Sigma Chemicals (Trizma base). All other chemicals were reagent grade. Once distilled water was redistilled from alkaline permanganate and then from dilute H2S04 before use. Anion exchange membranes tested were the AMF 104 E B
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9. AUGUST 1975
1605
Table I. Ammonium Ion Enrichment by the AMF 104-Glutaraldehyde-BSA-Urease Membrane Acccptor ammonium ion buildup ( d P l d t P h f / r n i n ) a
Ammonium ion concentration, a t 30 min (u.U)*
Donor w e 3 , Experiment
U
Uncorrected
Blank corrected
Acceptor P2
Donor P I
Ratio P Z I P ,
*
0.041 0.002 ... 3 .O 1.5 2 0.051 + 0.002 0.01 3.5 1 .o 3.5 0.001 0.65 0.69 i 0.006 9 .o 2.3 3.9 0.01 8.32 0.08 8.3 320 62 5.2 0.1 52.7 + 1.4 52.6 1,064 110 9.7 B (Buffer) 0.15 i 0.005 ... 5.9 ... 0.10 0.002 2.8 3.2 1.2 0.07 i 0.002 1.7 1.4 1.2 0.0001 0.13 i 0.001 0.06 3.7 1.o 3.7 0.001 0.59 0.002 0.52 18.2 2.3 7.9 0.54 i 0.007 0.47 13.6 0.66 0.009 18.6 0.59 0.01 4.9 0.01 107 3.1 35 4.8 5.2 i 0.09 103 5.1 a V, = 1.0 ml, Vd = 50 ml, Buffer = Tris, O.O5M, p H 8.0. Uncorrected column data represent linear slopes and standard deviation of the slopes, For Experiment B, buffer values are triplicate measurements run at varying times during the trials, but in the order shown. All other replicates are in random order. The slope of the third buffer run was used to make the blank correction. since it was made closest in time to the urea measurements. (. . .) indicates value not measured. A
(Buffer)
0.0001
*
*
*
*
(American Machine and Foundry Corp., Springdale, Conn.) and the RAI P-1025 (RAI Research Corporation, Hauppauge, L.I., N.Y.). The AMF 104 E B is a graft membrane having polystyrene quaternary amine groups attached to a polyethylene backbone. I t has an ion exchange capacity of 1.5 mequiv per dry gram and a wet thickness of 0.006 inch. The RAI P-1025 contains methyl pyridinium groups grafted to a polytetrafluoroethylene matrix. This membrane has a capacity of 1.0 mequiv per dry gram and a wet thickness of 0.0011 inch. Membrane Preparation. The reactor-separator membranes were prepared by casting the urease gel directly onto the surface of the desired anion exchange membrane. In a typical formulation, an enzyme solution containing 1-5 mg/ml of urease and 6% by weight BSA was made up in a 0.05M maleic acid-NaOH buffer a t pH 6.5. An aliquot of a dilute stock glutaraldehyde solution was added to bring the final volume to 2-4 ml, with a 0.5 to 0.75% V/V glutaraldehyde concentration. After thorough mixing, this gel solution was poured immediately onto one surface of a 2-inch square piece of the anion exchange membrane that was held flat against a horizontal glass plate by a circular aluminum mold. The metal mold defined the area of gel coverage and prevented the gel from coating the reverse surface of the anion exchanger. The anion exchanger had been pre-washed first in triply distilled water and then in 0.05M maleate buffer. To prevent marked dimensional changes upon addition of the enzyme gel, the anion exchange membrane was left wet with buffer solution before laying it on the glass plate. The gel solution was then allowed to evaporate for 8-10 hr, during which time it became dry and polymerization occurred. The air-dried reactor-separator membrane could be easily peeled away from the glass plate. Dry thicknesses ranged from 0.003 to 0.015 inch, depending upon the type of anion exchange membrane and volume of enzyme gel employed. The membranes were stored dry a t 5 OC and then rinsed for several hours in 0.05M Tris-sulfate buffer, p H 8.0, before use. Adhesion of the enzyme gel layer to the anion membrane surface during solution testing was excellent using the RAI P-1025 as the base. However, separation of the two layers was observed for a few samples of the AMF 104 E B composite since this anion exchanger had less tendency to swell than did the enzyme gel layer. Measurements of Transport Behavior. The electrodes were calibrated for ammonium ion response before a series of tests by measurement of known standard ((NH4)$304 solutions in 0.05M Tris-SOd buffer, p H 8.0) using 1- to 2-ml volumes in the transport cell itself. For the transport measurements, a disk (0.75-inch diameter) of reactor-separator membrane was punched out of the stock sheet, rinsed in several portions of the Tris buffer, and placed in the cell. The cell was then positioned in the stirring-bath arrangement and Tris buffer added to both donor and acceptor solutions. Initial acceptor concentration measurments were taken on this buffer-only system to ascertain if any blank increase existed. After this was done, the buffer was removed and fresh Tris added again to donor and acceptor. To begin a transport run, an aliquot of a buffered concentrated urea solution was pipetted into the donor 1606
ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
... ...
...
... ...
...
... ... ...
solution and acceptor ammonium ion buildup measured over a 15to 30-minute reaction period. After this reaction period, the donor ammonium ion level (and occasionally the acceptor pH) was measured. Donor and acceptor solutions were removed by aspiration, and the membrane was rinsed by adding several portions of fresh Tris buffer to both the donor and acceptor compartments. Measurements of the ammonium concentration in the acceptor compartment during the rinsing indicated when the original blank value had been reached. At this time, fresh buffer was added to both acceptor and donor sides and the next urea run started. After a series of runs, the assembled cell was stored a t 4 "C with Tris buffer inside until needed. Data Analysis. The raw data output from the transport measurements was a series of millivolt-time chart recordings. These chart readings were inputted to a Tektronix 31 calculator program with the aid of an X-Y positional digitizer (Model 224-116 Digitizer, Numonics Corp., North Wales, Pa.) interfaced to the calculator. The program included the application of activity coefficient corrections and electrode calibration corrections to the raw digitized data to convert the millivolt chart readings into ammonium ion concentrations. Linear regression subroutines (Tektronix Statistics Program No. 4-1) were used to give the rate of ammonium ion concentration buildup in the acceptor solution, and also to give the slopes of plots of the rate of ammonium ion concentration buildup vs. urea concentration.
RESULTS AND DISCUSSION Typical data obtained from experiments using the AMF 104 and RAI P-1025 anion membrane-based reactor-separators are given in Tables I and 11, respectively. For the AMF 104 reactor-separator (Table I), linear rates of acceptor ammonium ion buildup were obtained after a 5 - to 10minute lag period (Experiments A and B represent membrane disks from separate syntheses). A residual acceptor ammonium rise was also noted when Tris buffer alone was used as the donor solution. This rise was attributed to incomplete rinseout of acceptor product or to residual cation presence stemming from membrane synthesis. The blank was never completely eliminated but settled to a nearly constant level with increased membrane use. In a given apparatus, and a t controlled volumes and stirring rate, a measure of the quality of the reactor-separator is given by the P2/P1 ratio a t the end of the reaction period. This ratio builds to significant values with increasing donor urea concentration, indicating that the anion exchange layer is effectively trapping the charged ammonium ion reaction product within the acceptor solution. The accuracy of the P*/P1 ratio a t low donor substrate levels was limited by the accuracy of measurements of the small amount of product
~~
Table 11. Ammonium Ion Enrichment by the RAI P-1025-Glutaraldehyde-BSA-UreaseMembrane rimmonium ion concentration, at 30 min (UL.(l)*
Acceptor ammonium ion buildup ( d p l d f u , M / m h ) a Donor urea m hf
(Buffer)
Uncorrected
Blank corrected
Acceptor P2
Donor P i
Ratio P 2 1 P I
...
0.58 i 0.02 21 4.5 4.7 ... 19 2.8 6.8 0.43 i 0.01 *.. 10 ... 0.31 i 0.01 0.01 0.52 i 0.01 0.15 21 4.9 4.3 0.02 0.84 i 0.01 0.47 30 4 .O 7.5 0.04 1.28 i 0.01 0.91 45 3.3 13.5 1.82 74 7.8 9.3 0.08 2.19 i 0.01 0.10 2.82 i 0.02 2.45 90 4.8 19 6 .O 15.5 2.38 93 2.75 i 0.02 3.4 80 7.7 270 0.40 8.03 i 0.06 790 11.0 72 22.1 0.80 22.5 i 0.40 870 5.6 155 28.0 1.o 28.3 i 0.40 12.9 200 81.6 2,570 3 .O 82.0 i 1.0 V d = 50 ml, V , = 1.0 ml. Buffer = Tris, 0.05.W, p H 8.0. Cncorrected column data represent linear slopes and standard deviations of the slopes. Blank value used for correction is simple average of latter two buffer values, which were taken during the experimental urea measurements. (, , ,) indicates concentration was not measured.
...
found in both solutions. However, the ratios do show that product in the acceptor solution is increasing very much faster than product in the donor solution, especially a t high urea concentrations. The data obtained from a representative experiment with the RAI P-1025 based membrane are given in Table 11. This reactor-separator membrane exhibited increased efficiency over the AMF 104-based system, apparent from the large acceptor ammonium ion levels that were obtained from only millimolar donor urea levels. The rates of ammonium ion buildup in the acceptor solutions were again linear with time in all cases. T h e lag time before steady state was reached was also reduced to 2-5 minutes with this reactor-separator. A buffer blank was again noticed and was attributed to the same sources as before. Replicate measurements on the same urea solutions a t different times in an experiment revealed a 4-6% repeatability in the measurement of any particular acceptor ammonium ion buildup rate. The measured product ratio P*/Pl after the 30minute reaction period again indicated that 100-fold enrichments of ammonium ion occurred in the acceptor compartment. Because these enrichments were obtained from much lower donor urea levels than used in the AMF 104 reactor-separator, the RAI 1025 system was deemed to be a much more efficient reactor-separator. Calibration plots of blank-corrected acceptor product buildup rates against donor urea concentration for the two reactor-separator membranes are shown in Figure 5 . Linear correlation within a 1-2% error range was observed for these and other similar calibration plots. T h e non-coincidence of the calibration plots reflects the difference in efficiencies of the two reactor-separator membranes. The calibration plots all exhibited log-log slopes of unity within an error range of 1-296, indicating a strictly linear dependence of ammonium ion buildup rate upon donor urea concentration. Numerous measurements were repeated over narrower, one-decade ranges of donor urea concentration, to confirm the accuracy and linearity of the calibration plots, and no discrepancies were found. The theoretical model of the reactor-separator indicated a linear dependence of acceptor ammonium ion buildup rate upon the donor urea concentration for both diffusionlimited and enzyme-limited cases. Experimental data obtained over periods of several weeks with the same membrane revealed little change in slope of the calibration plots, whereas enzyme activity measured on separate pieces of enzyme gel alone showed definite loss of activity over the
Y
1
1
000001
I
0000l
I
0001 DONOR UREA (M1
001
I
01
Figure 5. Rates of acceptor ammonium ion buildup a s a function of donor urea concentration All data are blank corrected values obtained from the experiments described in Tables I and il. When multiple determinations of one donor urea concentration were made, data were averaged to a single value. Curve A represents the RAi P- 1025-glutaraldehyde-BSA-urease membrane; curves B and C represent two separate syntheses of the AMF 104-glutaraldehyde-BSA-urease membrane
same time period, indicating that diffusion-limited transport occurred in the reactor-separator membrane. An experiment designed to check this hypothesis was performed by preparing several RAI P-1025 reactor-separator membranes having different added enzyme activities but otherwise identical formulations. The amount of enzyme activity remaining in the membranes after synthesis was checked by monitoring separate disks of the enzyme gel according to a previously described technique (12). Linear calibration plots obtained from the reactor-separator membranes are shown in Figure 6. The slopes obtained from the two enzyme concentrations used in the experiment did not differ within the 20% membrane-to-membrane error level common to all studies. In addition, the theoretical model predicted changes in slope varying from 20 to 50% a t these two levels of enzyme activity, a larger variation than was experimentally obtained. Difficulty was encountered in testing a wider range of added membrane enzyme activity because of protein precipitation a t higher loadings or analytical inaccuracies a t lower enzyme levels. Over this limited range, a range of enzyme activity a t which nearly all experiments were performed, the data seemed to support the diffusionlimited assumption. Experimental support for the simplified theoretical ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
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Table 111. Comparison of Urea Diffusion Coefficients Calculated from RAI P-1025 Reactor-Separator Experiments and from Urea Flux Measurements in the Anion Exchange Membrane Calculated
Esperimenta
1 2 3 4
5 6 Flgure 6. Effect of added enzyme o n the rate of acceptor ammonium ion buildup The membrane employed was the RAI P-1025-glutaraldehyde-BSA-urease reactor-separator, with 5.0 mg/ml ( 0 )or 2.0 mg/ml (0)urease added to the synthesis formulation. Linear slopes are 0.0173and 0.0144 min-', respectively
model of the reactor-separator membrane was sought by calculating a diffusion coefficient for urea within the anion exchange layer from reactor-separator data, and checking this value against a diffusion coefficient obtained through independent flux measurements on the anion exchange membrane alone. The reactor-separator value was derived from Equation 20 by assuming diffusion limitation, whereby the slope of the rate of acceptor product vs. substrate plot would yield the constant given in the second term of the equation (nDs,,6s,BA/dL2).The urea diffusion coefficient could then easily be obtained from this slope. Table I11 presents the calculated values of the diffusion coefficient from experiments with the RAI P-1025 based reactorseparator membranes and the value obtained from a twosolution urea flux study on the RAI P-1025 anion exchange membrane alone. Agreement was excellent within the error range of the experiments on the RAI P-1025 membrane. Agreement of the urea diffusion coefficients was not so good for the AMF 104 based membrane (3.3 X cm2/sec from the model, and 7.9 X 10-8 cm2/sec from the anion exchange membrane measurements), but the low efficiency of the AMF 104 reactor-separator limited the comparison. Nonetheless, both of these comparisons indicated that the limiting factor in the reactor-separator performance was the substrate diffusion through the anion exchange layer. The comparisons also suggested that the theoretical model adequately represented the reactor-separator membrane behavior a t high-enzyme conditions. I t is particularly noteworthy that the rate of product buildup remains linearly dependent upon the donor urea concentration up to a t least 0.1M (Table I and Figure 51, which is much higher than the value observed for the homogeneous reactions, where K , is 0.001-0.01M. This is in agreement with the assumption (No. 2) stated earlier and may prove to be analytically useful for the quantitation of urea a t very high concentrations. Other workers have also noted such linearity of response to high substrate concentrations in immobilized enzyme systems ( 1 5 ) .
CONCLUSIONS The work described in this paper indicates that the simplified theoretical model satisfactorily describes the experi-
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ANALYTICAL CHEMISTRY, VOL. 47, NO. 9, AUGUST 1975
Slope of rate YS. substrate plot (nifii-l)b
0.026 0.027 0.0274 0.0289 0.0173
+ 0.001 = 0.001
0.0006 0.0007 i. 0.0004 0.0144 i 0.0003 i i
DS,a, cm2 / s e c x 107,
2.9 3 .O 3 .O 3.1 3.2 2.7
Mean and'Standard Deviation for DS,= 3.0 i 0.2 calculated from the model Es.afrom anion membrane flux experiment 2.8 a Each experiment performed with a different reactor-separator membrane. Standard deviation of slopes is given. Calculated according t o second term of Equation 20. L Z 1.0 ml; d = 0.00254 cm; A = 1.94 cmZ except in 5 and 6 where A = 1.13 cmz; Js., = 1.0.
mental behavior of a reactor-separator membrane. Analytical promise is indicated by the linear dependence of product ammonium ion buildup in the acceptor solution upon the substrate urea concentration in the donor solution. T o realize the promise, analytical devices should be constructed with minimal acceptor volumes, so as to minimize response times. A possible configuration might be to wrap an ion selective electrode with a reactor-separator membrane. Another possible configuration might be a tubular anion exchanger with enzyme immobilized on the internal surface, and with a product sensor located downstream.
LITERATURE CITED (1) W. R. Vieth and K. Venkatasubramanian. Chern Tech., 7, 434 (1974). (2)S.A. Barker and R. F. Burns, Chern. lnd. (London), 16,801 (1973). (3)H. P. Gregor and P. W. Rauf, Report of the 2nd NSF Enzyme Grantees Conf.. Purdue University, Lafayette, Ind., 1974. (4)T. Anfailt, A. Granelli, and D. Jagner, Anal. Lett., 6,969 (1973). (5)W. J. Blaedel and T. J. Haupert, Anal. Chem., 38, 1305 (1966). (6)W. J. Blaedel and T. R. Kissel, Anal. Chem., 44, 2109 (1972). (7)L. Goidstein, Biochem. Biopbys. Acta, 315, 1 (1973). (8)G. P. Royer and G. M. Green, Abstracts, 167th National Meeting, American Chemical Society, Los Angeles, Calif., April 1974. (9)G. Broun, D. Thomas, and E. Selegny, J. Membr. Biol., 8, 313 (1972). (10)T. Kissel, Ph.D. Thesis, University of Wisconsin, 1974. (11) N. Lakshminarayanaiah, "Transport Phenomena in Membranes", Academic Press, New York, 1969. (12)W. J. Blaedel, T. R. Kissel, and R. C. Boguslaski, Anal. Chern., 44, 2030 ( 1972). (13)R. Goldman, 0.Kedem, and E. Katchalski, Biochern., 7, 4518 (1968). (14)M. J. D. Brand and G. A. Rechnitz. Anal. Chem., 42, 616 (1970). (15)L. D. Mell and J. T. Maloy, Anal. Chem., 47, 299 (1975).
RECEIVEDfor review March 10, 1975. Accepted May 8, 1975. During 1972-73, T.R.K. was the holder of an American Chemical Society Analytical Division Fellowship, sponsored by Perkin-Elmer Corporation. T.R.K. also gratefully acknowledges reception of a Wisconsin Alumni Foundation Fellowship during 1973-74. This work was supported in part by grants from National Science Foundation (No. MPS73-04991-A01), and from Ames Research Laboratory, Division of Miles Laboratories.
