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Diffusion-reaction of urea through multimembrane containing urease — Effects of microenvironments around urease and asymmetry of the membrane
Journal of Membrane Science, 54 (1990) 145-162 Elsevier Science Publishers B.V., Amsterdam
145
Diffusion-reaction of urea through multimembrane containing urease - Effects of microenvironments around urease and asymmetry of the membrane Masakatsu Yonese*, Hideki Murabayashi and Hiroshi Kishimoto Faculty of Pharmaceutical Sciences, Nagoya City University, Tanabe-dori, Mizuhoku Nagoya, 467 (Japan) (Received June 19,1989; accepted in revised form June 4,199O)
Abstract Diffusion-reactions through enzyme membranes were studied by using a multimembrane, consisting of an enzyme layer sandwiched between films. The multimembrane was shown to possess the following characteristics: (1) the microenvironments around the enzyme can be altered arbitrarily by adding polymers etc., and (2 ) the asymmetries of the multimembranes can be controlled easily by using various films. Diffusion-reactions of urea through symmetric and asymmetric multimembranes having a urease layer were studied by measuring total fluxes Jz and flux ratios - Jb/Jz of one of the products (NH: ion) into a donor and an acceptor compartment. By adding sodium alginate NaAlg to the urease layer, the pH showing the maximum Jf shifted towards the alkaline pH region by 0.6 pH unit, and the maximum JF increased. From the value of the pH shift, the electrostatic potential yl” around the active site of the urease was calculated to be - 0.0343 V. The values of Jk/JF through the symmetric multimembrane were in the range 1.2-1.7, and those for the asymmetric multimembrane were in the range 0.2-0.3. In the diffusion-reaction through the latter membrane, carbamate anions were found to play an important role. Diffusionreaction through the multimembranes was analyzed by assuming that the reactions in the enzyme layer obey a first order reaction.
Introduction Basic studies of immobilized enzyme membranes were developed by Katchalski and co-workers, who pointed out their significance as a model of enzymes in biomembranes [ 1,2]. Recently, immobilized enzyme membranes have been studied, not only with respect to the elucidation of diffusion-reaction of substrates due to enzymes in biomembranes, but also as to their application in sensors such as enzyme electrodes [ 31. Effects of asymmetries of the immobilized enzyme membranes and systematic arrangements of multienzymes on the diffusion-reaction have led to new functional membranes which one cannot *To whom correspondence should be addressed.
0376-7388/90/$03.50
0 1990 -
Elsevier Science Publishers B.V.
146
expect to achieve with homogeneous membranes containing an enzyme [4-71. However, such asymmetric membranes containing enzymes are difficult to prepare and their reproducibilities are not guaranteed. To elucidate the effects of microenvironments around the immobilized enzymes and of the asymmetry of the membranes on the diffusion-reaction, a multimembrane consisting of an enzyme layer sandwiched between supporting films: Solution
II film 11 enzyme
layer 1film 2 1solution
II
is very convenient to basic studies of the diffusion-reaction. The multimembrane has the following characteristics: (1) the microenvironments around the enzyme can be altered arbitrarily by adding polymers or liposomes etc., and (2 ) by using various supporting films, the asymmetries of the multimembrane can be easily controlled. In this research, the diffusion-reactions of urea through symmetric and asymmetric multimembranes having a urease layer were studied. Furthermore, an alginate ( Alg) , which is type of polysaccharide, was used as a polymer additive, and the effects of such addition on the diffusion-reaction were studied. Alginate is a linear block copolymer composed of /3-D-mannuronate and a-L-guluronate, and is gelled by adding divalent metal ions, such as Ca ions [8,9]. In our previous paper [lo], the effects of the sol-gel transition on the charge density of Alg were studied by the use of the membrane potential method. Alginate gels have been examined with respect to their applications as matrices for immobilized enzymes and organelles [ 111, and in drug delivery systems [12]. The effects of the sol-gel transition of Alg in the enzyme layer on the diffusion-reaction are very important. However, in this study, the effects could not be evaluated because CO;- ions produced by the hydrolysis of urea form a precipitate of CaCO, in the presence of Ca ion added for the gellation of Alg. Experimental
Materials Urease was of commercial origin (Cooper Biochemical, 82 U-mg-‘, Lot. No. G4P6952) extracted from soy beans, and was used without any purification. Purified sodium alginate (NaAlg) used as an additive was prepared from commercial NaAlg (Tokyo Kasei Kogyo Co., Ltd.) by dialyzing against distilled water and by filtering to remove insoluble substances, as described in previous work [ 9,101. The purified NaAlg was stored refrigerated after freeze drying. The weight average molar mass of NaAlg was determined to be M, = 1.32 x lo5 g-mol-’ by using an LS-8 light scattering photometer (Toy0 Soda Manufacturing Co., Ltd., Japan). The guluronate fraction FG and the consecutive guluronate one FGG were determined as being 0.37 and 0.28 by circular dichroism [ 131 and proton-NMR [ 141 methods. Urea, ammonium chloride and all other reagents were of special grade (Katayama Kogyo Co., Ltd.). Distilled and
147
deionized water was used for preparation of aqueous solutions. The pH values of all solutions were adjusted by using maleic acid-Tris buffer solutions ranging from pH = 6.0 (ionic strength I= 0.115 mol-1-l) to pH = 8.0 (I= 0.148 mol1-l). As the support films sandwiching the enzyme layer of the multimembrane, two types of film were used, i.e. Spectrapor 2 (SP) (Spectrum Medical Industries, Inc. ), which is a kind of cellulosic dialysis membrane, and Selemion DMV (SDMV) (A sah’1 G arasu Co., Ltd.), which is an anion exchange membrane. Determination of kinetic parameters of urease To measure the initial velocity of the urease-catalyzed hydrolysis of urea, a urease solution (3 ml, 0.05% w/v) or a mixed solution (3 ml) composed of urease and NaAlg (0.05 and 1.0% w/v) was added to urea solutions (50 ml) of concentrations ranging from 0.001-0.3 mol-1-l. The reaction mixtures were incubated at 25’ C, and the concentrations of NH,+ ions, as one of the products, were determined by using an NH, electrode (Orion 95-12) connected to a digital pH/mV meter (Orion 701 A). The time dependences of NH,+ production were confirmed to be linear during 5 min as reported by Nichol et al. [ 151. From the results of 5 min reactions, initial reaction velocities were determined in the pH range 6.0-8.6. Multimembrane cell The multimembrane cell shown in Fig. 1 (a) was constructed of acrylic resin, and contained the enzyme layer sandwiched between support films as described in the previous paper [lo], i.e. solution I 1film 1) enzyme layer 1film 2 1solution II. Enzyme solutions were put into holes (E) (radius = 0.25 cm) in a perforated Teflon plate, T, (0.049 cm thick, with seven holes in it). To prevent deformation of the support films due to the osmotic pressure of the enzyme layer, and their vibration due to stirring of the solutions I and II, the support films on both sides were fixed by means of perforated Teflon plates T1 and Tz. The volumes of compartments I and II were 51-52 ml, and solutions I and II (50 ml) were poured into them. The total permeable area, A, of the multimembrane was 1.374 cm’. Diffusion-reaction of multimembrane containing urease Symmetric multimembrane The SP films were used as the support films on both sides of the enzyme layer, i.e. solution I I SP I enzyme layer ) SP I solution II. As the enzyme layer, urease solution (0.06% w/v) or a mixed solution composed of urease and NaAlg (0.06 and 0.6% w/v) were used, and compartments I and II were usually a donor and an acceptor part respectively. The initial concentration of urea in compartment I was usually 0.01 mol-1-l. Time courses of NH,+ concentrations
(a)
(b)
4x
-I’
0
le
Fig. 1. Schemes of multimembrane. (a) Multimembrane cell containing enzyme layer. A: compartment I (donor part); B: compartment II (acceptor part); D: stirrer; E: sample injection holes; F: support films 1 and 2; G: silicone rubber; J: inlet for solution injection; T1 and T,: perforated Teflon plate for support; T,: perforated Teflon plate (0.049 cm). (b) Notations of concentrations and diffusion coefficients in multimembrane.
in compartments I and II that had flowed out from the urease layer were measured by using the ammonia electrode in the pH range 6.046. Linear relationships between C&n4’ and time t were obtained under steady state, and from their slopes the fluxes of NH,+ into compartment I, Ji, and compartment II, JF (mol-cm -%ec-‘), were determined. The direction of flux from compartment I to II was considered positive. Asymmetric multimembrane A pair of films, such as SDMV and SP, was used as the support films 1 and 2, and the urease solution in the enzyme layer had the same concentration as in the case of the symmetric multimembrane. The fluxes of the product NH,+ were determined as for the symmetric multimembrane. Measurements of permeabilities and unstirred layer The fluxes of NaCl through single and dual SP films were measured under various stirring conditions by using the same cell except for the absence of T, in Fig. 1 (a), i.e. the SP films were fixed between the perforated Teflon supports T, and T,. The thickness of an unstirred layer 6 and the permeability coeffi-
149
cients P without unstirred layer effects were obtained from the following equations [ 161: =26/D
(1)
l/P& - l/P’ = L/P
(2)
2/P’ -l/P&
where D is the diffusion coefficient in solution, L is film thickness, and P’ and P& are the permeability coefficients of the single and the dual films defined by J=P’dC, in which J is flux and AC is the concentration difference between compartments I and II (Cn - C’ ) . The permeability coefficients of NH,+ and urea through the support films (SP and SDMV ) were measured by the same method as mentioned above. Results Thickness of unstirred layer and permeability coefficient of support films The permeability coefficients of NaCl through the single and the dual SP films, P’ and Ph respectively, were obtained under various stirring conditions (R= 100-500 rpm) from the steady state fluxes. The initial NaCl concentration of solutions I and II were C’=O.l and C”=O mol-1-l. The results for P’ and P& increased with increasing R and become almost constant in the region of R > 300 rpm. The permeability coefficients P obtained from eqn. (2) were found to be independent of R, and their average value was 2.22 x 10e6 cm2set-‘. In obtaining these P values, the water flows due to AC were estimated to be negligible. The thickness of the unstirred layer 6 obtained from eqn. (1) decreased with increasing R, as shown in Fig. 2. In the region of R=300-500 rpm, the value of 6 was found to be almost 0.003 cm. Subsequently, solutions I and II were stirred at 300 rpm in measuring the permeabilities of the support films and the diffusion-reaction through the multimembrane. The permeability coefficients of NH: and urea through the support films (SP and SDMV) were measured, and the results for pH = 7.0 are shown in Table 1.
1.0-
E
u % iii
0.5 -
0’
I
0
I
200
I
400 R1r.p.m.
Fig. 2. Variation of unstirred layer 6 with stirring rate R in bulk solutions.
150 TABLE 1 Permeability coefficients of support films and diffusion coefficients D or P ( low5 cm*-set-I)
1 (cm)
SP SDMV
0.0035 0.0145
urea
NH:
1.371” 0.206 0.0209
1.998” 0.276 0.00285
“Diffusion coefficient in solution.
0
2
4
6
8
t/hr
Fig. 3. Time courses of concentration of product in compartments I and II. (0 ) Compartment I; (A )compartment II.
Diffusion-reaction of urea through multimembrane containing urease layer Symmetric multimembrane Urea solution (Ci = 0.01 mol-1 -’ ) 1SP 1urease layer ] SP ]urea solution (CH’=O.Ol mol-1-l). To confirm the symmetry of the multimembrane, the fluxes of the product NH,+ ions into compartments I and II were measured at pH = 7.0 using the symmetric multimembrane, in which the concentration of urea in both compartments I and II, Ci and Ct’, was 0.01 mol-1-l. As shown in Fig. 3, the time courses of concentrations of NH,+ in compartments I and II were found to be almost equal, and to be in steady state after ca. 30 min. From these results, the cell was confirmed to be symmetrical for the diffusion-reaction through the multimembrane. Diffusion-reactions of urea through the multimembrane [urea solution (Ci = 0.01 mol-1 - ’ ) 1SP 1urease layer 1SP ] CE’= 0] were measured in the pH
151
range 6.5-8.6. The urease solution (0.06% w/v) or the mixed solution composed of urease and NaAlg (0.06 and 0.6% w/v) were used as the urease layer, and the fluxes of the product NH,+ into compartments I and II, Ji and JF, were obtained under the steady state condition. The total fluxes of NH,+, JF ( = - JL + Jg ), and the flux ratios - JL/Jb’, are shown in Figs. 4 and 5 as a function of pH. By adding NaAlg, the optimum pH, i.e. the value of pH showing the maximum JT, was shifted toward the alkaline pH region by 0.6 pH unit, from pH 6.9 to pH 7.5, and the maximum JpTincreased slightly. The values of pH showing the maximum value of - Jk/JF were almost the same as that for JT, and the values of - Jk/JF were greater than unity, i.e. the fluxes of the
0' 6
8 7
1
8
9
PH
Fig. 4. pH of solution vs. total flux of product JT through symmetric multimembrane. (0 ) Urease in enzyme layer; (0, X ) urease and NaAlg in enzyme layer, (63 ) JT vs. pH of the solutions in the compartments I and II, ( x ) JTvs. pH in the enzyme layer calculated from the Donnan equilibrium.
0
6
7
PH
8
9
Fig. 5. pH of solution vs. flux ratio of product - JpJz through symmetric and asymmetric multimembrane. Symmetric multimembrane: (0 ) urease in enzyme layer; (0 ) urease and NaAlg in enzyme layer. Asymmetric multimembrane; (A ) urease in enzyme layer; (A ) urease and NaAlg in enzyme layer. Dotted and broken curves show theoretical values for the symmetric multimembrane containing, respectively, urease and urease and NaAlg in the enzyme layer; (-.-. ) theoretical values for the asymmetric multimembranes containing urease, or urease and NaAlg.
152
product into compartment I (donor part) were larger than those into compartment II (acceptor part) under all experimental conditions. Asymmetric multimembrane 1SDMV 1urease layer 1SP I. The diffusion-reaction of urea through the asymmetric multimembrane composed of SDMV and SP as support films 1 and 2 was measured to elucidate the asymmetric effects, i.e. the effects of the anion exchange membrane used as film 1. The concentrations of urea in compartments I and II were Cfi= 0.01 mol-1 -’ and Ci’ = 0. The results for JF are shown in Fig. 6, and those for Ji/JF are shown in Fig. 5 together with the results for the symmetric multimembrane. The values of JT were much less than those of the symmetric multimembranes. Lower values of J,’ through the asymmetric multimembranes are considered to result from the reduced permeability of urea through the SDMV film 1. However, by adding Alg, the maximum JT was increased slightly (as well as that for the symmetric membrane). The flux ratios - Ji/Jg were much less than unity, in the range 0.2-0.3. As expected from the effects of the positively charged SDMV used as support film 1, the fluxes JF were much greater than the absolute value of Jk. The optimum pH of the asymmetric multimembrane containing only urease was 6.3, which was slightly more acidic compared with the symmetric multimembrane. By adding Alg, the value of pH was shifted to the alkaline region (by 0.3 pH unit) as well as that for the asymmetric multimembrane. However, the pH shift was smaller than for the symmetric one. Kinetics of urea hydrolysis in urease solutions To elucidate the effects of adding NaAlg to the urease solutions on the hydrolysis of urea, the kinetics in the solutions were studied in the pH range 6.58.6. The initial velocities for various urea concentrations were analyzed by 1.5 xl T 5 73 E o 70 E c-a
to-
0.5 -
01 5.5
I
I
!
6
I
8 PH
Fig. 6. pH of solution vs. total flux of product J,’ through asymmetric in enzyme layer; (A ) urease and NaAlg in enzyme layer.
multimembrane:
(A
)urease
153
-6
7
PH
0
9
Fig. 7. V,,,,, vs. pH profiles of urease and mixed solutions composed of urease and NaAlg: (0 ) urease; ( 0 ) urease + NaAlg.
Lineweaver-Burke plots, and maximum velocities V,,, and Michaelis-Menten constants KM were obtained. The values for V,,, are shown in Fig. 7 as a function of pH. By adding NaAlg, the optimum pH of urease was shifted to the alkaline region by 0.5 pH unit, from pH 7.0 to pH 7.5, and the value of V,,, at the optimum pH increased slightly. These results show relationships similar to the values of JT shown in Fig. 4. The values of I& were in the range 3.47.3 X 10m3mol-1-l. Discussion Effects of adding NaAlg to urease solutions on hydrolysis of urea The optimum pH of urease for the hydrolysis of urea in the solutions shifted to the more alkaline pH region on adding NaAlg, as shown in Fig. 7. As alginate is an anionic polysaccharide having one carboxylate group per uronate unit, the pH shift, dpH, results from the pH decrease in the microenvironment around the active sites of urease [ 171. The active site of urease is surrounded by anionic groups, and the negative electrostatic potential w” prevails in the region. Under equilibrium conditions, the electrochemical potential ,ii” of H+ ions in the region a! around the active site is equal to that of H+ ions pp in the region p away from region a: p”=~*+kTlna”+ery”=~~=~*+KTlnaB
(3)
where acuand aP are the activities of H+ ions in the (x and /3 regions, and p0 is the standard chemical potential. Then the pH difference between these regions can be expressed as: pHP-pH”=
- 0.434ey/“/kT
(4)
154
The optimum pH shift dpH due to the addition of NaAlg corresponds to pHB-pH”, i.e. when the optimum pH of the system with NaAlg is pHB, the local pH around the active site pH” should be equal to the optimum pH for the system without NaAlg. From dpH=0.5, the value v/” was calculated to be - 0.0296 V. Chondroitin 6-sulfate (Chs-C) is a linear polysaccharide and is composed of a disaccharide repeating unit, i.e. N-aCetyl-D-galaCtOSamine 6-sulfate and D-gluculonic acid. Chs-C possesses an ionizable group on one saccharide unit, similarly to Alg. The surface electrostatic potential v/” of the sodium salt of Chs-C, as obtained by the electrophoretic method [ 181, was reported to be v/“= -0.0245 V f or an ionic strength I=O.l mol-1-l. The local electrostatic potential v/” induced by Alg at 1=0.12-0.15 mol-1-l was found to be almost equal to the surface potential of Chs-C. Effects of adding NaAlg to urease layer of symmetric multimembrane on diffusion-reaction For the diffusion-reaction of urea through the urease layer of the symmetric multimembrane, the optimum pH shift due to the addition of Alg is considered to result from the pH decrease in the microenvironment around the active site described above and the H+ ion distributions between the urease la.yerand the bulk solution. When the effective charge density of the urease layer is known, the H+ ion distribution between the urease layer and the bulk solution can be obtained by assuming Donnan equilibrium and electroneutrality [ 191. As described in our previous paper, the effective charge densities of the Alg layers were obtained from the membrane potentials of the multimembrane [lo]. In that paper, the ratio of the effective charge density to the total concentration of the carboxylic groups of Alg, S*/&,, was reported to be 0.45. Thus, the effective charge density of the NaAlg layer ( WAlg=0.06% w/v) is -0.014 mol-1-l. The isoelectric point of urease is reported to be pH = 5.0 [ 201. Thus, the net charge of urease was negative in our experimental region, pH = 6.0-8.6. However, since the concentrations of urease were very small compared with that of Alg, the effect of the urease on the effective charge density can be neglected. The H+ ion concentration in the urease layer containing Alg can be estimated to be almost the same as that in the solution layer containing only Alg. In the calculations of H+ ion distribution, the ions from the buffer were taken into consideration. The pH difference between the NaAlg layer and the bulk solution was calculated to be almost -0.02 in the pH range 6-9. In Fig. 4, J,’ values are also shown as a function of pH in the urease layer obtained as above. The deviations of H + ion concentrations due to the Donnan equilibrium were found to be too small to explain the shift of optimum pH. Therefore, the optimum pH shift to the alkaline region by 0.6 pH unit must result predominantly from an additional pH decrease in the microenvironment around the active sites of the
155
urease. As discussed for the effects of adding NaAlg to the urease solutions, the local electrostatic potential v/” induced by Alg can be obtained from the pH decrease ( - 0.58) in the microenvironment by eqn. (4 ). The value y/” was calculated to be -0.0343 V; this values is that relative to the /? region of the urease layer. The result was almost equal to that obtained from the optimum pH shift in the solution. The optimum pH shifts of the asymmetric multimembrane will be discussed later. At the optimum pH, the V_, value of the urease solutions and the value of JT through the multimembrane were increased slightly by adding NaAlg, as shown in Figs. 4 and 7. These results coincide with those of Nichol et al. [ 15,211, who studied the effects of adding polymers to urease solutions on the hydrolysis of urea, and showed that V,,, was increased slightly by adding polymers such as bovine serum albumin, ovalbumin and dextran. They attributed these effects to the change in conformation due to the excluded volume of the added polymers. Theoretical analysis of diffusion-reaction of urea through multimembrane Urease catalyzes the hydrolysis of urea: NH2CONHz +2H20=2NH4+
+CO;-
(5)
Paying attention to NH,+ which is one of the products P, the reaction of urea S in the urease layer is expressed by S*2P. In the urease layer, if the concentrations of urea are much less than the KM value, the enzymic reaction approximates to a first order reaction [ 2,3]. Under steady state conditions, diffusion-reaction of S and P can be expressed by the following equations in the urease layer: D;(d2C,/dx2)
-kc,
=O
D;(d2C,/d.r2) +2kC, =O
(6) (7)
where k is a first order reaction rate constant, 0: and 0; are the diffusion coefficients of S and P, and C, and C, are the concentrations of S and P at position x of the urease layer, as shown in Fig. 1 (b) . Concentrations of S and P in the urease layer are obtained by solving eqns. (6) and (7) under the following boundary conditions, viz. the interfacial concentrations of S and P between support film 1 and the enzyme layer are C,‘seand CF , and those between film 2 and the enzyme layer are Cp and Cr respectively. c
s=
C,‘*“sinh{cr(Z”-x)}+C$esinh(ax) sinh(&)
(8)
156
c
_2~.C?sinh{cu(l”-x)}+C?sinh(ax) sinh ( ale) 0;
= P
+D;(C~-C~)+2D:(C;+-C:+)x+2D:
+:+?
D;le
+ cp
(9)
P
where cy is (k/D~)““, which is a parameter relating to the reaction rate constant. At each interface, the consecutive law of the fluxes of S and P must be satisfied according to the following equations: -D;(dC,/&)l,”
(10)
-D~(dC,/d_x)2*“=P~(C,2+--C:1)/12
(11)
J,‘,“=P,‘(C:-C$“)/ll= J$“=
JP =P;(
= -D;(dC,/d+”
-CF/ll)
(12)
JF = -D;(dCp/dx)2*“=P;(C~/12)
(13)
where P,‘, Pz, Pi and Pi are permeability coefficients of urea and NH,f through support films 1 and 2. The fluxes of S are discussed first. From eqns. (8), (10) and (ll), (dC,/dx)l+and (dC,/&)2,“canbeobtainedwithoutusing the interfacial concentrations of S and P by the following equations:
1[ -C:
a!
1+
al’
ck!
sinh ( ale)
-3 P,’
2
B =sinh(cul”) 1
crl’
B =sinh(al”) 2
al2
1[ -C:
1
1+
2
cosh(cr1”) -$
cosh(oll’)-; al1
cosh(al’)-$
l-
cosh(cr1”) B1
es
sinh(cx1”) P,” cosh(a1”) -$
1
1
P,’
.D”+cosh(&) s
Pz
*D”+cosh(c@) s
1
(14)
(15) (16) (17)
Then, Jt," , J $” , C,l+ and C,“pecan be obtained by using eqns. (lo), (11 ), (14) and ( 15 ) . The enzyme reaction rate in the enzyme layer V can be obtained by: V=
J,‘,” _ Jfp”
In the same manner as in the case of the substrate:
(18)
157
+C;-C:, 1”
2cuD3’ -_’ PEl”
(Cf,e+C:*e)
sinh ( ale) 1” Dell B,=l+L+L P’le P
PAI’
(19)
sinh(cuZ”)
2cuD; C$“cosh(aZ”) -C,l*’ +C;-C:,+2crD:Z’
[l-cosh(aZ”)]
20: _(CpL__C,l,e) +leD;
(C;,e+C,l,e)[l-cosh(aZ”)] sinh(aZ”)
-1 &
(20)
De12 P212 P
(21)
From eqn. (12 ), (13 ) , ( 19) and (20)) the concentration profiles of P can be calculated. The total of the fluxes of P into compartments I and II is equal to 2v. J;=-Jp+Jp
(22)
The flux ratio of P, - Jk/Jk’, can be obtained by:
J:,
(23)
Symmetric multimembrane The diffusion-reactions of urea through the symmetric multimembrane, 1SP 1urease layer 1SP I, are discussed theoretically. The permeability coefficients of urea and ammonium ion NH,+ through the SP film as shown in Table 1, were used in the calculations, the diffusion coefficients in the urease layer being obtained by Wang’s equation [ 22,231 D”=D,(l-1.5~~)
(24)
where Do is the diffusion coefficient in water and VAis the volume fraction of Alg. Some of the calculated concentration profiles of S and P in the multimembrane are shown in Fig. 8. The concentrations of the substrate were found to be less than or almost the same as the KM values of urease. The diffusionreaction of urea through the urease layer can thus be considered approximately to obey eqns. (6) and (7). Figure 9 shows the total flux of P, J,’ as a function of CYZ”. The values of J,’ increase with increasing al” and approach asymptotically to a constant value. The flux ratios of P, - Jk/JF , are greater than 1, as
-I’
0
x/cm
19 2
Fig. 8. Calculated concentration profiles for substrate (S) and product (P) in symmetric multimembrane. 1s: Substrate (al’c0.7); 1P: product (al”~0.7); 2s: substrate (ale= 1.2); 2P: product (&“=1.2); Ct =O.l, Cf =O mol-1-l. Data shown in Table 1 are used in the calculations.
Fig. 9. Variation with cyle of calculated total flux of product J,’ for symmetric and asymmetric multimembrane; SM: symmetric multimembrane; AM: asymmetric multimembrane. Data shown in Table 1 are used in the calculations.
shown in Fig. 10, and increase with increasing CYZ”, i.e. the flux of P into the donor part is greater than that into the acceptor part. From the experimental results for J,’ shown in Fig. 4 and the theoretical values in Fig. 9, the reaction rate constant, k, in the urease layer was obtained. The results are shown in Fig. 11. The value of k showed maxima at the optimum pH for the multimembranes both without and with NaAlg. By using these k values, the efflux ratio of the product, - Jk/JF, can be obtained from Fig. 10, and the expected values are shown in Fig. 5 together with the experimental results. The expected values were slightly smaller than the experimental results. However, neglecting the water flow due to osmotic pressure, the perme-
159
-A SM
!i
0.02
-
-,P . ..a
7 - 0.01 AM-
0'
I
0
4
2
ale
6
6
'0
Fig. 10. Variation with al” of calculated flux ratio of product - Ji/Jz for symmetric and asymmetric multimembrane. SM: symmetric multimembrane; AM: asymmetric multimembrane. Data shown in Table 1 are used in the calculations.
- a0
1
6
8
7
'0
9
PH
Fig. 11. Rate constant k of urease vs. pH. Rate constant k obtained from J;f through the multimembranes: ( 0 ) urease; (0 ) urease and NaAlg. Rate constant k’ obtained from V,, and KM: ( A ) urease; ( A ) urease and NaAlg.
ability coefficients of the support films were overestimated slightly. Taking this effect into consideration, the theoretical results - JL/JF increase slightly. We can thus consider that the theoretical values coincide semi-quantitatively with the experimental results. When the concentration of urea is much less than the KM of urease, k is estimated approximately to be k= V,,,/&. V,, is proportional to the concentration of an enzyme Cn, i.e. V_= k+2CE, where k+z is the rate constant of breakdown of the enzyme-substrate complex. Taking the concentration differences of the urease into consideration, the k values for urease in the multimembrane can be estimated from the results for V,,, and KM shown in Fig. 7.
160
Denoting k thus obtained as k’, the values of k’ are shown in Fig. 11 together with the k values obtained from J,‘. The values of k were found to be much less than k’ and the profiles of pH vs. k to be much sharper than those of pH vs. k’. As shown in Fig. 8, the concentrations of urea in the urease layer are in almost the same region as Khl. Thus, one of the factors resulting in the lower k values is considered to be the fact that the reaction is of Michaelis-Menten type. Effects of asymmetry of multimembrane on diffusion-reaction The permeabilities of S and P through the support films on both sides of the urease layer affect significantly both JpTand - JL/JF. The theoretical values for the asymmetric multimembrane, ) SDMV 1urease layer ] SP ] , are shown in Figs. 9 and 10 together with those for the symmetric multimembrane. Due to the lower permeability of urea and NH,+ ions through the SDMV support film 1,the values of J,’ through the asymmetric multimembrane are less than those for the symmetric one, and the calculated values of - Jk/Jz are near 0.006, much lower than those for the symmetric multimembrane. Comparing the theoretical results with the experimental ones, the results for J,’ shown in Fig. 6 were more than the theoretical values obtained using k values of the synthetic multimembrane and the results for - Jk/Ji’ shown in Fig. 5 were in the range 0.2-0.6, more than 10 times as high as the theoretical values. Tanny et al. [6] studied precisely the ion flows in a membrane composed of an anion exchanger and an urease phase, and showed that carbamate ions NH, COO -, an intermediate in the hydrolysis of urea, take part in the diffusion-reaction: NH, CONH, + Hz 0 =NH, COO - + NH,+
(25)
i.e. the carbamate ions produced near the interface between the anion exchanger and the urease phase exchange through the anion exchanger with anions in the donor solution, in which the carbamates decompose spontaneously with a halflife of several msec [ 241. NH,COO-
+H,O=NH,+
+CO:-
(26)
As pointed out by Tanny, the carbamate ions diffuse into the SDMV film 1 and the products NH: and CO:- diffuse out to the donor compartment due to their concentration gradients. Consequently, the value of - Jk/JF become greater than the theoretical values, which do not take the presence of the carbamates into consideration. To analyze them more precisely, we must take the unstirred boundary layer in the compartment containing the urease into consideration. This layer does most of the work in decomposing the urea. Utilizing the free solution value of urea diffusion and a halflife of several msec, it is found, by using the relation 6=2Dt, that almost all the reaction must take place within 10 ym of the urease solution/support film interface. This being the case, the concentration profiles are more complex than indicated in Fig.
161
1 (b). If these situations are taken in consideration, the theoretical values of - Jb/JF may become closer to the experimental ones. The values of pH showing the maximum J,’ for the asymmetric multimembrane shifted to more acidic regions, both for the cases with and without Alg, than the corresponding values for the symmetric multimembrane. From these facts, the values of pH in the urease layers are considered to become more acidic, an effect resulting from the efflux of carbamate anions through the SDMV film. For the diffusion-reaction of urea through the asymmetric multimembrane containing urease, carbamate ions are suggested as playing important roles in the total flux of product JpT, the flux ratio of product - Jk/Jk’, and the optimum pH of the urease.
References 1
2
3
4 5
6
7
8 9 10 11 12 13 14
R. Goldman, 0. Kedem, I.H. Silman, S.R. Caplan and E. Katchalski, Papain-collodion membranes. I. Preparation and properties, Biochemistry, 7 (1968) 486-500. R. Goldman, 0. Kedem and E. Katchalsik, Papain-collodion membranes. II. Analysis of the kinetic behavior of enzymes immobilized in artificial membranes, Biochemistry, 7 (1968) 4518-4532. D. Thomas, Artificial enzyme membrane; diffusion reaction and sensors, 1987 International Congress on Membranes and Membrane Process, Membrane Society of Japan, Tokyo, 1987, p. 35. D. Thomas, G. Broun and E. Selegny, Monoenzymatic model membranes: diffusion reaction kinetics and phenomena, Biochemistry, 54 (1972) 229-244. G. Broun, D. Thomas and E. Selegny, Structured bienzymatical models formed by sequential enzymes bound into artificial supports: active glucose transport effect, J. Membrane Biol., 8 (1972) 313-332. G.B. Tanny, 0. Kedem and Z. Bohak, Coupling of transport and enzymic reaction in a membrane composed of an anion exchanger and immobilized urease, J. Membrane Sci., 4 (1979) 363-377. K. Ishihara, M. Kobayashi and I. Shinohara, Control of insulin permeation through a polymer membrane with responsive function for glucose, Makromol. Chem., Rapid Commun., 4 (1983) 327-331. A. Sugget, Polysaccharides, in: F. Franks (Ed.), Water, Vol. 4, Plenum Press, New York, NY, 1975, p. 519. M. Yonese, K. Baba and H. Kishimoto, Stress relaxation of alginate gels crosslinked by various divalent metal ions, Bull. Chem. Sot. Jpn., 61 (1988) 1857-1863. M. Yonese, K. Baba and H. Kishimoto, The effects of the sol-gel transition of alginates on effective charge densities, Bull. Chem. Sot. Jpn., 61 (1988) 1077-1083. H. Tanaka, M. Matsumura and I.A. Veliky, Diffusion characteristics of substrates in Caalginate gel beads, Biotechnol. Bioeng., 26 (1984) 53-58. Y.F. Leung, G.M. O’Shea, M.F.A. Goosen and A.M. Sun, Microencapsulation of crystalline insulin or islets of Langerhans, Artif. Organs, 7 (1983) 208-212. E.R. Morris, D.A. Rees and D. Thorn, Characterization of a&ate composition and block structure by circular dichroism, Carbohydr. Res., 81 (1980) 305-314. H. Grasdalen, B. Larsen and 0. Smidsrod, Study of the composition and sequence of uronate residues in alginates, Carbohydr. Res., 68 (1979) 23-31.
162 15
16 17
18 19 20 21 22
23
24
L.W. Nichol, E.A. Owen and D.J. Winzor, Effect of thermodynamic nonideality in kinetic studies: evidence for reversible unfolding of urease during urea hydrolysis, Arch. Biochem. Biophys., 239 (1985) 147-154. C.T. Everit, W.R. Redwood and D.A. Haydon, Problem of boundary layers in the exchange diffusion of water across biomolecular lipid membranes, J. Theor. Biol., 22 (1969) 20-32. L. Goldstein, Y. Levin and E. Katchalski, A water insoluble polyanionic derivative of trypsin. II. Effect of the polyelectrolyte carrier on the kinetic behavior of the bound trypsin, Biochemistry, 3 (1964) 1913-1919. M.B. Mathews, Macromolecular properties of isomeric chondroitin sulfates, Biochim. Biophys. Acta, 35 (1959) 9-17. P.C. Hiemenz, Principles of Colloid and Surface Chemistry, Marcel Dekker, New York, NY, 1977, p. 145. A.L. Lehninger, Biochemistry, Worth, New York, NY, 1975, p. 162. L.W. Nichol, M.J. Sculley, L.D. Ward and D.J. Winzor, Effects of thermodynamic nonideality in kinetic studies, Arch. Biochem. Biophys., 222 (1983) 574-581. J.H. Wang, Theory of the self-diffusion of water in protein solutions. A new method for studying the hydration and shape of protein molecules, J. Am. Chem. Sot., 76 (1954) 47554763. M. Nakagaki and M. Yonese, Permeability of potassium chloride, tetra-alkyl ammonium chloride and dodecyl amine chloride in the inside and at the interface of the gelatin membrane, Yakugaku Zasshi, 94 (1974) 1170-1177. R.L. Blakely, J.A. Hinds, H.E. Kunze, E.C. Webb and B. Zerner, Demonstration of a carbamoyl-transfer reaction and inhibition by hydroxamic acids, Biochemistry, 8 (1969) 19912000.
145
Diffusion-reaction of urea through multimembrane containing urease - Effects of microenvironments around urease and asymmetry of the membrane Masakatsu Yonese*, Hideki Murabayashi and Hiroshi Kishimoto Faculty of Pharmaceutical Sciences, Nagoya City University, Tanabe-dori, Mizuhoku Nagoya, 467 (Japan) (Received June 19,1989; accepted in revised form June 4,199O)
Abstract Diffusion-reactions through enzyme membranes were studied by using a multimembrane, consisting of an enzyme layer sandwiched between films. The multimembrane was shown to possess the following characteristics: (1) the microenvironments around the enzyme can be altered arbitrarily by adding polymers etc., and (2 ) the asymmetries of the multimembranes can be controlled easily by using various films. Diffusion-reactions of urea through symmetric and asymmetric multimembranes having a urease layer were studied by measuring total fluxes Jz and flux ratios - Jb/Jz of one of the products (NH: ion) into a donor and an acceptor compartment. By adding sodium alginate NaAlg to the urease layer, the pH showing the maximum Jf shifted towards the alkaline pH region by 0.6 pH unit, and the maximum JF increased. From the value of the pH shift, the electrostatic potential yl” around the active site of the urease was calculated to be - 0.0343 V. The values of Jk/JF through the symmetric multimembrane were in the range 1.2-1.7, and those for the asymmetric multimembrane were in the range 0.2-0.3. In the diffusion-reaction through the latter membrane, carbamate anions were found to play an important role. Diffusionreaction through the multimembranes was analyzed by assuming that the reactions in the enzyme layer obey a first order reaction.
Introduction Basic studies of immobilized enzyme membranes were developed by Katchalski and co-workers, who pointed out their significance as a model of enzymes in biomembranes [ 1,2]. Recently, immobilized enzyme membranes have been studied, not only with respect to the elucidation of diffusion-reaction of substrates due to enzymes in biomembranes, but also as to their application in sensors such as enzyme electrodes [ 31. Effects of asymmetries of the immobilized enzyme membranes and systematic arrangements of multienzymes on the diffusion-reaction have led to new functional membranes which one cannot *To whom correspondence should be addressed.
0376-7388/90/$03.50
0 1990 -
Elsevier Science Publishers B.V.
146
expect to achieve with homogeneous membranes containing an enzyme [4-71. However, such asymmetric membranes containing enzymes are difficult to prepare and their reproducibilities are not guaranteed. To elucidate the effects of microenvironments around the immobilized enzymes and of the asymmetry of the membranes on the diffusion-reaction, a multimembrane consisting of an enzyme layer sandwiched between supporting films: Solution
II film 11 enzyme
layer 1film 2 1solution
II
is very convenient to basic studies of the diffusion-reaction. The multimembrane has the following characteristics: (1) the microenvironments around the enzyme can be altered arbitrarily by adding polymers or liposomes etc., and (2 ) by using various supporting films, the asymmetries of the multimembrane can be easily controlled. In this research, the diffusion-reactions of urea through symmetric and asymmetric multimembranes having a urease layer were studied. Furthermore, an alginate ( Alg) , which is type of polysaccharide, was used as a polymer additive, and the effects of such addition on the diffusion-reaction were studied. Alginate is a linear block copolymer composed of /3-D-mannuronate and a-L-guluronate, and is gelled by adding divalent metal ions, such as Ca ions [8,9]. In our previous paper [lo], the effects of the sol-gel transition on the charge density of Alg were studied by the use of the membrane potential method. Alginate gels have been examined with respect to their applications as matrices for immobilized enzymes and organelles [ 111, and in drug delivery systems [12]. The effects of the sol-gel transition of Alg in the enzyme layer on the diffusion-reaction are very important. However, in this study, the effects could not be evaluated because CO;- ions produced by the hydrolysis of urea form a precipitate of CaCO, in the presence of Ca ion added for the gellation of Alg. Experimental
Materials Urease was of commercial origin (Cooper Biochemical, 82 U-mg-‘, Lot. No. G4P6952) extracted from soy beans, and was used without any purification. Purified sodium alginate (NaAlg) used as an additive was prepared from commercial NaAlg (Tokyo Kasei Kogyo Co., Ltd.) by dialyzing against distilled water and by filtering to remove insoluble substances, as described in previous work [ 9,101. The purified NaAlg was stored refrigerated after freeze drying. The weight average molar mass of NaAlg was determined to be M, = 1.32 x lo5 g-mol-’ by using an LS-8 light scattering photometer (Toy0 Soda Manufacturing Co., Ltd., Japan). The guluronate fraction FG and the consecutive guluronate one FGG were determined as being 0.37 and 0.28 by circular dichroism [ 131 and proton-NMR [ 141 methods. Urea, ammonium chloride and all other reagents were of special grade (Katayama Kogyo Co., Ltd.). Distilled and
147
deionized water was used for preparation of aqueous solutions. The pH values of all solutions were adjusted by using maleic acid-Tris buffer solutions ranging from pH = 6.0 (ionic strength I= 0.115 mol-1-l) to pH = 8.0 (I= 0.148 mol1-l). As the support films sandwiching the enzyme layer of the multimembrane, two types of film were used, i.e. Spectrapor 2 (SP) (Spectrum Medical Industries, Inc. ), which is a kind of cellulosic dialysis membrane, and Selemion DMV (SDMV) (A sah’1 G arasu Co., Ltd.), which is an anion exchange membrane. Determination of kinetic parameters of urease To measure the initial velocity of the urease-catalyzed hydrolysis of urea, a urease solution (3 ml, 0.05% w/v) or a mixed solution (3 ml) composed of urease and NaAlg (0.05 and 1.0% w/v) was added to urea solutions (50 ml) of concentrations ranging from 0.001-0.3 mol-1-l. The reaction mixtures were incubated at 25’ C, and the concentrations of NH,+ ions, as one of the products, were determined by using an NH, electrode (Orion 95-12) connected to a digital pH/mV meter (Orion 701 A). The time dependences of NH,+ production were confirmed to be linear during 5 min as reported by Nichol et al. [ 151. From the results of 5 min reactions, initial reaction velocities were determined in the pH range 6.0-8.6. Multimembrane cell The multimembrane cell shown in Fig. 1 (a) was constructed of acrylic resin, and contained the enzyme layer sandwiched between support films as described in the previous paper [lo], i.e. solution I 1film 1) enzyme layer 1film 2 1solution II. Enzyme solutions were put into holes (E) (radius = 0.25 cm) in a perforated Teflon plate, T, (0.049 cm thick, with seven holes in it). To prevent deformation of the support films due to the osmotic pressure of the enzyme layer, and their vibration due to stirring of the solutions I and II, the support films on both sides were fixed by means of perforated Teflon plates T1 and Tz. The volumes of compartments I and II were 51-52 ml, and solutions I and II (50 ml) were poured into them. The total permeable area, A, of the multimembrane was 1.374 cm’. Diffusion-reaction of multimembrane containing urease Symmetric multimembrane The SP films were used as the support films on both sides of the enzyme layer, i.e. solution I I SP I enzyme layer ) SP I solution II. As the enzyme layer, urease solution (0.06% w/v) or a mixed solution composed of urease and NaAlg (0.06 and 0.6% w/v) were used, and compartments I and II were usually a donor and an acceptor part respectively. The initial concentration of urea in compartment I was usually 0.01 mol-1-l. Time courses of NH,+ concentrations
(a)
(b)
4x
-I’
0
le
Fig. 1. Schemes of multimembrane. (a) Multimembrane cell containing enzyme layer. A: compartment I (donor part); B: compartment II (acceptor part); D: stirrer; E: sample injection holes; F: support films 1 and 2; G: silicone rubber; J: inlet for solution injection; T1 and T,: perforated Teflon plate for support; T,: perforated Teflon plate (0.049 cm). (b) Notations of concentrations and diffusion coefficients in multimembrane.
in compartments I and II that had flowed out from the urease layer were measured by using the ammonia electrode in the pH range 6.046. Linear relationships between C&n4’ and time t were obtained under steady state, and from their slopes the fluxes of NH,+ into compartment I, Ji, and compartment II, JF (mol-cm -%ec-‘), were determined. The direction of flux from compartment I to II was considered positive. Asymmetric multimembrane A pair of films, such as SDMV and SP, was used as the support films 1 and 2, and the urease solution in the enzyme layer had the same concentration as in the case of the symmetric multimembrane. The fluxes of the product NH,+ were determined as for the symmetric multimembrane. Measurements of permeabilities and unstirred layer The fluxes of NaCl through single and dual SP films were measured under various stirring conditions by using the same cell except for the absence of T, in Fig. 1 (a), i.e. the SP films were fixed between the perforated Teflon supports T, and T,. The thickness of an unstirred layer 6 and the permeability coeffi-
149
cients P without unstirred layer effects were obtained from the following equations [ 161: =26/D
(1)
l/P& - l/P’ = L/P
(2)
2/P’ -l/P&
where D is the diffusion coefficient in solution, L is film thickness, and P’ and P& are the permeability coefficients of the single and the dual films defined by J=P’dC, in which J is flux and AC is the concentration difference between compartments I and II (Cn - C’ ) . The permeability coefficients of NH,+ and urea through the support films (SP and SDMV ) were measured by the same method as mentioned above. Results Thickness of unstirred layer and permeability coefficient of support films The permeability coefficients of NaCl through the single and the dual SP films, P’ and Ph respectively, were obtained under various stirring conditions (R= 100-500 rpm) from the steady state fluxes. The initial NaCl concentration of solutions I and II were C’=O.l and C”=O mol-1-l. The results for P’ and P& increased with increasing R and become almost constant in the region of R > 300 rpm. The permeability coefficients P obtained from eqn. (2) were found to be independent of R, and their average value was 2.22 x 10e6 cm2set-‘. In obtaining these P values, the water flows due to AC were estimated to be negligible. The thickness of the unstirred layer 6 obtained from eqn. (1) decreased with increasing R, as shown in Fig. 2. In the region of R=300-500 rpm, the value of 6 was found to be almost 0.003 cm. Subsequently, solutions I and II were stirred at 300 rpm in measuring the permeabilities of the support films and the diffusion-reaction through the multimembrane. The permeability coefficients of NH: and urea through the support films (SP and SDMV) were measured, and the results for pH = 7.0 are shown in Table 1.
1.0-
E
u % iii
0.5 -
0’
I
0
I
200
I
400 R1r.p.m.
Fig. 2. Variation of unstirred layer 6 with stirring rate R in bulk solutions.
150 TABLE 1 Permeability coefficients of support films and diffusion coefficients D or P ( low5 cm*-set-I)
1 (cm)
SP SDMV
0.0035 0.0145
urea
NH:
1.371” 0.206 0.0209
1.998” 0.276 0.00285
“Diffusion coefficient in solution.
0
2
4
6
8
t/hr
Fig. 3. Time courses of concentration of product in compartments I and II. (0 ) Compartment I; (A )compartment II.
Diffusion-reaction of urea through multimembrane containing urease layer Symmetric multimembrane Urea solution (Ci = 0.01 mol-1 -’ ) 1SP 1urease layer ] SP ]urea solution (CH’=O.Ol mol-1-l). To confirm the symmetry of the multimembrane, the fluxes of the product NH,+ ions into compartments I and II were measured at pH = 7.0 using the symmetric multimembrane, in which the concentration of urea in both compartments I and II, Ci and Ct’, was 0.01 mol-1-l. As shown in Fig. 3, the time courses of concentrations of NH,+ in compartments I and II were found to be almost equal, and to be in steady state after ca. 30 min. From these results, the cell was confirmed to be symmetrical for the diffusion-reaction through the multimembrane. Diffusion-reactions of urea through the multimembrane [urea solution (Ci = 0.01 mol-1 - ’ ) 1SP 1urease layer 1SP ] CE’= 0] were measured in the pH
151
range 6.5-8.6. The urease solution (0.06% w/v) or the mixed solution composed of urease and NaAlg (0.06 and 0.6% w/v) were used as the urease layer, and the fluxes of the product NH,+ into compartments I and II, Ji and JF, were obtained under the steady state condition. The total fluxes of NH,+, JF ( = - JL + Jg ), and the flux ratios - JL/Jb’, are shown in Figs. 4 and 5 as a function of pH. By adding NaAlg, the optimum pH, i.e. the value of pH showing the maximum JT, was shifted toward the alkaline pH region by 0.6 pH unit, from pH 6.9 to pH 7.5, and the maximum JpTincreased slightly. The values of pH showing the maximum value of - Jk/JF were almost the same as that for JT, and the values of - Jk/JF were greater than unity, i.e. the fluxes of the
0' 6
8 7
1
8
9
PH
Fig. 4. pH of solution vs. total flux of product JT through symmetric multimembrane. (0 ) Urease in enzyme layer; (0, X ) urease and NaAlg in enzyme layer, (63 ) JT vs. pH of the solutions in the compartments I and II, ( x ) JTvs. pH in the enzyme layer calculated from the Donnan equilibrium.
0
6
7
PH
8
9
Fig. 5. pH of solution vs. flux ratio of product - JpJz through symmetric and asymmetric multimembrane. Symmetric multimembrane: (0 ) urease in enzyme layer; (0 ) urease and NaAlg in enzyme layer. Asymmetric multimembrane; (A ) urease in enzyme layer; (A ) urease and NaAlg in enzyme layer. Dotted and broken curves show theoretical values for the symmetric multimembrane containing, respectively, urease and urease and NaAlg in the enzyme layer; (-.-. ) theoretical values for the asymmetric multimembranes containing urease, or urease and NaAlg.
152
product into compartment I (donor part) were larger than those into compartment II (acceptor part) under all experimental conditions. Asymmetric multimembrane 1SDMV 1urease layer 1SP I. The diffusion-reaction of urea through the asymmetric multimembrane composed of SDMV and SP as support films 1 and 2 was measured to elucidate the asymmetric effects, i.e. the effects of the anion exchange membrane used as film 1. The concentrations of urea in compartments I and II were Cfi= 0.01 mol-1 -’ and Ci’ = 0. The results for JF are shown in Fig. 6, and those for Ji/JF are shown in Fig. 5 together with the results for the symmetric multimembrane. The values of JT were much less than those of the symmetric multimembranes. Lower values of J,’ through the asymmetric multimembranes are considered to result from the reduced permeability of urea through the SDMV film 1. However, by adding Alg, the maximum JT was increased slightly (as well as that for the symmetric membrane). The flux ratios - Ji/Jg were much less than unity, in the range 0.2-0.3. As expected from the effects of the positively charged SDMV used as support film 1, the fluxes JF were much greater than the absolute value of Jk. The optimum pH of the asymmetric multimembrane containing only urease was 6.3, which was slightly more acidic compared with the symmetric multimembrane. By adding Alg, the value of pH was shifted to the alkaline region (by 0.3 pH unit) as well as that for the asymmetric multimembrane. However, the pH shift was smaller than for the symmetric one. Kinetics of urea hydrolysis in urease solutions To elucidate the effects of adding NaAlg to the urease solutions on the hydrolysis of urea, the kinetics in the solutions were studied in the pH range 6.58.6. The initial velocities for various urea concentrations were analyzed by 1.5 xl T 5 73 E o 70 E c-a
to-
0.5 -
01 5.5
I
I
!
6
I
8 PH
Fig. 6. pH of solution vs. total flux of product J,’ through asymmetric in enzyme layer; (A ) urease and NaAlg in enzyme layer.
multimembrane:
(A
)urease
153
-6
7
PH
0
9
Fig. 7. V,,,,, vs. pH profiles of urease and mixed solutions composed of urease and NaAlg: (0 ) urease; ( 0 ) urease + NaAlg.
Lineweaver-Burke plots, and maximum velocities V,,, and Michaelis-Menten constants KM were obtained. The values for V,,, are shown in Fig. 7 as a function of pH. By adding NaAlg, the optimum pH of urease was shifted to the alkaline region by 0.5 pH unit, from pH 7.0 to pH 7.5, and the value of V,,, at the optimum pH increased slightly. These results show relationships similar to the values of JT shown in Fig. 4. The values of I& were in the range 3.47.3 X 10m3mol-1-l. Discussion Effects of adding NaAlg to urease solutions on hydrolysis of urea The optimum pH of urease for the hydrolysis of urea in the solutions shifted to the more alkaline pH region on adding NaAlg, as shown in Fig. 7. As alginate is an anionic polysaccharide having one carboxylate group per uronate unit, the pH shift, dpH, results from the pH decrease in the microenvironment around the active sites of urease [ 171. The active site of urease is surrounded by anionic groups, and the negative electrostatic potential w” prevails in the region. Under equilibrium conditions, the electrochemical potential ,ii” of H+ ions in the region a! around the active site is equal to that of H+ ions pp in the region p away from region a: p”=~*+kTlna”+ery”=~~=~*+KTlnaB
(3)
where acuand aP are the activities of H+ ions in the (x and /3 regions, and p0 is the standard chemical potential. Then the pH difference between these regions can be expressed as: pHP-pH”=
- 0.434ey/“/kT
(4)
154
The optimum pH shift dpH due to the addition of NaAlg corresponds to pHB-pH”, i.e. when the optimum pH of the system with NaAlg is pHB, the local pH around the active site pH” should be equal to the optimum pH for the system without NaAlg. From dpH=0.5, the value v/” was calculated to be - 0.0296 V. Chondroitin 6-sulfate (Chs-C) is a linear polysaccharide and is composed of a disaccharide repeating unit, i.e. N-aCetyl-D-galaCtOSamine 6-sulfate and D-gluculonic acid. Chs-C possesses an ionizable group on one saccharide unit, similarly to Alg. The surface electrostatic potential v/” of the sodium salt of Chs-C, as obtained by the electrophoretic method [ 181, was reported to be v/“= -0.0245 V f or an ionic strength I=O.l mol-1-l. The local electrostatic potential v/” induced by Alg at 1=0.12-0.15 mol-1-l was found to be almost equal to the surface potential of Chs-C. Effects of adding NaAlg to urease layer of symmetric multimembrane on diffusion-reaction For the diffusion-reaction of urea through the urease layer of the symmetric multimembrane, the optimum pH shift due to the addition of Alg is considered to result from the pH decrease in the microenvironment around the active site described above and the H+ ion distributions between the urease la.yerand the bulk solution. When the effective charge density of the urease layer is known, the H+ ion distribution between the urease layer and the bulk solution can be obtained by assuming Donnan equilibrium and electroneutrality [ 191. As described in our previous paper, the effective charge densities of the Alg layers were obtained from the membrane potentials of the multimembrane [lo]. In that paper, the ratio of the effective charge density to the total concentration of the carboxylic groups of Alg, S*/&,, was reported to be 0.45. Thus, the effective charge density of the NaAlg layer ( WAlg=0.06% w/v) is -0.014 mol-1-l. The isoelectric point of urease is reported to be pH = 5.0 [ 201. Thus, the net charge of urease was negative in our experimental region, pH = 6.0-8.6. However, since the concentrations of urease were very small compared with that of Alg, the effect of the urease on the effective charge density can be neglected. The H+ ion concentration in the urease layer containing Alg can be estimated to be almost the same as that in the solution layer containing only Alg. In the calculations of H+ ion distribution, the ions from the buffer were taken into consideration. The pH difference between the NaAlg layer and the bulk solution was calculated to be almost -0.02 in the pH range 6-9. In Fig. 4, J,’ values are also shown as a function of pH in the urease layer obtained as above. The deviations of H + ion concentrations due to the Donnan equilibrium were found to be too small to explain the shift of optimum pH. Therefore, the optimum pH shift to the alkaline region by 0.6 pH unit must result predominantly from an additional pH decrease in the microenvironment around the active sites of the
155
urease. As discussed for the effects of adding NaAlg to the urease solutions, the local electrostatic potential v/” induced by Alg can be obtained from the pH decrease ( - 0.58) in the microenvironment by eqn. (4 ). The value y/” was calculated to be -0.0343 V; this values is that relative to the /? region of the urease layer. The result was almost equal to that obtained from the optimum pH shift in the solution. The optimum pH shifts of the asymmetric multimembrane will be discussed later. At the optimum pH, the V_, value of the urease solutions and the value of JT through the multimembrane were increased slightly by adding NaAlg, as shown in Figs. 4 and 7. These results coincide with those of Nichol et al. [ 15,211, who studied the effects of adding polymers to urease solutions on the hydrolysis of urea, and showed that V,,, was increased slightly by adding polymers such as bovine serum albumin, ovalbumin and dextran. They attributed these effects to the change in conformation due to the excluded volume of the added polymers. Theoretical analysis of diffusion-reaction of urea through multimembrane Urease catalyzes the hydrolysis of urea: NH2CONHz +2H20=2NH4+
+CO;-
(5)
Paying attention to NH,+ which is one of the products P, the reaction of urea S in the urease layer is expressed by S*2P. In the urease layer, if the concentrations of urea are much less than the KM value, the enzymic reaction approximates to a first order reaction [ 2,3]. Under steady state conditions, diffusion-reaction of S and P can be expressed by the following equations in the urease layer: D;(d2C,/dx2)
-kc,
=O
D;(d2C,/d.r2) +2kC, =O
(6) (7)
where k is a first order reaction rate constant, 0: and 0; are the diffusion coefficients of S and P, and C, and C, are the concentrations of S and P at position x of the urease layer, as shown in Fig. 1 (b) . Concentrations of S and P in the urease layer are obtained by solving eqns. (6) and (7) under the following boundary conditions, viz. the interfacial concentrations of S and P between support film 1 and the enzyme layer are C,‘seand CF , and those between film 2 and the enzyme layer are Cp and Cr respectively. c
s=
C,‘*“sinh{cr(Z”-x)}+C$esinh(ax) sinh(&)
(8)
156
c
_2~.C?sinh{cu(l”-x)}+C?sinh(ax) sinh ( ale) 0;
= P
+D;(C~-C~)+2D:(C;+-C:+)x+2D:
+:+?
D;le
+ cp
(9)
P
where cy is (k/D~)““, which is a parameter relating to the reaction rate constant. At each interface, the consecutive law of the fluxes of S and P must be satisfied according to the following equations: -D;(dC,/&)l,”
(10)
-D~(dC,/d_x)2*“=P~(C,2+--C:1)/12
(11)
J,‘,“=P,‘(C:-C$“)/ll= J$“=
JP =P;(
= -D;(dC,/d+”
-CF/ll)
(12)
JF = -D;(dCp/dx)2*“=P;(C~/12)
(13)
where P,‘, Pz, Pi and Pi are permeability coefficients of urea and NH,f through support films 1 and 2. The fluxes of S are discussed first. From eqns. (8), (10) and (ll), (dC,/dx)l+and (dC,/&)2,“canbeobtainedwithoutusing the interfacial concentrations of S and P by the following equations:
1[ -C:
a!
1+
al’
ck!
sinh ( ale)
-3 P,’
2
B =sinh(cul”) 1
crl’
B =sinh(al”) 2
al2
1[ -C:
1
1+
2
cosh(cr1”) -$
cosh(oll’)-; al1
cosh(al’)-$
l-
cosh(cr1”) B1
es
sinh(cx1”) P,” cosh(a1”) -$
1
1
P,’
.D”+cosh(&) s
Pz
*D”+cosh(c@) s
1
(14)
(15) (16) (17)
Then, Jt," , J $” , C,l+ and C,“pecan be obtained by using eqns. (lo), (11 ), (14) and ( 15 ) . The enzyme reaction rate in the enzyme layer V can be obtained by: V=
J,‘,” _ Jfp”
In the same manner as in the case of the substrate:
(18)
157
+C;-C:, 1”
2cuD3’ -_’ PEl”
(Cf,e+C:*e)
sinh ( ale) 1” Dell B,=l+L+L P’le P
PAI’
(19)
sinh(cuZ”)
2cuD; C$“cosh(aZ”) -C,l*’ +C;-C:,+2crD:Z’
[l-cosh(aZ”)]
20: _(CpL__C,l,e) +leD;
(C;,e+C,l,e)[l-cosh(aZ”)] sinh(aZ”)
-1 &
(20)
De12 P212 P
(21)
From eqn. (12 ), (13 ) , ( 19) and (20)) the concentration profiles of P can be calculated. The total of the fluxes of P into compartments I and II is equal to 2v. J;=-Jp+Jp
(22)
The flux ratio of P, - Jk/Jk’, can be obtained by:
J:,
(23)
Symmetric multimembrane The diffusion-reactions of urea through the symmetric multimembrane, 1SP 1urease layer 1SP I, are discussed theoretically. The permeability coefficients of urea and ammonium ion NH,+ through the SP film as shown in Table 1, were used in the calculations, the diffusion coefficients in the urease layer being obtained by Wang’s equation [ 22,231 D”=D,(l-1.5~~)
(24)
where Do is the diffusion coefficient in water and VAis the volume fraction of Alg. Some of the calculated concentration profiles of S and P in the multimembrane are shown in Fig. 8. The concentrations of the substrate were found to be less than or almost the same as the KM values of urease. The diffusionreaction of urea through the urease layer can thus be considered approximately to obey eqns. (6) and (7). Figure 9 shows the total flux of P, J,’ as a function of CYZ”. The values of J,’ increase with increasing al” and approach asymptotically to a constant value. The flux ratios of P, - Jk/JF , are greater than 1, as
-I’
0
x/cm
19 2
Fig. 8. Calculated concentration profiles for substrate (S) and product (P) in symmetric multimembrane. 1s: Substrate (al’c0.7); 1P: product (al”~0.7); 2s: substrate (ale= 1.2); 2P: product (&“=1.2); Ct =O.l, Cf =O mol-1-l. Data shown in Table 1 are used in the calculations.
Fig. 9. Variation with cyle of calculated total flux of product J,’ for symmetric and asymmetric multimembrane; SM: symmetric multimembrane; AM: asymmetric multimembrane. Data shown in Table 1 are used in the calculations.
shown in Fig. 10, and increase with increasing CYZ”, i.e. the flux of P into the donor part is greater than that into the acceptor part. From the experimental results for J,’ shown in Fig. 4 and the theoretical values in Fig. 9, the reaction rate constant, k, in the urease layer was obtained. The results are shown in Fig. 11. The value of k showed maxima at the optimum pH for the multimembranes both without and with NaAlg. By using these k values, the efflux ratio of the product, - Jk/JF, can be obtained from Fig. 10, and the expected values are shown in Fig. 5 together with the experimental results. The expected values were slightly smaller than the experimental results. However, neglecting the water flow due to osmotic pressure, the perme-
159
-A SM
!i
0.02
-
-,P . ..a
7 - 0.01 AM-
0'
I
0
4
2
ale
6
6
'0
Fig. 10. Variation with al” of calculated flux ratio of product - Ji/Jz for symmetric and asymmetric multimembrane. SM: symmetric multimembrane; AM: asymmetric multimembrane. Data shown in Table 1 are used in the calculations.
- a0
1
6
8
7
'0
9
PH
Fig. 11. Rate constant k of urease vs. pH. Rate constant k obtained from J;f through the multimembranes: ( 0 ) urease; (0 ) urease and NaAlg. Rate constant k’ obtained from V,, and KM: ( A ) urease; ( A ) urease and NaAlg.
ability coefficients of the support films were overestimated slightly. Taking this effect into consideration, the theoretical results - JL/JF increase slightly. We can thus consider that the theoretical values coincide semi-quantitatively with the experimental results. When the concentration of urea is much less than the KM of urease, k is estimated approximately to be k= V,,,/&. V,, is proportional to the concentration of an enzyme Cn, i.e. V_= k+2CE, where k+z is the rate constant of breakdown of the enzyme-substrate complex. Taking the concentration differences of the urease into consideration, the k values for urease in the multimembrane can be estimated from the results for V,,, and KM shown in Fig. 7.
160
Denoting k thus obtained as k’, the values of k’ are shown in Fig. 11 together with the k values obtained from J,‘. The values of k were found to be much less than k’ and the profiles of pH vs. k to be much sharper than those of pH vs. k’. As shown in Fig. 8, the concentrations of urea in the urease layer are in almost the same region as Khl. Thus, one of the factors resulting in the lower k values is considered to be the fact that the reaction is of Michaelis-Menten type. Effects of asymmetry of multimembrane on diffusion-reaction The permeabilities of S and P through the support films on both sides of the urease layer affect significantly both JpTand - JL/JF. The theoretical values for the asymmetric multimembrane, ) SDMV 1urease layer ] SP ] , are shown in Figs. 9 and 10 together with those for the symmetric multimembrane. Due to the lower permeability of urea and NH,+ ions through the SDMV support film 1,the values of J,’ through the asymmetric multimembrane are less than those for the symmetric one, and the calculated values of - Jk/Jz are near 0.006, much lower than those for the symmetric multimembrane. Comparing the theoretical results with the experimental ones, the results for J,’ shown in Fig. 6 were more than the theoretical values obtained using k values of the synthetic multimembrane and the results for - Jk/Ji’ shown in Fig. 5 were in the range 0.2-0.6, more than 10 times as high as the theoretical values. Tanny et al. [6] studied precisely the ion flows in a membrane composed of an anion exchanger and an urease phase, and showed that carbamate ions NH, COO -, an intermediate in the hydrolysis of urea, take part in the diffusion-reaction: NH, CONH, + Hz 0 =NH, COO - + NH,+
(25)
i.e. the carbamate ions produced near the interface between the anion exchanger and the urease phase exchange through the anion exchanger with anions in the donor solution, in which the carbamates decompose spontaneously with a halflife of several msec [ 241. NH,COO-
+H,O=NH,+
+CO:-
(26)
As pointed out by Tanny, the carbamate ions diffuse into the SDMV film 1 and the products NH: and CO:- diffuse out to the donor compartment due to their concentration gradients. Consequently, the value of - Jk/JF become greater than the theoretical values, which do not take the presence of the carbamates into consideration. To analyze them more precisely, we must take the unstirred boundary layer in the compartment containing the urease into consideration. This layer does most of the work in decomposing the urea. Utilizing the free solution value of urea diffusion and a halflife of several msec, it is found, by using the relation 6=2Dt, that almost all the reaction must take place within 10 ym of the urease solution/support film interface. This being the case, the concentration profiles are more complex than indicated in Fig.
161
1 (b). If these situations are taken in consideration, the theoretical values of - Jb/JF may become closer to the experimental ones. The values of pH showing the maximum J,’ for the asymmetric multimembrane shifted to more acidic regions, both for the cases with and without Alg, than the corresponding values for the symmetric multimembrane. From these facts, the values of pH in the urease layers are considered to become more acidic, an effect resulting from the efflux of carbamate anions through the SDMV film. For the diffusion-reaction of urea through the asymmetric multimembrane containing urease, carbamate ions are suggested as playing important roles in the total flux of product JpT, the flux ratio of product - Jk/Jk’, and the optimum pH of the urease.
References 1
2
3
4 5
6
7
8 9 10 11 12 13 14
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