Phosphatase Active Cross-Flow Microfiltration Poly(vinylidene Difluoride) Bioreactor

Polymer International 39 (1996) 17-30

Phosphatase Active Cross- Flow Microf iltration Poly(viny1idene

Difluoride) Bioreactor

M. G. Roig, J. F. Bello, S. Rodriguez

Departamento de Quimica Fisica, Facultad de Farmacia, Apartado 449, Universidad de Salamanca, Salamanca 37080, Spain

J. F. Kennedy & D. W. Taylor

Birmingham Carbohydrate and Protein Technology Group, School of Chemistry, The University of Birmingham, Birmingham B15 2TT, UK

(Received 9 September 1994; revised version received 20 July 1995; accepted 27 July 1995)

Abstract: Alkaline phosphatase from human placenta has been chemically immobilized on a hydrophilic cross-flow microfiltration membrane made from poly(viny1idene difluoride) (PVDF) derivatized with 1,l'-carbonyldiimidazole. The physicochemical characterization of the immobilized biocatalyst paid special attention to the irreversibility of the bonding of the enzyme to the support, the effects of pH, temperature and ionic strength on this activity, the existence of limitations of internal and external diffusion for H +, substrate and/or products, and the kinetic behaviour (intrinsic and/or effective) of the immobilized enzyme. With respect to enzyme stability, patterns of hysteresis or memory are proposed, to account for a catalytic activity affected by previous experimental events and situations. The intrinsic kinetic behaviour, rate versus substrate concentration in the absence of diffusional restrictions, was analysed graphically and numerically (by non-linear regression and by utilizing the F statistical test for model discrimination), postulating a minimum rational rate equation of 2 : 2 degree in substrate concentration. In concordance, a mechanistic kinetic scheme for the catalytic enzyme action has been postulated.

Key words: Membrane, microfiltration, poly(viny1idene difluoride), alkaline phosphatase, immobilization.

I NTR 0 D U CTlO N some important enzyme-phosphate complexes.6 These complexes are covalent (phosphoryl-enzyme (E-P)) at

The profusion of studies on alkaline phosphatase has acid pH values and addition complex type (E.P) at alka- provided a comprehensive knowledge of the enzyme line pH.3,7,8 which has been set forth in a book by McComb, Alkaline phosphatase from human placenta is a dimer Bowers & Posen' and in various reviews.' Alkaline consisting of two identical subunits' with molecular phosphatases (EC 3.1.3.1) are enzymes which show non- weight 125000 and 116000 Daltons."." It would be specific phosphohydrolase activity on many phosphate expected to show the majority of the kinetic character- esters and anhydrides independently of the nature of the istics and mechanisms of alkaline phosphatases in leaving group. The enzyme thus shows both hydrolytic general. With respect to steady state kinetic data, it and phosphotransferase but has also been should be noted that all the studies carried out with shown to function as a phosphate carrier since it forms purified enzyme have been treated from a Michaelian

point of view; that is, by determining the different K , * To whom correspondence should be addressed. and V,,, values for the conditions and methods studied.

Polymer International 0959-8103/96/$09.00 0 1996 SCI. Printed in Great Britain 17

18 M . G. Roig et al.

In 1960, Ahmed & King” published one of the first kinetic studies for the enzyme, finding Eadie-Hofstee linear plots and determining a K , of 5 . 7 r n ~ for 4- phenyl phosphate and 25 mM for the glycerophosphate. The only objection one could posit to this study is that the substrate concentration range was small (0.1- 0-04 mM). Harkness’ also treated the enzyme as Michaelian (using a more purified and crystallized enzyme) and published the K , values of 11 different substrates (0.8 mM for 4-nitrophenyl phosphate and 1.4 mM for B-glycerophosphate), although again the range of substrate concentration used to determine these K , values was small (1-0.2m~). In 1968 Fishman and c o w ~ r k e r s ’ ~ determined the K , values of the enzyme with phenyl phosphate as substrate at different pH values, ranging from 0.31 mM at pH 9-2 to 1 7 . 0 m ~ at a pH of 10.7. In later studies, Lin et al.,14 Van Bell’s and Sugiura et ~ 1 . ‘ ~ also showed a Michaelian behaviour for the enzyme in their studies on inhibition by tryptophan, levamisol and the effects of Zn2+ and Mgz+. Again, the ranges of substrate concentration were not wide enough to permit the observation of devi- ations from Michaelian kinetics.

Moss & WhitakerI7 incubated radioactive 0-

phosphate with the enzyme at pH 5 and subsequently measured the radioactivity incorporated into the enzyme. They showed two phosphate binding sites for each molecule of enzyme. Linear Scatchard plots indi- cated the absence of cooperative effects between the sites, i.e. the two sites of the enzyme seem to be func- tionally and structurally equal. If this were true at an alkaline pH it would favour the Michaelian kinetic behaviour. In this sense, a few questions arise: Are there also two independent sites at an alkaline pH? Might not phenomena of cooperativity occur between the sites at an alkaline pH such as those observed with phosphatase from Escherichia coli.?’* With alkaline phosphatase from human placenta, there is an additional and quite important problem underlying all that has been commented on so far, i.e. the heterogeneity of the molecular forms found for the enzyme. Do the three genetic isoenzymes have different kinetic behaviour ? Do the units of molecular aggregation or association formed with other ligands have the same catalytic activity? Fortunately, there appear to be no problems with respect to the activity-heterogeneity of the enzyme. Byers et al.” observed that the three homozygotic variants of the enzyme (FF, 11, SS) did not show differ- ences in catalytic activity, either at acid or alkaline pH, calculating the K , values for 4-nitrophenyl phosphate at a pH of 9.6 as 54, 71 and 7 6 p ~ for FF, I1 and SS, respectively. They concluded that any difference with respect to K , and V,,, among the different variants seems to be marginal.

Heterogeneity of aggregation or association also seems to be present. Thus Ghosh” reported that the two purified molecular variants exhibited similar kinetic

properties. The results of Doellgast et ~ 1 . ’ ~ seem consis- tent with this idea; when their ‘B’ form (the largest) was subjected to electrophoresis with sodium dodecylsulfate (separation of the subunits), a band appeared in the same position as for their ‘A’ form, under the same treatment. They also observed that the ‘A’/’B’ ratio for protein concentration was almost the same (about 3) as that found for their specific activities in the native state. This would mean that the ‘B’ form, although in a greater state of aggregation and associated with other inert proteins, maintains its unit of phosphatase with the same catalytic activity as the ‘A’ form. These find- ings are important for kinetic studies with commercially purified enzymes, since these are a mixture of the different molecular forms described for the enzyme. Evi- dently, it would not be particularly relevant, from a kinetic viewpoint, to work with mixtures of isoenzymes if they had the same catalytic behaviour and only dif- fered in aspects which do not substantially affect activity.

Immobilization of enzymes, as well as making it possible to utilize their unique properties (high activity and specificity) in analytical chemistry, medicine, fine organic synthesis, food and pharmaceutical technology, etc., is also of use in fundamental research for solving basic problems of a biochemical, enzymological, molecular biological nature.22 In this sense, enzymes adsorbed on to synthetic membranes may serve as approximate models for the study of the mode of action of enzymes associated with biological membranes, e.g. of alkaline phosphatase from placenta (anchored to a cell membrane via a phosphatidylinositol linkage through its C-terminal amino acid).23 The non- Michaelian kinetic behaviour of various artificial alkaline phosphatase membranes was shown to depend on the presence of an undisturbed layer in the interphase between the membrane and the solution, and on the effect of inhibition by the product ph~sphate . ’~ Kat- chalski et al. conducted theoretical analyses on the role played by the Nernst---Planck diffusion layer at the time of determining the apparent kinetic behaviour of the enzyme membrane. They confirmed that the global reaction rate is affected by the substrate concentration in the membrane/solution interphase and by the catalytic and physical parameters of the enzyme membrane. The crosslinking of human placental alkaline phosphatase with human serum albumin protein by means of glutaraldehyde provides monoenzyme membranes” whose action is regulated by the enzymatic reaction itself, as well as by diffusion of metabolites through the membranesz6 Physicochemical characterization and kinetic information on alkaline phosphatase immobilized by tannin,27 soil,28 and sepiolites” have been recently reported.

I n uiuo it is frequently the case that enzymes are immobilized on/within structural material, cellular membranes and other ‘solid phases’,30 e.g. human pla-

POLYMER INTERNATIONAL VOL. 39, NO. 1, 1996

PVDF bioreactor 19

cental alkaline phosphatase, a non-specific membrane enzyme with transport, functions by means of hydrolysing phosphorylated intermediates involved in the movement of a multitude of substances across membranes. To get closer to the in-viuo situation, the enzyme has been immobilized by a multisite attachment on a cross-flow microfiltration hydrophilic poly(viny1idene difluoride) (PVDF) membrane. The aim of this work was to carry out a systematic study of its kinetic behaviour hydrolysing a crossing substrate before postulating a mechanism of its catalytic action.

MATERIALS A N D METHODS

Materials

Enzyme. Alkaline phosphatase (AP) from human placenta (EC 3.1.3.1) was supplied by Sigma Chemical Co. (St Louis, USA) in lyophilysed form and with a specific activity of 15.6 Sigma units ml-'. The stock solution of the alkaline phosphatase was prepared by weighing and dissolving a known quantity of alkaline phosphatase in 5 ml of cold 10mM Tris/chloride buffer, pH 7.5. In order to use enzyme free from possible denatured fractions, the enzyme was microfiltered through a 0.4 pm Millex- HA Millipore filter. A spectrophotometric scan was then carried out between 200 and 350nm and the concentration of the enzyme was calculated (2-3 mg mlK ') from the Beer-Lambert law at 280 nm, the extinction coefficient of the enzyme being 1 mgK' mlcm-'. Intermediate enzyme solutions ( ~ 0 . 6 mg ml- ') were prepared by dilution in cold l m ~ Tris, pH 7.5, stock solution. The enzyme solutions were kept at 0-5°C to avoid deactivation. The stability of the enzyme in solution at 5°C was such that at 0-5-4pgml-' it lost practi- cally no activity over the first 7h, with no losses of activity greater than 5% being detected in general within the first 14h. On the other hand, at 37°C the enzyme began to lose activity by approximately 20% in 1-2h of storage (enzyme concentrations of 0.5- 2 pg ml- '). This loss of activity generally reached 50% after 6 h storage. Therefore, freshly prepared enzyme solutions were used.

Substrate. The substrate used was 4-nitrophenyl phosphate (4-Npp) (Sigma 104 substrate, Sigma Chemical Co., USA). The reagent contained <0.5% 4- nitrophenol (4-Np) and phosphate, and it was therefore used without further purification. Substrate solutions were prepared in 10 mM bicarbonate/carbonate buffer, pH 10.0, ionic strength Z = 0 . 0 2 ~ or in 5 0 m ~ bicarbonate/carbonate buffer, pH 8.0-1 1.5, ionic strength Z = 0 . 1 4 ~ . Sodium phosphate (Merck), ammonium chloride, sodium chloride (Panreac), sodium azide, Tris, ethanolamine and Tween-20 (Sigma) were also used.

Instrumentation

The determination of reaction rates in the kinetic studies (rate versus pH, enzyme stability) as well as of the UV-visible spectra, was carried out on a Beckman spectrophotometer (Beckman Instruments Inc., Ful- lerton, CA), model DU-7, with a wavelength of between 190 and 800nm, fitted with a Hewlett-Packard 26716 recorder (Hewlett-Packard, Irvine, CA). Determinations of pH were carried out on a pH meter (PHM 84) (Radiometer, Copenhagen) with a temperature com- pensation device and electrodes K 4040 (HY-I) and G-2040 C (KJ-I) (Radiometer, Copenhagen). A Selecta 389 thermostat was used to maintain the temperature within a range of +O.I"C. A PSEM-500 Philips scan- ning electron microscope (Philips, Eindhoven) was used for obtaining micrographs of the PVDF support. Minitan-S (Millipore Spain SA, Madrid, Spain) is a cross-flow ultramicrofiltration system that was utilized throughout this work simultaneously as a bioreactor due to fact that the PVDF filtration membrane was partially loaded with immobilized enzyme. A Gilson Minipuls peristaltic pump (Gilson, Villiers-le-Bel) was employed.

The statistical fitting of certain kinetic data was carried out with the Simplex algorithm implemented on an IBM-AT microcomputer.

Support

A Millipore affinity membrane (Immobilon AV) kindly supplied by Millipore Spain SA (Madrid) was used as support. This hydrophilic PVDF membrane (140 pm, micrcporous-70% void) had been chemically activated with 1-carbonylimidazole groups by reacting with 1,l'- carbonyldiimidazole (Fig. l), the aim being to covalently bond the amino groups of lysine from protein^.^' PVDF is a semi-crystalline polymer of 1,l-difluoroethyl- ene (vinylidene difluoride), containing 59.4% fluorine. The symmetrical arrangement of the hydrogen and fluorine atoms in the chain contributes to the unique polarity, due to the two distinct dipole moments of the alternating CF, and CH, groups. This is influential in the polymer's dielectric properties and solubility. Its uniform pore size (0.65 pm) confers peculiar character- istics to this activated microporous membrane, such as facilitating the uniform flow of liquids. Its large specific surface area (155cm' per cm2 sheet area) permits bonding of proteins within and on the external surface of the membrane, and prevents membrane fouling. These properties have been utilized for acting as a cross-flow passive filter and a biocatalyst. Its bonding capacity for proteins is around 1OOpg per external square ent ti metre,^' a little less than the 190pg per external square centimetre of another PVDF Millipore membrane for hydrophobic adsorption of proteins. Nevertheless, for the direct immobilization method, the



PVDF 1. 1 '- Carbonyldirmidazole Activated PVDF

N H - C - - N 'by\=/

N

N +

N

+

NH L

Enzyme Immobilized Enzyme

H2N. P 3 II

I / 0

PVDF afllndy membrane c

NH c

Fig. 1. Derivatization of a PVDF membrane (Immobilon AV Millipore affinity membrane) for chemical immobilization of

proteins.

irreversibility of the bonding and the high mechanical strength and resistance of the support (which permits a wider range of experimental conditions) show the hydrophilic affinity PVDF membrane to be a versatile and convenient support for chemically immobilizing enzymes.

Immobilization method

The immobilization method (Fig. 1) comprises the nucleophilic attack of the &-amino groups of lysine and arginine from the enzyme to be immobilized on the car- bony1 moiety of the carbonylimidazole group of the activated PVDF membrane. The amount of protein immobilized is dependent upon the protein concentration and the time of immobilization. pH, ionic strength and temperature have little impact on the rate, or extent, of protein immobilization (pH 4-10, 0.01-1.0 M ionic strength, 0-37°C temperature). The protein coup- ling efficiency (40-60%) with a high capability of covalent protein immobilization (92% of the immobilized protein) is an important feature of the membrane. Co- valent immobilization results in improved kinetics between the interacting partners3* and reduces the like- lihood of displacement of the immobilized ligand by non-specific proteins.33 The technique was carried out by incubating the enzyme solution with the piece of membrane fitted in the Minitan bioreactor at 2 ml min- ' flow rate.31 The cross-flow microfiltration

through the Minitan system minimizes the shear forces, being advantageous for immobilizing the enzyme without denaturing it.

A possible drawback of this method is that amino groups of catalytically essential amino acid residues in the enzyme may be involved in this reaction. Often the active groups on the support (in this case the imidazole groups) preferentially attack the active site of the enzyme, thereby inactivating it. Accordingly, a 0.1 M phosphate buffer, pH 7.4, was used to dissolve the enzyme. This is a competitive inhibitor of the enzyme (Z5,, = 1 . 5 m ~ at pH 10.5) which preserves the enzyme from possible inactivation during its immobilization.

Spectrometric study of products and reagents

4-Nitrophenyl phosphate (pK, < 2; pK, = 5)34 exhibits a spectrum with maximum UV absorption between 310 and 314nm. The molar extinction coefficient of 4-nitrophenyl phosphate dissolved in 10mM NaOH is 9 9 9 0 c m - ' ~ - ' at 311 nm and 25°C. Interference from 4-nitrophenol at 400 nm is minimal. At alkaline pH, 4-nitrophenol, one of the reaction products, is found in the form of the 4-nitrophenolate anion (pK = 7.15),35 a species that absorbs in the visible region with a maximum centred on 400nm. This species was chosen for following the reaction kinetics.

Most of the studies were carried out at pHs above 9, the extinction coefficient of 4-nitrophenol was therefore taken directly at an alkaline pH (in 0 . 0 1 ~ NaOH, pH 11.7 and ionic strength 0.01 M), being 182OOcm-'M- '. In the studies carried out at only a slightly alkaline pH (pH 7.5), 4-nitrophenol is found in both its dissociated and undissociated forms so that the total concentration of 4-nitrophenol is given by

where A, is the total absorbance at 410nm and E~~~ is the apparent extinction coefficient given by

eA- and being the molar extinction coefficients at 410 nm of the basic and acid forms, respectively, and K: the dissociation constant of 4-nitrophenol. was measured in an acetic/acetate buffer solution at pH 3.9, yielding a value of 29.1 cm- ' M - ' ; cA- was measured in ~ O - ' M NaOH, pH 11.7, giving a value of 1.82 x lO4crn- '~- ' . The values of [H'] and of the equilibrium constant Kg at different ionic strength were determined by considering the effects of the activity coefficients by means of the Debye-Huckel equation as modified by D a v i e ~ . ~ ~ Once the extinction coefficients,


P V D F bioreactor 21

the values of [H’] and of Kg are known, it is possible to calculate the apparent extinction coefficients of 4- nitrophenol at different pH values and ionic strengths.

Kinetic procedure

Phosphate-ester hydrolyses catalysed by alkaline phosphatase were followed by a dynamic method measuring initial reaction rates, to avoid the strong inhibition that takes place due to the phosphate reaction product. The alkaline phosphatase activity was measured as absorbance at 410 nm of the product 4-nitrophenol (4-Np) released during the kinetic run.

To follow the kinetics catalysed by the immobilized enzyme, the following technique was used : The substrate solution in 10 mM carbonate/bicarbonate buffer, pH 10.0, was thermostatted in a plastic vessel to the desired temperature. Using a Gilson Minipuls 2 peristaltic pump-normally at a recirculation flow rate of 2 ml min- ‘-the substrate solution was passed through Teflon tubes into the Minitan-S cross-flow microfilter/ bioreactor, where the human placental alkaline phosphate immobilized in the PVDF microfiltration membrane was fitted. The partially transformed substrates and products were channelled into a spectrophotometric flow cell (Hellma, GmbH and Co., Mulheim/Baden, Germany, 80 pl), and the increase in absorbance at 410 nm measured as a function of time in a Beckman DU-7 spectrophotometer coupled to a Hewlett-Packard 267 1G recorder. Finally, the circuit was closed with a connection between the optical cell and the vessel originally containing the substrate.

The kinetic curves appearing on the screen of the spectrophotometer were used to collect data on the initial linear stretch of the absorbance-time plot; the values of the initial rates ( V ) were deduced in pmol 4-Np min - ’, considering the apparent extinction coefficient and the total volume of the aqueous solution. Throughout this work the rate values refer to the total amount of enzyme immobilized on 244cm2 of membrane surface.

Curve- fitting

For an enzyme exhibiting a more complex kinetic behaviour than ‘Michaelian’, its rate equation at steady state would be of the following type:

V u = - [El0

thus making it necessary to fit the experimental data to rate equations of degree 1 : 1, 2 : 2, . . ., n : n. The theoretical justifications for this behaviour have been well

although experimental application has

not been sufficiently extended. We used the Snedecor F test, which has been proposed as the most suitable for this purpose.39 The range of substrate concentrations should be as broad as possible and a suitable number of points would be 10-15.

Accordingly, in the present work the aforementioned philosophy was applied, beginning with a visualization of the data through graphical plotting in different spaces, using the program ‘EnzygraphlO’ which auto- matically provides the different v[S] plots (direct, Lineweaver-Burk, Eadie-Hofstee). Following this, the data were fitted numerically to the successive rate equations of degree l : l , 2 : 2, 3 : 3, . . . , etc., by a non-linear regression program written in Fortran on an IBM microcomputer.

Non -linear regression program

None of the several algorithms for dealing with the problem of non-linear regression offers absolute cer- tainty. However, if the fitting between the experimental data and those calculated seems satisfactory and if the same minimum is found with different initial systems, then one may assume that the minimum reached is the overall minimum. In all fittings in this study this strat- egy was followed precisely.

The algorithm used was of the type known as ‘sequential’ and is called the ‘simplex method, improved by Nelder & Mead.40 The method involves calculation of the sum of the square residuals at the three corners of a triangle; the highest summatory is then inverted to form a new triangle, and so on, successively. The program deals with the fitting of rate versus [substrate] data to the generic rate equation (eqn 3), an expression that is in keeping with enzyme kinetics.37

F Test

To discriminate between the fittings to rate equations of successive degree and hence be able to determine the degree n : n of the equation after which an increase in degree will not significantly improve the sum of square residuals, the statistical F test was applied according to the formula proposed by Lindgren:41

(4)

where Qj’ and Qf+l represent the sum of squared residuals for models 1 and 2, mj and mjt are the corresponding numbers of parameters and n IS the number of experimental data points. The value of F thus obtained is compared with tabulated values of F for confidence levels of 95 and 99% if calculated F is greater than tabulated F , the improvement is significant; and if calculated F is less than tabulated F , then the improvement is not significant.



RESULTS AND DISCUSSION

Enzyme adsorption isotherms

Chemical adsorption (e.g. human placental alkaline phosphatase on the hydrophilic PVDF membrane) is due to the formation of chemical bonds between the adsorbent and the adsorbate. The bond is short-range in nature and can only be formed by molecules directly in contact with the surface of the adsorbent, that is, only those situated within bonding distance. As a result, a monolayer of adsorbed biomolecules is formed. Simi- larly, since the adsorbent-adsorbate interactions are intense, the heterogeneity of the surface is important. The force of attraction between the adsorbent and the adsorbate decreases progressively as the surface covered increases.

Batch adsorption isotherms were determined at 25°C. Six 1.0 ml solutions of various enzyme concentrations were added to six 2.25 cm2 PVDF sheets (0.0180 g dried weight) for 4 h with gentle shaking to immobilize the alkaline phosphatase. The final six enzyme concentrations were measured, and found to be between 0.1 and 11.2 mg ml- '. After washing the six PVDF membranes (by recirculating a flow of 10 mM carbonate/bicarbonate, pH 10.0, for 1 h), the amount of alkaline phosphatase immobilized was quantified by means of kinetic assays. As the enzyme activity is directly related to the enzyme loading, the corresponding enzyme activity per gram of dried support (E) versus enzyme concentration ([El) at equilibrium data were fitted to the following Langmuir isotherm:

Emax represents the number of molecules of enzyme per unit mass of the adsorbent required to occupy all the active sites of the surface of the adsorbent, E is the number of molecules of enzyme adsorbed per unit mass of the adsorbent at a given moment and [El is the enzyme concentration at equilibrium. K,d is the equilibrium constant for the adsorption process (immobilization reaction). Linear regression fitting of the double reciprocals of E versus [El data gives the following adsorption parameters: Em,, = 0-343 pmol min- 'g- ' ;Kad = 21.5mgml-' = 1.85 x 1 0 - 4 ~ .

To interpret the phenomenon of adsorption, Lang- muir proposed a simple model, based on the following hypothesis: (a) The surface of the adsorbent displays a certain number of active sites for adsorption. (b) Only one molecule of adsorbate can adsorb on to each active site (monolayers). (c) The adsorbate-adsorbent interaction energy is the same for all active sites, that is, they have the same probability of being occupied. (d) There are no lateral interactions among different molecules adsorbed on to the active sites of the surface of the adsorbent. However, interaction between biomolecule

and absorbent is rarely that simple. Many configu- rations of binding sites on the surface of the adsorbent present themselves to, for example, a protein, which itself may offer more than one surface to bind to. Con- sequently, a polydispersity of interaction strengths exists, that is, a range of possible adsorption constants is expected. Is it possible to average the spread of values and use a single figure that approximates the interaction of most molecules? Sorption experiments indicate that much of the binding can be described by a single apparent adsorption constant. Nevertheless, its average value will vary depending on the percentage of occupied sites.

The intensity of the adsorbent-adsorbate interactions will become smaller as the fraction of covered surface increases (4 = E/Emax). Additionally, lateral interactions will increase as 4 increases. As a result, in most cases these two effects will tend to cancel each other, such that the Langmuir isotherm usually interprets empirical behaviour acceptably well. Nevertheless, adsorption theory for proteins is a compromise of approximations and assumptions.

Stability kinetics

The stability of human placental alkaline phosphatase immobilized on PVDF affinity membrane was studied under storage conditions (in 10mM Tris buffer, pH 7.5, 0 . 0 2 ~ ionic strength, 5°C (storage)) and under various experimental conditions, pH (carbonate/bicarbonate buffer, pH 8.1-1 1.0), ionic strength (0-1.2 M), temperature (5-50 "C), flow rate (2-30 ml min- '), [substrate] (0.01-1 mM) by intermittent operation.

The A P activity (u ) of this immobilized preparation was measured under standard conditions (10 mM carbonate/bicarbonate buffer, pH 10.0, 0-02 M ionic strength, 6 ml min- flow rate, [CNpp] 0.2 m ~ , 25°C with continuous stirring. The stability data, activity versus time, from Fig. 2 show two periods of inactivation (14-36th day, 62-83rd day) separated by a period of activation of the immobilized alkaline phosphatase (36-62nd day). After 82 days, the immobilized A P maintained 33% of its initial activity.

Increasing the ionic strength of the experimental environment during the kinetic runs carried out during the second period of time representing activation (Fig. 2) should facilitate a dynamic conformational transition from a stretched enzyme configuration to a globular one (refolding), due to the partial electrostatic neutral- ization of the charges over the protein.

The foldings-unfoldings of protein chains are intra- molecular processes. The kinetics of these reactions can always be described in terms of first-order rate equations. This means that the concentration of a given species is described by a sum of one or more exponen- tial terms, ci Ai exp( - ki t) , where the ki parameters are characteristic time constants and the Ai terms are constant amplitude parameters. The corresponding semi-


P V D F bioreactor

100

23

0 - - . /'

\

82 n m c l day

Fig. 2. Operation/storage stability of alkaline phosphatase covalently immobilized on PVDF affinity membrane. Storage (0.01 M Tris buffer, pH 7.5, ionic strength 0.02 M, 5 O C ) . Stan- dard assay of A P activity (0.2 mM 4-Npp, 0.01 M carbonate/ bicarbonate buffer, pH 10.0, ionic strength 0.02M, 25"C,

recirculation flow rate 6 ml min- I).

logarithmic plots of the data u versus time for human placental alkaline phosphatase immobilized on PVDF membrane are linear, with the slope being -ki, the inactivation or activation kinetic constants (function of temperature, microenvironment, immobilization procedure, etc.) (k = 0*03day-', tllz = 23 day for the two inactivation processes; k = 0.05 day- ', t1/2 = 14 day for the activation process). The stability profile of 1 pgml-' human placental alkaline phosphatase in solution (10 mM carbonate/bicarbonate, pH 9-8, 0.025 M I , 5°C) was checked by GhaYs4* with the first-order inactivation parameters k = 0.2day-', tlj2 = 3-5 day.

Logically these folding-unfolding processes are much slower for immobilized proteins than for soluble proteins. The dynamic structural response of the enzyme- support to new environments takes time to achieve a quasi-static equilibrium configuration. This may explain the slow first-order inactivation (activation) processes found as well as the following fact. The activity of the stored immobilized enzyme was checked three times daily (30 days) in standard conditions (see Experimental procedures) before beginning kinetic experiments (uJ. At the end of the day, after the kinetic protocol was completed, the standard kinetic assay of the activity of the immobilized enzyme was again checked three times ( u , ~ ) . In 72% cases, significantly, ula > u,, and in the 28% cases where the contrary was true the samples always corresponded to experimental protocols where the conditions were maintained for repressed AP activities (low flow rate, low substrate concentration).

The most potent effect of immobilizing an enzyme on a rigorous support of regular structure is that the structure of the enzyme must fit into a unique position, because there are numerous bonds between the enzyme and supporting matrix. This seems to point to the fairly

well accepted notion that the enzyme becomes stabil- ized in the process. However, such a hypothesis should be viewed with certain provisos. Accordingly, direct comparison of the stabilities of the enzyme in solution and when immobilized, without consideration being given to concentration effects, should be devalued.

Activity versus pH profiles

Since protons participate in the hydrolysis catalysed by AP,43 it was suggested that its catalytic activity would depend on the pH. The following experimental protocol was designed to investigate this: flow rate 2.0 (6.0)mlmin-', 0-2 (0.2, 1-0, 10)mM 4-Npp, 5 p m ~ carbonate/bicarbonate buffer, 0.14 M I , 25"C, pH varying between 8.1 and 11-&a total of 27 kinetic runs. The results are shown in Fig. 3, where the typical bell-shaped profiles show a pH optimum increasing from 9.5 up to 10.6 when substrate concentration is increased from 0.2 up to 10.0mM. On comparing this with the profile for human placental alkaline phosphatase activity in solution, which is similar (optimum pH increasing from 9.0 up 10.5),44 a slight shift of optimum pH towards more alkaline pHs is observed when alkaline phosphatase from human placenta is covalently immobilized with PVDF affinity membrane. These A P activity versus pH profiles suggest that under these conditions the limitation to the free diffusion of protons is particularly important (AP activity is less dependent on pH at decreasing substrate concentration and recirculation flow rate). Alternatively, proton transport is facili- tated by the presence of buffer anions. If total concentration of the buffer is sufficiently high, the protons will be rapidly removed from the microenvironment of the enzyme and only a small disturbance will be

I

l 0

0 9.0 10.0 11.0

PH

Fig. 3. Overall enzyme activity versus pH profiles for alkaline phosphatase covalently immobilized on PVDF affinity membrane. Experimental conditions. 0 , 10 mM; B, 1.0 mM and A, 0, 0.2 mM 4-Npp; 0.05 M carbonate/bicarbonate buffer, ionic strength 0.14 M, 25"C, recirculation flow rate 6 ml min- or 0,

2mlmin-'.



seen in the activity/pH profile unless there is severe con- straint on proton diffusion. Accordingly, protons will accumulate on the surface of the support and the internal pH will be significantly less than in the bulk solution, provoking a disturbance in the activity versus pH profile.

Substrate concentration influences reaction rate (high substrate: high reaction rate), the internal pH of the enzyme-support will therefore differ notably from that of the bulk solution. Accordingly, in this catalytic system the accumulation of ionized products in the inte- rior of the membrane strongly affects the local pH (decrease of in-situ pH) and so optimum pH (increases). The importance of this effect depends upon the diffusion coefficient, the dissociation constants of the ionized products and on the buffer capacity of the reacting medium. At the alkaline working pH, this AP-PVDF membrane acts as a polyanionic matrix (isoelectric point of alkaline phosphatase from human placenta = 4.2-4.3, 6.9-7.0), so that there is a tendency to accumulate H + , thus decreasing the pH, around the immobilized enzyme. Accordingly, in the bulk of the solution, the external pH (which is what is measured) is greater than the pH in the microenvironment of the enzyme (operational pH). Therefore, if the catalytic activity versus pH profile of the enzyme in solution is bell-shaped with a given optimum pH, when the enzyme is immobilized the profile will continue to be similar but with an optimum pH displaced to more alkaline values.

Arrhenius profile and thermodynamic parameters

The experimental protocol followed for studying the temperature effect on immobilized A P activity was 0.1 mM (5-0 mM) 4-Npp, 10 mM carbonate/bicarbonate buffer, pH 10.0, 0.02 M I , 3.5 ml min- ' (10.0 ml min- ') recirculation flow rate, working temperature range 5- 50 "C. In conditions favouring slow external diffusional processes (low substrate concentration and low recirculation flow rate), almost no temperature influence is seen on the global enzymatic activity. At high substrate concentration and recirculation flow rate, favouring non-kinetic relevance of the external diffusional transport throughout the Nernst-Planck layer, temperature has a clear influence on the catalytic activity of immobilized A P (data not shown). The optimum temperature is higher than 50°C (optimum temperature of AP-PVDF in a stirred tank reactor was 70°C). For human placental alkaline phosphatase immobilized by crosslinking with human serum albumin, the optimum temperature26 was 40°C, showing the importance of support (structure, mechanical strength and resistance) type for temperature stability.

Assuming substrate concentration is sufficiently high (5.0mM) to consider the initial rates determined are the maximum rates, referred to the enzyme loaded in a

1 cm2 membrane these would be the true k,,, . As k,,, is a general catalytic constant, which may include more than a single rate constant, in principle the activation energy E , that can be obtained from the Arrhenius plot cannot be applied to any particular step of the reaction and must remain, until the reaction mechanism is known, as a catalytic or apparent activation energy. If different steps are involved in k,,, , having different temperature coefficients, the different steps may control the rate at differing temperatures; in this case the Arrhenius plots would not be linear. A possible explanation for the curved Arrhenius profile shown in Fig. 4 could be that at low temperatures the controlling factors are kinetic (catalysis), while as temperature increases, the substrate (products) diffusion becomes the limiting factor on reaction rate. This is because temperature has a more marked accelerating effect on the enzymatic reaction rates than on the diffusion rates. In this sense, in the Arrhenius plot for immobilized alkaline phosphatase the low temperature section is controlled kinetically (catalytically) and the slope of the curve in that range would represent the true activation energy ( E , =

4.5kcalmol-'). At the high temperature section of the plot, the limiting factor is the rate of substrate (products) diffusion within the matrix, which (compared with the enzymatic reaction rate) is so insensitive to changes in temperature that the slope of the Arrhenius plot is close to zero ( E , diffusional control 1.2 kcal mol- '). The activation energy for the enzyme in solution,' pH 10.0, is 10.4 kcal mol- '. Using the V ( T ) data in the range of kinetic control shown in Fig. 4, and carrying out the corresponding linear regression fitting of the respective data of ln(V/T) against (1/T), it is possible to determine the activation thermodynamic parameters, enthalpy (AH* = 4.5 kcalmol- l) , entropy (AS* = -42calmol-' K - ') and Gibbs free energy (at

I -5.40

t 3.0 3.2 3.4 3.6

1 103 T/ K-1

Fig. 4. Effect of temperature on global activity of alkaline phosphatase covalently immobilized on PVDF affinity membrane. Experimental conditions: 5.0 mM 4-Npp, recirculation flow rate 10 ml min- ', 0.01 M carbonate/bicarbonate buffer,

pH 10.0,0.02 M ionic strength.


P V D F bioreactor 25

298 K) (AGt = 17 kcal mol- '). The thermodynamic activation parameters for k,,, can be explained in terms of the number of the weak bonds formed during the activation process. The breakage of each weak bond is assumed to be accompanied by A H of 4 kcal and A S of 12calK-'. Accordingly, lower values of A H f and AS* are associated with the breakage of fewer weak bonds or the formation of a greater number of weak bonds. With no knowledge of the individual constants when V is a complex function, the activation parameters A H * and AGf are likely to be complex functions and difficult to interpret.

Activity versus ionic strength profiles

A kinetic study was carried out with 0 . 2 r n ~ 4-Npp in 10 mM carbonate/bicarbonate buffer, pH 10.0, 25"C, recirculating flow rate 6 ml min- ', ionic strength (with NaCl, NaBr, CH,COONa and Na,SO,) ranging from 0.02 to 1 . 2 ~ . This study of the effect of ionic strength on the immobilized AP activity was carried out to test for the possible existence of electrostatic interactions between the enzyme-support and the substrate (product) with influence on the kinetics. This kind of interaction could result in partition of the substrate (product) between the bulk solution and the heterogeneous phase (immobilized enzyme) and modulating diffusional limitations. The experimental results are shown in Fig. 5, where rate increased up to about 1 . 0 ~ ionic strength. The anion effect seen for SO:- can be explained on the basis of competition between the global accelerating effect and an inhibitory anion effect, due to the chelating action of the Zn2+, an essential cation for the catalytic mechanism."

To examine a possible cation effect on immobilized AP activity, a second experimental protocol was carried out with 0-2 mM 4-Npp in 10 mM carbonate/bicarbonate buffer, pH 10.0, 25"C, recirculating flow rate 6 ml min- ', ionic strength (with NaCl, KCl, NH,Cl and MgCl,) ranging from 0.02 to 1 . 2 ~ . The experimental results showed a global activating effect of the ionic strength besides cation effects (Fig. 6). The Mgz+ cation (according its positive charge 2 +) exhibits the highest activating effect on the immobilized AP activity (100% activation up to 0 . 0 5 ~ ) . For NH: cation, there is an activating effect followed by an inhibiting effect on the immobilized A P activity profile that again could be explained on the basis of competition between the global accelerating effect, due to the ionic strength, and an inhibitory cation effect. This species at pH 10.0 (working pH) is mainly in the NH, form (pK = 9-25),45 which is likely to complex to a certain extent to the Znz+ of the active site of the enzyme, forming Zn(NH,):+ (stability equilibrium constant around 10') thus inhibiting it considerably.

With regards to human placental alkaline phosphatase in solution there is contradictory information on

NaBr

NaOAc

I 2oo t

0 0.4 0.8 1.2

Ionic Strength I M

Fig. 5. Effect of the ionic strength on global activity of alkaline phosphatase covalently immobilized on PVDF affinity membrane for different sodium salts. Experimental conditions : 0.01 M carbonate/bicarbonate buffer, pH 10.0, 25"C, recircula-

tion flow rate 6 ml min -

the effect of ionic ~trength.".~' Perhaps this disparity is due to the effect of salt concentration on the activity of alkaline phosphatases being dependent on the pH of the reaction m i x t ~ r e , ~ . ~ ~ , ~ ' the type of ions i n v ~ l v e d , ' ~ ~ ~ * and the source of the enzyme. Harkness" found a slight inhibiting effect of the ionic strength (20% at 1 . 0 ~ NaCl, pH 10.0) on the catalytic activity of human placental alkaline phosphatase ; however, for GhaYs,,* this enzyme was activated by ionic strength (0.05 up to 0.60 M) at pH 9.7 (7 mM carbonate/bicarbonate buffer), 27°C. The accelerating effect due to the ionic strength may be caused by small variations in the constants of the acidic dissociation and of the basic protonation (which increase and decrease, respectively, with the ionic strength) of the functional groups of the amino acids involved in the catalysis. In this way, the acidic and nucleophilic catalysis, which is a s s ~ m e d ~ ~ - ~ ~ to act in the steps of the reaction mechanism, would be favoured by increasing the ionic strength. Dissociation of the enzyme-phosphate complex(es) could be rate- determining and hence susceptible to the influence of ionic strength. Halford5, measured the conformational changes induced to E . coli alkaline phosphatase by binding experiments with a competitive inhibitor (2-



200 * t; 0 0.4 0.8 1.2

Ionic Strength / M

Fig. 6. Effect of the ionic strength on global activity of alkaline phosphatase covalently immobilized on PVDF affinity membrane for different chloride salts. Experimental conditions: 0.01 M carbonate/bicarbonate buffer, pH 10.0, 25"C,

recirculation flow rate 6 ml min -

hydroxy-5-nitrobenzyl phosphonate). These conformational changes were strongly dependent on NaCl concentration. This suggests that conformational changes (which may accelerate the overall rate) are also induced by NaCl during the action of alkaline phosphatase on substrates.

At working pH, the AP-PVDF membrane is thought to retain some negatively charged residues (isoelastic point of human placental AP is 4-2-4.3, 6.9-7.0). Repulsive anion-anion electrostatic molecular interaction between the charged residues of the immobilized preparation and the molecules of the substrate 4-Npp, negatively charged (pK, < 2, pK, = 5),34 and of the product 4-Np, negatively charged (pK = 7.15),33 may occur. This electrostatic repulsion between charged enzyme-support and substrate first delays external diffusion of the substrate towards the supported enzyme and secondly favours external diffusion of the product 4-Np from the immobilized enzyme towards the bulk solution. Moreover, this repulsive electrostatic interaction causes the partitioning of substrate (product) between the enzyme-support and the bulk phase, the concentration of the substrate being lower in the support.

The addition of a background electrolyte (NaCl, NaBr, sodium acetate, KCl, MgCl,) increases the ionic strength, which causes a disturbance, which means a smaller limitation to external diffusion of the substrate, a faster diffusion rate of the substrate (partially controlling process) and thus a higher overall reaction rate.

Transfer of matter

In the majority of immobilized enzyme systems there are diffusional gradients that distort and complicate kinetic study. A possible way to overcome these limitations is to use flow reactors at sufficiently high flow rates. To check this hypothesis an experimental protocol was designed to test the effects of the recirculation flow rate on the effective/global enzymatic activity. The experimental conditions were 5 mM 4-Npp, 10 mM carbonate/bicarbonate, pH 10.0, 0-02 M I , 25°C and varying flow rates between 2 and 30mlmin-' (recirculating the reaction sample). The results show (Fig. 7) an increase in alkaline phosphatase activity as flow rate is increased, for both high and low substrate concentrations. This effect shows a contribution of limitation of free diffusion of the substrate to the overall reaction rate. In summary, a more vigorous stirring of the solution around the immobilized enzyme, plus an increased flow rate, leads to a decrease in the diffusional limitation of substrate (products). There is a greater relative increase in velocity when flow rate is increased, as the concentration of 4-Npp decreases. At low substrate concentrations, the limitation to free diffusion of the substrate (products) should be considerable (according to the Fick diffusional mass flow equation that assumes a faster diffusional transport at a higher substrate (products) gradient). Hence, at high substrate concentrations, the external diffusion of substrate (products) should be less a rate-controlling step than the

0 10 20 30 Recirculation flow rate / ml min''

Fig. 7. Influence of recirculation flow rate on global activity of alkaline phosphatase covalently immobilized on PVDF affinity membrane for different substrate concentrations (0, 0.2mM and 0, 5 . 0 m ~ 4-Npp). Other experimental conditions: 0.01 M carbonate/bicarbonate buffer, pH 10.0, 0 . 0 2 M

ionic strength, 25°C.

POLYMER INTERNATIONAL VOL. 39, NO. 1 , 1996

PVDF bioreactor 27

chemical rate-limiting step. This will have a determinant effect on the kinetic behaviour of the immobilized AP, as detailed below. Thus, results show that enzymatic activity increases with flow rate until it reaches a plateau between 10.0 and 25.0mlmin-'. A further increase in the flow rate up to 30*0mlmin-' causes a decrease in the rate of the reaction catalysed by this immobilized AP. This may be due to high rates of recirculation at which certain parts of the support are stretched in such a way that access of the substrates to the enzyme is diminished or the configuration of the immobilized enzyme modified. This could also explain the diminished enzymatic activity when flow rate is decreased from 30.0 to 18.0mlmin-'. The external diffusion limitation disappears (or becomes kinetically irrelevant) from a flow rate of 10.0 ml min- ' onwards.

Mechanistic schemes for enzyme kinetic behaviour

In 1977 Hill et aLS4 made an extensive review of studies carried out on enzyme kinetics in solution performed between 1965 and 1976. They found that in more than 800 studies performed with various enzymes, the kinetic behaviour observed corresponded to the 'non- Michaelian' type, which generally needs rate equations of degree 2 : 2, or greater. However, in uiuo most enzymes exist associated with highly organized cellular material (even glycolytic enzymes are physically or chemically immobilized in the cytoplasmic matrix). This is an important basic reason for our interest in investi- gating the reaction kinetics of enzymes immobilized on heterogeneous supports as approximate models of their action in viuo.

In view of the difficulty of carrying out well- characterized and controlled experiments with immobilized biocatalysts (cells or enzymes), considerable effort has been made to apply mathematical treatments of reaction and diffusion/partitioning kinetics in porous media to these systems. The literature offers a large number of solutions for the differential equations involved and for cases of particular geometries and different reaction rate equation^.^' The results of these cal- culations provide an estimate of the effective reaction rate of an immobilized system, based on estimates of the intrinsic reactivity and of diffusion/partitioning of substrates, intermediates and products in the heterogeneous aggregate. The aim is to gain insight into the effects of partitioning and diffusion for an immobilized enzyme and in this way better understand the conformational and microenvironmental factors which may directly affect the values of the kinetic parameters k,,, and K,. The final result should be a better understanding of the factors determining enzymatic behaviour in the living cell.

In the overall kinetics of the transformation of a substrate by an immobilized enzyme, apart from the actual

enzyme (catalyst) kinetics, physicochemical kinetic processes, such as diffusion and partitioning, may participate. Logically, such processes will modify apparent, global or effective kinetics. There are some experimental conditions, in this case high flow rate (>lOmlmin-', uide supra) in which the limitations to free external diffusion of the substrate are minimal. Assuming the absence of a partitioning effect of the substrate ( P = 1) (the PVDF support is electrically neutral), it may be speculated that the system works under conditions close to those in which the intrinsic kinetics of the immobilized enzyme could be discovered. Thus, to a first approximation, at high flow rates (> lOml min- I) ,

immobilized AP could exhibit its intrinsic kinetics. In order to analyse the intrinsic kinetic behaviour of

AP immobilized on PVDF affinity membrane, a series of rate versus [4-Npp] (replicated) kinetics runs was carried out. The experimental conditions were lOmM carbonate/bicarbonate buffer, pH 10.0, 0.02 M ionic strength, 25"C, recirculation flow rate 10 ml min- ', 4-Npp concentration between 0.01 and 1.0mM. The results of the experimental protocol for lOml min-' flow rate are shown in Fig. 8. This corresponds to the Eadie-Hofstee plots of rate versus [CNpp] (u versus u/[S]). Besides the data with standard deviation, the resulting lines of the statistical fittings of these points to the respective rate equations u [ S ] of degree 1 : 1, 2 : 2 and 3 : 3 are shown. For these kinetic data obtained at high flow rate (10 ml min- I), the limitations to external diffusion may be assumed to disappear (uide supra), and hence overall or effective kinetic behaviour of the immobilized enzyme is closer to its intrinsic kinetic behaviour, which, at least graphically, seems to fit better to an equation of degree 2 : 2 or 3 : 3 than to one of 1 : 1. That is, non-linear tendencies of the experimental points u [ S ] in the corresponding Eadie-Hofstee plots are

40 c E - E - 0

9 5 . N

Y

>

-

x

\ 1:l

Fig. 8. Kinetic behaviour of alkaline phosphatase covalently immobilized on PVDF affinity membrane against 4-Npp concentration at high recirculation flow rate (10 ml min - '). Other conditions: 0.01-1 mM 4-Npp, 0.01 M carbonate/bicarbonate

buffer, pH 10.0,0.02 M ionic strength, 25°C.



obseved. Linearity would have been found if the data had been fitted to an equation of degree 1 : 1 (Michaelis-Menten).

It is necessary to check this hypothesis, based on the graphical aspect of the data, by methods of numerical fitting and statistical tests. With this aim, the F statistical test was applied in order to discriminate between the goodness of different fits. From statistical tests, it can be concluded that, under the experimental conditions used, the equation of minimum rate for the reaction would be of degree 2 : 2 for all the cases analysed. However, as has been observed in simulation studies,39 experimental conditions could exist in which the F test will not detect the true degree but a lower one regarding the reaction mechanism. From the graphical and numerical-statistical analysis carried out it seems that the global or effective kinetic behaviour of the immobilized enzyme at high and low flow rates can be expressed as a polynomial quotient rate equation in [S] of at least degree 2 : 2. Consequently, a u[S] rate equation of at least degree 2 : 2 is proposed as representative kinetic behaviour for AP immobilized on this PVDF affinity membrane :

In free solution alkaline phosphatase from human placenta catalyses the hydrolysis of p-nitro- and u- carboxyphenyl phosphates according to a rate equation of at least grade 3 : 3, which means that the enzyme behaves in solution in a non-Michaelian way.5

Since alkaline phosphatase from human placenta is a dimer, it could be proposed that the cause of the non- Michaelian kinetics is the cooperativity between the two active sites of the enzyme molecules, either of binding and catalysis of the substrate, or only the former.

For an enzyme with two active sites, such as alkaline phosphatase, the simplest scheme which considers these effects of cooperativity and aspects such as the phos- phorylation and dephosphorylation of the enzyme and its inhibition by inorganic phosphate is that proposed by Waight et al.;57 this mechanism is represented in Fig. 9 (Mechanism I), where Q is phosphate, P is phenol and the rest are described according to the normal sym- bolism. This six-noded mechanism corresponds to a 3 : 3 rate equation when resolved by computer according to steady-state treatment. Our u[S] experimental results show that a 2 : 2 fitting seems to be sufficient and that a 3 : 3 degree does not improve the fitting significantly. It is possible that our fitting program converges slightly better than Waight’s does and the good 2 : 2 fitting, found in this work, might therefore indicate that, under given conditions, the general 3 : 3 equation from Mechanism I will be reduced to a 2 : 2 fitting. Waight et al.56 themselves have studied this reduction in degree in a number of reports and have established that these reductions originate when the numerator and denomi-

n

n

) ‘ k * I

W Fig. 9. Mechanisms proposed for human placental alkaline phosphatase: (I) Two-sited cooperatively linked Ping-Pong Uni-Bi mechanism. (11) Ping-Pong Uni-Bi mechanism obtained by simplifying Mechanism I, proposed as valid when there are negligible amounts of the final products 4- nitrophenol (P) and phosphate (Q) in the reaction medium. In both schemes, EE represents the enzyme with its two sites, S represents 4-nitrophenyl phosphate, and EES, SEE, EEQ, represent the different states the enzyme may be found in. The pathways corresponding to kL3, k - , and k - , of Mechanism I have not been considered in Mechanism I1 because 4- nitrophenol (P) is not a good acceptor of inorganic phosphate since it has been shown that the extent of the reaction

P + Q + S would be negligible.

nator of the function share a common linear factor and take place when the Silvester resultants cancel out. Thus for a reduction from 3 : 3 to 2 : 2 the next resultant would have to be zero:

But the fact that Ro must be cancelled says nothing in molecular terms, since ell, z12 and g13 are parameters which depend on the individual rate constants in such a complex manner that it is not possible to reach an explanation in terms of one or two rate constant^.^' Its


PVDF bioreactor 29

only meaning is mathematical and, in general, it is only when any given values of the rate constants are concur- rent that the Silvester resultant can be made equal to zero. It would be necessary to make similar arguments to carry out reductions from 3 : 3 to 1 : 1, or from 2 : 2 to 1 : 1. According to this, all changes in fittings and in the form of the curves can be explained in mathematical terms without it being necessary that some type of cooperativity should have to disappear.

A more intuitive treatment might be to approach the problem from a molecular point of view, i.e. which steps of Mechanism I would be negligible under the experimental conditions of our study? Does the elimination of these steps lead to a mechanism of 2 : 2? Two important aspects should be borne in mind: (1) In all the kinetic studies carried out, initial rates were measured (<3-5% of the reaction). (2) In the reaction medium, initially there were no end products present (phosphate, 4-nitrophenol). Under these conditions, the general Mechanism I could be simplified to Mechanism I1 (Fig. 9). That is, according to (2) the EEQ o SEEQ pathway is completely eliminated, since in conditions of absence of phosphate the EEQ concentrations would be so low that the participation of such a pathway would be negligible compared with the rest. By the same cause, the utilization of the following direction EE + EEQ +

QEEQ is also negligible. Furthermore, the pathways corresponding to EEQ + EES, SEEQ + SEES, QEEQ + SEEQ of Mechanism I are not considered because 4-nitrophenol (P) is not a good acceptor of inorganic phosphate and the extent of the reaction P + Q + S is negligible.

Mechanism I1 leads to a 2 : 2 degree rate equation when the steady-state treatment is applied. In principle, this Ping-Pong Uni-Bi mechanism, where products are released before all substrates can react and the reaction being unimolecular in reactants and bimolecular in products, could adequately explain the intrinsic kinetic behaviour (2 : 2 rate equation fitting of rate versus [4- Npp] data) found for human placental alkaline phosphatase in free solution58 and immobilized on affinity PVDF cross-flow microfiltration membrane. These non- Michaelian kinetics of the enzyme, due to cooperativity phenomena, would confer greater versatility for alkaline phosphatase in the control and/or modulation of its physiological functions.

ACKNOWLEDGEMENTS

The authors express their thanks to La Junta de Cas- tilla y Leon, DGICYT (Spain) and the British Council for invaluable collaboration.

REFERENCES

1 McComb, R. B., Bowers, G. N. Jr & Posen, S., Alkaline Phospha- tase. Plenum Press, New York, 1979.

2 Meyer-Sabellek, W., Sinha, P. & Kottgen, E., J. Chromatogr., 429

3 Wilson, I. B., Dayan, J. & Cyr, K., J. Biol. Chem., 239 (1964) 4182. 4 Fernley, H. N. & Walker, P. G., Biochem. J., 104 (1967) 1011. 5 Roig, M. G., Burguillo, F. J., Del Arco, A,, Usero, J. L., Izquierdo,

C. & Herraez, M. A., Int. J. Biochem., 14 (1982) 655. 6 Hildebrandt, E. & Fried, V. A,, Anal. Biochem., 177 (1989) 407. 7 Bloch, W. & Bickar, D., J. Biol. Chem., 253 (1978) 6211. 8 Herraez, M. A,, Burguillo, F. J., Roig, M. G. & Usero, J. L., Int. J.

9 Harkness, D. R., Arch. Biochem. Biophys., 126 (1968) 503. 10 Harkness, D. R., Arch. Biochem. Biophys., 126 (1968) 513. 11 Gottlieb, A. J. & Sussman, H. H., Biochim. Biophys. Acta, 160

12 Ahmed, Z. & King, E. J., Biochim. Biophys. Acta, 45 (1960) 581. 13 Fishman, W. H., Inglis, N. R. & Ghosh, N., Clin. Chem. Acta, 19

(1968) 71. 14 Lin, C. H., Sie, H. G. & Fishman, W. H., Biochem. J., 124 (1971)

509; Lindgren, B. W., Statistical Theory. Macmillan, New York, 1976.

(1988) 419.

Biochem., 11 (1980) 511.

(1968) 167.

15 Van Bell, H., Clin. Chem., 22 (1976) 972. 16 Sugiura, M., Hirano, K., Iino, S., Suzuki, H. & Oda, T., Chem.

17 Moss, D. W. & Whitaker, K. B., Probides Biol. Fluids, 24 (1976)

18 Del Arco, A,, Burguillo, F. J., Roig, M. G., Usero, J. L., Izquierdo,

19 Byers, D. A., Fernley, H. N. & Walker, P. G., Eur. J . Biochem., 29

20 Ghosh, N., Annals NY Acad. Sci. Biochem., IV (1969) 626. 21 Doellgast, G., Beckman, G. & Beckman, L., Clin. Chim. Acta, 75

22 Martinek, K. & Mozhaev, V. V., Ado. Enzymol., 57 (1985) 179. 23 Low, M. G., Futerman, A. H., Ackerman, K. E., Sherman, W. R. &

24 Katchalski, E., Silman, I. & Goldman, R., Ado. Enzymol. Relat.

25 Trevan, M. D., Immobilized Enzymes. John Wiley and Sons, New

26 Roig, M. G., Serrano, M. A., Bello, J. F., Cachaza, J. M. &

27 Ittah, Y., J . Agric. Food Chem., 40 (1992) 953. 28 Perez-Mateos, M., Busto, M. D. & Rad, J. C., J . Sci. Food Agric.,

29 Carrasco, M. S., Rad, J. C. & Gonzalez-Carcedo, S., Bioresour.

30 Low, M. G. & Saltiel, A. R., Science, 239 (1988) 268. 31 Blankstein, L. A. & Dohrman, L., Am. Clin. Prod. Review, Novem-

32 Kennel, S. J., J. Immunol. Methods, 55 (1982) 1. 33 Kenny, G. E. & Dunsmoor, C. L., J . Clin. Micro., 47 (1983) 655. 34 Holbrook, K. A., & Ouellet, Can. J. Chem., 36 (1958) 686. 35 Weast, R. C. (Ed.), Handbook of Chemistry and Physics, 61st edn.

36 Davies, C. W., Ions Association. Butterworth, Oxford, 1962. 37 Wong, J. T-F., Kinetics of Enzyme Mechanism. Academic Press,

38 Bardsley, W. G., Leff, P., Kavanagh, J. & Waight, R. D., Biochem.

39 Burguillo, J. F., Wright, A. J. & Bardsley, W. G., Biochem. J., 211

40 Nelder, J. & Mead, R., Comput. J., 4 (1965) 308. 41 Lindgren, B. W., Statistical Theory. Macmillan, New York, 1976. 42 Ghai's, N. I., Masters thesis, University of Salamanca, Spain, 1984. 43 Roig, M. G., Serrano, M. A., Bello, J. F., Cachaza, J. M. &

44 Roig, M. G., Serrano, M. A,, Bello, J. F., Cachaza, J. M. &

45 Perrin, D. D. & Dempsey, B., Buffers for pH and Metal Ion

46 Neumann, H., Boross, L. & Katchalski, E., J . Biol. Chem., 242

47 Chappelet-Tordo, D., Fosset, M., Iwatsubo, M., Gache, C. & Laz-

48 Hayashi, M., Unemoto, T. & Hayashi, M., Biochim. Biophys. Acta,

Pharm. Bull., 25(4) (1977) 653.

81.

C. & Herraez, M. A., Int. J . Biochem., 14 (1982) 127.

(1972) 205.

(1977) 501.

Silman, I., Biochem. J., 241 (1987) 615.

Areas Mol. Biol., 34 (1971) 445.

York, 1980, p. 130.

Kennedy, J. F., J. Biomat. Sci., Polymer Edn, 2 (1991) 287.

55 (1991) 229.

Technol., 51 (1995) 175.

ber (1985) 17.

The Chemical Rubber Co., Cleveland, Ohio, 1980.

New York, 1975, pp. 15-35.

J., 187 (1980) 739.

(1983) 23.

Kennedy, J. F., Polymer Int., 24 (1991) 45.

Kennedy, J. F., Polymer Int., 25 (1991) 75.

Control. Chapman and Hall, London, 1979.

(1967) 3142.

dunski, M., Biochemistry, 13 (1974) 1788.

315 (1973) 83.


30 M . G . Roig et al.

49 Schwartz, J. H., Proc. Nat . Sci. USA, 49 (1963) 871. 50 Lazdunski, C. & Lazdunski, M., Biochim. Biophys. Acta, 113 (1966)

51 Katz, I. & Breslow, R., J. Am. Chem. Soc., 90 (1968) 7376. 52 Williams, A. & Naylor, R. A., J . Chem. Soc. B (1971) 1973. 53 Halford, S. E., Biochem. J . , 126 (1972) 727. 54 Hill, C. H. M., Waight, R. D. & Bardsley, W. G., Mol. Cell. Bio-

55 Rees, D. C., Bull. Mathematical Biology, 46 (1984) 229. 56 Waight, R D. & Bardsley, W. G., Biochem. Soc. Trans., 5 (1977)

57 Waight, R. D., Leff, P. & Bardsley, W. G., Biochem. J . , 167 (1977)

58. Roig, M. G., Burguillo, F. J., Cha'is, N. I., Velasco, B. & Chachaza,

551. 758.

787.

J. M., Biocatalysis, 7 (1993) 97. chemistry, 15 (1977) 173.

POLYMER INTERNATIONAL VOL. 39, NO. 1. 1996

Phosphatase Active Cross-Flow Microfiltration Poly(vinylidene Difluoride) Bioreactor

Documents

Transcript of Phosphatase Active Cross-Flow Microfiltration Poly(vinylidene Difluoride) Bioreactor