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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.
K e y words: Membrane, microfiltration, poly(viny1idene difluoride), alkaline
phosphatase, immobilization.
some important enzyme-phosphate complexes.6 These
complexes are covalent (phosphoryl-enzyme (E-P)) at
acid pH values and addition complex type (E.P) at alkaline pH.3,7,8
Alkaline phosphatase from human placenta is a dimer
consisting of two identical subunits' with molecular
weight 125000 and 116000 Daltons."." It would be
expected to show the majority of the kinetic characteristics and mechanisms of alkaline phosphatases in
general. With respect to steady state kinetic data, it
should be noted that all the studies carried out with
purified enzyme have been treated from a Michaelian
point of view; that is, by determining the different K ,
and V,,, values for the conditions and methods studied.
The profusion of studies on alkaline phosphatase has
provided a comprehensive knowledge of the enzyme
which has been set forth in a book by McComb,
Bowers & Posen' and in various reviews.' Alkaline
phosphatases (EC are enzymes which show nonspecific phosphohydrolase activity on many phosphate
esters and anhydrides independently of the nature of the
leaving group. The enzyme thus shows both hydrolytic
and phosphotransferase
but has also been
shown to function as a phosphate carrier since it forms
* To whom correspondence should be addressed.
Polymer International 0959-8103/96/$09.00
0 1996 SCI. Printed in Great Britain
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 4phenyl phosphate and 25 mM for the glycerophosphate.
The only objection one could posit to this study is that
the substrate concentration range was small (0.10-04mM). 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
M g z + . Again, the ranges of substrate concentration
were not wide enough to permit the observation of deviations from Michaelian kinetics.
Moss & WhitakerI7 incubated radioactive 0phosphate 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 indicated the absence of cooperative effects between the
sites, i.e. the two sites of the enzyme seem to be functionally 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 differences 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
M . G. Roig et al.
properties. The results of Doellgast et ~ 1 . ’ seem
consistent 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 findings are important for kinetic studies with commercially
purified enzymes, since these are a mixture of the different molecular forms described for the enzyme. Evidently, 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 differed 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 nonMichaelian 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 p h ~ s p h a t e . ’ ~
Katchalski 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 plaPOLYMER INTERNATIONAL VOL. 39, NO. 1, 1996
PVDF bioreactor
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.
Enzyme. Alkaline phosphatase (AP) from human placenta (EC 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 MillexHA 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 . mg
6 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 practically 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 0.52 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% 4nitrophenol (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.
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., Fullerton, 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 compensation 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 scanning 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
The statistical fitting of certain kinetic data was
carried out with the Simplex algorithm implemented on
an IBM-AT microcomputer.
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-difluoroethylene (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 characteristics 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
M . G . Roig et al.
1. 1 '- Carbonyldirmidazole
Activated PVDF
Immobilized Enzyme
H2N. P
PVDF afllndy membrane
c NH
Fig. 1. Derivatization of a PVDF membrane (Immobilon AV
Millipore affinity membrane) for chemical immobilization of
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
Immobilization method
The immobilization method (Fig. 1) comprises the
nucleophilic attack of the &-aminogroups of lysine and
arginine from the enzyme to be immobilized on the carbony1 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 coupling efficiency (40-60%) with a high capability of covalent protein immobilization (92% of the immobilized
protein) is an important feature of the membrane. Covalent immobilization results in improved kinetics
between the interacting partners3* and reduces the likelihood 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),35a
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,
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
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 l O 4 c r n - ' ~ - ' . 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
the values of [H’] and of Kg are known, it is possible
to calculate the apparent extinction coefficients of 4nitrophenol 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:
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 automatically 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
Non -linear regression program
None of the several algorithms for dealing with the
problem of non-linear regression offers absolute certainty. 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 strategy 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
where Qj’ and Qf+l represent the sum of squared
residuals for models 1 and 2, mj and m j t 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.
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. Similarly, 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
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 10mM 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
Emaxrepresents 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,, = 0-343pmol
min-'g-';Kad = 21.5mgml-' = 1.85 x 1 0 - 4 ~ .
To interpret the phenomenon of adsorption, Langmuir 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
M . G . Roig et al.
and absorbent is rarely that simple. Many configurations 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. Consequently, 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, 0-02M 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 neutralization of the charges over the protein.
The foldings-unfoldings of protein chains are intramolecular 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 exponential terms,
Ai exp( - kit), where the ki parameters are
characteristic time constants and the A i terms are constant amplitude parameters. The corresponding semi-
P V D F bioreactor
well accepted notion that the enzyme becomes stabilized 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
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 ) . Standard 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 = 3-5day.
Logically these folding-unfolding processes are much
slower for immobilized proteins than for soluble proteins. The dynamic structural response of the enzymesupport 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
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 facilitated 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
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,
0.2 mM 4-Npp; 0.05 M carbonate/bicarbonate buffer, ionic
strength 0.14 M, 25"C, recirculation flow rate 6 ml min- or 0,
seen in the activity/pH profile unless there is severe constraint 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
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 interior 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
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 (5-0mM) 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 550 "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
M . G. Roig et al.
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
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 10.0,0.02M ionic strength.
P V D F bioreactor
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 A G f 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 0-2mM 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
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
Z n z + 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
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, recirculation 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
complex(es) could be ratedetermining 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-
M . G. Roig et al.
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
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
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
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, 0-02M 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
Recirculationflow 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.
PVDF bioreactor
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 aLS4made 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 'nonMichaelian' 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 investigating 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 wellcharacterized 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 calculations 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
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 min4-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
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
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 ucarboxyphenyl 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 nonMichaelian 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 phosphorylation 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 symbolism. 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.56themselves have studied this reduction in degree in
a number of reports and have established that these
reductions originate when the numerator and denomi-
M . G. Roig et al.
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 4nitrophenol (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 4nitrophenol (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 g 1 3 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
P V D F bioreactor
only meaning is mathematical and, in general, it is only
when any given values of the rate constants are concurrent 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 [4Npp] data) found for human placental alkaline phosphatase in free solution58 and immobilized on affinity
PVDF cross-flow microfiltration membrane. These nonMichaelian 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.
The authors express their thanks to La Junta de Castilla y Leon, DGICYT (Spain) and the British Council
for invaluable collaboration.
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