Kinetic analysis of chemical reactions coupled to an enzymic step. Application to acid phosphatase assay with Fast Red.

Abstract

Acid phosphatase assay with alpha-naphthyl phosphate as substrate and the use of diazonium salt (Fast Red TR) for chromophore formation was kinetically analysed as a system of two chemical reactions coupled to an enzymic reaction. This system follows a mechanism defined as enzymic-chemical-chemical (EzCC). The accumulation of chromophore with reaction time presented a marked lag period, which was only dependent on the rate constants of the chemical reactions and was independent of the enzymic step. The specific rate constants of each chemical step were determined in 3.8-5.0 pH and 10-35 degrees C temperature ranges. Thermodynamic parameters of the chemical steps were also obtained. Measurement of acid phosphatase activity can be carried out in the pH range 3.8-5.0 (4.8 was optimal pH) without the need to eliminate the lag period.

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Biochem. J. (1984) 223, 633-638
Printed in Great Britain
633
Kinetic analysis of chemical reactions coupled to an enzymic step
Application to acid phosphatase assay with Fast Red
Josefa ESCRIBANO, Francisco GARCIA-CARMONA,* Francisco GARCIA-CANOVAS,
Jose Luis IBORRA and Jose Antonio LOZANO
Departamento Interfacultativo de Bioquimica, Facultad de Medicina, Universidad de Murcia, Murcia, Spain
(Received 26 March 1984/Accepted 25 July 1984)
1. Acid phosphatase assay with oa-naphthyl phosphate as substrate and the use of
diazonium salt (Fast Red TR) for chromophore formation was kinetically analysed as
a system of two chemical reactions coupled to an enzymic reaction. This system
follows a mechanism defined as enzymic-chemical-chemical (EzCC).
accumulation of chromophore with reaction time presented a marked lag period,
which was only dependent on the rate constants of the chemical reactions and was
independent ofthe enzymic step. 3. The specific rate constants ofeach chemical step
were determined in 3.8-5.OpH and 10-350C temperature ranges. Thermodynamic
parameters of the chemical steps were also obtained. 4. Measurement of acid
phosphatase activity can be carried out in the pH range 3.8-5.0 (4.8 was optimal pH)
without the need to eliminate the lag period.
2. The
Enzymic reactions where the products are un-
stable and undergo achemical process ofdecompo-
sition, deprotonation or, in general, stabilization
by a first-order or second-order kinetics have
previously been described (Childs & Bardsley,
1975; Claiborne & Fridovich, 1979; Boekeheide et
al., 1980; Frere et al., 1982). On the other hand,
chemical reactions have been coupled to many
enzymic reactions in order to determine the time-
dependent behaviour of the products (Ellman et
al., 1961; Jolley & Mason, 1965; Esterbauer et al.,
1977). Usually it has been considered that the
velocity of an enzymic step, provided that it is the
limiting one, can be measured by monitoring the
formation ofthe chemical reaction product (Ester-
bauer et al., 1977). A kinetic analysis has recently
been made ofthe pathway ofdopa (3,4-dihydroxy-
phenylalanine) oxidation by tyrosinase to dopa-
chrome, as a system of several chemical reactions
coupled to an enzymic step (Garcia-Carmona et
al., 1982), although with peculiar pathway charac-
teristics such that it is not applicable for a study of
a linear pathway of an enzymic reaction followed
by various chemical reactions.
In the present work, kinetic analysis of a system
Abbreviations used: Fast Red TR salt, 5-chloro-2-
toluidinediazonium chloride (hemizinc chloride salt).
*To whom correspondence should be addressed.
of two chemical reactions coupled to an enzymic
reaction has been carried out, designating this type
of mechanism
as enzymic-chemical-chemical
(E,CC).This theoretical studywas applied to assay
for determination of acid phosphatase activity by
the method of Hillman (1971), with a-naphthyl
phosphate as substrate and the use ofFast RedTR
for chromophore formation, as expressed in the
mechanism shown in Scheme 1.
The formation of the chromophore shows a
marked lag period, which strongly depended on
pH. This method is not accepted by most clinical
laboratories (Bais& Edwards, 1976) because ofthe
existence of this lag period. Various modifications
have been introduced to minimize the lag period,
since according to several authors its existence
means that the limiting step for this assay is the
formation of the complex between the reaction
product (a-naphthol) and Fast Red TR (Bais &
Edwards, 1976), and therefore the reaction be-
tween a-naphthol and Fast Red TR must be rapid
to reflect the enzyme activity accurately (Cooper et
al., 1982), suggesting that a pH range of 5.5-6.0
must be used to measure the enzyme activity (Bais
& Edwards, 1976; Warren & Moss, 1977; von
Gundlach & Miihlhausen, 1980; Cooper et al.,
1982).
The present paper shows that the need to
eliminate the lag period, in order to measure
Vol. 223

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J. Escribano and others
O-PO3H2
OH
X
N~
Acid phosphatase
<
k+l
N
-
H20
Pi
cx-Naphthyl phosphate (A)
a-Naphthol (B)
Scheme 1
0-
i
.
<
~+H+
oa-Naphthyl (C)
k+ 2
Fast Red
Chromophore (P)
accurately the enzyme activity in an EZCC mecha-
nism, is unfounded. Furthermore, analysis of this
type of mechanism allows the specific rate con-
stants ofeach chemical step to be easily evaluated.
On the basis of the kinetic results obtained, some
modifications to the assay of the acid phosphatase
are proposed.
Theory
The hydrolysis of the a-naphthyl phosphate by
acid phosphatase and the reaction of the product
with Fast Red TR can be described as follows:
Enzyme
A
B
(1)
B
k+
C
(2)
c -k'+2
p
(3)
where A is oc-naphthyl phosphate, B is oa-naphthol,
C is a-naphthyl and P is the chromophore obtained
from the reaction between a-naphthyl and Fast
Red TR; k'1 = k 4[H+] and k' 2 = k+2[Fast Red].
Eqn. (1) shows the enzymic hydrolysis of a-
naphthyl phosphate, eqn. (2) the deprotonation
equilibrium of a-naphthol and eqn. (3) the chemi-
cal reaction between a-naphthyl and Fast Red TR.
On the assumption that the a-naphthyl phos-
phate concentration is saturating or its variation
during reaction time is very small, we ought to
consider that the enzymic reaction rate remains
constant (V0). On the other hand, the Fast Red TR
concentration in the reaction medium should be
high enough
to remain constant during the
reaction time.
Taking into account these assumptions, velocity
equations for B and C accumulation are:
d[B_
dt~~~~~~~~
(4)
d[CI~~= k+,[B1-(k'i1+k'+2)[C]
Frmen.()ad()asetdodreuto
Fromeqns. (4)and (5)a second-orderequationcan
be defined, the general solution of which is:
a
(5)
[C]=
1
(A2 eAlt+Al.eA2))
(6)
k+2
(A2- A1)
whereAland A2 solutions are negative. From eqns.
(5) and (6) it can be deduced that:
[B]-k+,.kf 2 (k-1+kf+2)- (A2_s1)
k' 1 + ki 2),A2.eAit+(A2+k'1 +k' ))A1*eA2]
For -Al -t>l and -A22t>l, [B] and [C] in the
steady state can be defined as:
[C]
_ VO
kf++~2
(k'1+k'+2)
Vn
ss
[BOSSnth o
h
On the other hand:
d[P]=k'+2[CI
dt
(7)
From eqns. (6) and (7) and integrating, the
following expression for[P] as a function ofAland
A2 can be established:
[PI=Vo
t
('e-t) (.
e
+
Al
'1
Al
Al'
12J
l.eA2t+_--A1
142
1984
63-4

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Acid phosphatase assay with Fast Red
For -A1 *t» 1 and -A2't» 1, it is possible to define
how P is accumulated when the system reaches its
steady state:
[P]SS=Vo(t+AA)
Substituting A1 and A2 as a function of the rate
constants, the following expression is obtained for
the P accumulation in the steady state:
[P]SS= Vo[t(k+k
I'
k+
l
+2)
Therefore the lag period, L, is defined as:
[H+]
L = ~ ~
Ka. k+2[FastRed]
11
~
k+,
k+2[FastRed]
(9)
where Ka = k +I/k-
naphthol. A similar equation has been obtained by
Easterby (1981), applying the mass-conservation
balance.
A plot oflag period against proton concentration
gives straight lines, the slopes ofwhich allow us to
evaluatekI2,since Ka is known, and the intercept
on the ordinate axis allows the k,j values to
be calculated.
With reference to eqn. (9), it is important to
point out that the transition time depends on the
rate constant of the chemical reactions, but it is
independent of the rate of the enzymic step. How-
ever, concentrations of intermediates in the steady
state depend on both enzymic and chemical
reactions, and increase with enzymic reaction rate.
is the ionization constant ofa-
Materials and methods
Acid phosphatase (orthophosphoric-monoester
phosphohydrolase, acid optimum, EC 3.1.3.2)
(0.36 unit/mg), Fast Red TR salt and a-naphthyl
phosphate were obtained from Sigma Chemical
Co., Kingston-upon-Thames, Surrey, U.K. All
other reagents commercially obtained were of
analytical grade. One unit of enzyme is defined as
the amount of enzyme that hydrolyses 1.O4mol of
p-nitrophenyl phosphate/min at pH4.8 at 37°C.
Spectrophotometric measurements were carried
out with an Aminco DW-2 spectrophotometer
equipped with a Hewlett-Packard recorder with
kinetic response, which allows the dead recording
time to be minimized; when the rate constant of
the chemical reaction was greater than 0.1s-1,
an Aminco-Morrow Stopped Flow
equipped with a Dasar T.M. unit was also used.
Temperature was controlled by a Gilson bath with
a precision of +0.1°C. Acid phosphatase activity
accessory
was determined by the Hillman's (1971) method,
where chromophore accumulation was monitored
spectrophotometrically at Amax. = 405nm. The re-
action medium conitained 0.1 M-sodium citrate
buffer (pH as indicated in each case), 3mM-a-
naphthylphosphate,
62.5,ug
phatase/ml and Fast Red TR concentration varied
in the 1.3-13mm range. The reaction study was
undertaken in the temperature range 10-35°C. The
a-naphthyl phosphate and Fast Red TR solutions
were prepared fresh every day.
of
acid
phos-
Results
Variation oflagperiodand the steady-state rate with
the enzyme concentration
The hydrolysis of a-naphthyl phosphate by acid
phosphatase was followed by the absorbance
increase
at 405nm, where
formed by the reaction of a-naphthyl with Fast
Red TR dye shows maximum absorbance. The
reaction progress presented a marked lag period,
which was strongly dependent on pH and tempera-
ture, but was independent of the enzyme concen-
tration. Fig. 1 shows the chromophore formation
the chromophore
0.3
0
100
200
300
Time (s)
Fig. 1. Chromophore accumulation with time
This is followed by the absorbance increase at
405nm at different enzyme concentrations(gg/ml):
1, 77; 2, 59; 3, 40.3; 4, 30.6; 5, 20.6. The reaction
medium contained 0.1 M-citrate buffer, pH4.5,
5.7mM-Fast Red TR and 1.5mM-a-naphthyl phos-
phate at 23°C. The inset shows a plot of chromo-
phore accumulation rate in steady-state conditions
against enzyme concentration. The same experi-
mental conditions as indicated for the main Figure
were used.
Vol. 223
635
V}
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J. Escribano and others
for different enzyme concentrations at 230C and
pH4.5. The transient phase was defined by the lag
period, the value of which was independent of the
enzyme concentration, according to eqn. (9). How-
ever, the slope of the linear zone of the curve
depended directly on the enzyme concentration, as
shown by Fig.
accordance with eqn. (8).
1 (inset), and its value is V0, in
Evaluation of the specific rate constants
The specific rate constants of each step were
calculated from eqn. (9). The lag period was
evaluated for each different concentration of Fast
Red TR in the concentration range 1.3-13mM, for
the same enzyme concentration (62.5pg/ml), at
23°C in 0.1M-citrate buffer in the pH range 3.8-
5.0. The plot of the lag period against the
reciprocal of the Fast Red TR concentration, as
shown in Fig. 2, gives straight lines for each pH
value studied, the ordinate value of which is
identical for all pH values, being the inverse ofthe
rate constant k+ 1. This value k+ 1 = 3.1 x 10-2s-1
was independent of proton concentration. On
the other hand, the plot of the value of each
slope against proton concentration was a straight
line, as shown in Fig. 2 inset. The second-order
rate
constantk+2
(k+2=3.8x105M-Is-1)
m= l/Ka-k+2,
by
taking
(Weast, 1973).
can
be
evaluated
its
from
slope
Ka=4.6x10-10M
Variation of lag period with pH and temperature
The rate constants for different values ofpH and
temperature were evaluated. The reaction medium
500
400
0e
0.
.9
2501
200
X
10
S.o
150
0.
oo
Cu
-.
100
50
0.4
0.6
1/[Fast Red] (mM-')
Fig.
2. Variation of lag period with Fast Red TR
concentration
The data are presented as plots of the lag period
against the reciprocal ofFast Red TR concentration
at the different pH values: 0, pH 3.8; A, pH4.0; A,
pH4.5;
contained
phosphate and 62.5pg of acid phosphatase/ml at
23°C. The inset shows a plot ofeach slope ofstraight
lines obtained in the main Figure, according to eqn.
(9), against proton concentration.
El, pH4.8; 0, pH 5.0. The reaction medium
0.1 M-citrate buffer, 1.5mM-c-naphthyl
300
200
100
0
0.5
1.0
1.5
2.0
10-4 x [HI] (M)
Fig. 3. Lag period variation at several pH values and
temperatures
The reaction medium contained 0.1 M-citrate buffer,
1.5mM-ox-naphthyl phosphate, 5.7mM-Fast Red TR
and62.5jugof acid phosphatase/ml. Temperatures:
*, 10°C; 0, 15°C; A, 20°C; A, 25-C; *, 30°C;
350C.
E,
Table 1. First-order rate constantsfor the deprotonation of
a-naphthol and the reaction between a-naphthyl and Fast
Red TR at several temperatures
The formation of the chromophore presents a lag
period, which depended on temperature. From eqn.
(9) the specific rate constants at several tempera-
tures values can be evaluated.
Temperature (°C) 10-2Xk
10
1.73
15
2.53
20
2.86
25
3.41
30
5.95
35
6.84
1 (s- 1)
103 xk'+ 2 (S-')
0.99
1.07
1.54
2.39
2.88
3.69
1984
//0
0OZ~~~~
A
~~~~A
0~~~
I'l
0
/01
1
636

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Acid phosphatase assay with Fast Red
637
Table 2. Thermodynamic activation parametersfor the deprotonation ofot-naphthol andfor the reaction between oa-naphthyl
and Fast Red TR
Ea (kJ*mol- 1)
AH$ (kJ*mol-1)
Deprotonation (k+1)
46.0
Union to Fast Red (k'+.2)
36.4
33.8
AGI (kJ*mol-1)
81.1
53.5
ASt (kJ*mol1*K-1)
0.12
0.07
48.5
contained 0.1 M-citrate buffer in the pH range 3.8-
5.0,
62.5jg of acid phosphatase/ml, 3mM-a-
naphthyl phosphate and 5.7mM-Fast Red TR. The
lag period increased when pH and/or temperature
were decreased. From eqn. (9) the plot of the lag
period against proton concentration for the same
concentration ofFast Red TR gives linear plots, as
shown in Fig. 3. From these linear-regression-
fitted plots, k+ 1 can be evaluated from the inter-
cepts on the ordinate axis andk'+2 from the slope of
the straight lines. The different rate constants at
several temperatures are given in Table 1.
For the evaluation ofthe activation energies for
the deprotonation of a-naphthol and the reaction
between a-naphthyl and Fast Red TR, Arrhenius
plots were made with thek+Iand k'+2 values ob-
tained. The derived activation parameters are
summarized in Table 2.
Discussion
The theoretical analysis ofan EZCC mechanism
and its application for the determination of acid
phosphatase activity allows us to define a para-
meter, the lag periodofthe accumulation ofthe last
product, that
constants of the chemical reactions (eqn. 9) and is
independent of the enzymic step.
Thus, from a theoretical and experimental point
of view, this mechanism shows that the accumu-
lation rate ofthechromophore in the steady state is
independent ofthe existence ofchemical steps and
its rate constants, but depends on a linear
behaviourofthe enzyme concentration (eqn. 8 and
Fig. 1 inset). Enzymic activity can be determined
without the interference of the relatively slow
chemical step. Therefore
minimize the lag period (Bais & Edwards, 1976;
Cooper et al., 1982). Minimization of this lag
period with a determination of acid phosphatase
activity above pH5.5 has introduced several
further problems in the method of measurement.
At these pH values the diazonium salt itself is
unstable and may be precipitated from solution
(Warren & Moss, 1977); a significant hydrolysis of
Fast Red TR can also take place to yield 4-chloro-
2-methylphenol, subsequently undergoing coup-
ling with Fast Red TR to produce a chlorocresol-
azodye complex (Cooper et al., 1982); instability of
a a-naphthol-azodye complex chromophore (War-
is only dependent on the rate
it is unnecessary to
ren & Moss, 1977), probably due to the coupling of
a second diazonium ion to the complex already
formed between a-naphthol and diazonium ion
(Sanders et al., 1978), also occurs.
On the basis ofthe present paper, measurement
ofenzymic activity at a pH between 3.8 and 5.0 is
recommended, since the molar absorption coeffi-
cient of chromophore is then highest (Bais &
Edwards,
1976),
at pH4.8 the prostatic acid
phosphatase activity is also at amaximum (Walter
& Schuitt, 1974), and furthermore in this pH range
none of the problems present in the 5.5-6.0 range
appear.
The theoretical and practical analysis of the
transition phases of the EZCC mechanism allows
us to evaluate the specific rate constants of the
chemical steps easily and to establish with greater
accuracy the specific reactions that occur in the
chromophore formation.
This work was partially supported by grant 276/81
from the Comision Asesora de Investigacion Cientifica y
Tecnica.
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