Biochimica et Biophysica Acta, 1161 (1993) 311-316 311 © 1993 Elsevier Science Publishers B.V. All rights reserved 0167-4838/93/$06.00

BBAPRO 34401

A model for prosthetogenic enzyme amplification assays

Stuart Harbron, Mark Fisher and Brian R. Rabin London Biotechnology Limited, Department of Biochemistry and Molecular Biology, University College London, London (UK)

(Received 13 May 1992)

Key words: Enzyme amplification; Alkaline phosphatase; Kinetics; Mathematical modeling

A mathematical model describing the behaviour of a new class of prosthetogenic enzyme amplification assays is described. The predictions of the model are favourably compared with an enzyme amplification assay for alkaline phosphatase. The model is used to kinetically characterise and optimise the enzyme amplification assay.

Introduction

Since the introduction of enzyme-linked immunoas- says in the 1970's, their sensitivity has been improved by a variety of methodologies to give detection limits that are comparable to radioimmunoassays [1]. Thus, the relative amount of enzyme label can be increased by employing the avidin-biotin system [2] or through catalysed reporter deposition [3]. Alternatively, or ad- ditionally, substrates may be used that give products which can be measured at lower concentrations, e.g., by fluorescence or luminescence [4,5].

The sensitivity of enzyme-labelled systems can also be increased by amplification. Such systems generally employ primary enzyme labels catalysing the formation of a trigger molecule that activates a secondary enzyme system, resulting in a measurable change exceeding that capable of being produced by the primary enzyme alone. These secondary systems may be based on the release of enzymes from liposomes [6], the generation of an inhibitor of enzyme activity [7], or the production of a substrate or cofactor that is part of a cyclic system [8,9]. To date, the only amplification system that has been commercially exploited utilises a substrate cycle to amplify the primary label activity [8].

Prosthetogenic amplification systems [10-13] de- pend on the production of a prosthetic group to acti- vate a suitable apoenzyme through the action of the primary enzyme on a prosthetogenic substrate (Scheme I). In two of the systems that we have described so far, the primary enzyme catalyst is alkaline phosphatase (EC 3.1.3.1) which is used in many enzyme-linked immunoassays. The prosthetogen substrates used have been riboflavin 4'-phosphate [12] and flavin adenine dinucleotide phosphate (FADP) [11,13]. The former produces riboflavin which is converted by riboflavin kinase (EC 2.7.1.26) to FMN which reconstitutes apo- glycolate oxidase (EC 1.1.3.1); the latter produces FAD directly leading to the reconstitution of apo-o-amino acid oxidase (EC 1.4.3.3).

In this report we describe and analyse a simple model which adequately describes the behaviour of the FADP-based amplified assay of alkaline phosphatase [11,13] in which the DAAO formed is detected by coupling with horseradish peroxidase to yield a coloured product. The model enables the kinetic prop- erties of the primary catalyst to be defined and it can be used to optimise the design of assays for the pri- mary analyte.

Correspondence to: S. Harbron, London Biotechnology Ltd., De- partment of Biochemistry and Molecular Biology, University College London, London, WCIE 6BT, UK. Abbreviations: FADP, flavin adenine dinucleotide 3'-phosphate; aDAAO, apo-D-amino acid oxidase; hrp, horseradish peroxidase; DHSA, 3,5-dichloro-2-hydroxybenzenesulphonic acid; 4-AP, 4- aminoantipyrine.

Primary Possible further

catalyst reactions

Pros~etogen ) ) ) prosthetic O r o u p y Apoenzyme

R#colllciRttlon of hol~m~yll~ ~tivity

$ Visualisation ( Holoenzyme

Scheme I. Amplification cascade assay.

312

Theory

Binding of the prosthetic group by the apoenzyme The model used is as follows:

E + F . k ÷ 2 d e t e c t o r c o m p o n e n t s

( , . " E F

k 2 ~ , ~ 3 p

where E is the concentration of apoenzyme, F is the concentration of prosthetic group, P is the concentra- tion of detected product, EF is the concentration of active holoenzyme, k+2 and k_ 2 are apparent rate constants defining the process of formation and de- composition of the active holoenzyme, respectively, and k+3 is the apparent rate constant for the forma- tion of detected product, P, catalysed by the holoen- zyme, EF, and appropriate coupling enzymes.

The following analysis is valid provided E >> EF. The formation of EF can be multi-stage, in which case k+2 and k 2 are composite rate constants, but the analysis assumes that all intermediates are catalytically inactive. The formation of P can also be multi-stage, in which case it is assumed that the coupling components are present in excess.

The model is described by the following equations:

d E F d t = k + 2 F - k - 2 E F (1)

where k'+2 = k + 2 E

dP - - = k + 3 E F (2) d t

F o = F + E F (3)

from which it can be shown that:

k+2 E F = .Fo( l - e - a t ) (4)

a

where a = k '+ 2 + k 2

substituting (4) into (2) and integrating:

' k ( ( l - e - " ) ) k+2 +3 P -F 0 t -- (5)

a a

When e-a' << 1, the exponential term vanishes, and

P = A d - B I (6)

k + 2 k + 3 w h e r e A 1 - - .F o

a

k + 2 k + 3 a n d B i a2 • F 0

Amplification assay of the primary catalyst The model used is as follows:

FP > F . k + 2 d e t e c t o r c o m p o n e n t s

• E F k ~ + 3 p k_ 2

where FP is the concentration of prosthetogen, k ~1 = k+l[E p] F P / ( K m + F P ) , where k+l is the turnover number of the primary catalyst, Ep, and K m is its Michaelis constant. The other parameters are as de- fined above.

The same assumptions have been made as above in the derivation of the following equations. In addition, the formation of F may be multi-stage, in which case it is assumed that that the relevant coupling enzymes are present in excess.

dF d~- = k + l - k ~ - 2 F + k - 2 E F (7)

d E F = k ~ 2 F - k 2EF (8)

d t

dP - - = k + 3 E F (9) d t

from which it can be shown that:

k t k ' +1 +2 at E F ~ ( e - + a t - l ) (10) a -

substituting (10) into (9) and integrating gives:

p k ~ l k + 2 k + 3 ( ( 1 - e at) at2 ) - - + - - - t ( 1 1 ) a 2 a 2

or:

P= k'+z(Azt 2 - B e t + C 2 ( 1 - e ~t))

k+2k+3 w h e r e A 2 2 a

(12)

k+2k+3 B2 a 2

and

k + 2 k + 3 C2 a 3

w i t h a = k + 2 + k 2

when the exponential term vanishes, this gives

p = k + t ( A 2 t2 - B e t + C 2 ) (13)

Materials and Methods

Reagents. a D A A O was obtained from Calzyme Lab- oratories (San Luis Obispo, CA, USA) and used after

further purification [14]. FADP was supplied by Lon- don Biotechnology (London, UK). Horseradish peroxi- dase (Grade I) and calf intestinal alkaline phosphatase (EIA Grade) were supplied by Boehringer-Mannheim (Lewes, UK). FAD, D-proline, 4-AP, DHSA, 4- nitrophenyl phosphate and Tris base were obtained from Sigma (Poole, UK). Laboratory chemicals of Analar grade were from Fisons (Loughborough, UK).

Equipment. All microtitre-plate-based assays were performed using a MR7000 plate reader fitted with kinetics cartridge and thermostatically controlled plate holder (Dynatech, Billingshurst, UK).

FAD binding. The binding of FAD to aDAAO was monitored by following the activity of the resulting holoenzyme in a mixture comprised of 0.1 M Tris-HCl (pH 8.9, or as indicated), 35.0 mM D-proline, 2.0 mM DHSA, 0.4 mM 4-AP, 0.001 mg hrp, 0.1 /zM aDAAO and the appropriate concentration of FAD in a total volume of 0.1 ml. The concentration of the product [15] was calculated from the absorbance at 520 nm assum- ing it had an extinction coefficient of 23 000 for a 1-cm light path.

Alkaline phosphatase assay. Alkaline phosphatase was standardised using the following mixture: 0.1 M Tris-HCl buffer (pH 8.0), 0.1 mM MgSO 4, 1.0 /xM ZnSO4, 0.1 mM 4-nitrophenyl phosphate and alkaline phosphatase in a total volume of 1 ml. 10 pM of enzyme gave a change in absorbance per min of 0.00137 at 405 nm and 25°C for 1-cm light path.

The FADP-based amplified assays were performed in microtitre plates under the following conditions: 0.1 M Tris-HCl (pH 8.9, or as stated), 0.1 mM MgSO4, 1.0 /xM ZnSO4, 0.02 mM FADP, 35.0 mM D-proline, 2.0 mM DHSA, 0.4 mM 4-AP, 0.001 mg hrp, 0.1 /xM aDAAO and alkaline phosphatase in a total volume of 0.1 ml. The mixture was incubated at 25 or 37°C and the change in absorbance at 520 nm was monitored. The concentration of the product [15] was calculated from the absorbance at 520 nm assuming it had an extinction coefficient of 23 000 for a 1-cm light path.

The concentrations of Mg 2÷ and Zn 2÷ used were lower than often employed for alkaline phosphatase determinations, as higher levels, particularly of Zn 2÷, have a deleterious effect on the reconstitution of the apoenzyme.

Results

FAD binding The effect of pH on the activity of DAAO reconsti-

tuted in the presence of 5 nM FAD over a range of pH values at 25 and 37°C was studied. At both tempera- tures, the activity increased as the pH was raised, but above pH 8.9 the colour formed was increasingly unsta- ble resulting in a reduced colour fomation after 30-40 min. This was due to bleaching of the coloured dye by

313

0.7 -

0.6 + ~ _

0 .5+ wg

0.4 /'~m=•== Absorbance / = •

(520 nm) i /~'~m ~ ~--~ 0.3 i ~ ¢ " . - ~r,,-~r""

- r , ~

o.1

0 ~ ~ . . . . ~ ~ ~ • 0 5 10 15 20 25 30

Time (rain)

Fig. 1. Reaction time-course obtained for the assay of aDAAO. Each microtitre plate well contained (in a total volume of 0.1 ml): 0.1 M Tris/Tris-HCl (pH 8.9), 35.0 mM D-proline, 2.0 mM DHSA, 0.4 mM 4-AP, 1 ~g hrp, 0.1 /zM aDAAO and 5 nM FAD. The reaction was monitored at 520 nm using a Dynatech MR7000 plate reader fitted with a thermostatically controlled plate holder set to 25°C (rn) or 37°C ( • ). The solid lines were calculated using the model derived in

the text.

hrp, as the 4AP was consumed. Fig. 1 shows the increase in absorbance at 520 nm with time obtained when 5 nM FAD was incubated with 0.1 /zM aDAAO at 25 and 37°C at pH 8.9. From this, P (Eqns. 5 and 6) can be calculated at each point. After an initial lag time, a straight line of gradient A 1 and intercept B1 (see Eqn. 6) is obtained, from which k~_ 2 and k 2 can be calculated:

k+2 - - - B1F0k+3

h i k 2= ~-l - k + 2

Table I gives values for k ~ 2, k_ 2 and k + 3 over a range of pH values at the two temperatures. The values for k+3 were obtained by measuring the rate of reaction in the presence of a saturating concentration of FAD (0.24 mM).

TABLE I

Kinetic parameters of the amplification assay

pH k+3 k+2 k_ 2 k~_ 1 (min -I ) (min -1 ) (rain -1 ) (pM rain -1 )

at 25°C 8.0 1230 0.046 0.139 15.1 8.9 1330 0.085 0.126 50.2 9.2 1330 0.050 0.065 70.0 9.5 1320 0.049 0.056 74.3 9.8 1300 0.046 0.052 61.3

at 37°C 8.0 1540 0.219 0.493 91.8 8.2 1420 0.264 0.397 90.2 8.5 1340 0.211 0.230 89.6 8.7 1310 0.193 0.177 82.0 8.9 1290 0.163 0.145 123

314

I.,I-

1.2 /

0.8 ~ , Lu~-mmlmm Absorbance lllllll

(520 rim) 0.6 m uumuu nnlm m

0.4

0.2 ,~_~ ~ . ~ ~

0 0 l0 20 30 40 50 60

Time (min)

Fig. 2. Reaction time-course obtained for the amplified assay of alkaline phosphatase. Each microtitre plate well contained (in a total volume of 0.1 ml): 0.1 M Tris/Tris-HC1 (pH 8.9), 0.1 mM MgSO4, 1.0 ~zM ZnSO4, 20/xM FADP, 35.0 mM o-proline, 2.0 mM DHSA, 0.4 mM 4-AP, 1 /zg hrp, 0.1 ~ M aDAAO and 1 amol of alkaline phosphatase. The reaction was monitored at 520 nm using a Dynat- ech MR7000 plate reader fitted with a thermostatically controlled plate holder set to 25°C (D) or 37°C ( n ) . The solid lines were

calculated using the model described in the text.

The lines given in Fig. 1 were calculated using these parameters.

Alkaline phosphatase assay Eqn. 11 predicts that the concentration of hydrogen

peroxide, and hence absorbance, will rise exponentially at first and subsequently increase quadratically. This is what is observed in practice: Fig. 2 shows the increase in absorbance obtained during the assay of 1 amol of alkaline phosphatase at pH 8.9 at 25 and 37°C.

k+l can be calculated at each of the measured points using the following relationship obtained from Eqn. 12:

P k+:

A2 t2 - B z t + C 2 ( 1 - e - " ' )

Using values for A2, B 2 and C 2 calculated from the parameters in Table I, the mean values for k' calcu- +1 lated at 25 and 37°C are given in Table I.

The lines given in Fig. 2 were calculated using these parameters.

TABLE II

Kinetic parameters of alkaline phosphatase

pH kca t K m (s l) (/J,M)

at 25°C 8.0 40.9 12.5 8.9 124 9.6

at 37°C 8.0 159 0.8 8.2 167 2.2 8.5 214 8.7 8.7 270 19.5 8.9 364 35.5

Kinetic properties of alkaline phosphatase with FADP Estimates for K m and kca t for alkaline phosphatase

calculated from values for k' obtained at different +1 concentrations of FADP and pH values up to 8.9 are given in Table II. No measurements were made at higher pH values, because of the limitations imposed by the bleaching of the dye.

Discussion

Although Massey and Curti [16] clearly show that the binding of FAD by aDAAO is a two-stage process, enzyme activity does not appear until the completion of the second stage. Thus, the use of composite rate constants is a justifiable simplification of the overall binding process.

The fit between the observed and predicted be- haviour during the initial exponential period is very good (Figs. 1 and 2), indicating that the simple model used for the simulation is adequate to describe the behaviour of the system. The departure of the meas- ured points from the predicted lines at longer assay times at 37°C is due to the bleaching of the dye referred to above. For the assay of alkaline phos- phatase (Fig. 2) at 25°C, the assay performs better than predicted. This is because the assay mixture warms up in the plate reader which, although thermostatically controlled, has no cooling capability.

The value of k+l can be easily estimated from the progress curve obtained for the assay of alkaline phos- phatase. Using 1 amol of APase with 20/zM substrate there is effectively no change in substrate concentra- tion even after 1 h incubation. Thus, k+l is a good estimate of the initial rate and the approach described has been used to characterise the kinetic behaviour of APase with FADP.

An examination of Eqn. 12 shows that the kinetics of the amplification assay are controlled by two compo- nents; (i), k+l, which is the rate at which FAD is produced from FADP by the action of alkaline phos- phatase and (ii), A2t 2 - B2t + C2(1- e-at), which is related to the binding of the FAD by aDAAO and the activity of the DAAO thus reconstituted. The optimum pH occurs when the product of these two factors is highest. Both of these are dependent on pH and tem- perature. In addition, the first is sensitive to the con- centration of FADP, whilst the second is affected by the concentration of aDAAO and assay time (i.e., whether the kinetics are governed by the exponential or quadratic phases of the reaction).

Fig. 3 shows the variation of the first of these, k + j, with pH at 25 and 37°C. At the lower temperature, k + l increases as the pH is raised and reaches a plateau at pH 9.5 to 9.8, presumably because of the increase in K m [17]. At 37°C, k+~ decreases slightly as the pH is raised, but shows a steep rise between pH 8.7 and 9.0.

160

140 /

120 j~J~" ? 100 ~ _ ~ /

k ~ + l 80 (pM/min)

20 ~ - ~

0 . . . . . . q "~ I

8.5 9 9.5 10 pn

Fig. 3. Variation of the apparent turnover of alkaline phosphatase with pH. Values for k+l have been calculated as described in the text. (11), assayed at 25°C using 20 ~ M F A D P ; (D) , assayed at 37°C using 2 0 / x M F A D P ; (zx), predicted behaviour at 37°C using 75/.~M FADP. For all three curves, 1 amol (10 fM) alkaline phosphatase was

used.

This apparently anomalous behaviour results from the way that the g m increases as the pH is raised (see Table II). Values for k~_ 1 have been computed for 75 /zM FADP from the parameters in Table II to com- pensate for the increase in K m as the pH is raised and these show a progressive increase with pH, reflecting that obtained at 25°C (Fig. 3). Coefficients of variation for the experimentally determined values for k ~ 1 were typically 5% and 12% at 25 and 37°C, respectively.

Figs. 4 and 5 show the variation in the second of these components with concentration of aDAAO at different pH values at 25 and 37°C, respectively. Val- ues for A2 t 2 - B2t + C 2 ( 1 - e -at) at 5 and 60 min have been calculated to illustrate the difference in behaviour during the exponential and quadratic phases, respectively.

At 25°C (Fig. 4) A 2 t 2 - B 2 t + C 2 ( 1 - e -at) in- creases with concentration of aDAAO. During the exponential phase the optimum pH is 8.9, but in the

20000 ~ 2000000

18000 I ~...z.~ --/ _-

16000 • i- __ I_fI_ _~ ~--I- ~ 1500000

14000 -~--

12OOO f f ~ ~ ~ 1000000

t = 5 min 10~O0 t = 60 min 8000 ~ .... _-J 500000

4000 ~ ~ l J - 0

2000 ~ ~

0 - - ~ ~ ~ ~- . . . . . 500000 0.2 0.4 0.6 0.8

[~DAAOI (uM0 Fig. 4. Variation of A 2 t 2 × B2 t + C 2(1 - e - at) with concentration of aDAAO at different pH values at 25°C. Closed symbols represent the exponential phase of the assay (where t ffi 5 min, left-hand axis) and open symbols represent the quadratic phase of the assay (where t = 60 min, right-hand axis). (11, 13), p H 8.0; ( A , zx), p H 8.6; ( + ) ,

pH 8.9; ( × ) , p H 9.2; (<>, . ) , p H 9.5; (o, o ) , p H 9.8.

315

25000 2500000

2oooooo

150O0 t = 5ra in t = 60 min

10000 ~ 500000 5001) 0

0 --- q , - - - ~ ~ -500000 0.2 0.4 0.6 0.8

[aDAAOI (aM)

Fig. 5. Variation of A2t 2 - BEt + C2(1- e -at) with concentration of aDAAO at different pH values at 37°C. Closed symbols represent the exponential phase of the assay (where t = 5 rain, left-hand axis) and open symbols represent the quadratic phase of the assay (where t = 60 min, right-hand axis). (11, 13), pH 8.0; ( A , A), pH 8.2; (O, *) ,

pH 8.5; (e, o ) , pH 8.7; ( x ) , pH 8.9.

quadratic phase the optimum is over a broad range from 8.9 to 9.5. These effects of pH are not dependent on concentration of aDAAO.

At 37°C, a different picture is obtained (Fig. 5). Here, the effects of pH are dependent on concentra- tion of aDAAO during the quadratic phase, the opti- mum shifting from 8.7 at 0.1/zM aDAAO to pH 8.0 at 1.0 /zM aDAAO. In the exponential phase, however, the effects of pH do not vary greatly over the range of concentrations employed, with the optimum obtained at pH 8.2.

If Fig. 3 is compared with Figs. 4 and 5, k' shows +1 a greater sensitivity to pH than does A2 t 2 - B2t + C2(1 -e -a t ) . Clearly, for maximum sensitivity the higher the pH the better, although the higher substrate concentration should be used at 37°C. However, be- cause of possible deleterious effects of dye bleaching observed at higher pH values, pH 8.9 is the best compromise pH for the colorimetric assay. If luminol were to be used [18] instead of the dye forming compo- nents used here, then full advantage could be taken of the improved assay performance at the higher pH values.

References

1 Gosling, J.P. (1990) Clin. Chem. 36, 1408-1427. 2 Ternynck, T. and Avrameas, S. (1990) Methods Enzymol. t84,

469-481. 3 Bobrow, M.N., Harris, J.D., Shaughnessy, K.J. and Litt, G.J.

(1989) J. Immunol. Methods 125, 279-285. 4 Flore, M., Mitchell, J., Doan, T., Winter, G., Grandone, C.,

Zeng, K., Haraden, R., Smith, J., Morris, K., Leezezynski, J., Berry, D., Safford, S., Barnes, G., Scholnick, A. and Ludington, K. (1988) Clin. Chem. 34, 1726-1732.

5 Bronstein, I. and McGrath, P. (1989) Nature 338, 559-600. 6 Litchfield, W., Freytag, J.W. and Adamich, M. (1984) Clin. Chem.

30, 1441-1445. 7 Mize, P.D., Hoke, R.A., Linn, C.P., Reardon, J.E. and Schulte,

T.H. (1989) Anal. Biochem. 179, 229-235. 8 Johannsson, A., Ellis, D.M., Bates, D.L., Plumb, A.M. and Stan-

ley, C.J. (1986) J. Immunol. Methods 87, 7-11.

316

9 Harbron, S., Eggelte, H.J., Benson, S.M. and Rabin, B.R. (1991) J. Biolum. Chemilum. 6, 251-258.

10 Rabin, B.R., Hollaway, M.R. and Taylorson, C.J. (1991) US Patent US 5057412.

11 Rabin, B.R., Harbron, S., Eggelte, H.J. and Hollaway, M.R. (1992) UK Patent GB-B-2240845.

12 Harbron, S., Eggelte, H.J. and Rabin, B.R. (1991) Anal. Biochem. 198, 47-51.

13 Harbron, S., Eggelte, H.J., Fisher, M.R. and Rabin, B.R. (1993) Anal. Biochem. 206, in press.

14 Harbron, S., Fisher, M. and Rabin, B.R. (1992) Biotech. Tehniques 6, 55-60.

15 Fossatti, P., Principe, L. and Berti, G. (1980) Clin. Chem. 26, 227-231.

16 Massey, V. and Curti, B. (1966) J. Biol. Chem. 241, 3417-3423. 17 Chappelet-Tordo, D., Fosset, M., lwatsubo, M., Gache, C. and

Lazdunski, M. (1974) Biochemistry 13, 1788-1795. 18 Hinkannen, A. and Decker, K. (1983) Anal. Biochem. 132, 202-

208.