Kinetic delay of cyclization/elimination-coupled enzyme assays: Analysis and solution

Article abstract of DOI:10.1016/j.bmcl.2010.09.104

A kinetic analysis of an enzyme assay employing a synthetic substrate that produces a detectable signal through a spontaneous organic cyclization/ elimination reaction following the enzymatic reaction was conducted. The results from the calculation were used to predict the lag period and provide accurate measurements of the activity of alkaline phosphatase using the fluorogenic substrate (1).

Full text of DOI:10.1016/j.bmcl.2010.09.104

Bioorganic & Medicinal Chemistry Letters 21 (2011) 1069–1071
Contents lists available at ScienceDirect
Bioorganic & Medicinal Chemistry Letters
journal homepage: www.elsevier.com/locate/bmcl
Kinetic delay of cyclization/elimination-coupled enzyme assays: Analysis and
solution
Fengtian Xue a, , Christopher T. Seto b
⇑
a Department of Chemistry, University of Louisiana at Lafayette, PO Box 44370, Lafayette, LA 70504, USA
b Department of Chemistry, Brown University, 324 Brook Street, Providence, RI 02912, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 19 July 2010
Accepted 21 September 2010
Available online 25 September 2010
A kinetic analysis of an enzyme assay employing a synthetic substrate that produces a detectable signal
through a spontaneous organic cyclization/elimination reaction following the enzymatic reaction was
conducted. The results from the calculation were used to predict the lag period and provide accurate
measurements of the activity of alkaline phosphatase using the fluorogenic substrate (1).
Ó 2010 Published by Elsevier Ltd.
Keywords:
Enzyme assay
Steady state
Lag period
Half life
Enzyme assays such as chromogenic assays and fluorogenic as-
says allow simple, sensitive, and rapid measurements of enzyme
activities,1,2 which are of great importance in diverse fields includ-
ing diagnostics,3 drug discovery,4 cellular imaging,5 and enzyme
engineering and evolution.6,7 Depending on the process of signal
generation, enzyme assays are commonly classified into direct as-
says where substrates generate optical signals directly in response
to enzymatic reactions, and coupled assays where an additional
enzyme is usually employed to turn over the product of the initial
enzymatic reaction to produce detectable signals. The kinetics of
both types of enzyme assays have been well documented and
widely applied in following activities of enzymes.1,2,8,9 Recently,
an increasing number of organic reaction (e.g., cyclization and
elimination) coupled enzyme assays have been developed using
chromogenic/fluorogenic substrates. As outlined in Scheme 1,
these substrates function in two consecutive steps: (1) the enzy-
matic reaction of interest produces an unstable intermediate (I);
and (2) the intermediate rapidly breaks down through a spontane-
ous cyclization reaction or a b-elimination reaction, releasing a
chromogenic/fluorescent molecule (P). These assays can be viewed
as a new type of direct enzyme assay since no additional enzyme/
reagent is required to generate a detectable signal. Their kinetics,
however, shares some characteristics with the coupled enzyme as-
say; the organic reaction is an additional step following the enzy-
matic reaction, which plays an important role when considering
the kinetics of the whole process.8,9 Compared to direct assays,
the cyclization/elimination-coupled enzyme assays often show de-
creased background signal and improved substrate binding affin-
ity.2 More importantly, they provide
practical means for
a
measuring the activities of enzymes that have been a challenge
to evaluate by direct assays.1,2 In addition, they avoid the complex-
ities and potential errors involved in performing a coupled enzyme
assay.10 So far, this strategy has been successfully applied in
numerous enzyme systems including catalytic antibodies,11 prote-
ases,12,13 epoxide hydrolases,14 phosphatases,15–18 lipases and
esterases,18,19 b-lactamases,20,21 tyrosinase,22 coenzyme Q,23
monoamine oxidases,24,25 DT diaphorase,26 ceramidases,27 serum
paraoxonases,28 sphingosine-1-phosphate lyase,29 Baeyer–Villiger
monooxygenases,30 hydroxylases,30 lactonases,30 and prostate spe-
cific antigen.31
Even though cyclization/elimination-coupled enzyme assays
are widely used, to the best of our knowledge, there is no formal
report about the kinetics of the assays, which can be used to deter-
mine the rate of the enzymatic reaction accurately. To facilitate fu-
ture applications of these assays, herein, we carry out a detailed
kinetics analysis of this system (Scheme 1) by viewing the cycliza-
tion/elimination reaction as a coupled step to the enzymatic reac-
tion.8,9 To use this assay to accurately determine the rate of the
enzymatic reaction, it is important that one starts to record the
data when the measured rate of the cyclization/elimination reac-
tion (V2) becomes equal to the rate of the enzymatic reaction
(V1) under experimental conditions—in other words, only if a stea-
dy state is reached (Scheme 1). Since the measurements are taken
during the initial rate period when the concentration of the initial
substrate is bigger than the Michaelis constant (Km) and only a
small fraction of the substrate is turned over by the enzyme (E),
E is fully saturated by the substrate (S), therefore the rate equation
⇑
Corresponding author. Tel.: +1 401 441 1881; fax: +1 337 482 5676.
E-mail address: fxx6907@louisiana.edu (F. Xue).
0960-894X/$ - see front matter Ó 2010 Published by Elsevier Ltd.
doi:10.1016/j.bmcl.2010.09.104

1070
F. Xue, C. T. Seto / Bioorg. Med. Chem. Lett. 21 (2011) 1069–1071
Km
k1
k2
P
+
ES
I
S
E
V1
V2
enzymatic reaction
cyclization/elimination
Scheme 1. Kinetic scheme for a cyclization/elimination-coupled enzyme assay.
Table 1
Relationship between
accuracies
3500
*
t
and t1/2 for different assay
t*
3000
2500
2000
1500
1000
500
[I]/[I]ssꢄ100% (%)
99
95
90
6.65 ꢅ t1/2
4.32 ꢅ t1/2
3.32 ꢅ t1/2
0
0
300
600
900
1200
1500
1800
2100
of the enzymatic reaction is V1 = k1[ES] ꢀ k1[E0] (E0 is the total con-
centration of the enzyme used in the assay). The product of this
reaction, I is depleted irreversibly from the enzymatic reaction
through a first-order intramolecular cyclization/elimination reac-
tion with a rate constant of k2.
time (s)
Figure 1. Time courses of cyclization reactions of 2 in 10 mM Tris buffer at pH 8.0.
The initial concentration of 2 for the measurement was 100
fluorescence intensity (I, kem = 460 nm) was recorded.
l
M. The increase in
It is important to establish whether the steady state (i.e.,
V2 = V1) is likely to occur within a reasonable period of time. More-
over, a quantitative prediction of the lag period before the steady
state is reached would serve as an indispensable guideline for
when to begin collection of data points. Based on the discussion
above, the rate equation for the enzymatic reaction in Scheme 1
can be shown as
lnð1 ꢂ ½Iꢁ=½IꢁssÞ
tꢃ ¼ ꢂ
ð7Þ
k2
Since the conversion of I to P is a first-order reaction, the rate con-
stant is defined as
ln2
t1=2
k2 ¼
ð8Þ
d½Iꢁ
¼ k1½Eꢁ ꢂ k2½Iꢁ
ð1Þ
ð2Þ
ð3Þ
ð4Þ
dt
Thus
Integrate both sides of Eq. 1,
lnð1 ꢂ ½Iꢁ=½IꢁssÞ
tꢃ ¼ ꢂ
ꢄ t1=2
ð9Þ
k1½Eꢁ
2t
ln 2
½Iꢁ ¼
ð1 ꢂ eꢂk
Þ
k2
*
As shown in Eq. 9, the time required (t ) to reach a certain per-
centage of the steady state of the coupled enzyme system ([I]/[I]ss)
is directly and only dependent on the half life (t1/2) of the coupled
cyclization/elimination reaction that follows the enzymatic reac-
At the steady state (t?1)
d½Iꢁ
¼ k1½Eꢁ ꢂ k2½Iꢁss ¼ 0
dt
*
tion of interest. Table 1 lists simple calculations of t values that
Thus
can be used to obtain a desired assay accuracy. For a precise kinetic
study, the value of [I]/[I]ss should be >99%, so one needs to pre-
incubate the assay mixture for a period of 6.65 ꢅ t1/2 before collect-
ing the first data point. In more qualitative measurements, the cor-
responding value of [I]/[I]ss may be lowered to 95% or 90%. To
achieve these accuracies, one can start recording the data of the
corresponding assay after 4.32 ꢅ t1/2 and 3.32 ꢅ t1/2, respectively.
Next, we applied this kinetic analysis to the measurement of the
activity of alkaline phosphatase (AP) using fluorogenic substrate
(1).32 As outlined in Scheme 2, when treated with AP, the O–P bond
in the nonfluorescent substrate (1) is hydrolyzed generate the
unstable intermediate (2). This intermediate undergoes a rapid
cyclization reaction to produce 3 while releasing the strongly
fluorescent molecule 7-hydroxycoumarin.
k1½Eꢁ
½Iꢁss
¼
k2
Take the natural log of both sides of Eq. 2 and rewrite the equation
as
ꢀ
ꢁ
k2
k1½Eꢁ
ln 1 ꢂ
½Iꢁ ¼ ꢂk2t
ð5Þ
Plug Eq. 4 into Eq. 5,
Â
Ã
ln 1 ꢂ ½Iꢁ=½Iꢁss ¼ ꢂk2t
ð6Þ
Therefore, the time required to reach a certain [I] can be calculated
by
O
CO2Me
O
OH
OH
H
N
O
P
O
O
N
k2
3
k1
O
O
+
phosphatase
O
O
O
CO2Me
O
O
O
N
CO2Me
2
1
O
O
OH
nonfluorescent
highly fluorescent
Scheme 2. Function of fluorogenic substrate (1) of AP.

F. Xue, C. T. Seto / Bioorg. Med. Chem. Lett. 21 (2011) 1069–1071
1071
1600
1400
1200
1000
800
600
400
200
0
0
500
1000
1500
2000
2500
time (s)
Figure 2. The activity of AP (Sigma P6774, from bovine intestinal mucosa) was measured in 96-well microtiter plates with 1 as the substrate. The enzymatic reaction mixture
(50 L) consisted of 10 mM Tris buffer (pH 8.0) and 1 mM MgCl2. Substrates were added as solutions in DMSO. The overall concentration of DMSO was 10% for each
l
measurement. The enzymatic reaction was run at 37 °C and initiated by the addition of substrates. For fluorogenic substrate 1, the fluorescence emission generated from the
reaction was measured using a Galaxy microplate reader (FLUOStar, BMG Labtechnologies) with an excitation filter of 340 nm and an emission filter of 460 nm.
8. McClure, W. R. Biochemistry 1969, 8, 2782.
9. Storer, A. C.; Cornish-Bowden, A. Biochem. J. 1974, 141, 205.
10. Kruger, N. J. Phytochemistry 1995, 38, 1065.
Under the same conditions that were used for the AP activity
assay (10 mM Tris buffer, pH 8.0), the half life (t1/2) of the cyclization
reaction of 2 was determined to be 100 s (Fig. 1). The corresponding
AP assay using 1 as the fluorogenic substrate was conducted (Fig. 2).
The lag period of the assay before the steady state was reached lasted
from 0 to 600 s. At the same time, the predicted lag period for 99%
accuracy based on Table 1 is 665 s (calculated by 6.65 ꢅ 100 s). This
prediction matches the experimental data well.
In summary, we have studied the kinetics of a cyclization/
elimination-coupled enzyme assay, and established a simple rela-
tionship between the lag period of the assay and the half life of
the coupled organic reaction. This result may be applied to the
development of other novel assays for enzymes using indirect
colorimetric substrates.
11. Shamis, M.; Barbas, C. F., III; Shabat, D. Bioorg. Med. Chem. 2007, 17, 1172.
12. Richard, J.-A.; Jean, L.; Romieu, A.; Massonneau, M.; Noack-Fraissignes, P.;
Renard, P.-Y. Org. Lett. 2007, 9, 4853.
13. Meyer, Y.; Richard, J.-A.; Massonneau, M.; Renard, P.-Y.; Romieu, A. Org. Lett.
2008, 10, 1517.
14. Jones, P. D.; Wolf, N. M.; Morisseau, C.; Whetstone, P.; Hock, B.; Hammock, B. D.
Anal. Biochem. 2005, 343, 66.
15. Zhu, Q.; Uttamchandani, M.; Li, D.; Lesaicherre, M. L.; Yao, S. Q. Org. Lett. 2003,
5, 1257.
16. Zhu, Q.; Huang, X.; Chen, C. Y. J.; Yao, S. Q. Tetrahedron Lett. 2004, 45, 707.
17. Nicolaou, M. G.; Yuan, C.-S.; Borchardt, R. T. J. Org. Chem. 1996, 61, 8636.
18. Badalassi, F.; Wahler, D.; Klein, G.; Crotti, P.; Reymond, J.-L. Angew. Chem., Int.
Ed. 2000, 39, 4067.
19. Chandran, S. S.; Dickson, K. A.; Raines, R. T. J. Am. Chem. Soc. 2005, 127, 1652.
20. Gao, W.; Xing, B.; Tsien, R. Y.; Rao, J. J. Am. Chem. Soc. 2003, 125, 11146.
21. Xing, B.; Khanamiryan, A.; Rao, J. J. Am. Chem. Soc. 2005, 127, 4158.
22. Germanas, J. P.; Wang, S.; Miner, A.; Hao, W.; Ready, J. M. Bioorg. Med. Chem.
Lett. 2007, 17, 6871.
Acknowledgments
23. Tremblay, M. S.; Sames, D. Org. Lett. 2005, 7, 2417.
24. Zhou, W.; Valley, M. P.; Shultz, J.; Hawkins, E. M.; Bernad, L.; Good, T.; Good, D.;
Riss, T. L.; Klaubert, D. H.; Wood, K. V. J. Am. Chem. Soc. 2006, 128, 3122.
25. Chen, G.; Yee, D. J.; Gubernator, N. G.; Sames, D. J. Am. Chem. Soc. 2005, 127,
4544.
We thank Jeff Martell and Kristin Jansen Labby for valuable
discussions.
26. Huang, S.-T.; Lin, Y.-L. Org. Lett. 2006, 8, 265.
References and notes
27. Bedia, C.; Casas, J.; Garcia, V.; Levade, T.; Fabriàs, G. ChemBioChem 2007, 8, 642.
28. Khersonsky, O.; Tawfik, D. S. ChemBioChem 2006, 7, 49.
29. Bedia, C.; Camacho, L.; Casas, J.; Abad, J. L.; Delgado, A.; Veldhoven, P. P. V.;
Fabriàs, G. ChemBioChem 2009, 10, 820.
30. Sicard, R.; Chen, L. S.; Marsaioli, A. J.; Reymond, J.-L. Adv. Synth. Catal. 2005, 347,
1041.
31. Jones, G. B.; Crasto, C. F.; Mathews, J. E.; Xie, L.; Mitchell, M. O.; El-Shafey, A.;
D’Amico, A. V.; Bubley, G. J. Bioorg. Med. Chem. 2006, 14, 418.
32. Xue, F.; Seto, C. T. Org. Lett. 2010, 12, 1936.
1. Reymond, J.-L. Enzyme Assay; John Wiley: Weinheim, 2005.
2. Reymond, J.-L.; Fluxà, V. S.; Maillard, N. Chem. Commun. 2009, 41, 34.
3. Manafi, M.; Kneifel, W.; Bascomb, S. Microbiol. Rev. 1991, 55, 335.
4. Silverman, R. B. The Organic Chemistry of Drug Design and Drug Action, 2nd ed.;
Elsevier Academic Press: Burlington, 2003.
5. Haugland, R. P.; Spence, M. T. Z.; Johnson, I. D.; Basey, A. The Handbook: A Guide
to Fluorescent Probes and Labeling Technologies, 10th ed.; Eugene, 2005.
6. Goddard, J. P.; Reymond, J.-L. Trends Biotechnol. 2004, 22, 363.
7. Goddard, J.-P.; Reymond, J.-L. Curr. Opin. Biotechnol. 2004, 15, 314.