Anal. Chem. 1986, 58,2523-2527
to 25 ppm a t the full gain of the pneumatic amplifier albeit at the expense of the original dynamic range of 2.5 X lo4. The base line sensitivity of the pneumatic amplifier, when its gain is set 90 that 100% methane sample yields a full scale deflection, is 0.117 kPa/OC and 0.110 kPa/(mL/min) of flow. The insensitivity of the base line to these two parameters ensures a live zero which can always be software compensated a t the remote, peak processing end of the system.
CONCLUSIONS A sensitive optical version of a nonelectric, multicomponent, pneumatic-powered chromatograph suitable for process control applications has been described. The demonstrated insensitivity of the field-mounted package to temperature, pressure, flow, and electromagnetic interference while the system maintains its parts-per-million detectability argues for a consideration of this technology for the design of instruments to be located in hostile environments. ACKNOWLEDGMENT The authors gratefully acknowledge the contributions of Bent Norlund and Bill Sherwood for their electronic designs and Bill Cloyd for his machining skills. LITERATURE CITED (1) Annino, R.; Curren, J., Jr.; Kallnowskl, R.; Karas, E.;Linqulst, R.; Prescott. R., J. Chromafcgr. 1976. 126, 301. (2) Annino, R.; Voyksner, R. J. J. Chromatcgr. 1977, 142, 131.
2523
(3) Annino, R. CHEMTECH 1961. 482. (4) Bodge. P., unpubllshed work. (5) Bell, A. 0. Phibs. Mag. 1881. 7 1 , 510. (6) Tyndail, J. Roc. R . Soc. London 1881, 31, 307. (7) Rontgen, W. C. Phibs. Mag. 1881 1 7 , 308. (8) Gurney, John D. Photo-Nuidlc Interfaces; preliminary report; Harry Diamond Laboratories: Adelphi, MD, 1982. (9) Wade, R. L.; Cram, S. P. Anal. Chem. 1972, 44, 131. (10) Cram. S. P.; Chesler, S. N. J . Chromatogr. 1974. 99, 267. (11) Gaspar. G.; Arpino, P.; Guichon, G. J. Chromatcgr. Sci. 1977, 15, 256. (12) Gaspar, G.; Annino, R.; Vidai-Madjar, C.; Guiochon, G. Anal. Chem. 1978, 5 0 , 1512. (13) Annlno. R.; Gonnord, M.-F.; Guiochon. G. Anal. Chem. 1979, 5 1 , 379. (14) Annino, R.; Leone, J. J. Chromatogr. Sci. 1982, 20, 19. (15) Annino, R. "The Application of Fleurlc Devlces in Gas Chromatographic Instrumentation." I n "Advances in Chromatography;" Giddings, Grushka, Cams. Brown, Eds.; Marcel Dekker: New York. 1987; Vol. 28. (16) Schutjes, C. P. M.; Cramers, C. A.; Vidai-Madjar, C.; Guiochon G. J. Chromatcgr. 1983, 279, 269. (17) Kirshner. J. M.; Katz, S. Design Theory of Nuidic Componenfs; Academic Press: New York, 1975. (18) Eycon, M. F., Jr.; Schaffer, D. J. "Design Guide for Laminar Flow Fluidic Amplifiers and Sensors"; Report HDL-CR-82-288-1, April 27, 1982. (19) Manion, F. M.; Neurics: 33 ., Design and Staging of Laminar Proportional Amplifiers; Harry Diamond Laboratories: Washington, DC, 1972; AD-751, 181.
RECEIVED for review March 4,1986. Accepted June 9,1986. Presented in part at The Pittsburgh Conference and Exposition on Analytical Chemistry and Applied Spectroscopy, Atlantic City, NJ, March 10-14, 1986.
Multipoint Kinetic Method for the Immunochemical Quantitation of Isoenzymes Developed and Evaluated with Creatine Kinase Inhibition as a Model System William E. Weiser and Harry L. Pardue*
Department of Chemistry, Purdue University, West Lafayette, Indiana 47907
Thls paper descrlbes the development and evaluatlon of a new kinetlc approach for immunoassay procedures. I n particular, lt descrlbes a new approach for the slmultaneous quantltatlon of Isoenzymes that Interact dlfferently wlth antlbodies. The proposed approach Is evaluated by uslng the muscle (M) and braln (B) wbunlts of the Isoenzymes of creatine klnase (CK, EC 2.7.3.2) as a model system. The approach Is based on the selectlve lnhlbltlon of one of the subunlts (e.g., M) by an antibody and the use of nonllnear least-squares data processing to compute the M and B subuntt actMtles from the thne-dependent response curve. For several concentratlons of the two Isoenzymes In the range of diagnostk slgnlficance, leastaquares flts of computed ( y ) vs. expected ( x ) values yielded equatlons of y = 0 . 9 8 ~ (9.3 X and y = 1 . 0 4 ~ (3.6 X loJ) for the MM and BB Isoenzymes, respectively.
+
-
Because antibodies offer high degrees of selectivity for a variety of species, they are useful as analytical reagents. The most common immunoassay procedures involve measurements made after antigen/antibody reactions have approached equilibriu~.Although these equilibrium-based procedures have proven effective, they do not represent the only option 0003-2700/88/0358-2523$01.50/0
and it is probable that kinetic. -ssed procedures could offer complementary capabilities as has been the case with more traditional types of reactions. A few studies that involve measurements during the kinetic phases of antigen/antibody reactions have been reported (e.g., ref 1-3), but these studies only begin to exploit the capabilities of kinetic-based immunoassays. To date no one has reported the use of multipoint kinetic data to resolve two or more components simultaneously. The primary purpose of this study was to develop and evaluate a new kinetic approach for the simultaneous quantitation of isoenzymes that interact differently with antibodies. Quantitation of the muscle (M) and brain (B) subunits of the creatine kinase (CK) isoenzymes is used as a model to evaluate the new approach. The basic premises on which the study was based were that the antibody used would be completely selective for one subunit (M or B),the kinetic behavior of the inhibition reaction could be controlled to follow some welldefined kinetic order, and the percent inhibition of the affected subunit would be reproducible and independent of concentration. Assuming conditions could be established to satisfy these criteria, then the plan was to make multipoint measurements during the inhibition process and to use curvefitting methods to compute the initial (uninhibited) activity of each subunit. In addition to serving as a model for the 0 1986 American Chemical Society
2524
ANALYTICAL CHEMISTRY, VOL. 58, NO. 12, OCTOBER 1986
general approach, the creatine kinase isoenzymes are important because quantitation of the M and B subunits in blood serum is useful in the diagnosis of myocardial infarction ( 4 ) . Conditions were established for which the criteria mentioned above were satisfied. Using a polyclonal anti-MM antibody, it was possible to achieve virtually complete inhibition of the M subunit with virtually no inhibition of the B subunit. Also, conditions were established for which the inhibition process followed pseudo-fist-order kinetics to near 100% inhibition of the activity of the M subunit. A coupled reaction system involving the NADP/NADPH couple was used to monitor the primary enzymatic reaction involving the CK isoenzymes (5). After a preliminary induction period, the coupled reactions were fast relative to the zero-order primary reaction. This paper describes the basis for the method, conditions established for the simultaneous quantitation of the subunits, and quantitative performance features.
MATHEMATICAL DESCRIPTION For a zero-order enzyme-catalyzed reaction producing product, P, the velocity can be written as V,l = dPt/dt = k d t
(1)
in which V,l is the velocity, P is product concentration, ko is a zero-order rate constant, and Et is the instantaneous enzyme concentration. For the uninhibited subunit, the velocity will remain constant, and the time-dependent product concentration will be given by in which Pt,ois the time-dependent product concentration for the zero-order (uninhibited) component of the reaction and V’i,o is the initial velocity of the zero-order component. For the inhibited component following fit-order behavior, the time-dependent enzyme concentration is given by
(3) in which Et,land Ei,lare time-dependent and initial enzyme concentrations and k1 is the f i b o r d e r inhibition rate constant. Substituting from eq 3 into eq 1,integrating, and substituting V’i,l = kJ3i,l yields V’i,1
P,,l = Pi + -(I
kl
- e+)
(4)
The total time-dependent product concentration, Pt,is given by the s u m of concentrations from the two processes (eq 2 and 4) as follows
(5) in which the initial velocities for the first- and zero-order processes are expressed as rates of change of product (NADPH)concentration. The relationship can be expressed as absorbance by multiplying through by the product of the molar absorptivity, e, and path length, b, and by adding in a term for the sample absorbance. Multiplying eq 5 by tb, substituting tbV’ = dA/dt = V, we have
in which Ai is the initial absorbance from all sources and Vi,l and Vi,oare the initial rates for the inhibited and uninhibited processes, respectively, expressed as rates of absorbance change. This is the equation used in the curve-fitting process. T o use the equation, curve-fitting methods described previously (3,6-8)are used to obtain the values of Ai, kl, and initial velocities for the first-order ( Vi,J and zero-order ( Vi,o)
components that give the best fits of data for A, vs. t to the zero-order/first-order model represented by eq 6. The computed values of Vi,l and Vi,oare proportional to the activities of the inhibited and uninhibited components of the enzyme. As with other methods for enzymes, initial velocities for “standard” solutions are used to establish calibration plots or equations that are then used to compute enzyme activities in samples for which values of Vi,l and Vi,oare obtained with the curve-fitting process.
EXPERIMENTAL SECTION Instrumentation. A centrifugal mixing system (Rotochem IIA, AMINCO, Deerfield, IL) was used to mix samples and reagents and to measure time-dependent absorbances. Software was written to collect 200 data points, each the average of three readings on each of nine samples at a minimum time of 1.5 s per point. Data were transferred from the computer in the Fbtochem to a supermicroprocessor (Masscomp 510 workstation, Masscomp, Westford, MA) for processing. The computer utilizes a UNIX operating system and programs are written in C language so they are easily transferable to other similar systems (9). It was important for this study to know the dead time of the mixing system. The dead time, defined as the difference between the times when an instruction is given to start the rotor and when mixing occurs, was determined to be 0.7 s. The dead time was determined with the reaction between monochloramine and iodide to form iodine (10) by comparing the absorbance at 10 s with the calculated absorbance at that time based on the rate constant for the reaction and the absorbance of the unmixed solutions. Principles and procedures involved in the curve-fittingprocess have been discussed previously (3,6-8)and are not repeated here. Reagents. All solutions were prepared with distilled deionized water. Isoenzymes and Antibodies. The human isoenzymes, CK-MM, CK-MB, and CK-BB (lyophilized powders) and goat antibodies (neat anti-sera) to human CK-MM and CK-BB were obtained from Cambridge Medical Diagnostics (Billerica,MA) and stored at -20 “C until needed. Antibody solutions were prepared by diluting the neat anti-sera with imidazole buffer. Buffer. Imidazole buffer was prepared to contain per liter 0.100 mol of imidazole (grade I or grade 111, Sigma Chemical Co., St. Louis, MO), 0.010 mol of Mg(CzH302)2(MCB, Cincinnati, OH), and 0.002 mol of EDTA (Fisher Chemical Co., Fairlawn,NJ). The pH was adjusted to 6.7 using 1 mol/L acetic acid. This solution was stored frozen until needed. Stock Enzyme Solutions. All enzyme solutions were prepared in a diluent solution that contained per liter 30 g of bovine serum albumin (Sigma No. A-4503), 20 mmol of N-acetylcysteine (Sigma), 2 mmol 100 mmol of imidazole (Sigma), 10 mmol of Mg(CzH302)2, of EDTA, and 5 mol of glycerol, adjusted to pH 6.7 with 1 mol/L acetic acid. After refrigeration overnight, the solution was filtered with a 7-wm filter and stored at -20 “C. Enzyme Samples. Five enzyme solutions,two containing only one isoenzyme each and three containing two isoenzymes (MM and BB), were prepared from stock solutions. These solutions were diluted further to prepare test samples. Zero-order rates obtained for the single-component samples were used to standardize the mixtures. Reagent Kit. A kit containing the reagents for the quantitation of creatine kinase was used (CK-NAC, Boehringer Mannheim Diagnostics Division, Indianapolis, IN). The reagent was prepared according to the manufacturer’s directions. Temperature. Reactions were run at 37.0 f 0.1 “C and absorbance was monitored at 340 nm. All reagents were warmed in a 37.0 & 0.1 “C water bath for at least 20 min prior to mixing. Procedure. Because the antibodylantigen reaction occurs within the first few seconds after mixing, an extended lag phase would obscure the kinetics of that reaction. To avoid this problem, enzyme samples were mixed with the reagent 5 min before antibody was added so that a steady-state rate was achieved prior to addition of antibody. The exact procedure was to mix 0.10 mL of enzyme sample with 2.5 mL of CK reagent in the thermostated water bath where it was incubated for 5 min. In the meantime, a Rotochem transfer disk that had been warmed to reaction temperature was prepared
2525
ANALYTICAL CHEMISTRY, VOL. 58, NO. 12, OCTOBER 1986 n
1
6.0
4
4.0
01
+.I 3.0
Table I. Effect of Antibody Concentration on Computed Rates
rate, 10-~ s-l antibody dilution uninhibited factors Vi,l pi,,
t
5 5 9b 9b 10 10 15 15 17.5* 17.5b 20 20 42.5b 42.5b
2.0
.
.--I
0 3
1.0
’
4
v) (u
L2:
0.0
pi,o
.
U
E
rate constant
.
-
R
0:
,
0 0 0 0 L
Flgure 1. Effects of antibody concentration on extent of Inhibition.
with water as the reference solution. Then four 0.5-mL aliquots of the incubated reaction mixture were placed in separate positions in the transfer disk. Each of three aliquots was mixed with 0.1 mL of antibody solution and the fourth was mixed with 0.1 mL of imidazole buffer to serve as a reference for comparison and to provide assurance that the coupled reaction system followed zero-order kinetics throughout the experiment.
3.33 1.57 3.63 1.71 3.33 1.56 3.33 1.56 3.80 1.79 3.33 1.56 3.92 1.85
%
(hi), 10-2 s-l
33 48 30 43 33 50 2.4 13 -2.0 0.8 -5.6 -0.6 -24 -24
4.7 5.3 4.0 4.6 4.1 4.6 2.8 3.2 2.5 2.7 2.3 2.5 1.3 1.4
Error between initial rates determined with (pi,%) and without inhibition. *Dilution factor obtained by reducing reaction volume of antibody solution. ( Vi,J
1. 30
RESULTS AND DISCUSSION For convenience, activities are presented as rates of absorbance change per second (s-l); comparisons with international units are discussed near the end. All uncertainties are reported as one standard deviation. Antibody Concentration. Because conditions to obtain zero-order behavior for the enzyme reaction systems are well established, our primary focus was on the antibody concentration that would yield the desired kinetic behavior. One of the first questions that needed to be addressed was what concentration of antibody was needed to cause complete inhibition of the affected subunit. Figure 1shows the effect of dilution of antibody preparation on the residual rate. For the preparation used in this study, a dilution factor less than 15-fold is required to ensure complete inhibition. Having established this fact, several experiments were done to evaluate effects of antibody concentration on results obtained for CK-MM alone using the curve-fitting process. To do this, results for different dilutions of CK-MM were obtained with and without antibody present for comparison purposes. Representative results are summarized in Table 1. For each antibody concentration, the curve-fitting process (eq 6) was pedto compute the initial velocity for the inhibited reaction (Vi,l) as well as any residual zero-order component ( Vi,o) that would result from incomplete inhibition of the enzyme or other residual zero-order processes. Ideally, the computed value, Vi,l, should be the same as the rate, Vi,l, obtained for the uninhibited reaction and the zero-order rate should be near zero. The most important observation from the data in Table I is that the error (Vi,l vs. Vi,l) is relatively high for both the highest and lowest concentration of antibody used, and is quite small for intermediate concentrations. The zero-order component, Vi,o,increases from negative values at high antibody concentrations to large positive values at low antibody concentrations. The zero-order component remains moderately small for the range in which differences between inhibited and uninhibited values are smallest. Reasons for this behavior are illustrated by data in Figure 2, which illustrate effects of antibody concentration on shapes of response curves. For higher antibody concentration (curves a and b), the inhibition reaction exhibits the desired behavior early in the reaction process, but at longer times, there is a monotonic decrease in absorbance. To test the possibility that the decrease in absorbance could result from precipitation
~
4.45 -0.036 2.33 -0.017 0.017 4.71 2.45 0.008 4.42 0.028 2.35 0.007 3.41 0.036 0.015 1.77 3.73 0.083 1.81 0.039 3.42 0.087 0.043 1.56 2.96 0.58 0.24 1.40
error,”
f-.----d
01
1.25
.
_____._.____-.-
u c
1’’- --.---
0
13 1.20. L
------_
0 v)
n
