Anal. Chem. 1989, 6 1 , 309-313 (20) Fahey, P. M.; @&kin, H. E. DeSallnaHon 1971, 9 , 297. (21) Kestlng, R.; Bar&, M.; Vincent, A. J . Appl. folym. Scl. 1966, 9 , 1873. (22) Eiblcki, J. M., Weber, S. (3. BlosenscKs, in press. (23) Lwkowski, H.; Pannier, R.; Wende, A. J . Rakt. Chem. 1967, 35, 149. (24) Loeb, S.; Sourkajan, S. UCLA Report 60-60, 1960. (26) Sourirajan, S.; Kunst, E. I n Reverse Osmosis end Synthetic Membranes; ktbnal Research Councii mnade: Ottawa, 1977; Chapter 7. (26) Kutowy. 0.; Thayer, W. L.; Sourirajan, S. Desellnetfon 1978, 26, 195. (27) Wilson, 0. S.; Thevenot, D. R., pereonai communicatlon. (28) DeLlgny, C. L. J . chrometogr. 1970, 49, 393.
309
(29) Kesting, R. E. In Synthetic porvmeric Membranes; Wiley: New York, 1985; Chapter 7.
RECEIVED for review May 19,1988, AcceDted November 16. 1988. We gratefully acLowledge support from the National Institutes of Health under Grant GM28112. We also thank The Electrochemical Society for their permission to publish work previously presented at their 172nd meeting in October 1987.
Multifrequency Phase Fluorescence Study of Hapten-Antibody Cornplexation Frank V . Bright Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14214
The rotatlonal dynamlcs of a phenytoln fluorolmmunoassay system Is lnvestlgated by uslng multlfrequency phase and modulatlon fluorescence spectroscopy. Results lndlcate that the fluorescein label on thk rdathfdy small hapten undergoes dgnlflcant (>45 % ) local motion even when bound to the phenytoln antlbody. We attribute thls local motion to unhlndered rotatlon of the fluoresceln molety around the bond attachlng lt to phenytoln. Thls local motion affects the sensltMty d a steadystate polarlzatlon Immunoassay dramatkally.
INTRODUCTION In all chemical analysis schemes, selectivity has been traditionally sought by a myriad of instrumentrbased techniques. However, in terms of overall selectivity (ideally specificity), biologically based techniques have clearly offered the best results to date (1). In fact, with many enzyme- or monoclonal-antibody-based methods of analysis one can often achieve complete specificity. Of the many bioanalytical techniques available, the immunoassay, first described by Yalow and Berson (21, has found widespread use in many biochemical, chemical, clinical, and medical applications. In its simplest embodiment, the immunoassay is based on the competitive binding between an antigen (Ag), an appropriately labeled form of the antigen (Ag*), and a highly selective antibody (Ab) (3) Ag* Ab Ag = Ag*Ab AgAb (1) Fluoroimmunoassays (FIAs) (3,4), in which a fluorescent label is used as the marker, has offered one of the most promising alternatives to the original radioimmunoassays. In addition to providing good detection limits and high sensitivity, FIAs can be heterogeneous or homogeneous in nature (3,4). The distinction between each is that heterogeneous immunoassays require a physical separation of Ag* and AgAb whereas homogeneous immunoassays allow one to determine simultaneously the distribution between Ag* and Ag*Ab without separation. Thus,for routine analyses, homogeneous immunoassays are preferred because they offer shorter analysis times, are less expensive, and are simpler to perform. However, in order for a homogeneous immunoassay to “succeed”, one must have some means of selectively discriminating between the free (Ag*) and bound (Ag*Ab) species. In the past, fluorescence-based selectivity parameters have included in-
+
+
+
0003-2700/89/0361-0309$01.50/0
tensity (5),lifetimes (6),and steady-state polarization (7,8). Of these, the fluorescence-polarization-basedapproaches have enjoyed the most success. Fluorescence polarization immunoassays (FPIAs) are based on the fact that the fluorescent label has a nominal fluorescence lifetime that is on the order of the rotational diffusion rate for the fluorescing label (9). Thus, the steady-state polarization of a fluorescent label (tag) can be used to “track” rotational diffusion. Unfortunately,by employing steady-state measurements alone one can only acquire information regarding ensemble-averaged rotational motion of the tag. In this paper, we employ multifrequency differential phase and polarized modulation ratio measurements to explore directly the rotational dynamics of a simple hapten-antibody system. Multifrequency (dynamic) measurements offer the advantage that one can determine the individual rotational diffusion rates that describe a particular system. For example, if a system is described by two distinct rotational motions, dynamic measurements can be used to successfully ferret out these individual motions. As a model system we chose to study fluorescein-labeled phenytoin (Ag*) complexed to antiphenytoin antibody (Ab). Our results indicate that, in spite of the small size of phenytoin (molecular weight 252), local motion of the fluorescein label is still quite large (>&%I when Ag* is bound to Ab (molecular weight -150000). It is shown that this local motion of the fluorescein label limits the sensitivity of the classic FPIA.
THEORY The observed fluorescence polarization or for this discussion anisotropy (r) is given by the Perrin equation (9-12) ro/r = 1 + (7/4) (2) where ro denotes the limiting anisotropy for the fluorescent probe in a vitrified solvent (9-129,r is the fluorescence lifetime, and 4 is the rotational correlation time. For a simple spherical molecule (isotropic rotor) the rotational correlation time is given by 4 = nV/RT (3) where n is the solvent viscosity, T i s the Kelvin temperature, R is the gas constant, and Vis the volume of the rotating unit. Of course, for anisotropic rotation (nonsymmetric species) more complicated expressions result. Inspection of eq 1-3 shows that a species having a larger volume (V) will exhibit a concomitantlylarger anisotropy. In @ 1989 American Chemical Society
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relative terms, Ag* has a small anisotropy and because Ab is much more massive, Ag*Ab has a significantly larger anisotropy. Thus, by measuring the anisotropy of a given sample, one has the necessary selectivity to distinguish simultaneously between Ag* and Ag*Ab. However, one generally cannot accurately determine the rotational dynamics of a given system by using steady-state measurements alone. Fortunately, by utilizing dynamic depolarization measurments, one canobtain more accurate information regarding the rotational dynamics. In the frequency domain, rotational dynamics are determined from frequency-dependent measurements of the differential phase angle (DPA) and the polarized modulation ratio (PMR) (13). If the time-dependent decay of the total fluorescence is I@), the decay of the parallel and perpendicular components of the polarized fluorescence is given by (14)
I l , ( t )= 1/3[l(t)(l + 2r(t))l
(4)
and
I l ( t ) = 1/3[I(t)(l - r(t))l
(5) respectively,where r(t) is the decay of fluorescence anisotropy. For a simple isotropic rotor r(t) decays as a single exponential (6) r(t) = ro exp(-t/#) and for the more complicated anisotropic rotors r(t) generally takes the form n
r ( t ) = roCfi exp(-t/@i)
(7)
i=l
where fi and & are the fractional contributions and rotational correlation times attributed to the ith rotational diffusional motion, respectively. Regardless of the form of the anisotropy decay (eq 6 or 7)) DPA and PMR are given by the sine (Ni) and cosine (Q)transforms N i= Ii(t)sin wt d t (8)
Di = Ii(t) COS wt d t
(9)
where Ii(t) is given by eq 4 and 5 and w is the angular modulation frequency (15)
PMR(w) =
[
Nl12+
Dl12
]
N L 2+ D L 2
112
(11)
The parameters of interest, f i and $i, are subsequently obtained by fitting the experimental DPA(w) and PMR(w) data using nonlinear regression techniques (16). Time-resolved rotational diffusion studies have been employed previously to demonstrate that antibodies (IgG molecules) are extremely dynamic species that exhibit nanosecond segmental mobility of their F(abl and F,,, fragments ( I 7,18). In contrast, to the internal mobility within an IgG molecule we are concerned here with the effects of fluorescent probe mobility on the characteristics of a simple hapten-antibody system. Specifically, we are concerned with the effect of local fluorescent probe motion on the analytical characteristics of the steady-state polarization immunoassay. If we assume that the fluorescent label can rotate locally when Ag* complexes to Ab, then eq 2 takes the form ro/r = FA1 4- TF/&l + F d F L ( 1 + ~ L / @ L ) F G ( + ~ TG/#G)) (12) where Ff is the fraction of uncomplexed Ag*, F b is the fraction of Ag* in the Ag*Ab form (Ff+ Fb= l),FLis the fraction of Ag*Ab motion attributed to local motion of the fluorescent
A B
14 0.000
0.200
0.400
9 3
C
1
D E
0.33 0.1 1
0.600
0.800
1. 00
Fraction Free Ag*
Flgure 1. Theoretical representation of the normalizedanisotropy (rdr) versus fractional amount of free Ag’ as a function of the local to global motion ratio ( F L / F G ) .
label, F G is the fraction of Ag*Ab “global” motion (FL + Fc = l),and subscripts L and G denote the local and global parameters for Ag*Ab, respectively. Clearly, the fractional contribution of the local and global rotations dictate critically the ro/r value. FL dictates also the sensitivity of a given immunoassay system for target analyte quantification. To demonstrate this, Figure 1shows a series of normalized anisotropy (ro/r) versus Ff plots for a hypothetical immunoassay system undergoing local label motion within Ag*Ab (eq 12). A label fluorescence lifetime of 4.0 ne is assumed for both Ag* and Ag*Ab. This value was chosen because it is extremely close to the lifetime for fluorescein. In reality, these two lifetimes (Ag* and Ag*Ab) may differ slightly (6))but assuming they are equal simplifies our discussion. For this simulation, the Ag* and local Ag*Ab rotational correlation times are both fixed at 1ns and the rotational correlation time for the global motion is 30 ns. Each of the curves shown (A through E) represents different ratios of F L / F G (see inset). For example, the curves labeled E and A are generated for 10% and 90% local motion, respectively, within Ag*Ab molecule. Clearly, the system with the lower percentage of local rotational character (curve E) is the more analytical useful. That is, case E exhibits a much better sensitivity. Conversely, the system exhibiting almost complete local motion (curve A) results in a much poorer analytical technique (lower sensitivity). This arises because the disparity in mass (volume) between Ag* and Ag*Ab is more accurately reflected and thus exploited by a system exhibiting 100%global motion for Ag*Ab. Regardless of the analytical utility of the various hypothetical systems represented by Figure 1, it is important also to realize that steady-state anisotropy measurements are unable to recover these individual parameters (i.e., +i and Fi) contained within eq 12 (11). Again, the steady-state approach can only yield ensemble-averaged values for all the individual rotational correlation times and their fractional contributions. Thus, while a FPIA clearly “works” it is impossible to fully evaluate a given FPIA based solely on steady-state polarization and lifetime measurements. Parts A and B of Figure 2 show theoretical differential phase and polarized modulation ratio plots, respectively,for the same hypothetical systems presented in Figure 1. These sets of curves can be used to determine unequivocally the individual rotational parameters describing the system (eq 12) (14-16). Therefore, this frequency-domain approach provides the requisite information for more accurate and complete evaluation of the FPIA system.
EXPERIMENTAL SECTION Phenytoin fluoroimmunoassay kits were graciously provided by Bob Aiscnfeld of Sigma Chemical Co. and were used as re-
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4NALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989 22.000
16.500
t1
11.OOO
5.500
0.000
T
9
= 4.00
Phenytoin
4
rO= 0'40 91= 1.0 ns
- -318 ps p=116) -1.07 & 27.9 ns @=1.55)
v v
*2= 30 ns
- 1.01 ns @= 0.94)
0
I 1
0
10
100
.0
c
2
Frequency (MHz) 2.900
-
311
.
10
100
Frequency (MHz)
B
2.800
]B
2.500 -.
/
2.100-2.000 2*400:1.700 --
: _ - _ - - - e - -
1.6001.so0T 1.zoo '1 Frequency (MHz)
Figure 2. (A) Theoretical differential phase
angle versus modulation frequency plots for the system described in Figure 1. (B) Theoretical polarized modulation ratio plots for the system described in Figure 1. The numbers on each set of curves are the F , / F , values. ceived. The fluorescent label employed was fluorescein. All data collection was performed with an SLM 48000 multifrequency phase and modulation fluorometer (SLM-Aminco, Inc.). Excitation was from an Innova 90-6 argon-ion laser (Coherent, Inc.) operating at 488.0 nm. To avoid photobleaching the laser power at the sample was kept below 15 mW. The resulting fluorescence was detected through 515-nm long-pass filters (Oriel) and the temperature of the samples was maintained at 25 0.2 "C with a temperature circulator (Model A81, Haake).
*
RESULTS AND DISCUSSION Parts A and B of Figure 3 show experimental differential phase angle and polarized modulation versus frequency data sets, respectively, for fluorescein-labeled phenytoin (Ag*) with and without an excess (3:l; pL of Ab:pL of Ag*) of antibody (Ab). The rotational dynamics for the Ag* (triangles) species are well described as a single exponential decay with a rotational correlation time of approximately 1.0 ns. Therefore, fluorescein-labeled phenytoin acts as a simple spherical rotor. In contrast, the antibody-bound Ag* (circles) is not well described by a simple isotropic model (dashed curve). The Ag*Ab data is best described (solid curve) as an anisotropic rotor with two rotational correlation times having values of 1.1ns (47%) and 28 ns (53%), respectively. The precision of these recovered rotational correlation time values is depicted in Figure 4 by the chi-squared (x2)versus rotational correlation time plots. The chi-squared value is a measure of the goodness-of-fit between the model and the experimental data. The dotted line at 2.0 is used as a fit guage-values above 2.0 are considered a poor fit and values below 2.0 reflect a good fit, 1.0 being an optimum fit. Figure 4A shows the effects of the shorter rotational correlation time on the chi-squared value. In the case of the anisotropic Ag*Ab sytem (dashed curve), the second rotational correlation time is fiied at 28 ns. The fractional contributions are also fixed a t 47% and 53% for the shorter and longer rotational motions, respectively. Figure 4A shows that it is not possible to distinguish simultaneously the shorter rota-
Frequency (MHz)
Figure 3. (A) Experimental differential phase angle versus frequency
plots for fluorescein-labeled phenytoin (Ag , triangles) and antibodybound fluorescein-labeled phenytoin (Ag' Ab, circles). (B) Experimental polarized modulation versus frequency plots for the same phenytoin system. Same symbolism as A. 1000.000
A
- \
\
\
inn n o n l
- Age - - AgrAb
\
2
0.1004 0.000
0.400
1.200
0.800
1.600
2 100
Rotational Correlation Time (ns)
-20
25
30
35
40
Rotational Correlation Time (ns)
Figure 4. (A) Chi-squared (x2)versus rotational correlation time for the short-lived rotational motion. The dashed curve is for the local motion for Ag'Ab and the solid curve Is for unassociated Ag'. (8) Chi-squared (x2)surface versus rotational correlation time for the longer-lived global motion of Ag' Ab.
tional motion of the Ag*Ab species and the rotational motion for unassociated Ag* using this approach. Fortunately, the longer rotational motion is well resolved from either of these
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 4, FEBRUARY 15, 1989
A
47%
O Y
0
1
2
3
4
5
pl Ab/pI Agr
Flgure 5. Effects of the antibody to fluorescently labeled antigen ratio (AbIAg’) on the percentage of recovered global (28 ns) motion.
faster rotational motions (Figure 4B). From these experiments alone, it is not possible to determine if the shorter observed rotational motion for the Ag*Ab system is caused by local rotation of the fluorescein label when Ag* is associated with Ag*Ab or rotation from unassociated Ag*. To investigate further the origins of these anisotropic motions within the Ag*Ab system, a series of multifrequency runs were performed a t different Ab/Ag* ratios. Figure 5 shows the effect of added antibody on the recovered fraction of the 28-11s “global” rotational motion. From these results, one can see that after an approximately 2:l (volume of Ab: volume of Ag*) ratio we do not observe any significant increases in the fractional contribution for the longer rotational motion. Therefore, one can conclude that all Ag* would be completely complexed above this 2:l level. Thus, we are able to deduce that all Ag* that was available was bound by Ab and that the shorter rotational correlation time is somehow associated solely with Ag*Ab and not just free Ag*. One other possible cause for this shorter rotational correlation time could possibly be free fluorescein in the system. However, reversephase high-performance liquid chromatography (HPLC) experiments on the Ag* solution failed to yield anything other than a single chromatographic peak. Moreover, the retention time for this Ag* peak did not coincide with the fluorescein retention time. Therefore, we have ruled out free fluorescein as the cause of the shorter rotational correlation time. Another interesting aspect of the observed data is the magnitude of the longer (global) rotational correlation time. It would be expected that a protein the size of an IgG molecule should exhibit a rotational correlation time in excess of 100 ns for its true global rotation of the entire IgG molecule (19). However, we observe a value only one-fourth to one-third of the true global value. We attribute this shorter “global” rotational correlation time to rotation of a single F, fragment complexed to the Ag* species. Importantly, we believe that the global motion of the Ag*Ab is probably occurring also, but because of the lifetime for our fluorescent label (4 ns), we are not well poised to observe this significantly slower rotational motion. Figure 6 shows schematically the proposed motions observed for the Ag*Ab molecule. The sensitivity of the classic polarization immunoassay is dictated by the fractional contribution of the local rotational motion (Figure 1). To determine the degree to which this local motion affects the phenytoin immunoassay, we compare (Figure 7) the experimental results for the polarization assay to theoretically expected results. The theoretical results were generated assuming that the rotational correlation time for the Ag*Ab species was 28 ns and that the Ag*Ab motion was only due to this motion (i.e., no local motion of the fluorescent label occurred when Ag* is complexed with Ab). Clearly, at the lower concentration levels, the theoretical model offers
Global Flgure 6. Schematic representation of the motions observed in the phenytoin Ag’Ab system. The local motion of the fluorescein label (*) contributes 47 % and the remaining 53 % arises from the motion of a single F,,,, fragment. The true global motion is not observed for this system.
-. ,-”
I,
0.300 -f\
0.0004 0
0-0
---
10
Experimental Doto Theoretical w/o Local Motion
20
30
40
Phenytoin (pg/mL) Flgure 7. Anisotropy versus phenytoin concentration. The solid points represent the experimentally determined values and the dashed line is the theoretical limit.
significantly better sensitivity, but this sensitivity advantage tapers-off at the higher concentration levels.
CONCLUSION We conclude that the sensitivity of the polarization immunoassay is dictated in large part by the local motion of the fluorescent probe in the Ag*Ab complex and that this motion affects the lower concentration portion of the working curve to a greater degree than the upper end. However, it seems that it would be possible to approach the theoretical limit simply by selective chemical attachment of the fluorescent label with respect to the antibody. For example, one approach might involve orienting the label on Ag such that its local motion is more hindered upon Ag*-Ab complexation. Of course, one must weigh the degree of rotational hindrance induced versus the decrease in binding constant for the hapten-antibody complex. Registry No. Fluorescein, 2321-07-5; phenytoin, 57-41-0. LITERATURE CITED (1) Froehllch. P. Modern Nuorescence Spectroscopy; Wehry, E . L., Ed.; Plenum: New York, 1981; Vol. 2, Chapter 2. (2) Yalow, R . S.; Berson, S. A. J . Clin. Invest. 1960, 3 9 , 1157.
Anal. Chem. 1989, 6 1 , 313-320 (3) Smlth, D. S.; Hassan; Nargessi, R. D. Modern Fluorescence Spectroscopy; Wehry, E. L., Ed.; Plenum: New York, 1981; Vol. 3, Chapter 4. (4) Brlght, F. V. Anal. Chem. 1988, 6 0 , 1031A. (5) Amkraut, A. A. Immunochemrstry 1964, 1 , 231. (6) Bright, F. V.; McGown, L. 8. Telenta 1985, 3 2 , 15. (7) Spencer, R. D. Clln. Blochem. Anal. 1981, 10. 143. (8) Dandllker, W. 8.; Kelly, R. J.; Dandllker, J.; Farquhar, J.; Levin, J. I m munochemlstry 1973, 10, 219. (9) Spencer, R. D.; Toledo, F. 6.;Williams, 6. T.; Yoss, N. L. Clln. Chem. 1973. 19. 838. (10) Perrin. F. J . Phys. Radium 1928, 7 , 390. (11) Lakowicz, J. R. Principles of fluorescence Spectroscopy; Plenum: New York, 1983; Chapter 5. (12) Weber, G. A&. Protein Chem. 1953, 8 , 415. (13) Weber, G. J . Chem. Phys. 1977, 66, 4081. (14) Lekowlcz, J. R.; Cherek, H.; Maiiwal, B. P.; Gratton, E. Biochemistry 1985, 2 4 , 376. (15) Lekowicz, J. R.; Gratton, E.; Cherek. H.; Maliwal, 8. P.; Laczko. G. J . Bbl. Chem. 1984, 259, 10967. (16) Gratton. E.; Limkeman, M. Biophys. J . W83, 44, 315.
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(17) Yguerabide, J.; Epsteln, H. F.; Shyer, L. J . Mol. Bbl. 1970, 51, 573. (18) Holowka, D. A.; Cathou. R. E. Biochemrstry 1976, 15, 3379. (19) Tao, T. Biopo~mefs1989, 8 , 609.
RECEIVED for review August 22,1988. Accepted November 14,1988. This work was supported by BRSG SO7 RR 07066 awarded by the Biomedical Research Support Program, Division of Resources, National Institutes of Health, the donors of the Petroleum Research Fund, administered by the American Chemical Society, a New Faculty Development Award from New York State/United University Professions, a Non-Tenured Faculty Grant from 3M, Inc., a grant from the Health Care Instruments and Devices Institute at SUNYBuffalo, and the Center for Advanced Technology (SUNYBuffalo).
Prediction of Gasoline Octane Numbers from Near-Infrared Spectral Features in the Range 660-1215 nm Jeffrey J. Kelly,' Clyde H. Barlow,' Thomas M. Jinguji, and James B. Callis* Center for Process Analytical Chemistry, Department of Chemistry, BG-IO, University of Washington, Seattle, Washington 98195
The feasibility of predicting the quality parameters of gasoline from Its absorption spectrum in the wavelength range 660-1215 nm was investigated. I n this spectral region, vibrational overtones and combination bands of CH groups of methyl, methylene, aromatic, and olefinic functions were observed. With the aid of multivariate statistics, the spectral features could be correlated to various quality parameters of gasoline such as octane number. As an example, multivariate analysis of the spectra of 43 unleaded gasoline samples yielded a three-wavelength prediction equation for pump octane that gave excellent correlations ( R 2 = 0.95; standard error of estimate, 0.3-0.4 octane number; standard error of prediction, 0.4-0.5 octane number) with the ASTM motor determined octane numbers. Independent multivariate analysis using partial least-squares (PLS) regression yielded similar results. An additional set of nine sampler from the Pacific Coast Exchange Group of the ASTM were examined for ten different quality parameters (research and motor octane numbers, Reid vapor pressure, API gravity, bromine number, lead, sulfur, aromatic, oiefinlc, and saturate contents). Regression analysis of the spectra results in correlation of nine of the ten properties with R 2values ranging from 0.94 to 0.99 and standard errors near the independent reference test values.
Octane number is an experimentally measured, fuel-performance property of gasoline, strongly related to consumer satisfaction. The octane rating of a gasoline is determined by the measurement of a standard knock intensity in specially designed, ASTM-CFR test engines, where the sample's performance is compared to reference fuel blends ( 1 ) . The in-
* Corresponding author.
Permanent address: Department of Chemistry, The Evergreen State College, Olympia, WA 98505. 0003-2700/89/0361-0313$01.50/0
strumentation required for the measurement of octane numbers is expensive (over $100 OOO), requires constant maintenance, needs frequent standardization, consumes approximately 1pt of gasoline per test, and takes 20 min per sample. Such instruments are not well suited for on-line applications such as blending operations. In addition, catalysis research is made more time-consuming and expensive due to the large samples required. Clearly, an alternate test for octane number is highly desirable, especially one that is more rapid, more portable, less expensive, and suitable for on-line use. Clevett (2) has reviewed a number of alternative designs for on-line octane analysis. Many of these instruments use thermocouples to detect the partial oxidation reactions that are the precursors to knocking. These correlative instruments still rely on combustion measurements and are relatively expensive and time-consuming (5-20 min per sample) but do consume smaller amounts of gasoline than the knock engine. An alternative strategy for octane determination is based on the relationship of chemical structure and odane. Straight chain hydrocarbons have low octane numbers (normal heptane defines the zero of the octane scale), branched hydrocarbons have increased octane numbers (isooctane is used to define 100 on the octane scale), and aromatic hydrocarbons generally have high octane numbers. Given the octane numbers of a gasoline's constituents and the amounts of each present in a gasoline, one could hope to evolve an additive relationship that would predict the overall octane number. This approach was employed some years ago by Walsh and Mortimer (3), who used gas chromatography to identify and quantify the amount of each gasoline component and then applied linear multivariate statistics to predict octane number. Although this technique gives excellent predictions for octane number, it is too time-consumingfor on-line or even routine laboratory analysis. Yet another approach relies on the use of the number and types of functional groups in a gasoline sample to predict its 0 1989 American Chemical Society
