Anal. Chem. 1991, 63,2025-2028
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Prediction of Gas Chromatographic Relative Retention Times of Anabolic Steroids C. G. Georgakopoulos, 0. G. Tsika, and J. C. K i b u r i s Doping Control Laboratory, The Olympic Athletic Center of Athens, Kifissias 37,15123 Maroussi, Athens, Greece
P. C. Jurs* Department of Chemistry, The Pennsylvania State University, 152 Davey Laboratory, University Park, Pennsylvania 16802
lb predkWn al gas chromatographic relative retention times (RRTs) d anabolic steroids, used In the doping control d athletes, was performed by a quantitative structurwetentbn relatlonshlp (QSRR) and muitlple linear regression analysis study. A nine-varlabk model was generated with a multiple correlation coeffkht R = 0.991 and rdatlvo standard error of less than 3 % Preliminary resuits Indlcated that the a p pkatbn d the modd, especlaHy In the predktkn d RRTs of metabolites d the anabolic steroids, will be helpful.
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INTRODUCTION Doping control is performed on athletes to prevent drug abuse. Anabolic steroids form an important class of doping agents. Steroids and metabolites are found in urine in free or conjugated form. They are extracted from the urine and analyzed by capillary gas chromatography coupled with spectrometry. 'QpicaUy, a first screening is applied to all the unknown urine samples by using GC selective ion monitoring (SIM) MS analpis. A second full mass range GC/MS analysis is performed on samples that were found to probably contain an anabolic steroid. If this second analysis is positive, then as much data as possible are accumulated to support the positive result. A tool for predicting the relative retention times (RRTs) of anabolic steroids and metabolites that are mentioned in literature would be a valuable aid in this process. Quantitative structure-activity relationships (QSAR) is the field that relates molecular structures, described numerically, with chemical, physicochemical, and biological activities (1). The methodology of relating chemical structure with chromatographic retention parameters is known as quantitative structureretention relationships (QSRR) (2)and has two main goals, the prediction of retention coefficients and the explanation of the chromatographic mechanisms. Chromatographic retention is based on the interactions between the solute and the stationary phase, and the goal of the present work is to find which of the available topological, geometrical, electronic and physical descriptors that we computed are related to the retention of the anabolic steroids. In the past, this goal has been approached successfully for many compound classes and chromatographic systems (3-9). Multiple linear regression analysis was used to find the subset of descriptors that correlates the RRTs.
EXPERIMENTAL SECTION The procedure used in the present study comprised four fundamental stages: (a) GC/MS analysis of anabolic steroids, metabolites, and endogenous steroids of similar structure by the Doping Control Laboratory of Athens, (b) molecular structure entry and storage, (c) molecular descriptor generation, and (d) statistical analysis. All the computations were performed on a SUN 4/110 workstation at Penn State University using the ADAPT software system (10, 11). 0003-2700/91/0363-2025$02.50/0
Data Set. A set of 45 anabolic steroids, metabolites, and endogenous steroids was used for the study (Table I). These compounds come from either standards or metatmlic experiments. The overall doping analysis approach is described in detail elsewhere (12). Briefly, the isolation of the anabolic steroids from urine is performed in the following manner: (a) extraction via XAD-2 column, (b) acidic or enzymatic hydrolysis, and (c) 0-TMS and N-TMS derivatization. The instrument used for the analysis was a GC HP5890/MSD HP5970. The internal standard used was methyltestosterone. Other experimental conditions were as follows: helium carrier gas, port temperature 250 OC, split ratio l : l O , injection volume 1pL, column HP Ultra 1/25 m/0.2 mm i.d./O.ll pm film thickness, and the temperature program 180 OC for 1min, 8 OC/min to 220 OC, 3-250 OC, 14 "C/min to 280 OC with a total run and acquisition time of 25 min. For almost all of the compounds the retention time was assigned for the molecular ion signal psak. The range of RRTs for the compounds was from 0.669 to 1.393 and the range of molecular weights was from 286 to 642. The experimental relative retention times are given in Table I. Structure Entry. The molecular structures were entered into the ADAPT software system by sketching hydrogen-suppressed diagrams on a graphics terminal (13-15), and they were stored as connection tables. The next step involved the minimization of the strain energy of each structure by correcting bond lengths and angles with two molecular mechanics algorithms: MM2 (16, 17) and AM1 (18). Because of the inability of the software to estimate descriptor values for silicon atoms, all the silicon atoms of the TMS groups were replaced by carbons, which should have a minimum effect on the results because of the homogeneity of the data set. Descriptor Generation. A total of 127 descriptors were calculated (a) topological, (b) geometric, (c) electronic, and (d) physical. Topological descriptors include fragment descriptors, molecular connectivity descriptors, K indexes, and path descriptors. Fragment descriptors are evaluated from simple counts of atoms, bonds, rings, and substructures of the molecule. Molecular connectivity descriptors are based on work by RandiE (19) and by Kier and Hall (20,21). These descriptors encode information about the size and the degree of branching in a molecule. K indexes, developed by Kier (22),are based on graph theory and give information about the molecular shape of a molecule. Path descriptors, developed by RandiE (23),include information about the number of paths and their lengths (a connected path is a through-bond path from one atom to the next). Geometric descriptors are used to differentiate molecules that are topologically very similar. They are evaluated from modeled three-dimensional coordinates and include principal moments of van der Waals molecular volume (W), length-to-breath inertia (24), ratio (26,27),the principal axes of the molecule (Le. ulengthn, "width", and "thickness" of the molecule) and their ratios (27), structural symmetry descriptors (23, and solvent-accessible surface areas and volumes of the molecule (28). One physical descriptor was calculated, the whole-molecule molar refraction value, by using the fragment additivity method developed by Vogel (29). Three electronic descriptors were calculated using the Del Re method (30). These descriptors compute the approximate u electron density, the interatomic distance between the atoms with 0 1991 American Chemical Society
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Table I. Set of 45 Anabolic Steroids Studied anabolic steroids
Table 11. Fbgmssion Model for 45 Anabolic Steroids
exp RRT calc RRT
methyltestosterone di-TMS androsterone mono-TMS etiocholanolone mono-TMS cholesterol mono-TMS androsterone di-TMS etiocholanolone di-TMS 11@-hydroxyandrosteronetri-TMS androstenedione di-TMS androstenedione androstenediol di-TMS testosterone di-TMS testosterone proprionate epitestosterone di-TMS DHA di-TMS stanolone di-TMS androstanedione di-TMS androstanedione 17a-methy1-5@-androstan-3a,17j3-diol di-TMS (methandriol metabolite) methandriol di-TMS nandrolone di-TMS 19-norethiocholanolonedi-TMS fluoxymesterone tri-TMS fluoxymesterone di-TMS 17a-methyl-9a-fluoro-4-androsten3a,6@,17@-tetraol tetra-TMS (fluoxymesterone metabolite) norethandrolone mono-TMS oxandrolone mono-TMS 17-epioxandrolonemono-TMS boldenone di-TMS 2a-methyl-16(5a)-androsten-3a,l7-diol di-TMS (drostanolone metabolite) oxymetholone tri-TMS bolasterone di-TMS 7a,l7a-dimethyl-5@-androetan-3a,l7@-diol di-TMS (bolasterone metabolite) calusterone di-TMS oral-turinaboldi-TMS 4-chloro-l7a-methyl-l,4-androsten-3-one6&17@-dioldi-TMS (oral-turinabol metabolite) methenolone di-TMS 3’-hydroxy-l7a-methyl-5a-androstan-17@01-2-eno-[2,3-c]pyrazole tri-TMS (stanozolol metabolite) 17a-methyl-5a-androstan-4a,l7@-diol-2eno-[3,2-c]-pyrazoletri-TMS (stanozolol metabolite) quinbolone mono-TMS methandienone di-TMS 17a-methy1-1,3,5-androsten-3,6,17@-triol tri-TMS (methandienone metabolite) 4-chloro-4,16-androsten-3a,l7-diol di-TMS (clostebol metabolite) la-methyl-16(5a)-andr~aten-3a,l7-diol di-TMS (mesterolone metabolite) 17a-methyl-5a-androstan16@,17@-diol[2,3-c]-furazandi-TMS (furazabol metabolite) norethisterone di-TMS
0.685 0.702 1.279 0.751 0.755 0.911 0.885 0.773 0.851 0.902 1.036 0.851 0.828 0.876 0.849 0.709 0.848
0.987 0.691 0.715 1.263 0.745 0.781 0.889 0.838 0.744 0.898 0.891 1.074 0.849 0.848 0.890 0.833 0.738 0.858
0.945 0.852 0.717 1.145 1.160 1.075
0.991 0.837 0.701 1.144 1.152 1.100
0.953 1.033 0.921 0.884 0.787
0.963 1.009 0.895 0.869 0.834
1.186 0.931
1.139 1.016 0.890
1.021 1.154 1.199
1.019 1.132 1.195
0.935 1.369
0.952 1.402
1.393
1.390
1.199 0.987 1.107
1.185 0.979 1.136
0.931
0.937
0.843
0.825
1.327
1.305
0.979
1.005
1.OOO
1.010
the most positive and most negative u charges, and finally, the s u m of the absolute values of all atomic u charges in the structure. Statistical Analysis. Multiple linear regression analysis was used for variable selection and model construction. Initially, objective evaluation was used for descriptor elimination to reduce the pool of descriptors. For this purpose various criteria were implemented successively. Deacriptors with less than 10% nonzero values were removed. Pairwise correlations of the descriptors were calculated, and one descriptor from each pair with a pairwise correlation coefficient larger than 0.95 was removed. Vector space analysis was used to examine multicollinearities and select the pool of descriptors containing the minimum amount of redundant information. The Gram-Schmidt orthogonalization method was
variable
regression coeff
std error of regression coeff
partial F
GEOMl MOM14 v4c V5CH S4P S4PC S7CH SGCH WTPT3 intercept
0.021 82 1.01677 -0.543 79 2.40045 0.121 99 -0.061 17 1.74499 -3.212 62 0.026 22 -1.65865
0.001 83 0.177 69 0.067 76 0.350 70 0.014 28 0.016 17 0.199 19 0.396 38 0.003 31 0.13070
142.861 74.300 64.399 46.851 72.991 14.305 76.742 65.690 62.714 161.036
R = 0.991
n = 45
descriptor code
s = 0.027
F(9,35) = 213.7
definition
GEOMl first major moment encoded, Le. the ‘length”, taking into accunt the ( x , y, z ) coordinates and the atomic weights MOM14 ratio of the first versus the second major moments of inertia v4c sum of the fourth-order cluster indexes for all molecules using valences in the computationb V5CH sum of the fifth-order chain indexes using valences in the computation s u m of the fourth-order path indexes S4P S4PC sum of the fourth-order path cluster indexes S6CH sum of the sixth-order chain indexes S7CH s u m of the seventh-order chain indexes WTPT3 s u m of the fourth-order cluster indexes for all molecules using valences in the computationb Osee ref 35. bSee refs 20 and 21. also used. From the described procedure, 92 descriptors were removed. With the remaining pool of 35 descriptors, multiple linear regression analysis (31,32)was performed by a stepwise addition and deletion procedure using partial F-to-enter and F-to-delete statistics (33). Initially, descriptors are added to the model by stepwise addition using the F values. Then, a deletion process was employed, where each combination of one, two, ...,descriptors was held out successively, followed by model generation. This led to the generation of many additional statisticallyvalid models. Finally, the selection of the best model was performed by using the following criteria: (a) multiple correlation coefficient, (b) standard error, and (c) overall F value for analysis of variance.
RESULTS AND DISCUSSION With the procedures described above, the model that was selected is presented in Table 11. The statistical values are strong: R = 0.991 and s = 0.027 (less than 3% of the mean RRT value of 1.0). A plot of the calculated vs experimental RRTs is presented in Figure 1. It shows the high degree of correlation obtained. Figure 2 shows a plot of the residuals vs the calculated RRTs. The random pattern of this plot reveals that no further information can be extracted. In Table I1 the definition of each descriptor included in the proposed model is presented. From there, one can see the contribution of the topological descriptors (all but the first two), and mainly that of molecular connectivity (all but the first three). The correlation of the molecular connectivity descriptors, which are measures of the complexity and bonding within the molecule, to chromatographic retention parameters has been extensively studied in the past (34-38). The conflicting inferences stimulated the construction of a model including only molecular connectivity and fragment descriptors. In that model, the nine descriptors included were MW, number of oxygen atoms, and the s u m of the fourth-order path (valence), fourth-order pathcluster (valence), seventh-order
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Table 111. Correlation Matrix of Descriptors and RRTs Used RRT GEOMl
1.OOO 0.296 0.399 0.457 0.430 0.787 0.710 0.761 0.634 0.645
MOM14 v4c V5CH S4P S4PC S7CH S6CH
WTPT3
1.4
1.OOO -0.473 0.228 0.182 0.241 0.005 -0.027 0.022 -0.239
1.OOO 0.318 0.061 0.397 0.464 0.384 0.284 0.534
1.OOO -0.102 0.869 0.825 0.475 0.260 0.582
F
t
31.1 -
4 0.9 V
I/+
0.5 I/ 0.5 0.6
0.7
1.0 1.1 Observed RRT
0.8
1.2
0.9
1.3
1.4
1.5
Flgurs 1. Plot of calculated vs observed relative retention tlmes for 45 anabollc steroids. 0.05 T
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0.04
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0.03
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3
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1.OOO 0.875 0.692
118-hydroxyandrosteronetri-TMS 19-norandrosteronedi-TMS boldenone mono-TMS 1,3(58)-androsten-3,178-dioldi-TMS (boldenone metabolite) oxymetholone tri-TMS clostebol di-TMS furazabole mono-TMS norethandrolone di-TMS
f 1.0
I
1.OOO 0.763 0.461 0.771
steroid
~
F
0.7 0.6
1.OOO 0.902 0.697 0.524 0.727
1.OOO 0.561
1.OOO
Table IV. Comparison of Predicted RRTs vs Experimental RRTs for Anabolic Steroids and Metabolites Not Included in the Data Set
1.3 -
1.2
1.OOO 0.185 0.037 0.225 0.458 0.063
V
'
T '
'
'
'
'
'
"
'
?
exp pred residuals RRT RRT RRT 0.922 0.669 0.900 0.681
0.847 0.735 0.827 0.798
-0,075 0.066 -0.073 0.117
1.186 1.116 1.122 1.078
1.069 1.033 1.058 1.009
-0.117 -0.083 -0.064 -0.069
can be seen: 0.902 for S4P and S4PC. Also, in Table 11, the partial F value for S4PC is the lowest compared to the other descriptors, although enough higher than the rejection criterion, which is F(0.99,9,35) 1 4.65. This means that there is a multicollinearity between two descriptors in the model shown in Table 11. Actually, the mean variance inflation factor (VIF) (39) for this model is 14.9. Another model that was evaluated, keeping all the other descriptors the same and rejecting S4PC gave almost the same correlation: R = 0.987, s = 0.032, F(8, 36) = 174.2, a much better mean VIF = 5.7, but worse prediction values for the steroids not included in the data set. Therefore, the proposed model remained that of the Table 11. To test the model, we predicted the RRTs for eight anabolic steroids and metabolites that were not used in the analyses. This is an external prediction set. Table IV shows the experimental and predicted RRTs for these unknown steroids. The average residual for this set of eight compounds is 0.083 and the correlation coefficient between the experimental and predicted RRTs is 0.959, which shows that the model can be useful for prediction. In similar QSRR studies in the past, boiling points and partition coefficients were shown to be important descriptors. The lack of these data did not allow the investigation of models with these descriptors. Obviously, this model is valid only with the columns and the same temperature program specified above. Finally, the prediction of RRTs for new steroids will depend on the degree of similarity between the query molecules and those in the data set. CONCLUSIONS In this study a successful application of the ADAPT software system was performed for the prediction of RRTs of anabolic steroids and similar compounds that usually are detected in the doping control of athletes. The proposed statistical model shows a high degree of correlation between observed and calculated values. It was shown that the model has a good predictive ability that will allow its application. ACKNOWLEDGMENT
W. Szanzer and R. Mass6 are thanked for their assistance and L. Anker, S. Dixon, R. Lawson, J. Main, W. Murray, M. Needham, and D. Stanton for their guidance.
2020
Anal. Chem. 1001, 63,2028-2032
LITERATURE CITED Hansch, C. I n Ouentltatlve SbYchxe-ActMly Reletkmshlps In L k g Desp; Arlena, E. J., Ed.; Drug Design; Academlc: New York, 1971; VOl. 1. Kallsran, R. OuentltaNve Structufe-Chromtographlc Retentbn Rela tbnshlps; John Wlley & Sons: New York, 1967. Mlhara, S.; Masuda, H. J. ” a r o g r . 1987, 404, 309. Shotrl, P. Y.; Mokashl, A.; Mukesh, D. J. Chromatogr. 1987, 387, 399. Rohrbaugh, R. H.; Jurs, P. C. Anal. Chem. 1985, 57, 2770. Rohrbaugh, R. H.; Jurs, P. C. Anal. Chem. 1987, 59, 1048. Rohrbaugh, R. H.; Jurs, P. C. Anal. Chem. 1988, 60, 2249. Stanton, D. T.; Jurs, P. C. Anal. Chem. 1989, 61, 1328. Anker, L. S.; Jurs, P. C.: Edwards, P. A. Anal. Chem. 1990, 62, 2678. Stuper, A. J.; Brugger, W. E.; Jurs, P. C. Computer-Asslsted Studies of Chemlcal Structure and Bldoglcel Function; Wlley Intersclence: New York, 1979; pp 83-90. Jurs. P. C.: Chou, J. T.; Yuan, M. I n Computw-AssistedmDeslgn; Olson, E. C., Chrlstoffersen, R. E., Eds.; Amerlcan Chemical Soclety: Washington, DC, 1979: pp 103-129. Donike, M. Dope Analysis. WOrM Symposium on Lbplng In Sports, Omc&lRome&gs, Florence 5110-12f1967; Internatbnal Amatew Athletic Foundatlon: New York, 1987; pp 53-80. Bruggar, W. E.; Jus, P. C. Anal. Chem. 1975, 47, 761. Stuper, A. J.; Jurs, P. C. J. Chem. Inf. Comp. Scl. 1976, 16, 99. Rohrbaugh, R. H.; Jurs, P. C. ~ A W Quantum : Chemistry Exchange, Program 300; (3cPE: Indlana University: Bloomlngton, IN, 1968. Burcket, U.; Alllnger, N. L. Molecular Mechenlcs; ACS Monograph 177; American Chemical Society: Washington, DC, 1982. Clark, T. A. Handbook of ComputatlonelChem3by: A Fracllcel Gu& to Chemlcal Structure and Energy Calculetkms; Wlley: New York, 1985. Dewar, M. J. S.; Zoeblsch, E. G.; Healy. E. F.; Stewart, J. J. P. J. Am. Chem. Soc. 1985, 107, 3902. RandlE, M. J. Am. Chem. Soc. 1975, 07, 6604. Kler, L. B.; Hall. L. H. Mdecular ConnecMty In Chemlsby and Drug Research; Academic: New York, 1976.
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(21) Kier, L. B.; Hall, L. H. hW?cuk?r ConnectMly h ~ m Analysis; J. Wlley: New York, 1986. (22) Kler, L. B. Ouent. Stnrct.-Act. Relet. 1986, 5 , 7. (23) RandlE, M. Comput. Chem. 1979, 5 , 3. (24) Goldstein, H. Classical Mechenlcs; Addlson-Wesley: Readlng, MA, 1950. (25) Bondl, A. J. phys. Chem. 1964, 68, 441. (26) Wise, S. A.; Bonnett, W. J.; Guenther, F. R.; May, W. E. J. Chromatogr. Sei. 1981, 19, 457. (27) Jurs. P. C. ADAPT 4.0 Documentation, 1990. (28) Pearlman, R. S. I n Moleculer Surface Area and Vdumes and their Use In StryctwelActlMy Reletkmshlps; Yakowsky. S. H.; Slnkula. A. A., Valvani, S. C., Eds.; Marcel Dekker, Inc.: New York, 1980. (29) Vogel, A. I.Textbook of Ractlcal Oganlc Chemlstry;Chaucer: New York, 1977. (30) Del Re. G. J . Chem. Soc. 1958. 4031. (31) Draper, N.; Smlth, H. Applkd Re@ressbn Analysls, 2nd ed.;Wlley-Interscience: New York. 1981. (32) Neter, J.; Wasserman, W.; Kutner, M. H. AppW Llnear ~ t l p t l c a l Wls.2nd ed.; Richard D. Irwin: Homewccd, IL, 1985. (33) Small, G. W.; Jurs, P. C. Anal. Chem. 1983, 55, 1121. (34) Kler, L. B.; Hall, L. H. J. Pharm. Sei. 1979, 68, 120. (35) Kallszan, R. Chromatographla 1977, 10. 529. (36) McGregor, T. R. J. Chromatogr. Scl. 1979, 17, 314. (37) Doherty, P. J.; Hoes,R. M.; Robbat, A., Jr.; Whke, C. M. Anal. Chem. 1984, 56, 2697. (38) Mlchotte, Y.; Massart, D. L. J. Pharm. Scl. 1977. 66, 1630. (39) Belsley, D. A.; Kuh, E.; Welsch, R. E. Reguessbn Dla~ostlcs;John Wlley 8. Sons: New York, 1980.
RECEIVED for review March 1,1991. Accepted June 28,1991. C.G.G. wishes to thank the Greek Ministry of Sports for financial support. The Sun 4/110 Workstation was purchased with the partial financial support of the National Science Foundation.
Role of the Modulator in Gradient Elution Chromatography Ajoy Velayudhan’ and Michael R. Ladisch*S’f Laboratory of Renewable Resources Engineering and Department of Agricultural Engineering, Purdue University, West Lafayeke, Indiana 47907-1295 MoMIe-phase addltlves are frequently used in gradlent elution chromatography to modulate adsorbate retention. These additives are known to adsorb themelves onto the statkmary phase, resulng in solvent demixlng. I n this paper, the concentration of the mobile-phase additive In the mobile phase Is assumed to be high enough for lt to lie in the nonilnear region of lts own adsorption isotherm. Then the shape of the gradient would become deformed while passing down the column and could ultimately form a shock layer. A series of numerical simulations of a binary feed mlxture Is presented under condltlons where a shock layer Is formed, and the posslbie consequences are dlscwsed. Dependlng on the b catbn of the adsorbate peak wlth respect to the mobilephase shock layer, leading or haMng shoulders can r d , akng with dgnmcant peak sharpening. The lmpllcatkns of these effects on separation are presented, and condltlons under which the present analysis might be tested experimentally are Indicated.
INTRODUCTION In liquid chromatography, substances that modulate the retention of the sample components are frequently added to the mobile phase in order to facilitate the separation (1).
* To whom corres ondence regarding this aper should be addressed a t LORRE, burdue University, 1295 !otter Center, West Lafayette, IN 47907-1295. Laboratory o f Renewable Resources Engineering. *Department of Agricultural Engineering. 0003-2700/91/0363-2028$02.50/0
Examples include salts in ion-exchange and hydrophobic interaction chromatography and organic modifiers in reversed-phase chromatography. We shall use the general term “modulator” to refer to all such mobile-phase additives. Modulators are commonly used in gradient elution chromatography, which is a popular technique for both small molecules and biopolymers, a t the analytical as well as the preparative level. Gradient elution has been widely studied, and the theoretical predictions are, for the most part, in good agreement with experiment. Authoritative reviews of the subject have been offered by Snyder ( 2 , 3 ) and Jandera and Churacek (4). The modulator is usually regarded as a nonadsorbing component ( 2 , 4 ) for the purposes of predicting adsorbate retention, although some work on isocratic elution has accounted for modulator adsorption (5-8). Here, we examine quantitatively the consequences in gradient elution of accounting for the adsorption of the modulator. The effect, usually called “solvent demixing” in the chromatographic literature, is well understood qualitatively (2,4);for example, solvent demixing is expected to cause peaks to “clump up” in the middle of the chromatogram (2). However, a quantitative examination reveals the possibility of interesting additional effects. Modulators are commonly used at concentrations that are much higher than the sample concentrations; consequently, they could well be in the nonlinear region of their own adsorption isotherms. Then different modulator concentrations will move with different velocities, and deformation of the gradient shape becomes possible; as will be seen presently, a gradient that is linear at the inlet could be significantly 0 1991 American Chemical Society
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