Mobile phase optimization method for steroids separation

Applied Medical Informatics
Original Research
Vol. 18, No. 1, 2/2006, pp: 17-24

Mobile Phase Optimization Method for Steroids Separation

Carmen Elena Stoenoiu1, Sorana Daniela Bolboacă2, Lorentz Jäntschi1
1 Technical University of Cluj-Napoca, Cluj-Napoca, Romania
2 „Iuliu Haţieganu“University of Medicine and Pharmacy, Cluj-Napoca, Romania
Abstract - The paper presented a mathematical model developed for optimization of mobile phase
composition in thin layer chromatography applied on steroids separation. The proper solvents system
was experimental identify as being a mixture of chloroform, cyclohexan, and methyl-ethyl-cetone. An
original mathematical model was developed and used in order to identify the composition of mobile
phase. Starting with the mathematical model and with the optimization procedure a computer
program has been developed. The proposed model is able to optimize simultaneously many mobile
phases with respect of the shortest analysis time and of the selectivity of compounds. The efficiency of
the mathematical and optimization models is demonstrated on a sample of five androstane isomers.
Key words: Androstane Isomers, Thin-Layer Chromatography (TLC), Mobile Phase Optimization
Introduction
functions [4,5]; mineralocorticoids – maintain The steroids hormones are natural or synthetic blood volume and control renal excretion of compounds with physiological activities derived electrolytes [6]); sex steroids (androgens, from cholesterol. With a single exception, estrogens, and progestagens – produce sex differences and support reproduction [7]); cyclopentanophenanthrene skeleton and atomic phytosterols (steroids that naturally occur in numbering system as cholesterol (see Figure 1 plants [8]); and ergosterols (steroids that occur [1], note that the carbon 18 and above can be supplements [9]). Androstane is a steroid hydrocarbon from which androgens are derived and has the generic structure as is shown in Figure 1. Steroid nucleus
Figure 2. Androstane generic structure
The term “steroids” has been introduced by Callow R.K. & Young F. G. in 1936 [2] for the techniques used for the separation of a mixture group of compounds comprising the sterols, bile of compounds by their distribution between two phases, was introduced in 1901 by Mikhail steroids include: anabolic steroids (class of steroids that increase muscle and bone synthesis technique used since 1963 [11] for separation [3]), corticosteroids (glucocorticosteroids – chemical compounds including of steroids. The regulate aspects of metabolism and immune method is still used in separation of compound because of its advantages comparing with steps under different conditions. The most column chromatography [12]: (1) single use of delicate problem in steroids separation is to the layer simplifies sample preparation chouse the optimum mixture of solvents in order procedures; (2) simplicity of development by dipping the plate into a mobile phase in a chamber; (3) high sample through-put with low previous investigated for identification of operating cost because multiple samples can be run simultaneously with standards on a single experimental results were obtained by the plate using a very low volume of solvent; (4) solvent system with the following compounds: selective and sensitive post-chromatographic Chloroform – Cyclohexan - Methyl-Ethyl- detection and identification; (5) visual Cetone. The obtained experimental data are observation and direct recording of the entire presented in Table 1. The best results expressed chromatogram including all components, the as mobile phase composition and objective origin, and the mobile phase front; and (6) the function obtained by using Simplex, and Prisma ability to repeat detection and quantification Table 1. Experimental data obtained for separation of androstane isomers
5.51 6.10 6.09 2.45 3.32 0.50 0.31 0.19 0.26 0.64 7.76 7.43 7.92 7.91 6.14 6.48 0.51 0.21 0.19 0.31 0.32 8.84 2.05 2.97 2.76 0.15 0.28 0.27 0.21 0.22 0.23 0.15 9.64 3.45 5.03 4.59 0.58 1.33 0.54 0.31 0.29 0.21 0.35 8.91 0.53 0.96 0.75 0.15 0.20 0.41 0.31 0.22 0.25 0.25 9.04 6.23 0.85 6.89 4.00 4.82 0.56 0.31 0.24 0.29 0.51 8.85 6.44 6.83 6.80 5.64 4.10 0.52 0.21 0.11 0.21 0.82 8.55 0.92 1.89 2.47 0.24 0.26 0.43 0.32 0.21 0.22 0.22 8.77 0.00 0.00 0.00 0.00 0.00 0.46 0.32 0.15 0.24 0.21 8.41 8.26 8.42 8.34 7.29 7.00 0.31 0.16 0.15 0.21 0.47 8.93 I = amount of information; w = width of the compound spot; i = 1…4 (1 = 5α-androstane-3β-ol, 2 = 5α- androstane-3α-ol, 3 = 5α-androstane-17β-ol, 4 = 5β-androstane-3α,17β-diol, 5 = 5β-androstane-3β,17β-diol) Table 2. Mobile phase composition and corresponding values for objective function according
with applied method
No. Method Chloroform : Cyclohexan : Methyl-Ethyl- Fob Starting with the experience obtained in Mathematical Model and Optimization optimization of the mobile phase in High- Performance Thin-Layer Chromatography of a The quantitative measure of a chromatographic sample of benzodiazepines [14,15], the aim of parameter put in a mixture of three solvents the present research was to develop and to depends on the composition of mobile phase. The dependence equation could be one with six or with seven parameters (Eq.(1) and Eq.(2)): Material and Method
1,x2,x3) = a1x1 + a2x2 + a3x3 + a4x1x2 A sample of five androstane was the material of the present study. The following isomers were M7(x1,x2,x3) = a1x1 + a2x2 + a3x3 + a4x1x2 (2) included into analysis: 5α-androstane-3β-ol, 5α- androstane-3α-ol, 5α-androstane-17β-ol, 5β- androstane-3α,17β-diol, 5β-androstane-3β,17β- 1, x2, x3 are molar fraction of the three 1 + x2 + x3 = 1), M6 and M7 are estimators and then predictors of choused chromatographic parameter, and a1, a2, a3, a4, chromatographic parameter and then used in a5, a6, a7 are coefficients first determined based Figure 3. Androstane isomers include into analysis
The following chromatographic parameters of the separation compounds for the eluent e. were modeled starting from Eq.(1) and Eq.(2): By application of one of the above describe equations (Eq.(3)-Eq.(5)) on a series of p jFj(Sm(e),Inf(e,m),RSA(e),RRP(e)) ore more than one rows (one row for each where Fob is an objective function which characterized the separation with the eluent e in report with selection of coefficients aj, 1 ≤ j ≤ 4, parameter that is modeled by using Eq.(1) or Fj are functions that contain an expression of Eq.(2). The optimization model has a unique four parameters, aj are coefficients choused solution for p ≥ 6 (Eq.(1)), and for p ≥ 7 arbitrary or through of a defined ponderate mathematical relation of the Fj functions and A system can be build for each row from Mob respectively of the number of equidistant matrix with p linear equations (where p = 6 intervals m, RSA is the mean of separation resolution by using the eluent e, and RRP is the ob(j) = a1x1 + a2x2 + a3x3 + a4x1x2 + . resolutions used in separation with the eluent e. where xi are the molar fractions of each solvent (i = 1, 2, 3) that enter into the composition of RS(i,j,e) = 2·(l(i)-l(j))/(w(i)+w(j)) the ej eluent (j = 1, 2, …, p). where i, j are two separation compounds, w(i) To the above describe system (Eq.(6)) the least and w(j) are the width of the compound’s spots, squared method was applied for construction of and RS is the matrix of calculated resolution for the system with unique solution (MMCP); the separation of the compound i by the compound solution is obtained by applying the following where i is one of the separation compounds, e is the eluent used as mobile phase, l(i) is the where (k,0) = 1, 2, …, 6 for Eq.(1) and (k,0) = coordinate at which the e eluent had migrated, 1, 2, …, 7 for Eq.(2), A(k) are the series of terms l(e) is the coordinate at which the eluent had known from Eq.(6), M2 is the mean calculated migrated, and RF is the series of retention factor for the product of Mob series and A(k), and MMCP is the extended matrix of system of the optimum point was identified, this being the linear equations which is used in determination optimum composition of mobile phase (x1, x2, The Gaussian method was applied to found the solution for Eq.(7). The found solutions for the A0 = (a01, a02, …, a06) - for Eq.(1) A0 = (a01, a02, …, a07) - for Eq.(2) The A0 coefficients are used in prediction of the chromatographic parameter of interest by using integrated into a program dedicated to the one of the equations Eq.(1) or Eq.(2). For optimization of the mobile phase composition. example if Y is the choused chromatographic The program is freely available from the parameter, the Mob matrix (the predictor of Y), as well as the estimator of Y, had more than one http://vl.academicdirect.org/molecular_dynamic row. If z is the number of Mob matrix rows (and implicit the number of predictors) then the The generic equations that proved to obtained estimator of choused chromatographic performances in optimization of the mobile parameter Ŷ is: phase, according with the chromatographic parameter of interest and composition of The optimum can be obtained by application of a maximization or minimization function (as is for example the characterization of a separation The values of the retention factor obtained experimentally and by mathematical model, o = opt(Ŷ), where opt = "max" or opt = experimental and optimized retention factor, associated 95% confidence interval, the squared Moving through all domains of possible values correlation coefficient are presented in Table 5. for the composition of the mobile phase, the Table 3. Results of optimization procedure
∆rf = a1x1+a2x2+a3x3+a4x1x2+a5x1x3+a6x2x3+a7x1x2x3 a1x1+a2x2+a3x3+a4x1x2+a5x1x3+a6x2x3+a7x1x2x3 Objective function (Fob) Fob = a1x1+a2x2+a3x3+a4x1x2+a5x1x3+a6x2x3+a7x1x2x3 Table 4. Experimental and optimized retention factor for androstane isomers
Exp. = retention factor obtained from experimental data; MathM. = retention factor obtained by mathematical model Table 5. Results of correlation between
experimental and optimized values for
Cyclohexan – Methyl-Ethyl-Cetone = 60 : 0 : retention factor
36) are presented in Table 6. The correlation coefficient obtained between experimental and 5α-androstane 3β-ol 0.9934 [0.9714-0.9985] 0.9869 optimized values, associated 95% confidence 5α-androstane 3α-ol 0.9648 [0.8536-0.9918] 0.9307 intervals and squared correlation coefficients are 95% CIr = 95% confidence intervals for correlation The graphical representation of the retention factor estimated through optimization versus retention factor experimentally obtained for 5β- Figure 5. The plot of the retention factor
androstane-3β,17β-diol compound is presented obtained through optimization procedure
The squared correlation coefficient between objective function calculated based the experimental data and objective function calculated by using the mathematical model for the optimum mobile phase (Chloroform – Cyclohexan – Methyl-Ethyl-Cetone = 60 : 0 : 36) was equal with 0.8921 (95%CIr = [0.7769 – 0.9871]). Applying the mathematical model on experimental data presented in Table 1, the diagrams of the objective function obtained for presented in Figure 6 was obtained (the composition of the used optimum mobile phase was Chloroform – Cyclohexan – Methyl-Ethyl-Cetone = 60 : 0 : 36). Figure 4. Optimized versus experimental
retention factor for 5β-androstane-3β,17β-
experimental data the graphical representation of the retention factor at optimum mobile phase (Chloroform – Cyclohexan – Methyl-Ethyl-Cetone = 60 : 13 : 27) the graphical representation presented in Figure 5 was obtained. The spots of dark color indicate the optimum mobile phase obtained by the mathematical model (Chloroform – Cyclohexan Figure 6. The diagram of the objective
function (Cyclohexan & Methyl-Ethyl-
The values of the resolution for separation obtained from the experimental data and respectively by the mathematical model for the phase is increased. In the region where the spots diagram as darkest spots (Cyclohexan – Methyl- are darkest, the composition of the optimum Ethyl-Cetone = 0 : 36), the color becoming mobile phase can be established according with lighter as the distance from the optimum mobile the value of the objective function (Fob). Table 6. Experimental and optimized separation resolution for androstane isomers
1.3611 3.8333 3.7176 1.1944 12.3678 1.0685 2.5867 0.0000 0.6809 5α-androstane-3β-ol & MathM. 1.5995 2.8743 1.0491 4.3299 1.7656 11.7357 1.3874 2.2069 1.5223 0.0000 -1.5132 2.7842 -0.6123 -0.5712 0.6321 -0.3189 0.3798 -1.5223 0.6809 1.3714 2.8980 2.7470 0.6984 1.6500 1.1429 4.8438 0.0000 0.3478 5α-androstane-3β-ol & MathM. 2.0585 1.0231 1.1217 3.1298 0.9909 1.5426 1.6400 4.5318 0.8971 0.4453 0.3483 1.7763 -0.3828 -0.2925 0.1074 -0.4971 3.1463 7.6000 7.6533 1.1515 5.2471 2.1918 2.0923 0.0000 3.7308 MathM. 9.1778 4.6253 3.5548 5.0261 2.7285 5.2772 2.6190 3.2725 1.9742 2.6115 -1.1252 -1.479 4.0452 2.6272 -1.577 -0.0301 -0.4272 -1.1802 -1.9742 1.1193 2.2892 8.4286 4.7640 1.0000 2.6355 3.4925 2.0308 0.0000 3.2308 MathM. 5.0588 3.3510 3.4511 3.0638 2.5547 2.4993 4.2739 2.6682 2.4726 2.3214 -1.2167 -1.0618 4.9775 1.7002 -1.5547 0.1362 -0.7814 -0.6374 -2.4726 0.9094 0.0500 0.9767 1.4667 0.7925 21.9636 0.1875 2.1887 0.0000 0.5161 5α-androstane-3α-ol & MathM. 0.0000 3.5802 0.0000 4.7737 0.6087 20.3429 0.0000 0.6302 1.1904 0.0000 -3.307 0.1838 1.6207 0.1875 1.5585 -1.1904 0.5161 6.8462 12.8182 17.1154 2.8929 10.5000 5.6667 6.1111 0.0000 6.1081 MathM. 15.2315 8.5199 6.2142 10.8550 5.8671 11.1565 6.4194 8.9897 3.0710 4.5436 6.604 6.2604 -2.9742 -0.6565 -0.7527 -2.8786 -3.071 1.5645 5.4340 14.9444 11.2121 2.7143 9.6829 5.3010 6.0370 0.0000 4.5079 MathM. 8.3549 6.2852 5.7482 8.0072 5.5387 9.6940 6.9897 7.1844 4.5026 3.3839 -2.5023 -0.8512 9.1962 3.2049 -2.8244 -0.0111 -1.6887 -1.1474 -4.5026 1.124 7.0800 11.6000 16.0400 2.5532 10.9057 7.2500 10.3721 0.0000 5.8333 MathM. 17.6358 9.1133 6.3593 12.5177 4.6293 10.9451 7.7706 11.9674 2.5576 4.3175 -1.458 -2.0333 5.2407 3.5223 -2.0761 -0.0394 -0.5206 -1.5953 -2.5576 1.5158 5.6078 13.4054 10.1875 2.3404 5.5200 5.8065 10.2791 0.0000 4.3226 MathM. 8.7378 5.6239 5.4412 8.6127 4.4771 5.4223 7.4977 10.6272 3.9262 3.7798 -2.0631 -0.0161 7.9642 1.5748 -2.1367 0.0977 -1.6912 -0.3481 -3.9262 0.5428 1.0794 0.6842 2.6786 0.2000 2.0500 2.9903 0.0909 0.0000 0.8529 -diol & 5β-androstane MathM. 2.0475 1.7197 0.8932 1.3022 0.4973 2.2265 2.7229 0.8321 0.0000 0.4648-3β,17β-diol -0.209 1.3764 -0.2973 -0.1765 0.2674 -0.7412 0 Exp. = experimental resolution of separation; MathM. = resolution of separation obtained by mathematical model Table 7. Results of correlation between experimental and optimized values for separation
resolution
5α-androstane-3β-ol & 5α-androstane-3α-ol 0.9365 [0.7477 – 0.9851] 5α-androstane-3β-ol & 5α-androstane-17β-ol 0.8602 [0.5029 – 0.9663] 5α-androstane-3β-ol & 5β-androstane-3α,17β-diol 0.7262 [0.1778 – 0.9303] 5α-androstane-3β-ol & 5β-androstane-3β,17β-diol 0.3879 [0.3198 – 0.8177] 5α-androstane-3α-ol & 5α-androstane-17β-ol 0.9632 [0.8475 – 0.9915] 5α-androstane-3α-ol & 5β-androstane-3α,17β-diol 0.7021 [0.1298 – 0.9234] 5α-androstane-3α-ol & 5β-androstane-3β,17β-diol 0.4362 [0.2666 – 0.8361] 5α-androstane-17β-ol & 5β-androstane-3α,17β-diol 0.8682 [0.5261 – 0.9684] 5α-androstane-17β-ol & 5β-androstane-3β,17β-diol 0.5850 [0.0706 – 0.8876] 5β-androstane-3α,17β-diol & 5β-androstane-3β,17β-diol 0.8346 [0.4319 – 0.9598] r = correlation coefficient; 95% CIr = 95% confidence intervals for correlation coefficient; Discussion
The proposed mathematical model for minimum value obtained from experimental optimization of mobile phase of androstane isomers has been developed, the aim of the retention factor (experiment number 6), and from 0.0000 to 21.9636 for the resolution of As it can be observed from the Results chapter three parameters were optimized: the retention experimental and optimized value differ from factor, the separation resolution and the one experiment to other. For example, for the objective function. Analyzing the obtained first experiment with one exception (separation results (Table 3) two observation can be done. resolution between 5α-androstane-3α-ol and First observation refers the generic dependence 5α-androstane-17β-ol), the value obtained equation used: for all three parameters the best though optimization vas greater comparing with results were obtained with the seven parameters value obtained experimentally. The greater equation (Eq.(2)). The second observation refers difference in separation resolution of 2.5023 the optimum mobile phase which is identical for was observed for 5α-androstane-3α-ol and 5β- separation resolution and objective function androstane-3β,17β-diol compounds (first experiment, Table 6). At the opposite sides are Cetone = 64 : 0 : 36, see Table 3), and are very closed to the optimum mobile phase obtained experiments, with one exception the value for the retention factor that is of 60 : 13 : 27. obtained through optimization was smaller Analyzing the data from Table 4 it can be observed that the differences between retention experimentally. The greatest difference was of factor obtained from experimental data and the 9.1962 for the experiment number 3, resolution value obtained through optimization were very separation between 5α-androstane-3α-ol and small, this sustaining the abilities of the 5β-androstane-3β,17β-diol, and of 1.5645 for optimization procedure. The minimum value of experiment number ten (separation resolution the absolute difference between these values is of 0.0000 (see the results from the Table 4, the androstane-3α,17β-diol). Analyzing the experiment number 9) to 0.2390 (see the results performances of the optimization procedure, regarding the resolution separation, the best androstane-3α-ol isomer. Note that the value performances were obtained for 5α-androstane- obtained through optimization was less than the 3α-ol and 5α-androstane-17β-ol compounds (r value obtained from experimental data (see = 0.9632, see Table 7). Thus, for the separation resolution the mathematical model had not the The performances of the proposed optimization same stability as for the retention factor (the model can be analyzed thought the correlation value of the correlation coefficients vary from coefficient and associated squared value. The 0.3879 to 0.9632, with two values less than 0.5, closer the value of correlation coefficient is to - three values between 0.5-0.75, and five values 1 or +1 the better the optimization procedure is. Looking at the correlation coefficients presented Some performance was obtained in optimization in Table 5 it can be observed that in four cases of objective function, but this performance is out of five the value is greater than 0.99. The less comparing with the performances obtained exception is observed for the compound 5α- for optimization of the retention factor. androstane 3α-ol for each the correlation The assessment of the proposed mathematical coefficient is of 0.9648, being considered that model in optimization of the mobile phase of there is a strong relationship between the androstane isomers by thin layer experimental value and value obtained through chromatography with three solvents can be done by analyzing the obtained results and of The performances obtained by using of the advantages and disadvantages. The greatest proposed mathematical model for the separation advantage of the mathematical model results resolution parameter are not so good comparing from its faster ability in obtaining the optimum with those obtained for retention factor (see composition of the mobile phase. Looking at the Table 6). This difference can be explained by obtained composition of the optimum mobile the difference between the distributions of data: phase it can be observed that the optimization of the retention factor, of the separation resolution 8. Gül MK, Şeker M. Comparative analysis of and of the objective function lead to very similar compositions of mobile phases (see (Brassica napus L.) and olive (Olea europaea L.) Table 3). This observation can be explained by the moderately polar character of the androstane isomers and shown us that the small variations 9. Perera CO, Jasinghe VJ, Ng FL, Mujumdar in composition of the optimum mobile phase do AS. The effect of moisture content on the conversion of ergosterol to vitamin D in shiitake As a concluding remark it can be say that the proposed mathematical model proved to assure 10. Senchenkova EM. In: Gillispie (Ed.). accurate results on analysis of the separation of Dictionary of scientific biography; Charles androstane isomers. But, more researches are Scribner Sons: New York, 1976;13:486-488. necessary to be done in order to analyze the 11. Dyer WG, Gould JP, Maistrellis NA, Peng stability and validity of the proposed model. If TC, Ofner P. Thin-layer chromatography of the mathematical model will prove its stability and validity could become a useful method in standardized procedure. Steroids 1963;1:271- separation of androstane isomers from drugs, 12. Sherma J. Thin-Layer Chromatography of Pesticides – A Review of Applications for Acknowledgements
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