Journal of Chromatography Library, Vol. 57: Retention and Selectivity in Liquid Chromatography R.M. Smith, editor 0 199s Efsevier Science 8. V. All rights reserved 47

CHAPTER 2

Retention prediction of pharmaceutical compounds

Department of Pharmaceutical Chemistty, School of Pharmaq, University of London, 29-39 BrunswickSquare, London, WCIN IAX, UK

2.1 INTRODUCTION

The principle of chromatographic separation was based on the empirical observation of the separation of plant dye mixtures on a silica gel column by Zwett. Although, it hap- pened almost 100 years ago, the prediction and design of a chromatographic separation is still a trial-and-error method and needs experience and intuition. From the early stages however, separation scientists wanted to understand the separation mechanism and tried to find relationships between the chemical structure of the compounds and their behaviour in a certain chromatographic system. The variation of the stationary phases, mobile phases, flow rates, etc. did not allow precise determination and accuracy of the chroma- tographic retention, and it was always advisable to express it as a relative value. Comput- erized “high-tech” HPLC equipment and highly reproducible HPLC columns make pos- sible the precise measurement and repeatability of HPLC retention. It means that from a technical point of view, we are ready to define precisely the retention of a compound un- der certain HPLC conditions, which also helps in discovering possibilities for the predic- tion of retention.

Why is a retention prediction for pharmaceutical compounds useful and important? In pharmaceutical chemistry, usually the structure of the compound, its possible impurities or metabolites are known when the search starts for the most appropriate analytical method. On the basis of structureretention relationships, the HPLC analytical method can be more easily designed. Retention prediction can also be used for optimization of the separation. The other purpose of the prediction can be the identification of the observed peak in the chromatogram. This task, however, requires a more reliable and accurate re-

*Present address: Department of Physical Sciences, Wellcome Research Laboratories, Langley Court, Becken- ham, Kent, BR3 3BS, UK.

References pp. 90-92

48 Chapter 2

tention prediction, and the application of other spectroscopic methods for the peak iden- tification is essential.

Although there are three major HPLC separation mechanisms (reversed-phase, ab- sorption and ion-exchange) applied in pharmaceutical analysis, the retention prediction most widely applied is reversed-phase HPLC. The reason for this is that reversed-phase chromatography is used in approximately 80% of pharmaceutical HPLC analyses, the reproducibility of manufacturing reversed-phase columns is much higher than any other type of stationary phase, and the retention mechanism is much clearer in reversed-phase chromatography. Therefore, in this chapter, the retention prediction focuses mainly on reversed-phase chromatography.

There are several approaches for retention predictions. One is based on the known chemical structure. With the help of another method, quantitative information (topo- logical indices, connectivity indices, quantum chemical parameters, etc.) can be obtained from the chemical structure. The calculated numbers can be related to chromatographic retention data by mathematical functions, and this can be the basis of retention prediction.

The alternative empirical prediction methods are based on experimental retention data for the pharmaceutical compounds and these data are used to predict retention in other similar chromatographic conditions andor structurally similar compounds.

In general, much more accurate retention prediction methods have been described for structurally related alkylbenzene homologous or substituted aromatic compounds, than for pharmaceutical compounds. Pharmaceutical compounds can be completely unrelated in structure and contain a much wider variety of polar functional groups, which makes the retention prediction less accurate. In this chapter, the methods presented for retention prediction focus on pharmaceutical compounds that are structurally unrelated. First, the definition and determination of the retention parameters is discussed. The dependence of the retention parameters on the chromatographic conditions is examined in order to reveal the reliable range of the retention prediction. The retention prediction possibilities for pharmaceutical compounds are discussed based on molecular modelling calcula- tions and other molecular descriptors. The relationships between measured or calculated physicochemical parameters and the retention parameters are also demonstrated. A reten- tion prediction method based on the experimentally found retention increment values is presented as well as other empirical methods with a multiparameter approach. As a sum- mary of the results, several applications for retention prediction of pharmaceutically ac- tive compounds is demonstrated. The intention has been made to show our results in this field without providing a complete literature review and only related methods are dis- cussed.

2.2 DEFINITION AND DETERMINATION OF RETENTION

In order to be able to predict the retention of pharmaceutical compounds in reversed- phase high performance liquid chromatography (RP-HPLC) the retention should be de- fmed precisely. Also the measurements of the retention should be carefully carried out. The most widespread measure of the degree of the retention is the capacity ratio (k) or alternatively it is called the retention factor [l], which can be defined by Eq. (2.1).

Retention prediction of pharmaceutical compounds 49

(2.1) k=- t R

t o where tR is the retention time (the time passed from the injection to the appearance of the solute peak maximum) and to is the dead time. The same expression can be obtained by using retention volume and dead volume values, which can be obtained by multiplying the retention time values with the actual mobile phase flow rate.

As is clear from the Eq. (2.1), the retention is expressed relative to the unretained component in the system. Therefore, the exact dead time determination is essential for the accurate determination of the retention factor, k. There are several arguments in the litera- ture about the precise dead time determination of a given HF’LC system. The problem starts with the definition of the dead time, namely the retention time (or if it is multiplied with the flow rate, the retention volume) of an unretained solute. The question arises which, if any, solute is unretained. There are many possibilities described in the literature. The dead volume can be the elution volume of a solvent disturbance peak obtained by injecting an eluent component, or the elution volume of an unionized solute that gives the lowest retention volume, or the elution volume of an isotopically labelled component of the eluent, or isotopically labelled water molecule, or the elution volume of a salt ion, or the volume of the liquid the column contains, or the extrapolated elution volume of a “zero” member of a homolog series. In practice none of the above possibilities are ac- cepted as an absolute definition. Berendsen et al. [2], Wells and Clark [3], and Knox and Kaliszan [4] provided detailed reviews on the various techniques for experimental de- termination of dead volume in HPLC. Whatever method is used to determine to, the most important thing is to apply the same method throughout the measurements used for the retention predictions.

According to Eq. (2.1) for the determination of the retention factor (k), the retention time of the compound should also be accurately measured. Although the retention factor does not depend on the flow rate or column pressure, it is advisable to keep them constant during the measurements. The retention time determination is usually carried out by an integrator or other data handling computer program. It is advisable to connect the injector and the integrator electronically for an accurate start of the time measurements. As the peaks are wider in HPLC than in GC, the slope sensitivity and threshold values should be properly set up. Care has to be taken when the signal to noise ratio is less than 5. As the error of the retention prediction is usually much higher than the error of the measure- ments, the above-mentioned practical problems for retention measurements are negligible.

Unfortunately the retention index system which defines relative retention and is there- fore much more independent of slight changes in chromatographic conditions is not as widespread as in gas chromatography. Baker et ul. [5-71 has introduced a retention index scale similar to the gas chromatographic retention index. The scale is based on the rela- tive retention of a homologous series of C34& 2-keto alkanes. The retention index, Z, of a given solute i is calculated from its observed retention factor ki, the retention factor for a 2-keto alkane eluting before the test solute, kN, and the retention factor of a 2-keto alkane eluting after the test compound, kN+ as described by Eq. (2.2).

log/$ -logk, 1% k N + 1 - 1% k,

zi = lOOx + lOON

References pp. 9G92

50 Chapter 2

The retention index of a given 2-keto alkane standard is by definition equal to 100 times the carbon number (N) in the formula. A slightly modified retention index scale has been proposed by Smith [8,9]. He suggested replacing the terminal methyl group of the 2-keto alkane series of standards by a terminal phenyl group, which makes the UV detection of the reference homologous series easier. The advantages of using the retention index scale is discussed in detail in Chapter 1. It was also proved that the logarithmic values of the k of a homologous series showed linear relationships with the number of carbon atoms in reversed phase liquid chromatography. Baker and Ma [6] showed that the retention index, for example, of phenacetin was independent of the methanol content of the mobile phase. Both index scales have already been used for the study of quantitative structure-retention relationships. The precision and accuracy of the relative retention de- termination expressed in the retention index did not exceed significantly the accuracy and precision of the k determination and its determination is more time consuming. The variation in k values as a function of the mobile phase composition can be important in the retention prediction of pharmaceutical compounds, and is often used for method de- velopment and optimization. This information disappears when using the index scale. Therefore, in this chapter, the retention prediction based only on the retention factor is discussed.

2.3 DEPENDENCE OF RETENTION ON THE COLUMN AND MOBILE PHASE COMPOSITION

In HPLC, the retention of a compound is determined by the strength of the solute- stationary phase and solute-mobile phase interactions. Thus, it is important to reveal quantitatively, how the mobile phase composition effects solute retention, as this infor- mation is vital for retention prediction.

On the basis of numerous experimental data, we can assume that the dependence of the logarithmic retention factor (log k) on the volume fraction of organic component, rp, in the mobile phase can be described by Eq. (2.3).

log k = Sj + log k0 (2.3)

where the log k0 value (the intercept of the straight line) refers to the extrapolated log k value for the neat water as mobile phase. The slope value (5') shows the sensitivity of the retention of a given compound caused by the change of the organic phase concentration in the mobile phase (see also Fig. 2.1).

Using Eq. (2.3), two important RP-HPLC retention parameters can be determined (the slope, S, and the intercept, log k,,), which can be used for the retention prediction. We should keep in mind that the linearity is valid only in a limited range of the mobile phase composition. The deviation from linearity can be observed at high organic phase concen- trations (above 90%, v/v) due to the residual silanol groups. It has been observed that at high organic phase concentrations, the retention of the compounds increased again, mostly for compounds with basic nitrogen or other silanophil groups [lo]. Also it was found that the extrapolated log k values for the zero organic phase concentration are dif-

Retention prediction of pharmaceutical compounds 5 1

I I I I I I

I

I I I

0 5 0 100 @ %

Fig. 2.1. The dependence of log k values on the organic phase concentration (OP% or q5)

ferent when obtained using a different organic phase, and it has no realistic meaning, be- cause deviation from linearity can be observed at this region as well [l l l .

In practice the determination of these two parameters (S, log ko) can be carried out by measuring the log k values of compounds by using a minimum of five organic phase con- centrations. The organic phase concentration can be decreased by 5 or 10% steps. All of the log k values of the investigated series of compounds should be determined in a mini- mum of three consecutive measurements, and the average log k values should be plotted against the organic phase concentration. The fit of the data points to straight lines can be checked by calculating the correlation coefficient and the standard deviation of the slope and intercept (S and log b, respectively) values.

Unacceptable fits can be obtained for several reasons. Schoenmakers et al. [12] de- scribed a quadratic relationship between the log k and q5 values. It usually fits much better to the experimental data points, as it explains the deviation from the linearity in the ex- treme organic phase concentration range, and also introduces a second term (the quadratic q5) usually improves the statistical parameters as well. Wells and Clark [ 131 suggested the application of the solvophobic theory proposed by Horvath et al. [ 141 for describing the log k versus q5 relationship. Several results [ 15,161 show that the linearity of the plot is not valid in a wide range of organic phase concentrations, and the log values are not the same when they are derived from data obtained by using acetonitrile or methanol. The deviation from linearity can be observed when the mobile phase pH is varied by the variation of the organic phase concentration in the mobile phase, especially in the case of easily ionizable compounds. The exact definition and determination of the mobile phase pH is therefore very important. In order to avoid the effect of the changing mobile phase pH on the linearity of the log k versus q5 plot, it is suggested that measurements are made

References pp. 90-92

52 Chapter 2

CJI 0

0 - - -

1 ' 1 1

I t I t I 1 1 1 I t 1 1

I I I I I I I - I0 20 30 40 50 60 70 80 90 O/o 'f'

Fig. 2.2. Hypothetical possibilities for the plots of the log k versus organic phase concentration ($) relation- ships. 1, straight line; 2, curved parabolic relationship without silanophil effect; 3, straight lines crossing each other; 4, parabolic relationships for basic molecules showing silanophil effect. (Reprinted with permission from ref. 28)

in a buffer at a pH equivalent to the neutral form of the solute. Figure 2.2 shows the hypo- thetical possibilities for the plots of log k versus @ for the above-mentioned cases.

In spite of these limitations, the relationship described by Eq. (2.3) has great potential to predict the retention of pharmaceutical compounds at various organic phase concentra- tions (within the linear range) and is extremely valuable in the optimization of separa- tions. The prediction of these two retention parameters (S and log b) is discussed in this chapter in detail.

As the retention in chromatography reflects the solute distribution between the station- ary and the mobile phases, it also depends on the temperature. The effect of the tempera- ture on retention has been studied less extensively in RP-HPLC than the effect of solvent composition. In fact the use of aqueous eluents and silica-based stationary phases limits the practical column temperature range fiom 5 to 100°C. Over that temperature range one can expect a roughly tenfold decrease in retention factor if the enthalpy of solute- stationary phase interaction is -5 kcal/mol, which is a typical value in RP-HPLC. A re- tention change of similar magnitude occurs when the organic phase component of the mobile phase is changed by approximately 30%. So the effect of the mobile phase com- position on the retention is more significant. Usually, chromatographic measurements are carried out at ambient temperature or under controlled temperature at 20 or 25°C. The temperature can also affect the efficiency of the chromatographic system, since the d i f i - sion coefficient of a solute increases with the temperature. In most cases the selectivity or the relative retention is not greatly affected by changing the temperature in RP-HPLC. This is not surprising as enthalpies for solute binding by the stationary phase are usually

Retention prediction of pharmaceutical compounds 53

small and the difference is less than 1 kcal for closely related compounds. The effect of temperature on retention is largely determined by the enthalpy of the solute-stationary phase interaction. The enthalpy can be calculated fiom the slope of plots of log k versus the reciprocal of the absolute temperature; called van’t Hoff plots. Published results [ 17- 191 indicate that the logarithm of the retention factor is linearly related to the enthalpy in RP-HPLC. The increase in the logarithm of the retention factor with enthalpy, however, is much greater than expected. It can happen that the temperature effect can be important in the retention prediction; then the use of a column thermostat is suggested to control the temperature.

Bad column efficiency can be the result of secondary equilibria and it not only de- creases the accuracy of the retention determination but it can cause erroneous retention prediction. Therefore, in practice it is always advisable to check the column efficiency and the peak symmetry when the retention measurements are used for prediction.

In conclusion, the magnitude of chromatographic retention is determined by the ener- getics of the solute interactions with both the mobile and stationary phases. Consequently, retention data contain relevant thermodynamic information. The close relationship be- tween the retention factor and the equilibrium constant allows us to extract thermody- namic information from the chromatogram which can be used for understanding and pre- dicting the retention.

2.4 CORRELATION OF RETENTION PARAMETERS TO THE MOLECULAR PARAMETERS OBTAINED BY MOLECULAR MODELLING

Many methods have been devised for the determination of molecular structures. In more recent years it has been proven to be possible to determine accurate structures by compu- tational methods, typically ab initio calculations [20] for large molecules. Molecular me- chanics calculations can be carried out to determine the three-dimensional structures of molecules having pharmaceutical importance. The calculated molecular parameters can be correlated to retention data.

In the early work of Horvhth et al. [21], the retention was attributed to a reversible as- sociation of the solutes with the hydrocarbon ligand of the reversed-phase stationary phase. The energetics of the association process was also analyzed and the dependence of the retention factors on ionic strength of the eluent and the hydrophobic surface of the solute were revealed. The correlations of the octanol-water partition coefficients, molecu- lar surface areas, and reversed-phase retention factors were studied by Funasaki et al. [22]. The importance of the molecular cavity surface area and various connectivity indi- ces, which can be calculated from the chemical structure of the compounds was pointed out also by Funasaki et al. [23]. Eng et al. [24] showed the application of holistic con- formation and total surface area calculations for the prediction of chromatographic reten- tion parameters for triphenyl derivatives. Mockel et al. [25] investigated the effect of the molecular surface type and area to the retention of various hydrocarbon classes. It cannot be questioned that molecular parameters play an important role in the retention but the extent of possible generalization of the equations and their predictive power for the chro- matographic retention have not yet been explored.

References pp. 90-92

54 Chapter 2

TABLE 2.1

THE CHROMATOGRAPHIC RETENTION DATA AND HYDROPHOBICITY DATA OF STRUCTURALLY UNRELATED PHARMACEUTICAL COMPOUNDS

Compound 1% pc Slope 1% ko $0

1 Sulphadimidine 1.644 -0.0280 0.854 30.50 2 Sulphamerazine 0.612 -0.0283 0.892 31.52 3 Barbital -1.050 -0.0402 1.063 26.44 4 Phenobarbital -0.430 -0.0319 1.341 42.04 5 Chloramphenicol 0.464 -0.0414 1.625 39.25 6 Salicylamide 0.236 -0.02 5 5 0.871 34.16 7 Phenacetin 1.128 -0.0226 1.002 44.34 8 Vanillin 1.119 -0.0244 0.866 35.49 9 Benzaldehyde 1.535 -0.0303 1.575 51.98 10 Acetanilide 0.529 -0.0270 1.021 37.81 11 Nicotinamide -0.690 -0.0382 0.25 1 6.57 12 Benzoic acid 1.769 -0.0284 1.252 44.08

14 Acetyl salicylic acid 1.037 -0.0272 1.077 39.60 15 Caffeine -0.912 -0.0299 0.552 18.46 16 Hydrochlorothiazide -1.717 -0.0456 0.887 19.45 17 Dexamethasone -0.472 -0.0139 0.568 40.86 18 Deoxycorticosterone 3.795 -0.0147 1.120 76.19 19 Isoniazid -2.003 -0.0382 0.060 1.57 20 Methyl salicylate 2.528 -0.0244 1.727 70.78 21 Hydrocortisone 2.029 -0.0129 0.436 33.80 22 Progesterone 1.508 -0.0192 1.831 95.36 23 Testosterone 4.874 -0.0143 1.085 75.87

With permission from ref. 26.

13 Salicylic acid 2.140 -0.0301 1.425 47.34

Our investigation [26] was focused on 23 drug molecules with completely different chemical structures (Table 2.1). The retention parameters of the pharmaceutical com- pounds were measured on LiChrosorb RP-18 10-pm columns, 250 X 4.6mm (Merck, Darmstadt, Germany). The mobile phases were various compositions of acetonitrile and 0.05 M phosphate buffer (pH = 4.6). Lower pH (pH = 2) was used for the retention meas- urements of the acidic compounds to avoid dissociation. The detailed instrumentation of the measurements and also the retention data obtained have been published earlier [27]. The retention of the compounds was expressed by the logarithmic values of the retention factor, log k and it was plotted as a function of the acetonitrile concentration. On the basis of three to five points, the slope and the intercept values of the straight lines obtained have been calculated and are listed in Table 2.1. It has also been published earlier [28,29] that the r$o values, namely the acetonitrile concentration necessary for obtaining log k = 0 retention showed excellent correlation with the logarithmic values of the octanol-water partition coefficients (log P). These values are also presented in Table 2.1.

A Personal Computer (PC) Model approach was used to determine the three- dimensional structure of compounds based on energy minimization. After setting up the geometries of the molecules having the smallest mmx-energy, the non-polar (NP), non- polar unsaturated (NPU) and polar surface areas (PS), their energies were calculated. The water solvation shell was also considered in the calculations of the accessible polar (APS)

Retention prediction ofpharmaceutical compounds 55

and non-polar (ANP, ANPU) surface areas. The calculated total surface energy (TSE) was expressed in kcaVmol. The dipole moment (dm) values and van der Waals radii (vdw) of the molecules listed in Table 2.1 were also calculated. Correlation analysis was carried out to reveal which of these parameters show significant correlation with the re- versed-phase retention parameters. The multiple regression equations and their mathe- matical statistical characteristics also reveal their applicability for retention prediction.

It was assumed that some kind of correlation can be revealed between the chromato- graphic retention parameters (S and log b) and the calculated molecular parameters, by which retention prediction of the pharmaceutical compounds can be carried out with vari- ous mobile phase compositions. The calculated molecular parameters are listed in Table 2.2.

The linear regression analysis revealed two significant equations (Eqs. 2.4 and 2.5) by which the S (slope) values could be described by the molecular parameters investigated.

S = 1.42 (* 0.35) X lo9 X vdw + 9.29 (* 0.26) X X TSE - 0.04 (2.4)

n = 23, r = 0.845, s = 5.07 X F = 25.1

TABLE 2.2 THE CALCULATED MOLECULAR PARAMETERS FOR THE COMPOUNDS LISTED IN TABLE 2. I

~~~~

No. NP NPU dm vdw ANP TSE

1 261.8 62.5 5.44 10.43 246.7 -3.7 2 194.7 68.4 6.81 11.60 183.5 -8.3 3 193.3 0.0 0.84 5.1 1 182.2 -7.0 4 206.7 27.6 0.68 9.84 195.3 -6.3 5 246.1 27.9 6.30 11.01 205.9 -6.9 6 103.1 50.8 3.14 5.60 97.4 -7.2 7 286.4 53.3 4.83 9.95 169.7 4.1 8 164.1 40.2 2.89 7.33 154.6 -3.6 9 151.2 54.1 2.81 6.38 142.9 0.5 10 196.6 40.7 3.03 8.01 185.4 1.5 11 106.3 36.9 2.16 6.48 100.4 -5.4 12 125.5 54.3 1.51 6.88 118.6 -2.4 13 108.7 53.8 1.93 6.88 102.7 -5.5 14 182.6 42.4 2.58 7.01 172.0 -3.7 15 254.0 18.3 1.87 8.03 239.0 1.9 16 124.2 15.8 6.42 5.26 103.7 -14.8 17 370.2 12.2 4.92 17.36 348.8 -1.7 18 383.3 6.9 3.91 13.52 361.7 0.8 19 108.9 38.3 2.47 6.73 103.0 -7.6 20 201.2 31.9 2.22 7.86 189.4 0.2 21 356.6 6.8 4.36 15.21 336.4 -2.7 22 410.2 6.8 2.28 13.00 387.0 4.2 23 371.9 6.6 2.09 13.13 351.1 3.4

NP, non-polar surface area, A2, NPU, non-polar unsaturated surface area, A2; dm, dipole moment; vdw, van der Waals radii; ANP, accessible non-polar surface area, A2, TSE, total surface energy (kcal/mol). Reprinted with permission from ref 26.

References pp. 90-92

56

S = 6.98 (& 1.73) X lod3 X ANP - 5.95 (* 1.64) X lo” X NP - 0.04

Chapter 2

(2.5)

n = 23, r = 0.857, s = 4.90 X lo”, F = 27.6

where n is the number of compounds, r is the multiple regression coefficient, s is the standard error of the estimate, and F is the Fisher-test value (vdw, van der Waals radii; TSE, total surface energy in kcavmol; ANP, accessible non-polar surface area; NP, non- polar surface area).

Equation (2.4) means that the higher the van der Waals radius and the higher the total surface energy, the more sensitive is the compound retention to changes in the acetonitrile concentration in the mobile phase. This finding is in agreement with the previous suppo- sitions that the S (slope) values are in relation to the size of the molecules.

Equation (2.5) expresses the retention sensitivity of the compound to the organic phase concentration as a fimction of the difference between the total non-polar and the accessi- ble non-polar surface areas. This finding can also be understood if we consider that the solvent molecules should replace the compounds from the stationary phase, and the higher the difference between the accessible and non-accessible hydrophobic surface area, the higher the concentration of acetonitrile molecules needed to elute the compound from the hydrophobic stationary phase surface. The three-dimensional plots of hydrocor- tisone and progesterone (Fig. 2.3) illustrate the situation. The polar regions are darker. The two molecules differ from each other only in the presence or absence of one hydroxyl group. The non-polar surface area of the progesterone is interrupted by the polar hydroxyl group in the case of hydrocortisone. Also the slope values of the compounds differs markedly, -0.0192 and -0.0 129 for the progesterone and hydrocortisone, respectively. Although their size and polarity do not differ very much, the accessible non-polar surface area by the non-polar stationary phase decreased markedly in the case of hydrocortisone.

P r o g e a t e r on Hydr ocor t i a o n

Fig. 2.3. The three-dimensional plots of the electron clouds for progesterone and hydrocortisone. (Reprinted with permission from ref. 26.)

Retention prediction of pharmaceutical compounds

E S T I M A T C D

-0 . O(J0

57

I I c

-0.045 - - -n.o4u -0.042 -0.030 -nsn -0.021 -o.nia -0.012' -n.(m' *

S l o p e

Fig. 2.4. The plot of the measured and estimated slope values for the compounds listed in Table 2.1 according to Eq. (2.4). (Reprinted with permission from ref. 26.)

The plot of the measured and calculated S values on the basis of Eqs. (2.4) and (2.5) can be seen in Figs. 2.4 and 2.5, respectively. From the figures and the statistical parame- ters of Eqs. (2.4) and (2.5) it can be seen that the prediction of the slope (3 values is not really accurate. As the slope values commonly range fiom 0.01 to 0.05, the 0.005 stan- dard error means a minimum 10% error. The equations can be suggested for retention prediction in only 10-20% of organic solvent concentration range.

The most significant equation for describing the variance of the intercept (log k,,) val- ues was obtained when the calculated clog P values, the molecular parameters describing the slope values (non-polar surface area, NP and the non-polar accessible surface area, NPA) and the reciprocal value of the dipole moment (dm) were taken as independent variables as described by Eq. (2.6).

log k,, = 0.286 (k 0.036)~log P + 0.037 (* 0.008)NP - 0.040 (* 0.009)ANP

+ 0.652 (* 0.165)[l/(dm)]+ 39.58 (2.6)

n = 23, r = 0.896, s = 0.230, F = 17.4

Although the relationship is significant at higher than 95% probability level according to the Fisher-test value, the predictive power of the equation can be regarded as very poor with 0.230 log k values as the standard error.

The chromatographic hydrophobicity index ($,,), discussed in detail in Section 2.6,

References pp. 90-92

58 Chapter 2

ESTIMAI ED

Slope

Fig. 2.5. The plot of the measured and estimated slope values of the compounds listed in Table 2.1 according to Eq. (2.5). (Reprinted with permission from ref 26.)

could also be described by the calculated octanol-water partition coefficients (log P ) and the calculated non-polar unsaturated surface area (NPU) as shown by Eq. (2.7).

$0 = 11 .OO (* 1.06) log P - 0.25 (A 0.92)NPU + 39.58 (2.7)

n = 23, r = 0.924, s = 8.85, F = 58.7

As the hydrophobicity index, $o, means the organic phase concentration at which the retention time is double the dead time (log k = 0), it can be regarded as a retention pa- rameter, which can be calculated from the hydrophobicity and the non-polar unsaturated surface area of the molecules. As can be seen, the standard error is 8.85, which means the error of the mobile phase composition expressed in volume percent. It seems to be rela- tively high, but in practice it can be acceptable. With 9% change in the mobile phase composition, the chromatographic peak will still be within the measurable range, and can be detected in the chromatogram. The plot of the measured and calculated (by Eq. 2.7) chromatographic hydrophobicity index values can be seen in Fig. 2.6.

As a conclusion from the relationships described above, the investigated retention pa- rameters could be described by molecular parameters obtained from molecular modelling of structurally unrelated pharmaceutical compounds. The linear regression equations ob- tained were significant from the mathematical statistical point of view, but the standard deviations seem higher than would be sufficient for retention predictions without any ex- perimental trials. In spite of these drawbacks, the importance of the above correlations is outstanding. The molecular mechanics calculations can be improved easily in the future,

Retention prediction of pharmaceutical compounds 59

E S T I M A T E D

1 60

30

Fig. 2.6. The plot of the measured and calculated (Eq. 2.7) hydrophobicity indices of compounds listed in Ta- ble 2.1. (Reprinted with permission from ref. 26.)

as these calculations are based on ub initio calculations with the assumption that the cal- culated force fields are transferable to larger molecules. With the help of faster computers and less assumptions, the accuracy of the calculations can be increased, which will probably also increase the predictive power of this type of correlation. It is also remark- able that the relationships can be set up for completely non-congeneric compounds, as most of the published results up to now were achieved by investigating homologous series [30-331. Jinno and Kawasaki [30] used partition coefficients, hydrophobic and electronic constants, van der Waals volume, molecular area, molecular connectivity, length-to- breadth ratio for describing a multiparameter structure-retention correlations for com- puter-assisted retention prediction of alkylbenzenes, substituted benzenes, phenols, poly- cyclic hydrocarbons. Kaliszan et ul. [3 1,321 applied the calculated total energy values, maximum charge differences for quantitative structure-retention relationships of substi- tuted benzene derivatives which can be regarded as non-congeneric solutes. Hanai [33] reported the importance of energy effects, pK, values and van der Waals volumes in de- scribing the reversed-phase HPLC retention of aromatic acids. But according to our in- vestigations [34] on the basis of the correlation of the slope (s) and the intercept (log b) values, the substituted aromatic compounds (such as anilines and phenols) can be re- garded as structurally related compounds from their partition behaviour in W-HPLC. This means that the examples cited above all refer to structurally related compound series. This emphasizes the importance of the correlations obtained for the 23 structurally unre- lated pharmaceutical compounds.

References pp. 90-92

60 Chapter 2

2.5 RETENTION PREDICTION BASED ON TOPOLOGICAL MATRIX AND INFORMATION THEORY

For the description of quantitative structure-retention relationships on which retention predictions can be carried out, the efforts to translate molecular structure into unique characteristic structural descriptors expressed as numerical indices are very important. The most commonly used topological indices as retention descriptors are summarized by Kaliszan [29]. The topological indices can be calculated by means of the chemical graph theory, where a chemical structural formula is expressed as a mathematical graph. The formula shows how bonds connect different atoms in the molecule. The mathematical graph describes abstract vertices joined by edges. Each molecular graph may be repre- sented either by a matrix, a polynomial, a sequence of numbers, or a numerical index (topological index). The molecular connectivity index, at present the most popular topo- logical index, was introduced by Randic [35] for the characterization of molecular branching. Molecular connectivity indices have gained great popularity for describing quantitative structure-retention relationships. Karger et al. [36] found the molecular con- nectivity useful for the prediction of reversed-phase HPLC retention data of phenols and alcohols containing various normal, branched, and cyclic hydrocarbon moieties. Jinno and Kawasaki [37] reported the lack of correlation (r = 0.176) between log k values ob- tained in reversed-phase chromatography and the molecular connectivity for a set of ben- zene compounds containing common substituents such as NH2, NO2, CN, COOCH, and C1. The reason for this may be that the equations describing quantitative relationships between molecular connectivity indices and retention parameters are usually only true for closely generic series of solutes, usually non-polar in character, for which retention data are determined in non-polar chromatographic stationary phase systems. It is because the molecular connectivity indices contain only limited information about the properties of polar fimctional groups, the ability to form hydrogen bonding or the capability for other polar interactions. The predictive power of the derived equations depends on the true re- lationship which is valid only within the series of the compounds investigated.

Matsuda et al. [38] and Hayashi et al. [39] described the application of information theory for retention prediction. The retention prediction for PTH-amino acids using the information theory was first suggested by Jinno [40]. They described the chromatographic retention factor as a hnction of chromatographic conditions and physicochemical proper- ties as shown by Eq. (2.8).

log $ = (CXZ + DX+ E)Rj + ( F P + GX+ H)

where Rj denotes the retention-solubility parameter of PTH-amino acidj and is related to the aqueous solubility parameter S [40]. The formula shows also a relation to the volume fiaction, X , of a modifier. Coefficients C to H of the polynomials of X can be determined by the linear least squares method for real data. The physicochemical properties of PTH- amino acids are reflected by Rj and those of the mobile phase are described by the poly- nomials of X. They used the retention prediction method for the optimization of the sepa- ration of PTH-amino acids. The same approach was also used for the retention prediction of alkylbenzenes [38]. Table 2.3 shows the formulae used for retention prediction of al-

Retention prediction ofpharmaceutical compounds 61

TABLE 2.3

FORMULAE OF RETENTION PREDICTION FOR ALKnBENZENES WITH ACETONITRILE AS A MODIFIER ACCORDING TO MATSUDA et al. [38]

log($) = A(x) log(Pi) + B(X)$ + C(x)

j (analyte number) W P i ) 5

A(X) 5 0 . 1 0 2 ~ ~ - 0.746X2 + 0.427, B(x) = 1.022y2 - 1.051X+ 0.308, C(X) = -O.980X+ 0.084

1 Toluefle 2.60 4.0

3 n-Propylbenzene 3.66 6.0 4 n-Butylbenzene 4.19 7.0

2 Ethylbenzene 3.13 5.0

5 n-Pentylbenzene 4.12 8.0 6 n-Hexylbenzene 5.25 9.0

With permission from ref. 38.

kylbenzenes with acetonitrile as a modifier. Figure 2.7 shows the predicted retention fac- tor values (k) at various volume fiactions (%) of acetonitrile in water, as mobile phases.

In this approach, a great number of experimental data were involved in the retention prediction, and it referred only to the given chromatographic conditions, column, flow rate, etc. The maximum information was extracted from the experimental values, and the retention prediction was carried out only in a limited range of variable conditions for the optimum separation.

To gain maximum information fiom a large set of chromatographic retention data, factor analysis was proposed by Righezza and Chretien [4 11. The approach was applied to the retention data k of a large set of compounds in HPLC. The chromatographic informa- tion, i.e. affinity and selectivity, was extracted with the help of principal component analysis and correspondence factor analysis (CFA).

In conclusion, the application of topological indices or information theory for the pre- diction of chromatographic conditions are always based on experimental retention data. Quantitative relationships can be set up between the retention factors and the descriptors

Fig. 2.7. Retention prediction of alkylbenzenes for reversed-phase chromatography. X denotes the volume frac- tion (‘33) of acetonitrile in water. Lines (from bottom to top): toluene; ethylbenzene; n-propylbenzene; n- butylbenzene; n-pentylbenzene; n-hexylbenzene. (Reprinted with permission from ref. 38.)

References pp. 90-92

62 Chapter 2

of the chemical structure of the compounds and other chromatographic conditions. The equations derived can be used for retention predictions only within the series of com- pounds and HPLC conditions investigated. The advantages of these methods are that they do not require measured physicochemical properties for the compounds.

2.6 RETENTION PREDICTION BASED ON THE HYDROPHOBICITY OF DRUGS

Much better precision and a wider application range in pharmaceutical analysis can be gained by using retention prediction based on measured or calculated physicochemical properties of compounds.

Separation in chromatography is the result of differential migration. Differential mi- gration or in other words the movement of individual compounds through the column depends on the equilibrium distribution of each compound between the mobile and the stationary phases. The distribution depends on the composition of the mobile phase and the stationary phase, and on the temperature. There are four major interactions between the solute and solvent molecules involved in the distribution, namely dispersion, dipole, hydrogen bonding and dielectric interactions. The total interaction of a solvent molecule with a sample molecule can be described by the term polarity. Polarity can be defined as the ability of the sample or solvent molecule to interact in all of these forces. Thus, polar solvents attract polar solutes. The polarity can also be measured or related to other phys- icochemical parameters, such as partition coefficients, dipole moments, etc. These phys- icochemical parameters can then be related to the chromatographic retention.

The separation mechanism on chemically bonded non-polar phases (RP-HPLC) has been described by various theories in the literature. In 1977, Colin and Guiochon dis- cussed three possible retention mechanisms [42]. The RP-HPLC can be regarded as a kind of liquid-liquid partition chromatography, or it is similar to classical liquid-solid chromatography, but interactions between the solute and stationary phases are weaker than in adsorption so that the solute behaviour in the mobile phase is dominant, or parti- tion of the solutes takes place between the mobile and a “mixed” stationary phase formed by adsorption of the organic modifier on the stationary phase [43]. The preponderance of more recent experimental evidence and theoretical developments [44] support a mecha- nism for RP-HPLC that is largely partitioning, particularly for C-18 stationary phases. Wise et al. [45] have proposed that the selectivity RP-HPLC for polycyclic aromatic hy- drocarbons depends on the length-to-breadth ratio of the molecules. Martire et al. [46] have developed a unified molecular theory based on a lattice model to describe the solute distribution process. Dill [47] has developed another statistical-mechanical theory that accounts for bonded-chain re-organization energy. All of these theories indicate that re- tention energies are dominated by partitioning of the solutes into the bonded-phase. It means that in reversed-phase HPLC, the hydrophobicity of the compounds governs the retention. The hydrophobicity is often expressed by the measured or calculated octanol- water partition coefficients (log P). The log P values are also used in drug design and they are also important from the environmental protection point of view. Therefore, it has a great advantage over other physicochemical properties in that huge databases of meas-

Retention prediction ofpharmaceutical compounds 63

ured log P values are available [48]. Rekker [49] developed a calculation method for log P values based on fragmental constants for the fragments of the molecules. Several programs are on the market [50,51] by which log P values can be calculated from the chemical structure of the pharmaceutical compounds. The relationships between the log P values and RP-HPLC retention data provides the possibility of not only estimating hydro- phobicity by chromatography but also predicting reversed-phase chromatographic reten- tion. Numerous publications have been reported on the correlation of RP-HPLC retention data with log P values. There are three main approaches for the correlation of the log P values to the RP-HPLC retention data of pharmaceutical compounds.

The first, most simple approach describes linear correlation between the log P values and the log k values obtained in a given RP-HPLC system according to Eq. (2.9).

log k = a log P + b (2.9)

where a and b are constants. The values of the constants depend on the applied reversed- phase column, mobile phase composition, and the structure of the series of compounds being investigated. It can be noticed from the published data that Eq. (2.9) was valid only for structurally related series of compounds. When a similar equation successfully de- scribed the data of structurally unrelated compound series, the chromatographic system contained octanol and water. As our aim is to study the retention prediction of pharma- ceutical compounds under regularly used reversed-phase HPLC conditions, the applica- tion of octanol in the chromatography can be disregarded. Although many examples show that high correlation coefficients can be found for Eq. (2.9), it cannot be regarded as be- ing useful for retention prediction as the values of constants vary with the column, mobile phase composition and the compound structure.

The second approach overcomes the problem of mobile phase variation by using the extrapolated log k values to 0% organic phase concentration as described by Eq. (2.10).

log k,, = a log P + b (2.10)

where a and b are constants. This approach has the advantage that the retention data of the compounds investigated can be obtained from different mobile phase compositions, so a much wider range of hydrophobicity values can be covered, which means that the equa- tion is more general, and valid for a larger set of compounds than is the case with Eq. (2.9). However, there are two major problems with the general use of Eq. (2.10). First, problems arise with the extrapolation of the log k values to zero organic phase concentra- tion. Snyder et al. [52], Butte et al. [53] and Hammers et al. [54] showed that over a vol- ume fraction range of at most 0.1-0.9, the linear extrapolation from the log k versus vol- ume fraction of the organic phase relationship is acceptable for the estimation of log ko values. However, several results [13,55] showed that the linearity of the plot is not valid for a wide range of organic modifier concentrations, and the l o g b values are not the same when they are derived from data obtained by using acetonitrile or methanol [25]. Therefore, log is suggested instead of log h. Schoenmakers et al. [ 121 suggested a quadratic relationship between log k and the volume fraction of the organic modifier, at which the log values are different. The uncertainty of the derivation of log values

References pp. 90-92

64 Chapter 2

makes the application of Eq. (2.10) unreliable. Also the relationship is valid only for structurally related compounds. It is understandable ftom Leo's [56] findings, that the linear relationship between partition coefficients is valid only for structurally related compounds, or for similar partition systems.

The third approach can be regarded as the most general for describing the relationships between the log P values and the chromatographic retention parameters [57] by Eq. (2.1 1).

log P =US+ b log ko + c (2.1 1)

where a, b, and c are constants and S is the slope. The equation was found to be valid for structurally unrelated pharmaceutical compounds. The slope and the intercept (log b) values mathematically describe the linear portion of the log k versus organic phase con- centration. By applying the least squares method to determine the values of the coeffi- cients (a, b and c), essentially a backward extrapolation is carried out to express the log k

A

l o g K'

1 .oo

0.75

0.50

0 . 2 5

0

- 0 . 2 5

-0.50

-0.75

-1.00

I I

0 10 20 30 4 0 50 60 70 80 90 100 y ( % ) I I I I I 0 1 I I

Fig. 2.8. The graphical illustration of the backward extrapolation method for optimizing the RP-HPLC mobile phase composition for describing the best relationship of log k values with the octanol-water partition coefi- cients (log P). Straight lines 1 4 represent the linear portion of the log k versus organic phase concentration plot. The optimized organic phase concentration for which the extrapolated log k values show the best correla- tion to log P (vertical line) can be calculated from the regression coefficients of Eq. (2.1 1) (ah). The horizontal line refer to the log k = 0 retention, i.e. the retention time is double the dead time.

Retention prediction ofpharmaceutical compounds

0.540-

0.520-

65

f B 111

J 1 I I I 1 /

IU .N 40 50 60 70 80 90

OP % (acctonitrlle Concentration, v/v )

Fig. 2.9. The plots of the standard error (s) for the log P versus log k relationships as a function of acetonitrile concentration in the eluent obtained on Supelcosil LC-18 (S) and LiChrosorb RP-18 (L) stationary phases. The optimum mobile phase composition was found to be 33.5% (v/v) and 30.1% (v/v) acetonitrile for Supelcosil LC-18 and LiChrosorb RP-18 stationary phases, respectively. (Reprinted with permission from ref. 58.)

values at the organic phase concentration at which the log P (octanol-water partition) can be best modelled. That is why a statistically significant equation was found for structur- ally unrelated compounds as well. The optimum mobile phase composition can be calcu- lated as a quotient of a and b. Figure 2.8 represents the theoretical meaning of Eq. (2.1 1). As it is based on retention data obtained under more than one set of isocratic mobile phase conditions, a wide range of Rp-HPLC conditions and hydrophobicity values can be covered.

The effect of various reversed-phase columns is manifested in the a, b, and c constants. Even the optimum mobile phase composition may differ from column to column [58] . Figure 2.9 shows the difference in the optimum mobile phase compositions for the log k versus log P relationships on two different stationary phases (Supelcosil LC-18 and Li- Chrosorb Rp- 18).

The drawback of Eq. (2.1 1) is that it cannot be used for retention prediction from the log P values, as we cannot calculate two unknown values (S and log h) from one equa- tion. Figure 2.8 shows the other possibility of using the S and log k0 values for expressing one single chromatographic parameter. From the S and log k0 values, an organic phase concentration can be expressed- at which the compounds have the same retention (log k = 0). It was found [59] that the chromatographic hydrophobicity index values (&)

References pp. 90-92

66 Chapter 2

obtained in this way show correlation with the log P values for structurally unrelated pharmaceutical compounds as given by Eq. (2.12) for 140 compounds usine acetonitrile eluents.

$0,AcN=9.31 logP1-37.94, n=140, r=0.88, s=12.8 (2.12)

From the data of more than 400 pharmaceutical compounds obtained by using metha- nol as an organic modifier, Eq. (2.13) was obtained.

$O,MeOH = 7.08 log P + 42, n = 448, r = 0.787, s = 13.48 (2.13)

For Eqs. (2.12) and (2.13), n stands for the number of compounds, r is the correlation coefficient, s is the standard error of the estimate. It was found [59] that in general the $o = a log P + b relationship exists for a wide range of compounds, and a great variety of reversed-phase columns. It only depends on the type of organic modifier (methanol or acetonitrile). On the basis of the equation, a mobile phase composition can be estimated at which the retention time is expected to be double the dead time. As can be seen fiom the statistical parameters, the error is 12-13% concentration. This can be regarded as a rough prediction of the retention. The plot of log P values and $0,AcN values for 140 com- pounds (Eq. 2.12) can be seen in Fig. 2.10. The names of the compounds and the data were published by Valk6 and Slegel [59] and cover a wide range of pharmaceutically active sulphonamides, morphines, steroids, salicylates, benzodiazepines, barbiturates, etc.

It should be mentioned that the pH of the mobile phase is also very important. In most retention prediction studies, the model compounds are not ionizable, so the mobfie phase pH does not influence the retention prediction significantly. In the case of pharmaceutical compounds, the situation is different. Most are slightly basic or acidic, therefore the mo- bile phase pH influences their protonation or dissociation, and thus their partition. All of

A

AcN

120-

100-

- 4 - 2 0 2 4 6 0 10 Log P

Fig. 2.10. The plot of logP values and the chromatographic hydrophobicity index values ($0, A ~ N ) for 140 compounds according to Eq. (2.12). (Reprinted with permission from ref. 59.)

Retention prediction ofpharmaceutical compounds 67

the relationships described above are valid only in that pH where the molecules are not ionized, as the measured or calculated log P values refer to the neutral molecules. To overcome the pH problem, and the application of different pHs in the mobile phase for measuring different types of structures, a general mobile phase composition was sug- gested by Roos and Lau-Cam [60]. They applied 1.5% acetic acid and 0.5% triethylamine in the mobile phase consisting of various concentrations of methanol and water. The data obtained for 140 pharmaceutical compounds were also included in the calculation of Eq. (2.13). In the above mobile phase system, the acidic compounds are in neutral form, due to the low pH, higher acetic acid concentration, while the protonated form of the basic compounds probably form a neutral ion-pair with the triethylamine. It was found [61], that the relationships described by Eqs. (2.10) and (2.1 1) exist also in ion-pair reversed- phase chromatography. Similarly, good retention prediction has been reported in re- versed-phase ion-pair chromatography using sodium dodecyl sulphate as pairing ion [62]. The retention prediction was made on the basis of the retention data and hydrophobicity parameters of pharmaceutical compounds.

A similar approach to the third approach discussed above [58] was presented by Pate1 et al. in 1991 [63]. They also used Eq. (2.9) as the starting relationship. Their second equation was not Eq. (2.3) as in our case, but they described the dependence of the log k values on the quadratic relation to the organic modifier concentration (logk= a + bq5 + ~$2) . They also found that the volume percent of the organic phase concentra- tion can be related to the hydrophobicity of the solvent mixture, which can be calculated from the mole fraction of a solvent component and its hydrophobicity values according to Eq. (2.14):

(2.14)

where xi is the mole fiaction of the ith solvent component, log Ps,i is the logarithm of the partition coefficient of the ith solvent, and n is the total number of pure solvents present in the solvent mixture. The calculated log P,, values were found to be related to the vol- ume fraction of the organic solvent in the mobile phase according to Eq. (2.15).

9 = A' + B'( UPsm) (2.15)

Considering the quadratic relationship between the log k values and the 9 values and the linear relation between the log k and the log P values (Eq. 2.9), the following general equation was set up:

log k = A0 + @(log P/Ps& + P(l0g P/Psm2) (2.16)

Mathematically Eq. (2.16) is very similar to Eq. (2.1 1). By calculating the regression parameters (Ao, Bo and @), the mobile phase composition is optimized for the best modelling of the octanol-water partition of the molecule. Therefore this approach can be considered as analogous to our general approach for describing log P by the measured slope and the intercept values of the compounds. The only difference is that it allows even quadratic relationships between log k and organic phase concentration (while Eq. (2.1 1)

References pp. 9&92

68 Chapter 2

supposes only a linear relationship), and the organic phase concentration is expressed by the mobile phase hydrophobicity value. The validity and prediction power of the equation were checked for structurally similar compound series (substituted aromatic compounds), under a variety of reversed-phase HPLC conditions (various types of organic modifiers and reversed-phase stationary phases). Statistically the correlations were always signifi- cant, the standard error of the log k prediction ranged from 0.150 to 0.987, which can be considered acceptable. The advantage of Eq. (2.16) is that it allows direct retention pre- diction at various mobile phase compositions from the known log P values of the com- pounds and mobile phase additives. To date, Eq. (2.16) can be considered as the most general and reliable retention prediction method for structurally unrelated compounds and applying various reversed-phase chromatographic conditions.

Other approaches which use physicochemical descriptors but also other experimentally obtained constants which can be related to physicochemical parameters are discussed later.

2.7 RETENTION PREDICTION BASED ON EMPIRICAL INCREMENT VALUES

The calculation of the hydrophobicity of the molecule based on the chemical structure has more or less been solved. The calculation is based on the constant and additive hydro- phobicity contribution of molecular fragments. As the RP-HPLC retention is also gov- erned mainly by hydrophobicity of the compound, the question arises whether the calcu- lation of the RP-HPLC retention can be carried out in a similar way from the retention contributions of the molecular fragments. The contribution of the substituents to retention have often been found constant and additive for a given chromatographic system. Based on this observation, reliable predictions of retention behaviour have frequently been re- ported in RP-HPLC C65-671. The theoretical basis of a structural retention increment database can be supported with the following equations. It is well known that the loga- rithmic retention factor (log k) is linearly proportional to the logarithmic distribution co- efficients (log K ) of the compounds referring to the chromatographic partition system as described by Eq. (2.17).

log k = log K + log( V,/V,) (2.17)

where VJV, is the so-called phase ratio, the ratio of the stationary and mobile phase vol- umes. From Eq. (2.17) it is clear that if log K is a linear free-energy related parameter, log k is the same. As log K can be regarded as a logarithmic value of the chromatographic partition coefficients, on the basis of the Collander [64] relationship, linear correlation can be expected for the log P values as mentioned earlier in Eq. (2.9). By analogy with the log P predictions (Eq. 2.1 S), the log k values also can be regarded as a sum of the Q log k, values referring to all fragments in the molecule (Eq. 2.19)

log P = x n i or log P = C F , f, (2.18)

Retention prediction of pharmaceutical compounds 69

where xi is the Hansch ;n value [68],J; is the Rekker fragmental constant [49] and Fi rep- resents the number ofJ; fragments in the molecule.

log k = C d l o g k; (2.19)

From Eq. (2.19) it is clear that it is possible to predict the log k values of compounds if the dlog 4 values are available. But two important limitations of the retention prediction should be considered. First, as was also observed in the calculation of log P values, the group or fragment contributions are not always additive, the neighbouring substituents can influence each other’s partition or retention contributions. These effects are often negligible, or they can be involved in the calculations as a dlog k value attributed to the interactions. The second, more important limitation is that the log k value depends on the column and mobile phase composition to a great extent. The dlog 4 values can be col- lected from the log k values of two compounds differing from each other only in the pres- ence or absence of the i substituent. Let us consider the change in the dlog 4 values for a change in the mobile phase composition. Equations (2.20) and (2.21) describe the rela- tionship of the log k values with the organic phase concentration (@) by linear relation- ships discussed above.

where c refers to the compound without the i fragment and ci with the i fragment. On the basis of Eqs. (2.20) and (2.21), the dependence of the 61og Ki values on the mobile phase composition (@, volume fraction of the organic modifier), can be described by Eq. (2.22).

61og k, = (S,, - sc)$ + log /$Ic; - log k, (2.22)

It can be seen that the higher the difference between the S values of the two com- pounds, the higher will be the dependence of 6 log ki values on the mobile phase com- positions. If i refers to a small substituent, which does not influence the contact hydro- phobic surface area of the molecules very much, we can expect very similar S values for compound ci and c. Then the difference is zero, the 6 log k; value will be independent from the mobile phase compositions. If we consider an average S value for compound ci, as -0.02 and 25% lower value for compound c, as -0.015, then the difference will be 0.005, which means that a 10% change in the organic phase concentration will cause a 0.05 change in the d log ki values. This value is slightly greater then the general error in log k measurements. It means that the dependence of the fragmental retention contribution on the organic phase concentration is very small, but theoretically cannot be neglected.

On the basis of the above considerations, a huge database has been set up for the 6 log k values for structural fragments of pharmaceutical compounds for the most com- mon metabolic changes [69]. More than 400 metabolic transformation routes were col- lected, and the d log ki values were calculated from literature data. For example, the most

References pp. 90-92

70 Chapter 2

CH3 0

1

4

c?? CONH2

9

OH

10

FH2 1 5

1 3

Fig. 2.1 1. Structure of the compounds investigated. Compound 1-3, pyridopyrimidine derivative and its me- tabolites; compounds 4-10, diazepam, oxazepam, uxepam and their metabolites; compounds 11-13, 3- trifluoromethyla-ethylbenzhydrol derivatives.

common metabolic hydroxylation was characterized by two values of 6 log k, -0.35 and -0.15 for aliphatic and aromatic hydroxylation, respectively. These numbers were ob- tained from literature data for the differences of log k values of hydroxylated and dehy- droxylated compounds obtained in a reversed-phase HPLC system. In general, retention data of a minimum of four pairs of compounds were considered in the Q log ki value. When literature data were not available for a certain compound pair, the 6 log k value for the i metabolic transformation route was estimated fiom the Hansch n value. On the basis of Eqs. (2.12) and (2.13) and our observation that a 10% increase in acetonitrile and methanol causes 0.285 and 0.298 log k change, respectively, it can be calculated that a unit change in log P value will result in 0.204 and 0.270 change in log k values. Thus, for example, the presence of a methyl group which has a rc value of 0.56 can be expected to increase the retention by 0.149 and 0.1 14 log k value with acetonitrile and methanol, re- spectively, as the organic modifier. Although the change in retention time caused by a given substituent can vary over a wide range, the 6 log k value can be regarded as a con- stant, neglecting its dependence on the organic phase concentration. Similarly for the log P predictions, when n and f values of a molecular fragment can be changed by an adjacent substituent which influences the prediction, the 6 log k values can also be differ- ent, reflecting their neighbouring substituents for the same reason. Moreover, the 6 log k values may vary on different reversed-phase columns from different manufacturers, as the

Retention prediction of pharmaceutical compounds 71

TABLE 2.4 MEASURED (mtR) AND THE PREDICTED (ptd RETENTION TIME DATA (log k) VALUES FOR THE 15 INVESTIGATED COMPOUNDS

Column I (to = 1.40 min) Column I1 (to = 2.38 min) Column 111 (to = 1.60 min)

mtR PtR b g k mtR PtR b g k mtR PtR logk

1 2 3 4 5 6a

7 8 9 LO 11 12 13 14 15

7b

11.1 -c 0.84 24.4 4.7 6.0 ' 0.37 11.0 5.2 3.9 0.43 12.3

13.0 - 0.92 14.3 8.7 8.7 0.71 10.8 7.5 9.6 0.64 9.4 5.7 6.6 0.49 8.0 5.7 5.3 0.49 8.0

20.8 16.0 1.14 19.6 5.9 - 0.51 9.4 4.9 4.2 0.40 8.4 4.4 - 0.32 6.2

12.7 9.9 0.91 10.4 3.7 5.0 0.22 5.8 8.4 - 0.70 14.3 6.0 5.3 0.51 9.9

- 0.97 16.6 - 1.00 12.2 0.56 6.3 8.3 0.50 8.8 0.62 7.3 5.1 0.58

- 0.70 19.6 - 1.08 9.9 0.55 12.1 13.0 0.85

10.8 0.47 9.2 14.3 0.71 8.3 0.37 7.4 9.0 0.59 6.8 0.37 7.4 6.4 0.59

21.4 0.86 29.8 21.3 1.28 - 0.47 7.2 - 0.54

6.8 0.40 5.7 5.1 0.41 - 0.21 3.9 - 0.15 13.1 0.53 11.5 8.1 0.79 4.9 0.16 3.3 4.7 0.02

- 0.74 13.5 - 0.87 9.1 0.54 7.7 8.3 0.58

Reprinted with permission from ref. 69. All PtR vdues were calculated from the mtR of the parent compounds, except as indicated in the footnotes. Column I, Hypersil ODs; Column 11, LiChrosorb ODs; Column 111, Se- pharon RPS. a PtR calculated from mtR of 4. b PtR calculated from mtR of 5.

times of the metabolites. The measured retention times of the parent compounds were the input data for the prediction of the retention

log k values can be different. The effect of the adjacent groups and different reversed- phase columns on the 6 log k, values, and on the retention prediction has been investi- gated for a few pharmaceutical compounds [69]. The purpose of the work was the appli- cation of the retention prediction method described above for predicting the retention of metabolites of known pharmaceutically active compounds. The chemical structures of the compounds investigated can be seen in Fig. 2.1 1.

The retention prediction was carried out for hydroxylation, demethylation, decarboxy- lation on the various molecules. The retention measurements were carried out on three different RP columns in order to reveal the effect of the stationary phase. Hypersil ODS, LiChrosorb ODS, and Sepharon RPS stationary phases were involved in the study [69]. The measured and predicted retention values for the compounds investigated are listed in Table 2.4.

The observed 6 log k, values for the metabolic transformations on the various mole- cules are listed in Table 2.5. In order to reveal the retention changes on the three columns for the same structural change, the differences between the 6 log k, values obtained for the C-hydroxylation of compounds 1,4,5, and 12 and for the N-demethylation of compounds 4,6,9, and 14 are summarized in Table 2.6.

References pp. 90-92

12 Chapter 2

The average 6 log ki values and their standard deviations were also calculated. In com- parison with the average and the standard deviation for the measured 6 log k values on the three types of columns and for the same structural change obtained on the same columns, but different mobile phase compositions, it can be seen that the standard deviation is much higher for the 6 log k values measured for the same structural change (i) but in dif- ferent molecules. This suggests that the weakest point of the prediction is the effect of neighbouring molecular fragments, and not the application of different columns and mo- bile phase compositions. The average standard deviations were 0.049 (expressed in log k) for demethylation and 0.104 for hydroxylation, which are acceptable, especially when expressed as retention time values (1.8 min). The relatively high standard deviation of 6 log ki values obtained for the same structural change on various molecules can be ex- plained from a physicochemical point of view, namely the N-methyl group is not basic in compounds 4,6, and 9 as in 14, because the first three are carboxamides. For this reason, the change in hydrophobicity and as a consequence in RP-retention cannot be expected to be the same. The effect of C-hydroxylation in 6 log k when there is a possibility of intra- molecular hydrogen bond formation is much smaller. That is possibly the case for com- pound 2. It can be seen from the examples presented that the error in the prediction is higher than the variation of 6 log k values due to a different reversed-phase column or conditions. This retention prediction method was applied only for the retention prediction of metabolites on the basis of the measured retention parameters of the mother com- pounds. In each case a change of never more than one 6 log 4 value was used for the re- tention prediction. The method was not considered suitable for the prediction of the re- tention of a molecule by building up a summation of all its fragmental 6 log k values. With this restriction, the method seems to be reliable and it was compiled in an expert system developed by Compudrug [70] called HPLC-MetabolExpert for predicting the chemical structures and RP-HPLC retention of possible metabolites of drug molecules.

A very similar approach for retention prediction of basic drugs were developed by Hindriks et al. [71]. The aim of the work was to develop an expert system for the selec-

TABLE 2.5

MOLECULES ON THE THREE COLUMNS AND THE AVERAGE (A) Slog k VALUES AND THE Slog k VALUE TAKEN FROM THE DATABASE (DB)

THE OBSERVED Slog k1 VALUES FOR THE METABOLIC TRANSFORMATIONS ON THE VARIOUS

Metabolic route 6 log k

Column I Column I1 Column III A DB _ _ _ _ _ ~

+OH on 1 +OH on 4 +OH on 5 +OH on 12 -CH3 on 4 -CH3 on 6 -CH3 on 9 -CH3 on 14 -COOH on 1 1

-0.470 -0.279 -0.220 -0.723 -0.204 -0.152 -0.110 -0.183 +0.598

-0.407 -0.230 -0.180 -0.371 -0.151 -0.105 -0.068 -0.196 +0.323

-0.498 -0.274 -0.260 -0.773 -0.231 -0.115 -0.136 -0.290 +0.643

-0.458 -0.261 -0.220 -0.622 -0.195 -0. I24 -0.105 -0.223 +0.521

-0.35 -0.15 -0.15 -0.50 -0.20 -0.20 -0.20 -0.25 +0.45

Reprinted with permission from ref. 69.

Retention prediction of pharmaceutical compounds 73

TABLE 2.6

THE 61og k VALUES CAUSED BY THE METABOLIC HYDROXYLATION AND DEMETHYLATION OF THE COMPOUNDS ON THE THREE COLUMNS

Reaction Compound pair Column I Column I1 Column 111 Average

Hydroxylation 1-2 4-6 5-7

Average: Std. dev.

Phenolic OH 12-13 Demethylation 4-5

6-7 9-10

14-15 Average Std. dev.

-0.470 -0.279 -0.220 -0.323 f0.107 -0.723 -0.204 -0.152 -0.110 -0.183 -0.162 f0.047

-0.407 -0.230 -0.180 -0.272 f0.097 -0.371 -0.151 -0.105 -0.068 -0.196 -0.130 f0.064

-0.498 -0.274 -0.260

f0. 109

-0.231 -0 .115 -0.136 -0.290

f0.088

-0.344

-0.773

-0.193

-0.458 f 0.038 -0.261 f 0.022 -0.220 f 0.033

f0.104 -0.622h0.179 -0.195 f 0.040

-0.313 f 0.030

-0.124 f 0.024 -0.105 f 0.034 -0.223 f 0.053 -0.162 f 0.026 f0.049

(Reprinted with permission from ref. 69.

tion of initial HPLC conditions for the analysis of pharmaceuticals. They investigated the retention behaviour of 600 basic compounds belonging to the class of CNS-active and cardiovascular drugs. The relative measure of polarity of the compounds was expressed by retention index values, mentioned earlier [6,8,9], which can be used to characterize the polarity of the molecule and to link the structure elements to some type of polarity de- scriptor. Under strict conditions, it was shown that the retention index (RI) values are constant. RI values for 300 compounds in combination with chromatographic data on the purity analysis of more than 300 compounds were the basis of the knowledge base. They chose to estimate the polarity of a given molecule on the basis of the presence of polar and non-polar groups. The expert system developed calculates the polarity of a new com- pound from its structure and expresses the result as a percentage of organic modifier (methanol) in the mobile phase. Before this, the structure is subdivided into fragments or structural elements. These elements are so defined that they can describe a structure in a simple and unambiguous manner. Examples of such elements are phenyl, methyl, hy- droxyl and tertiary nitrogen. All initially selected structural elements are shown in Table 2.7. The percentages listed in Table 2.7 are essentially derived from experimental data and from the Rekker’s fragmental constant values [49] for hydrophobicity contributions.

The authors [71] explain the effect of the pH of the mobile phase on the fragment value of the protonated groups. They claim that most fragment contributions are inde- pendent of the pH. They did not mention the effect of the neighbouring substituents. The differences in reversed-phase columns from various manufacturers are expressed by the so-called zero-level contributions. They determined experimentally the zero level for a NovaPak C18 column at 43% of methanol. In other words, methanol (%) = Z(fiagment contributions) + 43%. The same holds for apBondapack C18 column, except that the zero level is 2% lower. For most applications, tetramethylammonium phosphate buffer was used to block the silanol sites of the reversed-phase material to avoid the silanol effects on the retention of the basic drug molecules. They stated that the most difficult task

References pp. 90-92

74 Chapter 2

TABLE 2.7

SOME STRUCTURAL ELEMENTS AND THEIR EFFECTS ON THE PREDICTED PERCENTAGE OF METHANOL AT pH 7.4 AND pH 4.0 ACCORDING TO HINDRIKS et al. [71]

Structural element Methanol (%)

pH 7.4 pH4.0

9

10

11 12 13 1 4 15 1 6 17 18

Phenyl, monosubstituted (c&) Phenyl, disubstituted (CsH4) Phenyl, trisubstituted (c&) CI on aromatic group CI on aliphatic group OH on aromatic group OH on aliphatic group 0 atom in ether. The oxygen is positioned between: a Two aromatic groups b An aromatic and an aliphatic group c Two aliphatic groups 0 atom in ketone. The carbon connected to the oxygen is positioned between: a Two aromatic groups b An aromatic and an aliphatic group c Two aliphatic groups S atom. The sulphur positioned between: a Two aromatic groups b An aromatic and an aliphatic group c Two aliphatic groups Pyridine CH3 CH2 CH C N atom in ring plus double bond N atom in two rings Other N atoms: first one

every next one

+ I 1 +I0 +9 +7 +1 -2

-10

+11 +I0 +9 +7 + I -2

-10

-5 -5

-10

-5 -6

-10

+3 + I -3 +3 +5 +3 +2 + I -5 0

-5 -5

-5 -5

-10

-5 -6

-1 0

+3 +I -3 -5 +5 +3 +2 +I -5

0 -3 0

-5

Reprinted with permission from ref. 7 1.

proved to be to describe correctly and yet in a simple way the polarity of a sample mole- cule on the basis of its chemical structure. The approach proved to be successful, but also showed limitations, However, the accuracy of the prediction of the initial methanol con- centration was not shown, and also the limitations were not discussed. It was not clear what was the expected retention for the calculated methanol concentration in the mobile phase. Theoretically this approach is very close to the approach of the chromatographic hydrophobicity index, discussed earlier [28], where the mobile phase composition is pre- dicted to provide log k = 0 retention from the log P values of the compounds.

The third important approach was published recently by Dimov and Moskovkina [72]. Equations for the dependence of the retention in RP-HPLC on molecular mass and se- lected structural fragments of 18 benzodiazepine derivatives were proposed. They sug-

Retention prediction ofpharmaceutical compounds 75

gested a biparametric model based on the additivity principle for a general description of chromatographic retention for predictive purposes as shown by Eq. (2.23).

n n+k R=bo + x b i B i + C b i T i (2.23)

/=l j=n+1

where R represents the corresponding retention (k), B, are basic and are tuning con- tributors to retention. The bo and bj are regression constants. It was accepted [73] that the B term in Eq. (2.23) includes solute properties, allowing the calculation of the retention parameter (R), which does not differ from the experimental value by more than *10-15%. The T term also includes solute properties, which can correlate insignificantly with reten- tion and do not correlate with the properties included in the B term. The retention data of the benzodiazepine derivatives were taken from the literature. The molecular mass, M,, as a general property was tested as a B contributor. Molecular fragments such as C=O, -OH, -F, -NOz, N-R2 and flat rings (phenyl, cyclopropane) were tested as T contribu- tors. An indicator variable was used to represent the presence or absence of the fragments in the molecule. On the basis of the data, the regression parameters were calculated for Eq. (2.23). Very good agreement between the measured and calculated retention parame- ters were found. The results showed that there are fragments selected from the solute molecule which are responsible for retention and these can be called chromatophores. Their contributions are additive, but in some instances the fragment evaluation can be tuned so that a more accurate equation can be obtained. The evaluation from both the first and second groups of equations allows quantitative considerations of the contributions of different solute fragments, while the difference in a given fragment evaluation could be used to consider intramolecular interactions.

In conclusion, the retention prediction of pharmaceutical compounds can be carried out on the basis of fragmental retention contributions. Three methods have been dis- cussed. The first method uses a large database (400 metabolic transformations) of the retention increment values caused by the change in chemical structure, which usually oc- curs on metabolic transformation. This expert system approach can be applied for the retention prediction of metabolites from the measured retention data of the mother com- pounds under certain chromatographic conditions. It was shown that the effect of the mobile phase composition, and the type of reversed-phase column are negligible. The effect of the neighbouring structural fragment on the molecule caused higher deviation from the predicted retention. The second approach also uses an expert system, and was developed mostly for basic drug molecules on the basis of the experimental retention data of 600 compounds. From the fragmental hydrophobicity constants, a methanol concentra- tion value was calculated which should be added to the mobile phase to achieve a certain retention, The effect of various columns and mobile phase pH were taken into considera- tion in the fragmental values and the calculation methods. This system is suggested for building up the retention of the whole molecule from its fragmental contribution values, however, the precision and accuracy of the system has not yet been tested. The effect of intramolecular interactions on the retention prediction is not known.

The third approach seemed to be applicable for other chromatographic systems as well, not only for RP-HPLC. The advantage of the method is that it takes into account the intramolecular interactions between the fragments of the molecules, and their role in the

References pp. 90-92

76 Chapter 2

retention. The disadvantage of the method is that it needs a large amount of experimental data to calculate the regression coefficients of the equation used for the prediction. Dif- ferent equations should be applied to different chromatographic conditions. It is also not explained how accurate is the retention prediction for non-congeneric compounds or for compounds differing in structure from the investigated series.

2.8 RETENTION PREDICTION BASED ON EXPERIMENTAL RETENTION VALUES, THERMODYNAMIC CONSIDERATIONS WITH MULTIPARAMETER APPROACHES

Structure-retention relationships have been studied by numerous chromatographers for predictive purposes. The derived quantitative structure-retention relationships usually allow the prediction of the retention behaviour of a given solute of a given class. The most common way is to convert the retention data to a linear free-energy related (LFER) value usually the log k, and a linear regression equation can be set up using other LFER parameters as independent variables. The relationships are more reliable and show wider range of validity if they are based on multivariate analysis of experimentally determined retention data and physicochemical data. Using more than one independent variable to describe the variation in the retention data increases the reliability and accuracy of the prediction. The drawback of using a great number of variables in the quantitative struc- ture-retention equation is that a large number of compounds with precisely measured retention data are needed to set up the equation and for calculating the regression coeffi- cients. In general, to introduce a new independent variable into the equation, a minimum of five compounds are required with their measured retention data and measured or calcu- lated physicochemical descriptors. This means that when an equation contains three inde- pendent variables, the data of a minimum of 15 compounds are necessary to calculate the regression coefficients and the mathematical statistical parameters of the equation. In or- der to reveal the true value and the predictive power of the equations, the multiple re- gression coefficients, the standard error of the estimates and the Fischer-test value should be given. The multiple correlation coefficient reflects the proportion of the explained and unexplained variance of the retention parameters for the compounds involved in the cal- culation. The standard error of the estimates expresses the =k deviations of the predicted retention value from the true value, i.e. it shows the predictive power of the equation. It is always worth checking how it is related to the experimental error of the retention deter- mination. The Fisher-test value shows the probability that the equation reveals a true re- lationship. It is also very important to check the significance level of the variables. The most common way to show that the application of a given variable significantly increases the explained variance of the dependent variable (usually the retention parameter) is to give the f values of the regression coefficients with 95% probability level. If it is signifi- cantly different from zero, the variable can be regarded as significant. In order to estimate the importance of a given variable in a multivariable regression equation to explain the variance of the dependent variable, the so-called b-weight can be calculated. The b- weight values show the role of the variable for the prediction and a real rank can be set up among the variables. The independence of the independent variables is also very impor-

Retention prediction of pharmaceutical compounds 77

tant. To reveal the correlation of the variables involved in the equation, the correlation matrix provides valuable information. Briefly, these are the most important mathematical statistical considerations in a multivariate quantitative structure-retention equation. A detailed description of the mathematical basis of step-wise regression analysis can be found in the monograph by Draper and Smith [74].

The application of regression analysis for setting up quantitative structure-retention relationships was given by Woodburn et al. [75]. Retention of several non-polar solutes on two reversed-phase liquid chromatographic supports (C-2 and (2-8) was examined during isocratic, isothermal elution with binary mixtures of methanol-water and acetoni- trile-water. The log k values were correlated with the following indices of solute hydro- phobicity and molecular topology: octanol-water partition coefficients (log P), hydro- phobic surface area (HSA), and first-order molecular connectivity indices k'). For each stationary phase-solvent combination, one regression equation was required to describe the data for polycyclic aromatic hydrocarbons and halobenzenes, and another for alkyl- benzenes, as can be seen from the following equations:

log k - 2 B ~ 0 . 8 0 (h 0.02) log P-2.70 (+ 0.2), n = 9, r = 0.959 (2.25)

log kc-8 A = 0.84 (*0.05) log P - 1.20 (* 0.2), n = 1 1, r = 0.996 (2.26)

log kC-8B = 1.00 (k 0.04) log P - 1.50 (+O.l), n = 9, r = 0.999 (2.27)

Equations (2.24X2.27) refer to 60:40 methanol-water mixture as mobile phase. A re- fers to the solute group of benzenes, polyaromatic hydrocarbons (PAHs), and haloben- zenes, while B refers to the group of alkylbenzenes. The following equations show the similar correlations obtained in a 50:50 acetonitrile-water mobile phase.

log kc-2 = 0.35 (* 0.30) log P - 0.5 1 (* 0.1),

log kc-z,B = 0.51 (* 0.02) log P - 0.91 (h 0.06),

log kc.S,A = 0.55 (* 0.55) log P - 0.19 (5 O.l),

n = 1 1, Y = 0.993

n = 9, r = 0.998

n = 11, r = 0.995

(2.28)

(2.29)

(2.30)

log k-8,B = 0.73 (+ 0.03) log P - 0.60 (* 0.07), n = 9, r = 0.999 (2.3 1)

From the above equation it is clear that every mobile phase composition and stationary phase produces different constant values in the correlation analysis. Also the parameters are different with different group of compounds. The same authors [75] found significant correlations between the retention data and hydrophobic surface area, and the molecular connectivity indices, again with different parameters with different mobile and stationary phase compositions. As the physicochemical and topological descriptors investigated showed high correlation with each other, the multiple regression analysis could not be used. The different parameters of the correlations for the data of polycyclic aromatic hy-

References pp. 90-92

78 Chapter 2

drocarbons and halobenzenes, and alkylbenzenes were attributed to the differences in the nature of the interaction of these two groups of solutes with the bonded, n-alkyl chains. Solute molecular size, shape, and conformation as well as hydrophobicity appear to be the dominant factors controlling the solute retention.

Several efforts have been made towards describing quantitative structure-retention re- lationships simultaneously accounting for changes in mobile and stationary phase com- positions and including structurally unrelated compounds. A very interesting and promis- ing approach was derived by Jandera [76-781. His starting point was the linear relation- ship between the log k values with the organic phase composition as described by Eq. (2.3) (log k = S#I + log b), investigating the retention data of a homologous series of sol- utes at several different concentrations of the organic solvent used in the binary mobile phase. From the experimental data, he found another two relationships for the parameters Sand log in Eq. (2.3) as described in Eqs. (2.32) and (2.33).

log ko = an, + b (2.32)

S = d log + e (2.33)

where a, b, d, and e are constants, n, is the number of carbon atom in the solute of the homologous series. Introducing these parameters to the original Eq. (2.3), the following equation can be set up:

log k = $(d log ko + e) + (an, + b)

= $d(an, + b) + $e + (an, + b)

= (an, + b)(l + $4 + $e (2.34)

This equation means that the dependence of the log k values can be described by the organic phase concentrations considering the a and d constants, which according to Jandera do not depend significantly on the character of the homologous series but on the organic solvent used as the less polar component of the mobile phase. The constants e and b depend also on the type of the homologous series and the stationary phase used. The constants can be estimated by the measured retention data of a homologous series in a given stationary phase with a given organic modifier. These constants are supposed to be generally valid for other non-homologous series of compounds as well. The n, values obtained in this way, which are originally the carbon numbers, are equivalent to the non- specific contributions, while e refers to the polar contribution to the retention. Jandera has verified experimentally his theoretical approach to retention prediction of substituted aromatic compounds. He also showed [77,78] that the constants obtained showed good correlations with the Hansch type hydrophobicity parameter, n, and the Snyder's P' po- larity indices [79]. The experimentally determined constants can be used as molecular descriptors for retention prediction in general. The theoretical approach seems to be very logical and supported by a large number of experimental data, but according to the author of the present chapter one of the early assumptions for the derivation is not always true.

Retention prediction ofpharmaceuticai compounds 79

Namely, the high correlation between the slope (8 and the intercept values (log k,,) can- not be expected, except for structurally related compounds [34]. The compound series investigated (substituted aromatic compounds) can be regarded as structurally related according to our investigations. The advantage of the approach is the application of two independent variables to describe the retention, which are not in correlation with each other and sufticiently good prediction can be achieved.

The other multiparameter approach which tries to include all three chromatographic variables (solute structure, mobile phase composition, and stationary phase properties) was published by Kaliszan et ul. [80,81]. A set of 12 substituted benzene derivatives with a wide range of substituent properties were selected for the investigations. Changes in composition of the methanol-water mobile phase ranged from 35 to 65% to assure the linear range of the log k versus organic phase concentration plot. A set of the equations (2.3) were investigated as a function of the solute ( i ) and stationary phase 0').

(2.35)

Using multivariate regression analyses, it was found that S!, and log k,,,i can satisfac- torily be described by a two-parameter equation involving the quantum chemically calcu- lated total energy of a solute, and its polarity parameters, defined as the maximum excess electronic charge difference in a molecule. An impressive agreement was found between the measured and the calculated retention data of the 12 solutes on three stationary phases and various mobile phase mixtures. As with all the multivariate approaches, this approach also has the limitation that it is valid only within the series of compounds investigated, which can be regarded as similar and simple in structure considering the wide variety of pharmaceutically active drug molecules. Increasing the number of measured data for a wider range of compounds can probably enhance the predictive power of the above-men- tioned quantitative structure-activity equations.

Another multivariate approach was introduced by Zou et ul. for predicting the S and the log k, values as important chromatographic retention parameters at which the reten- tion prediction can be carried out for various mobile phase compositions within the linear range. They suggested using the solvatochromic parameters as independent variables and solute descriptors. The foilowing molecular descriptors for the solvatochromic effect were suggested: V, as a cavity term, which measures the endoergic process of separating the solvent molecules to provide a suitably sized enclosure for the solute; n* measures the exoergic eXects of the solute-solvent dipoledipole and dipole-induced dipole dielectric interactions, B, and a, measure the exoergic effects of hydrogen bonding involving the solvent as a hydrogen bond donor acid and as a hydrogen bond acceptor base and the solvent as a base and the solute as an acid, respectively. V, can be estimated by simple additivity methods such as those of Bondi [84] or Abraham and McGowan [85 ] , n*, P, and am are solvatochromic parameters that can be found in a paper by Kamlet et ul. [86] or measured by UV, IR or NMR spectroscopic methods [87]. With the help of these pa- rameters, the following multivariate regression equations were suggested to predict the S and the log k, values:

(2.36)

References pp. 90-92

80 Chapter 2

where p i and qi (i = 1-5) are regression coefficients, derived using conventional linear regression analysis. With the help of Eqs. (2.36) and (2.37) the relative importance of the solvatochromic parameters for describing the variance of the important S and log k,,, re- tention parameters can be revealed. The authors [82] described significant correlations for a small number of substituted aromatic compounds in three different mobile phase sys- tems (methanol-water, acetonitrile-water, tetrahydrofurane-water). Table 2.8 shows the parameters obtained for Eqs. (2.36) and (2.37) in three different mobile phases. Table 2.9 shows the compounds investigated with their solvatochromic parameters. Table 2.10 re- veals the predictive power of the equations obtained by summarizing the experimental and the predicted log and S values and their differences referring to the acetonitrile- water mobile phases.

Unfortunately, only the data of 12 compounds were used to calculate the regression parameters of a multivariate equation with four independent variables, which makes the results questionable, and also the predictive power of the equations was not tested outside the series of compounds investigated. The differences in the regression parameters ob- tained (pi and qi) obtained with three different mobile phase are explained by the differ- ences in the Hildebrandt solubility parameters [88]. It was also found that the log val- ues extrapolated from the different binary mobile phase systems were not the same. The possible explanation may lie in the sorption of the organic modifiers in the stationary phase, and the extrapolated log values contain contributions from the cavity process and the adsorbed organic modifier. The method is worth considering for pharmaceutical compounds, but further evidence is needed for the underlying mathematical statistical significance of the theory.

Galushko [89] recently described a method for calculating the retention and selectivity in RP-HPLC based on the molecular structure of the analyte and the characteristics of the sorbents and mobile phases. The approach is based on solvophobic theory. The stationary

TABLE 2.8

THE PARAMETERS OF Eqs. (2.36) AND (2.37) AS WELL AS THE REGRESSION COEFFICIENTS WITH THREE DIFFERENT MOBILE PHASE SYSTEMS OBTAINED BY ZOU et al. [82]

Mobile p1 P2 P3 P4 P5 R phase

1 0.161 4.829 -0.1192 -0.5440 -3.417 0.983 2 0.355 3.664 0.0115 -0.4987 -2.841 0.991 3 1.104 2.428 -0.2731 0.1398 -2.307 0.953

41 42 43 44 45 R ~~ ~ ~~ ~ ~~

1 -1.029 -4.089 0.0859 0.1424 2.324 0.971 2 -1.060 -3.257 -0.2228 0.0026 2.263 0.962 3 -0.873 -3.858 -1.0555 -0.9422 3.325 0.962

Reprinted with permission from ref. 82. Mobile phases: 1 , methanol-water; 2, acetonitrile-water; 3, tetrahy- drofuran-water.

Retention prediction of pharmaceutical compounds 81

TABLE 2.9 SOLVATOCHROMIC PARAMETERS USED IN THE CORRELATION STUDY FOR Eqs. (2.36) AND (2.37) BY ZOU et al. [82]

Solute VJlOO ?c* Bm am

Aniline Acetophenone Anisole Benzaldehyde Benzene Benzonitrile Diethyl phthalate Ethylbenzene Methyl benzoate Nitrobenzene p-Nitrophenol Phenol n-Prop yl benzene

0.562 0.69 0.63 0.606 0.491 0.59 1.153 0.687 0.736 0.631 0.676 0.536 0.785

0.73 0.90 0.73 0.92 0.59 0.90 0.84 0.53 0.76 1.01 1.15 0.72 0.51

0.50 0.49 0.32 0.44 0.10 0.37 0.82 0.12 0.39 0.30 0.32 0.33 0.12

0.16 0.006 0 0 0 0 0 0 0 0 0.93 0.61 0

Reprinted With permission from ref. 82.

phase surface layer is regarded as a layer of a liquid hydrocarbon but as a specific layer containing surface-fixed alkyl radicals and some amount of mobile phase components. The basis of the theory is the general equation which describes the relationship between the retention (log k) and the free-energy change of solvation energies in the distribution system (AG).

-AG lnk=-+log(V, /Vm) RT

(2.38)

TABLE 2.10 COMPARISON OF EXPERIMENTAL DATA FOR LOG k, AND -5’ WITH VALUES CALCULATED FROM Eqs. (2.36) AND (2.37) WITH ACETONITRILE-WATER AS MOBILE PHASE ACCORDING TO ZOU et al. [82]

Solute 1% kw S

Exp. Calc. Diff. Exp. Calc. Diff.

Acetophenone 1.42 1.50 0.08 -2.28 -2.40 -0.12 Anisole 1.86 1.76 -0.10 -2.62 -2.55 0.07 Benzaldehyde 1.36 1.34 -0.02 -2.22 -2.24 -0.02 Benzene 1.86 1.88 0.02 -2.57 -2.56 0.01 Benzonitrile 1.54 1.48 -0.06 -2.44 -2.34 0.10 Diethyl phthal. 2.30 2.36 -0.04 -3.22 -3.15 0.07 Ethylbenzene 2.64 2.54 -0.10 -3.37 -3.14 0.23 Methyl benzoate 1.82 1.95 0.13 -2.61 -2.74 -0.13 Nitrobenzene 1.80 1.82 0.02 -2.66 -2.66 0 p-Nitrophenol 1.49 1.47 -0.02 -2.81 -2.79 0.02 Phenol 1.06 1.09 0.03 -2.19 -2.22 -0.03 nPropylbenzene 2.83 2.90 0.07 -3.27 -3.46 -0.19

Reprinted with permission from ref. 82

References pp. 9&92

82 Chapter 2

where V, lV, is the phase ratio. The energies required to generate a cavity of molecular size in the stationary phase layer and the mobile phase can be described by Eq. (2.39) according to Horviith and Melander [90].

(2.39)

where N is Avogadro’s number, A is the cavity surface area in the liquid, z is the surface tension, A l is the solvent molecule area and kel is the characteristic constant for every liquid [9 1,921.

Considering that the cavity shape is spherical the A molecular area values can be calcu- lated from the V, increments in partial molar volumes of fragments. A large set of experi- mental values of partial molar volumes for different compounds [93] and simple calcula- tion methods [94] are available. The van der Waals and electrostatic interactions also should be calculated for the estimation of AG. The author suggests that the molecule of a substance can be considered as consisting of dipoles, each of which separately interacts with the surrounding continuum. Thus, by using the dipole moment values, the effective radius of an imaginary sphere in which the dipole is located and epsil dielectric permit- tivity values, the interaction energy can be described. He says that such an approach does not need quantum chemical methods to calculate the atom charges. The bond dipole mo- ments are determined for almost all bonds for various compounds [95,96]. More pre- cisely, each dipole is not surrounded by a totally closed sphere of solvent molecules. The proposed approach is based on the assumption that in different compounds the parameters of a ball segment in which the same dipole is located vary within a small range, so that to

G, = NAz + NAl~(ke1- 1)

TABLE 2.11 INCREMENTS FOR THE FREE-ENERGY CHANGE ( A G e , s , ~ 2 0 ) FOR SOME DIPOLES ACCORDING TO GALUSHKO [89]

Dipole

csp2-H csp3-H csp2-csp3 csp2-csp csp3-csp C-O c=o C-N C=N 0-H (aromatic) 0-H N-H N-O N=O C-cl c-s

1.49 1.49 1.80 1.80 1.80 1.66 1.74 1.69 2.37 1.35 1.20 1.38 1.55 2.20 2.34 1.80

1.00 1 .oo 1 .oo 1 .oo 1.00 1 .oo 1.05 1.00 1.40 1.00 0.89 1 .oo 1 .oo 1.42 1.30 1.00

0.70 0.40 0.68 1.48 1.48 0.70 2.40 0.45 3.10 1.51 1.51 1.31 0.30 2.00 1.59 0.90

4.36 1.42 2.33 6.68

11.06 3.15

32.20 1.24

21.25 27.28 38.80 19.20 0.71

11.04 5.80 4.09

Reprinted with permission from ref. 89. aFor calculation of a, = (rl + r2)/2, the van der Waals radii (r) were used: c = 0.18; H = 0.117; 0 = 0.152; N = 0.15; Cl = 0.18 nm.

Retention prediction of pharmaceutical compounds 83

10

4

4 6 8 10 I n k f

Fig. 2.12. Comparison of the retention factors (Ink) in water on Merck RP-18 and ODs-Hypersil stationary phases. Compounds: 1, phenol; 3, nitrobenzene, 4, rn-dinitrobenzene; 6, chlorobenzene; 8, naphthalene; 9, benzophenone; 10, benzene. (Reprinted with permission from ref. 89.)

calculate the electrostatic energy, this parameter can be approximated by the effective radius of the sphere. However, a lot of parameters in the theoretical equation are not known. The author suggests measuring the retention data of a minimum of three model compounds differing in structure (i.e. benzene, phenol, benzophenone) on a given station- ary phases to estimate the stationary phase parameters. The paper [89] provides a list of parameters such as the increments of partial molar volumes for some fragments, free- energy change of increments for some dipoles, as can be seen in Table 2.1 1.

It was also found that retention data of ten substituted phenol derivatives obtained on two different reversed-phase stationary phases (Merck RP-18 and ODs-Hypersil) did not show correlation as can be seen in Fig. 2.12.

This problem can be overcome by the calculated stationary phase parameters from the retention of standard compounds. The predictive power of the equations and the theory was tested again on 32 substituted aromatic compounds. Some compounds showed large

Referencespp. 90-92

84 Chapter 2

TABLE 2.12 THE COMPARISON OF THE CALCULATED AND EXPERIMENTAL RETENTION DATA (Ink) OBTAINED BY GALUSHKO’S RETENTION PREDICTION METHOD [89] (STATIONARY PHASE: MERCK RP-18)

Compound In kcalc In kexp Difference

Aniline Dimethyl phthalate Phenol 2,4-Dimethylphenol Benzyl alcohol Quinoline Benzaldehyde Anisole o-Nitroaniline NJ-Dimethylaniline m-Nitrophenol Toluene 2-Phenylethanol Chlorobenzene m-Dinitrobenzene Diethyl 0-phthalate Benzonitrile Benzophenone 1 -Phenylethanol Ethylbenzene n-Nitroacetophenone Anethole 0-Cresol Diphenyl ether Acetophenone Biphenyl Nitrobenzene Naphthalene 3-Phenylpropanol Anthracene N-Methylaniline Benzene

2.63 4.84 3.10 5.13 3.26 5.13 3.80 6.20 2.34 7.38 2.74 5.86 4.22 6.08 4.14 6.40 4.00 6.57 3.91 7.12 4.01 8.60 4.30 8.18 4.47 8.34 4.45 7.17 4.85 9.22 5.08 4.95

2.94 5.09 3.13 5.22 3.26 5.58 3.72 5.77 3.81 6.26 3.89 6.27 3.89 6.44 3.99 6.46 4.00 6.96 4.04 7.38 4.18 8.13 4.23 8.58 4.34 8.91 4.42

11.81 4.94

12.84 5.01 4.95

0.31 -0.25

0.03 0.09

-0.45 -0.08

0.43 -1.47

1.12 -1.15 -0.41

0.33

0.15 -0.06

-0.39 -0.13 -0.26 -0.17

0.47 0.07

-0.40 0.13

-0.57

-4.64 -0.09

0.07

-

-0.36

-

-

-3.62

-

Rreprinted with permission from ref. 89.

deviations between the measured and predicted retention values as shown in Table 2.12. This was attributed to the effect of the neighbouring substituents which was not taken into account in the calculations; for example the decrease in the interaction of a molecule with water produced by an intramolecular hydrogen-bond in the case of o-nitroaniline.

The suggested method seems to be promising, but as it is difficult to obtain the neces- sary parameters for pharmaceutical molecules, the estimation of the stationary phase pa- rameters seems to be a bit uncertain. Figure 2.13 shows the determination of the station- ary phase parameter on the basis of four model compounds. It is not completely clear from the published paper whether the two arbitrary z values mean two different mobile phase compositions for the estimation of dielectric permittivity, and if three values are considered whether they are on a single straight line or not.

Retention prediction ofpharmaceutical compounds 85

f(€,)

0.5

0.4

0.3

Ic

2 0 4 0 6 0 T3

Fig. 2.13. Determination of the stationary phase parameter of Merck RP-18 stationary phase (Reprinted with permission from ref. 89.)

Also the predictive power of the theory was not tested on pharmaceutical compounds, and the effect of the neighbouring substituents can cause significant deviations in the predicted retention. The advantage of the method would be that it does not require pre- liminary experiments, only the determination of the stationary phase characteristics.

More reliable and general prediction methods are based on experimental retention val- ues. In this case, the retention data of a given compound series are determined on a given stationary phase, with given mobile phase mixtures and additives. The retention predic- tion is based on the retention data obtained under slightly different chromatographic conditions, so the retention change in the compounds can be monitored, a function can be set up, and the retention prediction can be carried out using these functions. One of the most well-known methods is used by the DryLab program, developed by Snyder [97], for mobile phase optimization. The retention prediction is based on the experimentally meas- ured retention parameters of the compounds by using two different gradient runs on a given column. The difference in retention parameters obtained by a slower and faster gradient run will reveal the slope (3 values of the compounds, namely the sensitivity of the retention to the mobile phase composition. The absolute values of the retention give

References pp. 90-92

86 Chapter 2

information about its log k, values. On the basis of these two values, the retention can be predicted within reasonable (linear) range of organic phase concentration applied in isocratic mode.

Another interesting method which was developed also for optimizing a chroma- tographic separation is the “Prisma” method described by Nyiredi et al. [98]. In this model the solvent composition is characterized by the solvent strength (S,) and the selec- tivity points (P,). At constant solvent strength, the correlation between the selectivity points and the retention was described by a quadratic function. For constant selectivity points, the solvent strength and retention data correlate with logarithmic function. These correlations are used to formulate a mathematical model for the dependence of retention times (retention fdctors) on the mobile phase composition. Unknown compounds are es- timated in the mathematical model from a sequence of standard chromatograms after having identified individual peaks by an automatic procedure. Only retention times, rela- tive peak areas, and information about the mobile phase compositions are required as input for the peak identification. The peak identification procedure involves a combina- tion of statistical methods which exploit both the basic properties of retention data and the mathematical relation between retention data, selectivity points and solvent strength as derived from the “Prisma” model (Fig. 2.14).

The mathematical model completed by the estimated constants predicts the expected retention times for each possible mobile phase composition. Peak start and peak end times are predicted in a similar way to the retention times, once the identification is per- formed. The most important aspect of a chromatogram can thus be predicted for arbitrary mobile phase compositions. The information required for peak identification and mobile phase optimization is derived from a series of chromatograms generated from the same sample by varying the mobile phase composition according to a standard scheme derived from the “Prisma” model [99]. On the basis of the results obtained from the preliminary experimental runs, a set of equations for the retention surfaces, which relate to the reten-

Fig. 2.14. The regular part of the “Prisma” model for RP-HPLC. ST^ stands for solvent selectivity points and Ps stands for the selectivity points. At a constant ST the correlation between the Ps and the retention data (horizontal function) can be described by a quadratic function. For constant Ps the solvent strengths and reten- tion data correlate (vertical function) with a logarithmic function. (Reprinted with permission from ref. 98.)

Retention prediction of pharmaceutical compounds 87

tion time for each peak with the mobile phase composition, is generated. Apart from the above-mentioned mathematical functions, no other assumption is used. The method re- quires 7-14 measurements depending on the mobile phase additive. For a ternary system, more preliminary measurements are needed than for the binary system. The suggested method is extremely advantageous for the development of the optimal separation of the components of biological extracts (for example plants) and identification of the peaks. Retention prediction is made only over the experimentally checked range of chroma- tographic conditions, so it is reliable.

In conclusion, the retention prediction methods based on multivariate statistical analy- sis should be based on strong theoretical backgrounds and sufficient amounts of experi- mental data. It is always advisable to check whether the mathematical statistical parame- ters of the equations used for the retention predictions are significant or not and at what level. The theoretical basis of the equation used for the predictions reveals the predictive power of the relationships, whether it is valid for structurally related or unrelated com- pounds. It also should be checked how the chromatographic conditions (mobile phase and stationary phase) influence the prediction. From the approaches presented above, it is clear that a general quantitative structure-retention relationship for describing chromato- graphic retention for a wide range of compounds in a wide variety of chromatographic conditions is still not known. Much higher accuracy in prediction can be achieved when only structurally related compounds are considered under certain chromatographic condi- tions.

2.9 APPLICATIONS OF RETENTION PREDICTIONS OF PHARMACEUTICAL COMPOUNDS

High performance liquid chromatography is gaining wider and wider application in phar- maceutical analysis [loo]. The application of chromatography starts with the design of new drug molecules [ 10 11, involving metabolite research, pharmacokinetic investigations, toxicity measurements, drug delivery and formulation research, and quality control in every step of the manufacturing process. Therefore, the prediction of the chromatographic retention of pharmaceutical compounds is of great importance. A few approaches pre- sented in this chapter were used to develop computer expert systems for promoting the application of HPLC in the pharmaceutical industry.

The ELUEX expert system developed by CompuDrug Chemistry Ltd. (Budapest, Hungary) suggests an initial mobile phase composition for the very first chromatography of a drug molecule [102,103]. The prediction is based on Eqs. (2.12) and (2.13). On the basis of the calculated log P values from the fragments of the chemical structure of the molecule, the organic phase concentration in the mobile phase can be estimated at which the retention time of the compound will double the dead time. As the calculation of the hydrophobicity (octanol-water partition coefficients, log P) of the molecules is more or less solved, its capability and error are well known. Also Eqs. (2.12) and (2.13) were de- rived from the retention data of structurally unrelated pharmaceutical compounds ob- tained on various reversed-phase stationary phases and mobile phase compositions. It seems from the theoretical background [28], that the relationship is valid in general, as the

References pp. 90-92

Chapter 2 88

chromatographic partition system is optimized to be the most similar to the octanol-water partition system, when the Collander type of relationship is valid [64]:

log K = a log P + b (2.40)

where P is the octanol-water partition coefficient of a compound, K is the partition coef- ficient of a compound obtained in a different partition system, a and b are constants. Leo [57] revealed the limitation of the above equation, namely it is valid only for structurally related compounds or similar partition systems. When the chromatographic partition sys- tem is set up to be similar to the octanol-water partition system, Eq. (2.40) is also as- sumed to be valid for structurally unrelated compounds. From the above considerations, it is clear that accuracy of the prediction of the mobile phase composition for the given re- tention of the pharmaceutical compounds will be higher when more related compounds are considered, or the chromatographic system is more similar to the octanol-water parti- tion system. In the most general case, the error of the prediction was less than 10% or- ganic phase concentration, which is still acceptable for a method which does not require any preliminary experimental data at all. The accuracy of the prediction can be enhanced by application of experimental data. On the basis of three experimental results, the expert system can carry out optimization for the required separation of a mixture of pharmaceu- tical compounds. The flow chart of the expert system is presented in Fig. 2.15.

CHEMICAL STRUCTURE J J

J J.

Sekchbn of mobile phase log P cakuhtion pH and additives

Basicgroups + p H = 7 . 8 &,cakuhtion + TBAH

Bothackiicandksic-+ p H = 2 estimation

Noneofthem + no buffer necessary

Acidicgroups -+ p H = 2 5.

+ion pair of organic phase volunu

J. First trial

goodpcak shape bad peak shape

Bask + pH=7.8+TBAH +pH=2+ionpOir

Acidic-, pH=2.0 + p H = 8 + TBAH

Both -, pH = 2.0 + ion pair + by wn-crchange

None -+ no buffer + tuUingpH = 7.8 leading pH = 2.0

J 4

Fig. 2.15. The rule system of the ELUEX expert system for predicting the initial mobile phase composition for the separation of drug mixtures with known chemical structures. (Reprinted with permission from ref. 103.)

Retention prediction ofpharmaceutical compounds 89

The second most important application of retention prediction is its use for mobile phase optimization. The most reliable optimization methods are based on experimental data. As discussed above, the basic relationship for mobile phase optimization is the de- pendence of the retention factor on the mobile phase composition. Within a limited range, the linear relationship between the logarithmic retention factor (log k) and the organic phase concentration (OP% or 9) is valid. The slope (S) and the intercept (log b) values of the straight lines can be used for calculating the log k values at arbitrary mobile phase compositions. This means that any prediction method for the S and log ko values are of great importance in retention prediction and mobile phase optimization. It was shown that molecular modelling and quantum-chemical parameters can be related to S and log ko. The accuracy of the prediction is, however, very low. Much higher accuracy can be achieved by applying experimental data, for example, as suggested by DryLab software. The retention measurements applying a slower and a faster gradient run (linear increase in the organic phase concentration of the mobile phase). This can reveal more reliable S and log ko values at which the mobile phase optimization can be carried out on the same col- umn and same type of organic modifier.

Another purpose of the retention prediction can be the identification of a compound through its chromatographic retention This requires much higher accuracy in retention prediction. An interesting application of retention prediction was developed for promot- ing the identification of metabolites (HPLC-MetabolExpert, CompuDrug Chemistry, Bu- dapest, Hungary). The retention prediction is based on a database containing more than 400 hundred possible metabolic transformations. Based on experimental data, retention increment values are compiled for each metabolic transformation. From these data, the change in the retention of the metabolite compared to the mother compound is predicted. The accuracy of the retention prediction is increased by the application of measured re- tention data of a mother compound and the application of only one or two retention in- crement values. The method is not applicable for predicting the retention of compounds from the increment values only. The accuracy of the prediction is limited by neglecting the effect of the mobile phase composition and stationary phase differences from different manufacturers. But it was shown [69] that neglecting the neighbour effect can cause much bigger errors in the retention prediction. In spite of these limitations, the expert system with its theoretical background can be used for predicting the reversed-phase HPLC re- tention of metabolites under given chromatographic conditions. It can help to develop analytical methods possible with hyphenated techniques (HPLC-MS) for the identifica- tion of metabolites of newly synthesized compounds.

The fourth application of retention prediction methods can be the estimation and measurement of chromatographic hydrophobicity indices of pharmaceutical molecules. It is well known that the hydrophobic properties of drug molecules are very important in their absorption, delivery, distributions and drug-receptor binding, etc. The measurements of partition coefficients are very time consuming and require special analytical techniques for the concentration determination of molecules in both partitioning liquids. Often chro- matographic methods are applied for the concentration determination. The new chroma- tographic hydrophobicity index [28] suggested recently, provides a relatively easy meas- urement of hydrophobicity of drug molecules, independent from the mobile phase com- position and from the origin of the reversed-phase stationary phase. The index ranges

References pp. 90-92

90 Chapter 2

from 1 to 100, and it means the volume percent of the organic phase, at which the log k values of the compounds are zero (i.e. the retention time is double the dead time). The hydrophobicity index values are dependent only on the type of the organic phase, the pH and the temperature. They also show significant correlation to the octanol-water partition coefficients. They can be used for retention prediction and mobile phase optimization.

Finally, the development and application of retention prediction methods can reveal the mechanism of chromatographic retention, which is still not clearly understood. The search for important molecular properties in the retention is still going on. Understanding the chromatographic retention of compounds helps not only retention prediction, but also the development of the chromatographic conditions for pharmaceutical analysis and the design of new stationary phases. A knowledge of the retention mechanism also helps the optimization procedure and hopefully at the end of the day, the chromatographic method developed will not be a trial and error method, but can be computerized, automated com- pletely, even to include the method development.

2.10 ACKNOWLEDGEMENTS

The author gratefully acknowledges support from the Maplethorpe Fellowship at the Department of Pharmaceutical Chemistry, School of Pharmacy, University of London. I thank Dr. Robert Watt for careful reading of the manuscript and valuable comments. The encouragement during the work by Professor William Gibbons is also gratefully appreci- ated.

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