Yoshihiro Saito

One of the major goals in separation science is to understand the mechanisms that govern the retention of solutes in a particular chromatographic system. Quantitative structure–retention relationships (QSRR) are useful in this respect.

  They are statistically derived relationships that relate chromatographic parameters determined for a group of analytes and the quantities or descriptors accounting for the structural differences among the analytes tested. The descriptors in QSRRs are properties of compounds that are related to their structures and can be generated for molecules with similar structural features to quantify their molecular characteristics.

  These descriptors can be constitutional, geometric, topological, electronic and physicochemical. QSRR models are not only useful as tools for optimization strategies, but also for gaining insights into the molecular mechanism of separation in chromatography.

Most QSRR models were derived for reversed-phase liquid chromatography (RPLC) because this technique is still the most widely used separation method. Bonded-silica stationary phases remain the first choice for most RPLC separations.

  However, it is not always the best one, particularly for separating some polar compounds, which often show inadequate retention or broad tailing peaks.

  Polar compounds also require highly aqueous mobile phases to achieve adequate retention on RP columns, which can cause problems such as dewetting of the stationary phase and decreased sensitivity in electrospray ionization mass spectrometry.

An alternative approach to effectively separate small polar compounds on polar stationary phases is hydrophilic interaction chromatography (HILIC).

  This is a variant of normal-phase liquid chromatography (NPLC), but the nonaqueous mobile phase in NPLC is replaced with an aqueous–organic mixture with water being the strongest eluting solvent.

  Polar analytes are separated in HILIC by passing aqueous–organic mobile phases across a polar stationary phase such as silica, cyano, diol, which causes solutes to elute in order of increasing hydrophilicity, which is the opposite of the RPLC mechanism.

The main objective of this study is to develop QSRR models that will describe the retention behaviour of the adrenoreceptor agonists and antagonists on a polyvinylalcohol (PVA)-bonded stationary phase operated in the HILIC mode. These drugs are widely used to treat several medical conditions such as hypertension, angina pectoris, arrhythmia and congestive heart failure, and asthma.

  These analytes are polar compounds containing basic amino groups, which makes them good candidates for separation by HILIC. 

 Hydrochloride salts of alprenolol, isoxsuprine, methoxamine, midodrine, oxymetazoline, phenylephrine, propranolol, ritodrine, and sotalol; free base form of carvedilol, nadolol; and pindolol, timolol maleate, metaproterenol hemisulfate and metaprolol tartrate were all from Sigma-Aldrich (Japan). Betaxolol hydrochloride and atenolol free base were purchased from Tocris (Ellisville, MO, USA). Acebutolol hydrochloride was obtained from MP Biomedicals, Inc. (Germany), and bambuterol hydrochloride and salbutamol free base were from LKT Laboratories Inc. (Japan). Acetonitrile used for the preparation of mobile phase and methanol used for sample preparation were of HPLC grade were purchased from Wako Pure Chemical Industries (Japan). Water was purified by a Milli-Q Water Purification System (Millipore, Japan). Ammonium formate and formic acid were also obtained from Wako Pure Chemical Industries. A 0.2 μm disposable nylon filter was obtained from Toyo Roshi Kaisha (Japan). 

Preparation of standard solutions and mobile phase.

 Standard solutions of 0.1 mg/mL concentration were prepared from the stock solutions (1.0 mg/mL) obtained by dissolving accurately weighed amounts of each compound in methanol. All standard solutions were filtered using a 0.2 μm disposable nylon filter prior to chromatographic analysis. Mobile phases were prepared in this manner. First, 100 mM stock solution of ammonium formate was obtained by dissolving approximately 63.07 mg ammonium formate in 95 mL purified water. The pH of the resulting solution was adjusted to the desired pH using 1.0 M formic acid solution and then transferred into a 100 mL volumetric flask and diluted up to the mark with purified water. The pH of the final solution was checked again and adjusted to the desired pH with formic acid if necessary. Appropriate amounts of acetonitrile and the buffered aqueous phase were mixed thoroughly and degassed for 5 min to obtain the mobile phase. The final concentration of the buffer was kept at 10 mM for all mobile phases used in the chromatographic procedure. 

 The chromatograph was a Jasco PU-980 Intelligent HPLC Pump (Jasco, Japan) equipped with a Rheodyne 7125 injector (Cotati, CA, USA) with a 20-μL sample loop and a Tosoh UV-8010 UV-Visible (UV-vis) detector. Separation of the analytes was performed on YMC-Pack PVA-Sil (PVA-bonded column; 5 μm, 250 mm=2 mm i.d.) purchased from YMC Co. Ltd. (Japan). Column temperature was maintained using an oven (Tosoh CO-8000, Japan). 

Determination of retention for QSRR studies.

 The retention of the analytes on the PVA-bonded column was measured using acetonitrile/buffer as mobile phase by an isocratic elution at 40 °C. The composition of the mobile phase was kept at 90:10 (acetonitrile–buffer) to give an HILIC mode of separation and to ensure adequate retention of all analytes. The mobile phase was pumped into the column at the rate of 0.20 mL/min for at least 1 h before testing to allow the column to reach the set temperature and to achieve a stable baseline. A constant volume of the analytes (20 μL) was injected manually using a 100 μL micro syringe. Chromatographic peaks were monitored at 225 nm for all analytes except timolol, which was measured at 300 nm. All measurements were performed in triplicates. Data acquisition was performed using Borwin Chromatography Data Handling Software (Jasco) running on a PC. 

The parameters involved include the logarithm of the retention factor (

) of the compounds as dependent variables while the molecular descriptors were used as independent variables. A total of 36 constitutional, geometric, electronic, topological and physicochemical descriptors were calculated using the software Cerius (Accelrys, Japan) and the free online version of PreADMET (http://

). As most of the molecular descriptors are highly correlated with each other, the number of descriptors applied to the actual regression analysis was reduced in the following manner.  

First, the descriptors were correlated with each other and then with 

. Descriptors were selected based on their correlation coefficient value with other descriptors and with 

. When the correlation coefficient of two descriptors is greater than 0.90, both are highly correlated with each other. The descriptor showing a higher correlation with 

 is used for the actual analysis, leaving out the descriptor showing a lower correlation. By performing this variable selection method, information overlap in descriptors is minimized and cross-correlation of predictors in the final regression model is prevented. After performing the selection method, the number of molecular descriptors was reduced from 36 to 14. In this study, a forward stepwise multiple linear regression (MLR) procedure using SPSS Version 12 for Windows (SPSS Inc., Chicago, IL, USA) is applied to the data for each pH value. The 

 values of the compounds were regressed with the 14 molecular descriptors. The optimal number of predictors and the best regression equations were selected on the basis of the following statistical parameters:   

square of the multiple correlation coefficient (

the significance of individual descriptors (

The predictive ability of the derived MLR models was tested by using leave-one-out cross validation (LOO-CV) procedure. 

In this study, QSRR models for the adrenoreceptor agonists and antagonists on a PVA-bonded stationary phase were derived using forward stepwise MLR. The 

 values of the analytes and the molecular descriptors were used as the dependent and independent variables, respectively, in deriving the MLR equations. Table 1 summarizes the derived MLR equations and the statistical parameters 

 standing for the cross-validation coefficient of determination), 

. As can be seen, at each pH value the retention of the studied compounds on the chromatographic system can be adequately described by four predictors. At pH 3.0, 4.0 and 5.0, the retention of the analytes was found to be dependent on the compound's logarithm of the partition coefficient (

). At pH 6.0, however, the predictors were 

 and the energy of the lowest unoccupied molecular orbital (

). As listed in Table 1, the relatively high values of 

 indicate that the derived models show adequate fits. 

Table 1: Multiple linear regression equations derived from the training set using forward stepwise regression. 

The predictive property of the derived MLR equations was assessed using the LOO-CV technique. In LOO-CV, one case is taken out of the entire data set of size 

 as the hold-out or validation case. The 

 cases are then used for model building and the resulting model is used to predict the hold-out case. This entire process is repeated so that each case becomes the hold-out case. The overall model fit is then assessed by putting together the hold-out predictions. The 

 values in Table 1 represent the coefficient of determination for the prediction of the hold-out cases. In all pH conditions, 

 , indicating good predictive properties of the derived MLR models. In Figures 1(a)–1(d), the plots of cross-validated 

 were superimposed to the plots of the predicted 

 calculated based on the derived equations (fitted 

. It is clearly seen in the plots that almost all of the cross-validated 

 values. Although there are some differences between the fitted and cross-validated 

 values, none are severe enough to indicate extreme leverage point, indicating that the derived models have good predictive abilities. 

Figure 1: Plots of the predicted versus observed  log k for (a) pH 3.0; (b) pH 4.0; (c) pH 5.0; and (d) pH 6.0. Lines represent regression when predicted log k is equal to observed log k. 

The derived MLR equations are not only useful for predicting the retention of the compounds being studied. Insights concerning the factors responsible for the retention behaviour of the analytes on the PVA-bonded phase are also reflected on these models. Incorporating the molecular descriptors as predictors of retention can give tentative conclusions on the possible solute–stationary phase interactions present in the chromatographic system. The coefficients of the predictors in the MLR equations only reflect the original units in which the variables were measured, thus, the relative effects of the descriptors on the retention of the analytes cannot be assessed by these coefficients. Conversely, the standardized coefficients (β) of the predictors give the number of standard deviations change on the dependent variable that will be produced by a change of one standard deviation on the descriptor concerned. The magnitude and sign of β can be used to describe the relative effect of each predictor on the dependent variable, 

. Table 2 summarizes the β value and significance of each predictor in the derived MLR equations. As listed in Table 2, all predictors were significant at 95% confidence interval. 

Table 2: Standardized coefficients and significance of each predictor in the derived MLR equations. 

Among the predictors that were included in the MLR models, 

 has the highest value in all pH conditions as shown in Table 2. The number of 

 can be interpreted as the ability of the solute to interact with the stationary and mobile phases through hydrogen bonding. The compounds being analysed contain functional groups such as hydroxyl and amino groups that can act as both hydrogen bond acceptors and donors, while the PVA-bonded phase contains hydroxyl groups, which are also capable of hydrogen bond formation. Based on these, the solute and the stationary phase can interact with each other through the formation of hydrogen bonds, and this explains the inclusion of 

 compared with the other predictors, especially at pH 3.0, 4.0 and 5.0, may indicate that hydrogen bond interaction is the predominant mechanism involved in the retention of the analytes. It is not clear, however, why the number of hydrogen bond acceptors was not included as a significant predictor of retention. It is possible that hydrogen bonding interactions between analytes as 

 and the stationary phase as hydrogen bond acceptors predominate over hydrogen bond interactions between analytes as hydrogen bond acceptors and the stationary phase as 

. This is consistent with the reports of Park 

. on polar-bonded phases and silica used in NP separations,

  but further studies must be undertaken to confirm these findings. 

 both pertain to the hydrophobic/hydrophilic character of a molecule. The inclusion of these descriptors indicates hydrohilic or hydrophobic interaction as another mechanism of retention in the chromatographic system being studied. 

, defined as the effective partition coefficient for dissociative systems, is the ratio of the equilibrium concentrations of ionized and un-ionized species of a molecule in 1-octanol to the same species in the water. 

 (1-octanol/water partition coefficient) in that the latter only considers the un-ionized form of the molecule. 

 because the analytes having basic amino groups are ionizable at the working pH conditions. 

, is a measure of the hydrophobic or hydrophilic character of a compound. A compound having a high 

 value indicates that the compound has high hydrophobicity or low hydrophilicity and 

. The chromatographic system being studied was operated in the HILIC mode, thus, in this system the more hydrophilic (low 

 value) the compound is, the longer it is to be retained in the stationary phase. Table 2 shows that the β for 

 is inversely proportional to the retention of the compounds. This is consistent with the stated fact that compounds with high 

 values have low hydrophilicity and, therefore, low retention under HILIC mode.

 in the MLR equations for all pH values may signify the involvement of ionic interaction between the analytes and the stationary phase and/or mobile phase. The PVA-bonded stationary phase does not contain ionizable groups that can interact with the ionizable analytes, therefore, the only possible ionic interaction that can occur is between the analytes and the residual ionized silanol groups of the stationary phase. In the present case, ionic interaction is possible because the analytes, having pKa values between 8.5–10, are positively charged at the working pH conditions while the residual silanol groups of the stationary phase are negatively charged at pH above 4.0. 

As can be seen from Table 2, the contribution of 

 as a predictor of retention increases as the pH increases, as indicated by its β values, the highest of which is observed at pH 6.0. This signifies that ionic interaction between the analytes and the residual silanol groups of the stationary phase is more effective at pH 6.0 presumably because at this pH value the silanol groups are most ionized.  

 are very close to each other as compared to the other pH values wherein the value for 

 is significantly higher than the other predictors. This may indicate that at pH 6.0 the present of hydrophilic interaction, hydrogen bonding and ionic interaction affect the retention of the analytes to almost the same degree. The inclusion of 

 as a predictor at pH 6.0 further supports the role of hydrogen bonding interaction as one mechanism of retention in the studied system because this descriptor may be interpreted as the hydrogen bond accepting ability of a molecule. 

The derived QSRR models were found to be adequate in describing the retention of adrenoreceptor agonists and antagonists on PVA-bonded stationary phase operated in the HILIC mode. The retention of the analytes on the chromatographic system is dependent on the molecular descriptors of the compound namely, 

. The incorporation of these molecular descriptors in the QSRR models revealed hydrogen bonding, hydrophilic and ionic interactions as possible mechanisms of retention of the analytes.  

 is a doctoral student at the School of Material Science, Toyohashi University of Technology (Japan), and currently an assistant professor in the Department of Physical Sciences and Mathematics, College of Arts and Sciences, University of the Philippines (Manila, Philippines). 

 is a doctoral student at the School of Material Science, Toyohashi University of Technology, and currently an assistant professor in the Department of Pharmaceutical Chemistry, College of Pharmacy, University of the Philippines (Manila, Philippines). 

 is an assistant professor in the School of Material Science, Toyohashi University of Technology (Japan). 

 is a professor in the School of Material Science, Toyohashi University of Technology, and vice president of the same school. 

1. M. Karelson, M. Lobanov and A.R. Katritzky, 

2. R. Kaliszan, "Methodology of Quantitative Structure-Retention Relationship Analysis" in Quantitative Structure-Chromatographic Retention Relationships (John Wiley and Sons, New York, NY, USA, 1987) pp 69–79.  

Yoshihiro Saito

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