Quantitative Structure Pharmacokinetic Relationship Studies for Drug Clearance of Quinolone Drugs
Yash Paul^{1}, Avinash S. Dhake^{2}, Milind Parle^{3} and Bhupinder Singh^{4*}
^{1}Lord Shiva College of Pharmacy, Sirsa (Haryana), India.
^{2}L.B. Rao Institute of Pharm. Education and Research, Anand, Gujarat, India.
^{3}Guru Jambheshwar University of Science & Technology, Hisar (Haryana), India.
^{4}Univ. Institute of Pharm. Sciences, Panjab University, Chandigarh, India.
* Corresponding Author Email bsbhoop@yahoo.com
ABSTRACT
Quantitative Structure Pharmacokinetic Relationships (QSPR) studies tend not only to establish the quantitative relationships between structural properties and the pharmacokinetic parameters of new compounds, but also provide great help for better elucidation of factors influencing the pharmacokinetic fate of drugs. Clearance (CL_{tot}) value is one of the most imperative pharmacokinetic parameters related directly to dispositional characteristics of drug(s). It can be used to determine the dosing rate and steady state concentration of a drug in clinical pharmacokinetics. The current study was conducted to investigate QSPR for CL_{tot} values in man amongst 24 quinolone drugs employing extrathermodynamic approach. Analysis of several hundreds of QSPR correlations developed in the current study revealed extremely high degree of crossvalidated coefficients (Q^{2}) using leaveoneout (LOO) method (p<0.001). CL_{tot} shows positive liner dependence on topological parameters (e.g., BLI and negative liner dependence on electrostatic parameters (e.g., Qmax, QOmax, QmaxQmin). Influences of lipophilic parameters like log P, geometrical parameters like ZXS/ZXR and constitutional parameters like Cn and Brel was also noticed during multiparameter studies. The joint dependence of clearance values on topological and electro parameters signifies the importance of diffusion and ionization of quinolones drugs in vivo. The overall predictability was found to be quite high (R^{2}=0.9132, F=26.78, S^{2}=6.72, Q^{2}=0.7256, p<0.001). Logarithmic transformation of clearance did not yield much improvement in the significance of correlations, but the inverse transforms showed improved correlation (R^{2}=0.9332, F=34.52, S^{2}=0.0014, Q^{2}=0.8136, p<0.001).
KEY WORDS Quantitative structure pharmacokinetic relationships (QSPR), clearance, ADME. .
INTRODUCTION:
After the first decade of QSAR in mid 1970s, it was vivid that relationship derived from a series of compounds investigated in isolated systems did not apply to in vivo situations. Hence, it was realized that Absorption, Distribution, Metabolism and Excretion (ADME) processes of a drug were important determinants, as these modulated the concentrationtime profile of the drug substances at the drug receptor site.^{1 }Good amount of work, therefore, has followed on the establishment of relationships between structural descriptors and pharmacokinetic parameters/properties of a drug. Being able to predict ADME properties quickly using computational means is of great importance because experimental ADME testing is both expensive and arduous yielding low throughput. The use of computational models in the prediction of ADME properties is growing rapidly in drug discovery,
as immense benefits they provide in throughput and early application of drug design^{2}.
The CL_{tot} value of a drug is a crucial pharmacokinetic parameter because it is directly related to the bioavailability and drug elimination and can be used to determined the dosing rate and steadystate concentration of a drug.^{3} Hence it is important to predict the CL_{tot} value of drug leads during drug discovery so that compounds with acceptable metabolic stability can be identified and those with poor bioavailability can be eliminated. Traditionally, the CL_{tot} value of a drug candidate is obtained via in vivo studies, which tends to be quite arduous, time consuming and expensive. Therefore, a computational QSPR modeling method, has recently been explored for predicting the CL_{tot} value of drug candidates in an effort to eliminate undesirable agents in a fast and costeffective manner.^{47 }The primary aim of QSPR studies is to enable the drug designer to modify the chemical structure of a pharmacodynamically active drug in such a manner as to alter its pharmacokinetic properties without diminishing its pharmacodynamic polental.^{8} The major advantage of QSPR lies in the fact that once such a relationship is ascertained with adequate statistical degree of confidence, it can be a valuable assistance in the prognosis of the behavior of new molecules, even before they are actually synthesized.^{ }An early assessment of ADME properties will help pharmaceutical scientists to select the best drug candidate for development as well as to reject those with a low plausibility of success.^{9} Also, not only these QSPR techniques tend to save considerable amount of time, money, animal life and involvement of “normal, healthy and drugfree human volunteers” required for conducting the experimental pharmacokinetic studies, but also the expertise of pharmacokinetists and drug designers.^{1}
The key objective of current study was to establish the quantitative relationship(s) of high prognostic relevance amongst the structural parameters (i.e., descriptors) and drug clearance values of various quinolone antimicrobial drugs. Quinolones were chosen for QSPR as; this category of drugs has extensively used as antimicrobial agents in the treatment of serious infections. Also, quinolones consist of significant number of compounds thoroughly investigated for their pharmacokinetic performance particularly CL_{tot }(n=24). Further, the congeners in this class have many common pharmacokinetic characteristics, mechanism and degree of affinity with body tissues, etc. Moreover, descriptors like experimental values of Log P, melting point, etc. of these drugs are known and are available in standard tests or journals.
Construction of QSPR
Construction of a typical QSPR involves pharmacokinetic parameters, structural parameters (descriptors) and statistical techniques (Fig.1).
Fig. 1. Quantitative StructurePharmacokinetic Relationship (QSPR): A Multidisciplinary Endeavor
QSPR was conducted amongst various quinolone drugs employing extrathermodynamic Multi Linear Regression Analysis (MLRA) approach. The QSPR correlations were duly analyzed using a battery of apt statistical procedures and validated using leaveoneout (LOO) approach.
The reported values of CL_{tot} of the quinolone drugs in humans were taken from the literature.^{1114} In order to ensure that experimental various in determining CL_{tot }does not significantly affect the quality of our datasets, only CL_{tot} values obtained from healthy adult males after oral administration were used for constructing the dataset. A total of 24 quinolone drugs were selected for this study. CL_{tot} values of these compounds were also logtransformed (log CL_{tot}) and inverse transformed (1/CL_{tot}) to normalize the data and to reduce unequal error variance.
Lipophilic and dissociation parameters viz. Log P, pKa and Log D of various quinolone drugs were calculated using Pallas 2.0 software. Chemical structures were drawn using suitable templates under Chem3D software pro v.3.5. (Cambridge Soft Corporation, Cambridge, MA) and HyperChem software. Energy minimization was carried out using MM2 force field routine(s) and the files were saved as MDL molfiles. Molfiles generated by Chem3D were exported to DRAGON software, and as many as 1497 diverse descriptors, viz. constitutional, geometrical, topological, Whim3D, electronic, etc. were calculated. Molfiles were also transferred to CODESSA (Semichem, Shawnee, USA) software for calculation of 165 more molecular descriptors.
Multivariate statistical analyses
Attempts were made to correlate lipophilic, constitutional, electrostatic, electronic, topological and steric descriptors with the CL_{tot }values. The initial regression analysis was carried out using heuristic analysis followed by best MLRA (RGMS) options of CODESSA software. In case of the heuristic method, a preselection of descriptors was accomplished. All the descriptors were checked to ensure that value of each descriptor was available for each structure and there is a significant variation in these values. Descriptors for which values were not available for every structure in the data in question were discarded. Thereafter, the oneparameter correlation equations for each descriptor were calculated. The number of descriptors in the starting set was further reduced by discarding them if:
¯ The F value for oneparameter correlation with the descriptor is < 1.00.
¯ The r^{2} value of oneparameter equation is less than assigned value of r^{2}_{min} (usually 0.10).
¯ The oneparameter tvalue is less than the assigned value (usually 1.50).
¯ The multiparameter tvalue is less than the assigned value (usually 1.95).
¯ Descriptors are highly intercorrelated with another descriptor (r^{2 }> 0.65).
Log P_{o/w} Wiener index, Balaban index
Dipole moments Polarity Parameter (q_{min}q_{max})
Molecular weight Molar volume (MV)
Taft’s steric parameter Molar refractivity (MR)
Number of atoms
Number of bonds
Number of rings
Data of pharmacokinetic parameters of CL_{tot} available for 24 quinolones were analyzed, limiting the ratio of descriptors: drug to 1:4.
As a final result, the heuristic method yields a list of the best ten correlations each with the highest r^{2} and Fvalues. Many such attempts were carried out to obtain significant correlations for quinolones. A set of important descriptors found to significantly ascribe the variation of CL_{tot}, was constructed. Further, a search for the multiparameter regression with the maximum predicting ability was performed. A number of sets of descriptors were thus made and MLRA performed with CL_{tot}. Regression plots of each correlation thus attempted were examined. Residual plots were also examined for absence of randomization and distinct patterns to eliminate chance correlations. Logarithmic and inverse transformations of CL_{tot} were also carried out in order to screen the correlation with improved values of R^{2} and/or F ratio.
The statistical significance of each correlation was determined on the basis of the value of Fcriterion and the magnitude of crossvalidated R^{2}, commonly referred to as Q^{2}, calculated according to Eq. no.1.
… (1)
A model with good predictive performance has a Q^{2 }value close to 1, models that do not predict better than merely chance alone can have negative values.
The Fvalues were computed according to Equation no.2:
…(2)
Where, S_{1} is variance between samples and S_{2 }variance within samples.
The values of computed Fratio were compared with the critical values tabulated in statistical texts and levels of significance discerned. The correlations found to be statistically significant were compiled from CODESSA software. The names of descriptors were conveniently coded using a WSMacro program and the files converted to appropriate ASCII formats through inhouse built program source codes. These ASCII files were further converted into tabular formats in MSWord.
RESULTS AND DISCUSSION:
Variable QSPR results were obtained following application of multivariate statistical analysis on Quinolone drugs. Concise results of only those correlations which were found to be statistical significant, usually at 5% level or less, and/or with important applications have been taken into consideration. CL_{tot} shows positive linear dependence on topological parameters (e.g., BLI) and negative linear
Table 1. Significant linear, logarithmic and inverse QSPR polynomial equations along with the statistical parameters for a series of 24 quinolones using total body clearance as the pharmacokinetic parameter
Equations 
m 
R^{2} 
F 
S^{2} 
Q^{2} 
p< 
Cl_{tot} =  167.45  1859.2 QOmax 
1 
0.4112 
16.76 
28.58 
0.3631 
0.001 
Cl_{tot} = 65.384  536.39 Qmax 
1 
0.3592 
13.45 
31.10 
0.3429 
0.001 
Cl_{tot} =  54.513 + 74.796 BLI 
1 
0.3347 
12.08 
32.29 
0.1340 
0.005 
Cl_{tot} = 96.083  324.77 QmaxQmin 
1 
0.2980 
10.19 
34.08 
0.1084 
0.005 
Cl_{tot} =  188.9  21342 QOmax  273.62 Brel 
2 
0.5819 
16.01 
21.17 
0.4310 
0.001 
Cl_{tot} = 84.982  665.53 Qmax  311.01 Brel 
2 
0.5705 
15.28 
21.75 
0.3968 
0.001 
Cl_{tot} =  162.96  1871.5 QOmax  0.98487 ABn 
2 
0.5599 
14.63 
22.29 
0.4563 
0.001 
Cl_{tot} =  172.57  1904.9 QOmax + 8.9337 LogP 
2 
0.5374 
13.36 
23.43 
0.4907 
0.001 
Cl_{tot} =  193.61  2186 QOmax  278.55 Brel + 9.1501 LogP 
3 
0.7143 
18.33 
15.13 
0.5277 
0.001 
Cl_{tot} =  177.91  1835.5 QOmax  238.98 Brel + 12.155 LogP + 38.674 E1m 
4 
0.7913 
19.91 
11.57 
0.6234 
0.001 
Cl_{tot} =  162.69  2387.2 QOmax  286.50 Brel + 13.993 LogP + 55.692 E1m  135.09 X0Av 
5 
0.8499 
22.65 
8.74 
0.7309 
0.001 
Cl_{tot} =  120.16  2875.5 QOmax  204.06 Brel + 16.210 LogP + 48.769 E1m  264.68 X0Av + 495.82 FNSA3 
6 
0.9132 
26.78 
6.72 
0.7256 
0.001 
Cl_{tot} = 156.98  1263 Qmax  283.13 Brel + 8.1700 LogP  45.289 ZXS/ZXR  14.37 Cn + 1127.5 FPSA3 
6 
0.8798 
23.17 
7.37 
0.3659

0.001 
Log Cl_{tot} = 84.179  55.791 RCI 
1 
0.2925 
9.92 
0.0627 
0.2129 
0.005 
Log Cl_{tot} =  1.1402 + 2.4301 BLI 
1 
0.1934 
5.75 
0.0715 
0.0711 
0.05 
Log Cl_{tot} =  4.2361  54.495 QOmax 
1 
0.1934 
5.75 
0.0715 
0.1072 
0.05 
Log Cl_{tot} =  9.6260  82.256 QOmax + 3.3991 
2 
0.4841 
10.79 
0.0477 
0.3865 
0.005 
Log Cl_{tot} = 89.803  60.807 RCI + 2.3328 SBRel 
2 
0.4507 
9.43 
0.0508 
0.2546 
0.005 
Log Cl_{tot} = 120.70  79.402 RCI + 0.22558 Hy  0.003412 QYYe + 5.1946 FPSA1 + 2.1412 E3s  7.5862 X0Av 
6 
0.8330 
15.79 
0.0187 
0.6348 
0.001 
1/ Cl_{tot} =  27.397 + 18.468 RCI 
1 
0.2622 
8.53 
0.0080 
0.0685 
0.01 
1/Cl_{tot} =  0.035233 + 2.0128 Orel 
1 
0.1929 
5.74 
0.0087 
0.0777 
0.05 
1/Cl_{tot} = 0.70258 + 4.9357 Qnmin 
1 
0.1716 
4.97 
0.0090 
0.1170 
0.05 
1/ Cl_{tot} =  29.860 + 20.665 RCI  1.0216 SBRel 
2 
0.5104 
11.99 
0.0055 
0.3883 
0.005 
1/ Cl_{tot} = 3.6172  1.3332 SBRel + 25.139 Qomax 
2 
0.4741 
10.37 
0.0059 
0.2261 
0.005 
1/Cl_{tot}=  27.397 + 18.468 RCI 
1 
0.2622 
8.53 
0.0080 
0.0685 
0.01 
1/Cl_{tot}=  0.035233 + 2.0128 Orel 
1 
0.1929 
5.74 
0.0087 
0.0777 
0.05 
1/Cl_{tot} =  29.860 + 20.665 RCI  1.0216 Single bond Rel 
2 
0.5104 
11.99 
0.0055 
0.3883 
0.005 
1/Cl_{tot} =  32.800 + 22.683 RCI  0.19698 IC2 
2 
0.4961 
11.32 
0.0057 
0.3789 
0.005 
1/Cl_{tot} =  34.456 + 23.885 RCI  25.312 IC2 + 0.020177 ABn 
3 
0.7566 
22.79 
0.0029 
0.6171 
0.001 
1/ Cl_{tot} =  50.263 + 33.644 RCI  0.41402 IC2 + 2.8431 Crel + 0.02946 Hn  2.4182 Hrel + 2.5808 X0Av 
6 
0.9332 
34.52 
0.0014 
0.8136 
0.001 
dependence on electrostatic parameters (e.g., QOmax, Qmax, QmaxQmin). Influence of topological parameters, e.g., BLI, KFI and X0Av, electrostatic parameters like Qmax, FNSA3 and QOmax, lipophilic parameters like log P and Mlog P, geometrical parameters like ZXS/ZXR and constitutional parameters like Cn and Brel was also noticed during multiparameter studies. The joint dependence of clearance values on topological and electrostatic parameters signifies the importance of diffusion and ionization of quinolone drugs in vivo. The geometric parameters, WHIM parameters and constitutional parameters like Cn further ratify the diffusional contribution in ascribing intraclass variation in clearance values. Further, only limited dependence upon lipophilic parameters corroborates that the diffusional and ionizational considerations outweigh the permeability considerations. The overall predictability was found to be quite high (R^{2}=0.9132, F=26.78, S^{2}=6.72, Q^{2}=0.7256, p<0.001) as shown in Table1. Logarithmic transformation of clearance did not yield much
Fig. 2. Linear correlation plot between the values of Cl_{tot} as reported in literature and those using multiparameter QSPR fora series of 24 quinolones. The inset shows the corresponding residual plot.
improvement in the significance of correlations, but the inverse transforms showed improved correlation (R^{2}=0.9332, F=34.52, S^{2}=0.0014, Q^{2}=0.8136, p<0.001). Highly significant decrease in S^{2} values was observed, attributable ostensibly to the lower magnitude of inverse transforms. The residual plots using the inverse transforms of clearance values also showed better uniformity in scatter and randomization (Fig.3), ratifying their superiority over untransformed (Fig.2) and logtransformed clearance values. Earlier studies^{1519} reported highly significant correlations of clearance values with drug lipophilicity, contrary to our findings. Much higher number of diverse descriptors as well as of drug compounds in this congeneric series, coupled with much higher degree of prognosis involved in the current studies, unequivocally point out the reliability of the current QSPR investigations.
Fig. 3.Linear correlation plot between the values of inverse transform of Cl_{tot} as reported in literature and those using multiparameter QSPR for a series of 24 quinolones. The inset shows the corresponding residual plot.
CONCLUSIONS:
In case of quinolones, the joint dependence of clearance values on topological and electrostatic parameters signifies the importance of diffusion and ionization of quinolone drugs in vivo. The geometric parameters and constitutional parameters like Cn further confirm the diffusional contribution in ascribing clearance. Only limited dependence upon lipophilic parameters signifies that diffusional and ionizational considerations outshine permeability considerations.
ACKNOWLEDGEMENTS:
The authors are thankful to Mr. Varun Sarpal and Mr. Lalit Khurana for providing significant inputs in compiling the current manuscript.
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Received on 20.04.2008 Modified on 30.04.2008
Accepted on 02.05.2008 © RJPT All right reserved
Research J. Pharm. and Tech. 1(2): AprilJune. 2008;Page 106111