Quantitative Structure Pharmacokinetic Relationship Studies for Drug Clearance of Quinolone Drugs

 

Yash Paul1, Avinash S. Dhake2, Milind Parle3 and Bhupinder Singh4*

1Lord Shiva College of Pharmacy, Sirsa (Haryana), India.

2L.B. Rao Institute of Pharm. Education and Research, Anand, Gujarat, India.

3Guru Jambheshwar University of Science & Technology, Hisar (Haryana), India.

4Univ. Institute of Pharm. Sciences, Panjab University, Chandigarh, India.

 

* Corresponding Author E-mail 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 (CLtot) 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 CLtot 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 cross-validated coefficients (Q2) using leave-one-out (LOO) method (p<0.001). CLtot shows positive liner dependence on topological parameters (e.g., BLI and negative liner dependence on electrostatic parameters (e.g., Qmax, QOmax, Qmax-Qmin). Influences of lipophilic parameters like log P, geometrical parameters like ZXS/ZXR and constitutional parameters like Cn and Brel was also noticed during multi-parameter 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  (R2=0.9132, F=26.78, S2=6.72, Q2=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 (R2=0.9332, F=34.52, S2=0.0014, Q2=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 concentration-time 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 design2.

 

The CLtot 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 steady-state concentration of a drug.3 Hence it is important to predict the CLtot 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 CLtot 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 CLtot value of drug candidates in an effort to eliminate undesirable agents in a fast and cost-effective manner.4-7 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 drug-free 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 CLtot (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 Structure-Pharmacokinetic Relationship (QSPR): A Multidisciplinary Endeavor

Methods:

QSPR was conducted amongst various quinolone drugs employing extra-thermodynamic Multi Linear Regression Analysis (MLRA) approach. The QSPR correlations were duly analyzed using a battery of apt statistical procedures and validated using leave-one-out (LOO) approach.

DATASET SELECTION:

The reported values of CLtot of the quinolone drugs in humans were taken from the literature.11-14 In order to ensure that experimental various in determining CLtot does not significantly affect the quality of our datasets, only CLtot 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. CLtot values of these compounds were also log-transformed (log CLtot) and inverse transformed (1/CLtot) to normalize the data and to reduce unequal error variance.

Molecular structure and descriptors

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 CLtot 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 pre-selection 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 one-parameter 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 one-parameter correlation with the descriptor is < 1.00.

¯  The r2 value of one-parameter equation is less than assigned value of r2min (usually 0.10).

¯  The one-parameter t-value is less than the assigned value (usually 1.50).

¯  The multi-parameter t-value is less than the assigned value (usually 1.95).

¯  Descriptors are highly inter-correlated with another descriptor (r> 0.65).


Box 1: Representative List of Descriptors Used in Current QSPR Studies (Singh et al., 2007)10

Lipophilic parameters                                                              Topological parameters

Log Po/w                                                                                   Wiener index, Balaban index

Rm value                                                                                   Randic and Kier & Hall indices

Capacity factor (log K’)                                                           Kier shape index Atomic connectivity

Geometrical parameters                                                           Electronic (ionic) parameters

Moment of inertia                                                                   Hammett constant (σ)

Shadow indices                                                                         UV spectroscopy (E 1%1cm and lmax)

Quantum-chemical parameters                                                                Electrostatic parameters

Atomic charge densities                                                           Minimum and Maximum partial charges in the  molecule

Dipole moments                                                                      Polarity Parameter (qmin-qmax)

Steric parameters                                                                     Polarizability parameters

Molecular weight                                                                      Molar volume (MV)

Taft’s steric parameter                                                            Molar refractivity (MR)

Constitutional parameters

Number of atoms

Number of bonds

Number of rings

                                                               


Data of pharmacokinetic parameters of CLtot 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 r2 and F-values. Many such attempts were carried out to obtain significant correlations for quinolones. A set of important descriptors found to significantly ascribe the variation of CLtot, was constructed. Further, a search for the multi-parameter regression with the maximum predicting ability was performed. A number of sets of descriptors were thus made and MLRA performed with CLtot. 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 CLtot were also carried out in order to screen the correlation with improved values of R2 and/or F ratio. 

Validation of Testing Set

The statistical significance of each correlation was determined on the basis of the value of F-criterion and the magnitude of cross-validated R2, commonly referred to as Q2, calculated according to Eq. no.1.

(1)

A model with good predictive performance has a Q2 value close to 1, models that do not predict better than merely chance alone can have negative values.

The F-values were computed according to Equation no.2:

            …(2)

Where, S1 is variance between samples and S2 variance within samples.

The values of computed F-ratio 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 WS-Macro program and the files converted to appropriate ASCII formats through in-house built program source codes. These ASCII files were further converted into tabular formats in MS-Word.

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. CLtot 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

R2

F

S2

Q2

p<

Cltot = - 167.45 - 1859.2 QOmax

1

0.4112

16.76

28.58

0.3631

0.001

Cltot = 65.384 - 536.39 Qmax

1

0.3592

13.45

31.10

0.3429

0.001

Cltot = - 54.513 + 74.796 BLI

1

0.3347

12.08

32.29

0.1340

0.005

Cltot = 96.083 - 324.77 Qmax-Qmin

1

0.2980

10.19

34.08

0.1084

0.005

Cltot = - 188.9 - 21342 QOmax - 273.62 Brel

2

0.5819

16.01

21.17

0.4310

0.001

Cltot = 84.982 - 665.53 Qmax - 311.01 Brel

2

0.5705

15.28

21.75

0.3968

0.001

Cltot = - 162.96 - 1871.5 QOmax - 0.98487 ABn

2

0.5599

14.63

22.29

0.4563

0.001

Cltot = - 172.57 - 1904.9 QOmax + 8.9337 LogP

2

0.5374

13.36

23.43

0.4907

0.001

Cltot = - 193.61 - 2186 QOmax - 278.55 Brel + 9.1501 LogP

3

0.7143

18.33

15.13

0.5277

0.001

Cltot = - 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

Cltot = - 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

Cltot = - 120.16 - 2875.5 QOmax - 204.06 Brel + 16.210 LogP + 48.769 E1m - 264.68 X0Av + 495.82 FNSA-3

6

0.9132

26.78

6.72

0.7256

0.001

Cltot = 156.98 - 1263 Qmax - 283.13 Brel + 8.1700 LogP - 45.289 ZXS/ZXR - 14.37 Cn + 1127.5 FPSA-3

6

0.8798

23.17

7.37

0.3659

 

0.001

Log Cltot = 84.179 - 55.791 RCI

1

0.2925

9.92

0.0627

0.2129

0.005

Log Cltot = - 1.1402 + 2.4301 BLI

1

0.1934

5.75

0.0715

0.0711

0.05

Log Cltot = - 4.2361 - 54.495 QOmax

1

0.1934

5.75

0.0715

0.1072

0.05

Log Cltot = - 9.6260 - 82.256 QOmax + 3.3991

2

0.4841

10.79

0.0477

0.3865

0.005

Log Cltot = 89.803 - 60.807 RCI + 2.3328 SBRel

2

0.4507

9.43

0.0508

0.2546

0.005

Log Cltot = 120.70 - 79.402 RCI + 0.22558 Hy - 0.003412 QYYe + 5.1946 FPSA-1 + 2.1412 E3s - 7.5862 X0Av

6

0.8330

15.79

0.0187

0.6348

0.001

1/ Cltot = - 27.397 + 18.468 RCI

1

0.2622

8.53

0.0080

0.0685

0.01

1/Cltot = - 0.035233 + 2.0128 Orel

1

0.1929

5.74

0.0087

0.0777

0.05

1/Cltot = 0.70258 + 4.9357 Qnmin

1

0.1716

4.97

0.0090

0.1170

0.05

1/ Cltot = - 29.860 + 20.665 RCI - 1.0216 SBRel

2

0.5104

11.99

0.0055

0.3883

0.005

1/ Cltot = 3.6172 - 1.3332 SBRel + 25.139 Qomax

2

0.4741

10.37

0.0059

0.2261

0.005

1/Cltot= - 27.397 + 18.468 RCI

1

0.2622

8.53

0.0080

0.0685

0.01

1/Cltot= - 0.035233 + 2.0128 Orel

1

0.1929

5.74

0.0087

0.0777

0.05

1/Cltot = - 29.860 + 20.665 RCI - 1.0216 Single bond Rel

2

0.5104

11.99

0.0055

0.3883

0.005

1/Cltot = - 32.800 + 22.683 RCI - 0.19698 IC2

2

0.4961

11.32

0.0057

0.3789

0.005

1/Cltot = - 34.456 + 23.885 RCI -  25.312 IC2 + 0.020177 ABn

3

0.7566

22.79

0.0029

0.6171

0.001

1/ Cltot = - 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


QOmax    -Max. partial charge for O atom [Zefirov’s PC]

Qmax       -Max. partial charge

BLI          -Kier benzene-Likeliness index

Qmin       -Min. partial charge

Brel         -Relative no. of bonds

ABn        -Number of aromatic bonds

Log P       -Log P values

Elm            -1st component accessibility directional WHIM

 

index/weighted by atomic masses.

X0Av      -average valence connectivity index chi-0

FNSA-3  -FNSA-3  Fractional PNSA (PNSA-3/TMSA)      [Zefirov’s PC]

RCI         -Jug RC index

SBRel      -Relative no. of single bonds

Hy           -Hydrophilic factor

QYYe      -QYY COMMA 2 value/weighted by atomic        sanderson  electronegativities.

FPSA-1   -FPSA-1 Fractional PPSA (PPSA-1/TMSA)         [Zefirov’s PC]

E3s          -3rd component accessibility directional WHIM    index/weighted by atomic electrotoplogical states

Orel         -Relative no. of O atoms

Qnmin     -Min. partial charge for N atom [Zefirov’s PC]

IC2          -Information content (order 2)

Crel         -Relative no. of C atoms

Hn           -No. of H-atoms

Hrel         -Relative no. of H atoms

Cn           -No. of carbon atoms

ZXS/ZXR -ZX Shadow/ZX Rectangle

FPSA-3   -FPSA-3 Fractional PPSA (PPSA-3TMSA)           [Zefirov’s PC]

 

dependence on electrostatic parameters (e.g., QOmax, Qmax, Qmax-Qmin). Influence of topological parameters, e.g., BLI, KFI and X0Av, electrostatic parameters like Qmax, FNSA-3 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 multi-parameter 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 intra-class 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 (R2=0.9132, F=26.78, S2=6.72, Q2=0.7256, p<0.001) as shown in Table-1. Logarithmic transformation of clearance did not yield much

 

Fig. 2. Linear correlation plot between the values of Cltot as reported in literature and those using multi-parameter 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 (R2=0.9332, F=34.52, S2=0.0014, Q2=0.8136, p<0.001). Highly significant decrease in S2 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 log-transformed clearance values. Earlier studies15-19 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 Cltot as reported in literature and those using multi-parameter 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.

 

 

REFERENCES:

 

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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):  April-June. 2008;Page 106-111