Quant. Struct.-Act. Relat. 16, 283289 (1997) Quantitative Structure-Time-Activity Relationships (QSTAR) 283

Quantitative S truc ture-Time-Ac tivity Relations hips (QSTAR) : pH-Dependent Growth Inhibition of Escherichia coli by Ionizable and Nonionizable Kojic Acid Derivatives. Part I1 Katarina PirHelova

Department of Biochemical Technology, Slovak Technical University, Radlinskeho 9, SK-8 1237 Bratislava, Slovakia

Stefan BalG*

Department of Pharmaceutical Sciences, College of Pharmacy, North Dakota State University, 108 Sudro Hall, Fargo, North Dakota 58105-5055, U.S.A.

Ernest Sturdik, Regina Ujhelyova

Department of Biochemical Technology, Slovak Technical University, Radlinskhho 9, SK-81237 Bratislava, Slovakia

Miroslav Veverka

Department of Inorganic Chemistry, Slovak Technical University, Radlinskeho 9, SK-8 1237 Bratislava, Slovakia

Michal Uher

Department of Organic Chemistry, Slovak Technical University, Radlinskeho 9, SK-8 1237 Bratislava, Slovakia

Julius Brtko

Institute of Endocrinology, Slovak Academy of Sciences, SK-83306 Bratislava, Slovakia

Abstract

The previously published model of the model-based quantitative structure-time-activity relationship (QSTAR) for growth inhibitory activity of nonionizable series of kojic acid (5-hydroxy-2- hydroxymethyl-4H-pyrane-4-one) derivatives against Escherichia coli has been extended for the complete set consisting of 21 nonionizable and 14 ionizable compounds. The inhibitory activity has been characterized by the isoeffective concentrations causing 50%-decrease in the specific growth rate in comparison with the untreated control after the five exposure periods in 7 media differing in their pH values (pH 5.6-8.0). For an acceptable fit of the model to the data the receptor binding of both ionized and nonionized molecules had to be considered and the model modified accordingly. The model describes the toxicity of the tested compounds as an explicit non-linear function of hydro- phobicity, pKa values, the size of the substituent in the position 2, the pH values of the external media, and the time of exposure. The results can be interpreted as follows. Elimination as well as binding to the receptor have been positively influenced by both size of the molecules and ionization. The ionized molecules exhibit about 2.6 x lo3 stronger binding to the receptors than their nonionized counterparts. The QSTAR model can be used for rational development of more effective derivatives.

Key words: QSTAR, model-based QSAR, kinetics of biological activity, hydrophobicity, acidity, semi-empirical models, non- linear models, ionization

* To receive all correspondence

1 Introduction

Kojic acid derivatives exhibit a number of interesting biological activities [l-71. As a chemical substance of microbial origin produced by species of the genera Aspergillus and Penicillium [8, 91, kojic acid provides a promising skeleton for development of new more potent derivatives. The search in this direction could be rationalized by the use of quantitative structure-time-activity relationships (QSTAR). In the preceding paper [lo], the results of the QSTAR analysis for growth impairment of Escherichia coli by nonionizable kojic acid derivatives, acting in the media with different pH values, were summarized. This communication presents the results of a similar attempt for the larger set of compounds including both original nonionizable compounds and added ionizable derivatives. The description of the distribution of the compounds in the bacteria1 suspension is based on our previously published treatment [ 101. The probable involvement of the interaction of both ionized and nonionized molecular species with the receptor required extension of the methodology for formulation of QSTAR.

2 Materials and Methods

2. I Chemicals

The kojic acid derivatives (structures in Table 1) were prepared by previously reported methods from kojic acid isolated from the fermentation medium of Aspergillus tamarii VIII (for references see [ I 11).

0 VCH Verlagsgesellschafi mbH, D-69469 Weinheim 093 1-8771/97/040%0283 $17.50+.50/0

284 Katanna Pirielova et al. Quant. Struct.-Act. Relat. 16, 2811-289 (1997)

Table 1. Structure of the studied kojic acid derivatives, their 1-octanol/water partition coefficient P, dissociation constant pKa, and the indicator variable I (f = 1 if Rz contains more than six bonds in the longest sequence, otherwise I = 0).

0

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

H H H H H H H H CH3 (C0)CHCIz (C0)CHZCHCIz ~ c ~ ) ( c o ) o c z H s (CO)C(CH3)3 (CO)CHz(2-Th)d (C0)-2,4,6-triC1-Phe

(CO)CH(CH3)O-2,4,6-diC1-Phe ( C O ) ( ~ , ~ - F U ) ( ~ - C ~ - P ~ ) ~ (CO)CHz0(2-Np)' CH3 CHzOH (CO)(~-(~-CH~)-AZ)~ ( C O W 3 (CO)CHZ(~-T~)~ CH3 (CO)CHz0(2,4-diCl-Ph)'

(CO)CH~0(2,4-diCl-Ph)~

OH OH OH OH OH OH

(CO)CH20-2,4,6-triC1-Phe

(CO)CH,0(2-CH3-4-CI-Ph)e

(CO)CH20(2-CH3-4-CI- Ph)e

H H H H H H H H H H H H H H H H H H H H H H H H H H H H H ( C O P 3 Br I CI Br (COICH3

-0.617 0.635 0.615

-0.086 -0.693

0.915 1 .650a 2.082

-0.257 -0.669a - 1, 103a - 1.646

0.705 0.681 1.921 1 .699a 1 .863a 1 .954a 1 .092a 0.161

1.349' 0.505 1.762= 1.139 2.851a 2.793" 3.301' 2.592a

0.272 0.546 0.950 1.085

-0.275a

-0.377

-0.509

7.722 7.368 7.204 7.567 7.703" 7.703' 7.703a 7.703a

14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 7.437 6.150 6.057 5.936 6.248 7.172

0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0

2.2 Antimicrobial Activity

Bacterial strain Escherichia coli CCM 2260 was used to assay the bacterial growth inhibitory activity of kojic acid derivatives during the aerobic cultivation in liquid peptone-broth media prepared into phosphate-citrate buffers with pH values 5.6, 6.0, 6.6, 7.0, 7.6 and 8.0 and the ionic strength 0.5. The growth in the presence of the tested compounds was monitored spectro- photometrically. The growth inhibitory activity was character- ized as the concentration of the respective derivative ( c ~ ~ in mol L-I) causing the decrease of the specific growth rate to 50% of that of the untreated control. The experiments and data processing are described in detail in the preceding paper [lo].

2.3 Partition CoefJicients

The partition coefficients, determined by a kinetic method in the system 1-octanol/water, were published previously [ I 11. For the compounds where a sufficient quantity for these experiments was not available, the partition coefficients were estimated as follows. The partition coefficients Pc were calculated by the Crippen method [12]. As this method does not take into account the interactions between more distant polar fragments which can be anticipated between the substituents R2 and the oxygens of the skeleton, the calculated values of Pc were correlated with the experimental values of P as log P = 1.136 log P, - 1.828 (n = 7, r = 0.965, SD =0.340, F = 68) and the missing values of P were estimated from this equation.

Quant. Struct.-Act. Relat. 16, 283289 (1997) Quantitative Structure-Time-Activity Relationships (QSTAR) 285

2.4 Dissociation Constants

The acid dissociation constants K,, determined by potentiometric titration method or calculated from the Hammett constants, were published previously [l 11.

2.5 Model Construction

If transport of the drug molecules is much faster than their elimination and the biological effect is: (1) a direct, immediate consequence of the fast and reversible 1 : 1 drug-receptor interaction and (2) proportional to the fraction of the receptors occupied, kinetics of the biological activity can be described as ~ 3 1

l / c , = [K(1 - X)/XV,]exp(-k,,t)

where the distribution volume Vd is

and the elimination rate constant k,, is given by the expression

k,,Vd = CPB + D (3)

Here cx is the equieffective concentration eliciting the fraction X of the maximum effect, K is the drug-receptor association constant, t is the time of exposure, and B is the exponent from the Collander equation relating hydrophobicity of the membranes, inert proteins and metabolizing enzymes to that of the reference (usually 1- octanol/water) system [ 141. The terms A-D quantitatively describe individual processes the compounds undergo in the biological system: membrane accumulation and non-covalent protein binding (A), distribution in extracellular and intracellular aqueous phases (B), hydrophobicity-dependent and -independent elimination (C and D, resp.) The terms A and B express structure- nonspecific interactions and their functional forms can contain only physicochemical properties of the drug molecules. In contrast, K, C, and D describe structure-specific properties and their functional forms should include, in general, molecular features of the tested compounds. In a limited series, however, also the terms K, C, and D can be expressed using physicochemical properties of the compounds.

If the tested compounds ionize to the maximum degree M and acidities of the media differ in individual experiments, the concentration of the molecular species ionized to the j-th degree in the i-th aqueous compartment is related to the concentration of free nonionized molecules (cA) by the factors qii

(4)

The term sgn= f 1 according to the sign of the charge of the originating ion (negative for acids, positive for bases). All intracellular compartments are assumed, in the first approximation, to change their pH values under the influence of the external pHE with the identical sensitivity 3 (0 5 3 5 1). Equation 4 results from the definition of the dissociation constants K, if the proton

concentrations in individual intracellular compartments are assumed to be influenced by the external PHE value but not by the drug distribution. Then the terms A-D in Eqs. 1-3 can be written as [15, 161

Here Y = A, B, C or D, the (first) subscript indicating the charge of the species and the second subscript the association with the external and intracellular aqueous phases (E and I, resp.) When various molecular species bind to the receptor, an expression similar to Eq. 5 can be, under the conditions specified at the beginning of this section, written also for the drug-receptor association constant K. It should be, however, kept in mind that the summations in Eq. 5 will include only the ionization degrees in which the molecules are actually bound to the receptors and that the term associated with the external medium will vanish if the receptors are localized inside the cells.

The data on kinetics of biological activity of a series of compounds are complex and a direct application of Eqs. 1-3 with the terms K, A, B, C, and D substituted by Eq. 5 could cause problems with the number of adjustable parameters and their initial estimates in the non-linear analysis. The search for the final form of the QSTAR equation consists mainly in determining which terms in Eqs. 2 and 3 are significant and what is the form of the relation between the properties of compounds and the drug-receptor association constant K. This task is in the present case facilitated by the fact that the analysis for the effects of nonionizable kojic acid derivatives measured under identical experimental conditions has been done previously [lo]. Now the terms in Eqs. 1-3 identified as significant for nonionizable compounds have to be developed for ionizable compounds according to Eq. 5.

3 Results and Discussion

The structure of the nonionizable and ionizable kojic acid derivatives, their 1-octanol/water partition coefficients, the aqu- eous dissociation constants, and the indicator variable characteriz- ing the size of the substituent R2 are given in Table 1. The growth impairment activities of ionizable derivatives expressed as logT (T= 1/c50) after 2 ,4 ,6 ,8 , and 10 h exposure in the media withpH 5.6, 6.0, 6.6, 7.0, 7.6, and 8.0 are summarized in Table 2. Finally, Table 3 contains the initial toxicities logTo and Table 4 the elimination rate constants k e l , both obtained by fitting the monoexponential function of time (c$ Eq. I-the linear coefficient corresponds to To and the exponential coefficient to k,,) to the kinetics of biological activity of ionizable derivatives at the given pH value of the medium. For ionized kojic acid derivatives both To (Table 3, Figure 1) and kel (Table 4, Figure 2) show significant variation with pH of the medium, in contrast to the nonionized compounds (the lines in Figures 1 and 2 [lo]). The quantities summarized in Tables 2-4 for nonionizable derivatives (Table 1, Nos. %29) have been published previously [lo]. The time course of biological activities for all tested compounds was monoexpo- nential (c$ Figure 3) and the fits of the monoexponential function to the experimental data (Table 2) were of satisfying quality as can

286 Katarina Pirielova et al. Quant. Struct.-Act. Relat. 16, 283-289 (1997)

Table 2. Experimental growth impairment activities of the ionizable kojic acid derivatives (the numbers are given in Table 1) in the medium with the given pH value at the given exposure times expressed as IogT (Tis 1/q0 where c5,, is the concentration, in mol L-’, causing 50% decrease in the specific growth rate). NST - not sufficient toxicity at the highest tested concentration.

No. Time (h) logT in pH -

5.6 6.0 6.6 7.0 7.6 8.0

exp. calc. exp. calc. exp. calc. exp. calc. exp. calc. exp. calc.

1

2

3

4

5

6

7

8

30

31

32

2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10

2.375 2.284 2.178 2.071 2.001 3.152 3.032 2.915 2.796 2.672 2.896 2.801 2.693 2.602 2.586 2.721 2.602 2.582 2.463 2.331 2.041 1.956 1.885 1.778 1.685 3.186 3.054 2.925 2.806 2.664 2.551 2.442 2.328 2.245 2.154 3.190 3.098 3.032 2.956 2.902 2.432 2.366 2.301 2.234 2.172 3.150 2.965 2.763 2.558 2.469 3.512 3.274 3.065 2.788 2.534

2.178 2.075 1.973 1.871 1.768 3.010 2.908 2.806 2.703 2.601 3.017 2.914 2.81 1 2.708 2.605 2.619 2.517 2.414 2.312 2.209 2.109 2.007 1.905 1.802 1.700 3.066 2.965 2.864 2.763 2.662 2.399 2.296 2.193 2.090 1.987 3.097 3.012 2.928 2.844 2.760 2.470 2.368 2.266 2.165 2.063 3.111 2.991 2.871 2.75 1 2.63 1 3.269 3.146 3.023 2.900 2.777

2.075 1.956 1.853 1.765 1.674 3.085 3.000 2.915 2.834 2.721 2.981 2.885 2.854 2.615 2.563 2.756 2.643 2.556 2.421 2.345 2.092 2.002 1.905 1.802 1.685 3.152 3.028 2.930 2.774 2.678 2.600 2.523 2.398 2.315 2.196 3.124 3.01 1 2.915 2.823 2.71 1 2.645 2.554 2.486 2.402 2.336 3.143 2.993 2.732 2.482 2.295 3.298 3.1 10 2.876 2.612 2.443

2.183 2.079 1.976 1.873 1.770 3.020 2.916 2.81 1 2.707 2.603 3.030 2.924 2.818 2.712 2.606 2.626 2.522 2.419 2.315 2.21 1 2.1 15 2.01 1 1.908 1.815 1.701 3.071 2.969 2.867 2.766 2.664 2.407 2.303 2.198 2.093 1.989 3.103 3.018 2.932 2.847 2.762 2.470 2.368 2.266 2.165 2.063 3.110 2.973 2.837 2.700 2.564 3.257 3.117 2.976 2.835 2.694

2.279 2.175 2.074 1.95 1 1.865 3.065 2.952 2.862 2.699 2.605 3.000 2.912 2.820 2.702 2.589 2.655 2.543 2.421 2.356 2.210 2.188 2.082 1.938 1.815 1.695 2.985 2.896 2.800 2.665 2.61 1 2.520 2.432 2.301 2.178 2.087 3.124 3.089 3.012 2.951 2.875 2.680 2.602 2.526 2.447 2.375 3.096 2.91 1 2.721 2.582 2.401 3.110 2.942 2.775 2.608 2.441

2.183 2.076 1.968 1.861 1.753 3.020 2.906 2.793 2.680 2.566 3.026 2.908 2.790 2.673 2.555 2.627 2.517 2.407 2.297 2.187 2.1 15 2.008 1.900 1.792 1.684 3.072 2.966 2.859 2.753 2.647 2.407 2.295 2.182 2.070 1.957 3.108 3.018 2.928 2.838 2.749 2.470 2.368 2.266 2.165 2.063 2.979 2.816 2.652 2.488 2.324 1.708 1.607 1.505 1.403 1.301

2.206 2.094 2.001 1.885 1.772 3.052 2.960 2.801 2.573 2.561 2.901 2.834 2.7 13 2.606 2.500 2.501 2.390 2.329 2.258 2.141 2.234 2.082 1.954 1.83 1 1.675 2.952 2.874 2.791 2.700 2.688 2.412 2.299 2.196 2.012 1.900 3.102 2.930 2.815 2.734 2.658 2.470 2.400 2.336 2.265 2.198 1.911 1.863 1.801 1.754 1.702 2.900 2.743 2.639 2.476 2.356

2.164 2.049 1.934 1.819 1.704 2.981 2.855 2.728 2.602 2.476 2.975 2.841 2.708 2.574 2.440 2.600 2.481 2.361 2.242 2.122 2.095 1.980 1.864 1.748 1.633 3.053 2.939 2.824 2.710 2.596 2.373 2.249 2.124 2.000 1.876 3.095 2.997 2.899 2.801 2.703 2.470 2.368 2.266 2.165 2.063 2.905 2.768 2.609 2.497 2.365 2.949 2.771 2.594 2.417 2.239

2.001 1.895 1.815 1.735 1.644 2.685 2.534 2.463 2.351 2.267 2.652 2.545 2.423 2.301 2.220 2.401 2.315 2.254 2.056 2.041 1 .886 1.815 1.689 1.612 NST 2.795 2.721 2.646 2.554 2.462 2.120 2.013 1.915 1.823 1.704 3.000 2.931 2.802 2.710 2.628 2.390 2.346 2.298 2.246 2.197 2.501 2.389 2.263 2.112 1.976 2.651 2.485 2.398 2.267 2.1 11

2.05 1 1.913 1.775 1.637 1.499 2.81 1 2.656 2.502 2.347 2.193 2.779 2.618 2.456 2.294 2.133 2.462 2.317 2.171 2.026 1.880 1.979 1.840 1.701 1.562 1.423 2.938 2.800 2.662 2.525 2.387 2.213 2.061 1.910 1.758 1.606 2.998 2.874 2.750 2.627 2.503 2.470 2.368 2.266 2.165 2.063 2.549 2.366 2.183 1.999 1.816 1.708 1.607 1.505 1.403 1.301

1.956 1.841 1.736 1.645 1.530 2.481 2.409 2.298 2.145 2.110 2.391 2.301 2.181 2.044 1.985 2.286 2.154 2.095 2.023 1901 1.800 1.721 1.645 NST NST 2.643 2.553 2.495 2.371 2.275 1.905 1.812 1.714 1.602 1.508 2.813 2.708 2.605 2.557 2.487 2.620 2.535 2.445 2 356 2.265 2.287 2.182 2.098 2.000 1.878 2.275 2.186 2.046 1.912 1.845

1.893 1.736 1.579 1.422 1.265 2.626 2.456 2.286 2.116 1.946 2.588 2.414 2.239 2.065 1.891 2.289 2.126 1.963 1.799 1.636 1.819 1.661 1.503 1.346 1.188 2.779 2.622 2.465 2.308 2.151 2.03 1 1.863 1.695 1.527 1.359 2.853 2.706 2.559 2.412 2.265 2.470 2.368 2.266 2.165 2.063 2.357 2.172 1.987 1.802 1.617 2.479 2.294 2.109 1.924 1.739

(continued)

Quant. Struct.-Act. Relat. 16, 283-289 (1997) Quantitative Structure-Time-Activity Relationships (QSTAR) 287

Table 2. (continued)

No. Time (h) logT in pH

5.6 6.0 6.6 7.0 7.6 8.0

exp. calc

33 2 4 6 8

10 34 2

4 6 8

10 35 2

4 6 8

10

3.500 3.21 1 2.996 2.694 2.515 3.512 3.321 3.184 2.965 2.732 2.267 2.178 2.056 1.976 1.865

3.424 3.297 3.170 3.043 2.916 3.332 3.217 3.101 2.986 2.871 2.306 2.203 2.099 1.995 1.891

exp. calc.

3.523 3.397 3.337 3.251 3.000 3.105 2.812 2.959 2.591 2.813 3.475 3.341 3.301 3.210 3.142 3.080 2.912 2.950 2.695 2.819 2.310 2.320 2.174 2.213 2.087 2.106 1.965 1.999 1.867 1.892

exp. calc. exp. calc. exp. calc.

3.201 3.228 3.100 3.061 2.767 2.782 3.067 3.058 2.955 2.882 2.632 2.598 2.856 2.887 2.834 2.703 2.510 2.413 2.711 2.716 2.689 2.524 2.382 2.229 2.532 2.546 2.521 2.344 2.278 2.045 3.354 3.231 3.052 3.084 2.800 2.812 3.189 3.072 2.931 2.911 2.651 2.630 3.050 2.913 2.775 2.738 2.576 2.447 2.792 2.754 2.612 2.566 2.442 2.265 2.643 2.595 2.510 2.393 2.312 2.083 2.300 2.315 2.251 2.260 2.089 2.059 2.178 2.195 2.174 2.125 2.000 1.896 2.093 2.076 2.038 1.989 1.825 1.733 1.978 1.956 1.971 1.853 1.702 1.570 1.864 1.837 1.854 1.718 NST 1.407

exp. calc.

2.511 2.590 2.401 2.405 2.276 2.219 2.167 2.034 2.074 1.849 2.419 2.619 2.310 2.435 2.211 2.250 2.089 2.066 2.011 1.881 1.905 1.867 1.811 1.692 1.702 1.517 NST 1.342 NST 1.166

Table 3. Initial toxicities of ionizable acid derivatives To ( T is I / C ~ ~ where c50 is the concentration, in mol L-I, causing 50% decrease in the specific growth rate) and standard deviations SD calculated by fitting the monoexponential function of time to the kinetics of biological activity at given p H of the medium

No. (TofSD)x lo3 i n p H

5.6 6.0 6.6 7 .O 7.6 8.0

1 2 3 4 5 6 7 8 30 31 32 33 34 35

0.297 f 0.005 1.867 f 0.005 0.949 f 0.047 0.639 & 0.042 0.135 f 0.003 2.062 f0 .016 1.903 & 0.204 1.808 & 0.042 0.446 f 0.009 2.171 f0.072 5.587f0.125 5.752 f0 .227 4.928 f0.193 0.234 f 0.005

0.149 f0 .003 1.494 f 0.023 1.215 f0.094 0.724i0.016 0.157f0.003 1.869 f 0.045 1.928 i 0.023 1.671 410.023 0.508 f0.015 2.285 10.166 3.288f0.125 5.828 f0.432 4.576 i 0.160 0.260 f 0.007

0.243 f0 .003 1.522 f 0.049 1.273 f 0.030 0.576 f0 .017 0.207 f 0.004 1.219 f 0.036 1.300 f 0.020 1.569 f 0.047 0.434 f 0.012 1.866 f 0.042 1.690 f 0.043 2.361 f 0.097 3.390f0.156 0.253 f 0.005

0.205 f 0.003 1.581 f0.122 1.025 f 0.038 0.380f0.013 0.234 f 0.004 1.050 f 0.043 1.269 f 0.028 1.610 f 0.1 14 0.349 f 0.014 1.102 f 0.022 1.079 f 0.03 1 1.733 f0 .033 1.572 f 0.044 0.226 f 0.008

0.121 f0 .002 0.602 f 0.030 0.582 f 0.010 0.318 f0.022 0.097 f 0.004 0.759 f 0.012 0.953 f 0.027 1.268 f 0.043 0.166 f 0.002 0.431 f0.011 0.594 f 0.026 0.776 f 0.01 1 0.817f0.032 0.169 & 0.01 1

0.155 f 0.000 0.388 f 0.020 0.318 fO.O1O 0.233 f 0.01 1 0.075 f 0.000 0.543 f0.019 0.643 f 0.014 0.773 & 0.033 0.102 f 0.00 1 0.243 f 0.004 0.248 f0.009 0.420 f 0.006 0.333 f 0.005 0.102 f 0.002

Table 4. The elimination rate parameters k,, in h-’ and standard deviations SD of the ionizable kojic acid derivatives calculated by fitting the monoexponential function of time to the kinetics of biological activity at given pH of the medium

No. (kel f SD) x 10 in pH

- I 2 3 4 5 6 7 8 30 31 32 33 34 35

5.6

I. 120 f 0.034 1.372 f 0.006 1.010f0.097 1.010 f 0.126 1.001 fO.039 1.486f0.017 1.691 f 0.250 0.853 f 0.043 1.177f0.042 2.156 f 0.087 2.705 f 0.066 3.033 10.125 2 081 fO.lOO 1 156 f0 .040

6.0

1.185 f0.048 1.008 f 0.030 1.107 10.154 1.2 12 f 0.046 1.136f0.032 1.377 1 0.051 1.215 f 0.024 1.176 f0 .028 1.144 f 0.057 2.354 f0 .198 2.460f0.107 2.704 10.219 2.094 f 0.090 1.291 f 0.059

6.6 7.0 7.6 8.0 ~~~~

1.214 f 0.025 1.321 f0.068 1.146 f 0.047 1.243 f 0.061 1.428 f 0.047 1.130 f0 .059 0.920 f 0.029 0.709 f 0.054 1.277 & 0.059 2.045 f 0.057 2.052 f 0.064 1.903f0.101 1.983 f 0.116 1.233 f 0.042

~~ ~

1.229 f 0.025 1.557 f 0.173 1.144 f 0.074 0.98 1 f 0.067 1.589 f 0.042 0.847 f 0.076 1.1 I6 f 0.045 1.401 f0 .152 1.442 f 0.088 1.594 & 0.046 1.577 f 0.066 1.601 f 0.043 1.610 f 0.064 1.139 f 0.069

1.025 f 0.038 1.237 f 0.101 1.296 f 0.037 1.103 f0.139 1.078 f 0.092 0.936 f 0.031 0.983 1 0.055 1.106 f 0.068 1.172 f 0.023 1.471 f 0.055 1.505 f 0.097 1.449 f 0.032 1.367 f 0.085 1.474 f 0.158

1.220 f 0.028 1.150 f 0.101 1.237 f 0.068 I .056f 0.095 0.895 f 0.010 1.020 f 0.066 1.128f0.043 0.982 f 0.082 1.144 f 0.022 1.132 f 0.035 1.3 12 f 0.080 1.299 f 0.030 1.210 f0 .031 1.155 f 0.050

288 Katarina Pidelova era]. Quant. Struct.-Act. Relat. 16, 283-289 (1997)

4.0

3.5

3.0 Lo rn 2 2.5

2.0

1 -2 -1 0 1 2 3 4

1.5' * ' I ' ' ' ' ' ' I ' I ' log P

Figure 1. The dependence of the initial toxicities (T= l /qo, c50 is in mol L-') of the ionizable kojic acid derivatives (Table 3) on hydro- phobicity (Table 1) for the media with the pH value: 5.6 (m), 6.0 (O), 6.6 (O), 7.0 (0), 7.6 (+), and 8.0 (0). The line is valid for nonionizable compounds [ 101.

0.4

0.3

A r

'c 0.2

x" v -

D.1

- , - - I 8 I ' I I '

Figure 2. The dependence of the elimination rate parameters of the ionizable kojic acid derivatives (Table 4) on hydrophobicity (Table 1) for the media with the p H value: 5.6 (W), 6.0 (O), 6.6 (O), 7.0 (O), 7.6 (e), and 8.0 (0). The line is valid for nonionizable compounds [lo].

be seen from the standard deviations of the parameters To (Table 3) and kel (Table 4) as well as from the values of the statistical indices (the lowest value of the correlation coefficient was 0.976, the highest standard deviation 0.098).

The search for suitable expression for the individual terms K, A-D in Eqs. 1-3 and for the initial estimates was facilitated by the QSTAR expression derived previously [ 101 for 2 1 nonionizable derivatives measured after five exposure times and at six p H values of the medium under identical conditions. This resulted in the following QSTAR equation based on Eq. 1, where the distribution

6000 1 1 I I I

.-- 3000 I- \ i

k 1000

0

12 -1000

0 3 6 9

time (h)

Figure 3. The kinetics of the toxic action (c50 in mol L-') of the following ionizable kojic acid derivatives (Table 1): No. 2 (m), No. 5 (O), No. 29 (O), No. 30 (0). The lines correspond to the model (Eq. 1 as combined with Eqs. 9, 10, and 11) with the optimized values of the adjustable parameters given in the text.

volume V, was described by Eq. 2, the drug-receptor association constant K was expressed as

logK = lOgP - lOg(EP + 1) + FI + G (6)

and for the elimination rate constant kel the expression

k,, V , = D + DII (7)

was valid. The fit of Eq. 1 as combined with Eqs. 2.6, and 7 to the experimental data of nonionizable kojic acid derivatives provided the following optimized values of the adjustable parameters A=(1.831 zt0.421) x D=(4.791 h 0 . 6 2 6 ) ~ lo-', DI = (9.851 f 0.971) x lo-', E = (4.870 f 0.452) x lo-', F = (7.806 f 0.593) x lo-', and G = 2.907 f 0.045. As can be seen in the values of the statistical indices (n = 606, r = 0.949, SD = 0.177, and F = I O U ) , the fit was satisfactory [ 101.

Equation I , as combined with Eqs. 2, 6, and 7 can be used directly for construction of the QSTAR expression for ionizable com- pounds under the conditions of the differing pH of the medium using the substitution of the individual terms K, A, B and D by Eq. 5 .

The best fit was obtained when for the drug-receptor association constant the binding of both nonionized and ionized molecules of the kojic acid derivatives was considered. For this case the global drug-receptor association constant K can be expressed as

where the second equality comes from Eq. 4 or 5. The subscripts 0 and I refer to nonionized and ionized species, resp. It was assumed that the binding to the receptor of ionized species can be described by the same properties of the compounds as that of nonionized molecules besides a contribution of the ionized hydroxyl group, which was expected, in the fust approximation, to be constant for all the ionizable derivatives. The term w in the third equality

Quant. Struct.-Act. Relat. 16, 283-289 (1997) Quantitative Structure-Time-Activity Relationships (QSTAR) 289

represents the ratio of the drug-receptor association constants of ionized and nonionized molecules.

After trying all the possible combinations of the parameters in Eq. 5 , the following modification of Eqs. 2. 6, 7, and 8 for the distribution volume v d , the drug-receptor association constant K, and for the elimination rate constant kel resp., provided the best fit of Eq. 1 to the experimental data (Table 2 for ionizable compounds and Table 2 in [lo] for nonionizable compounds):

(9)

The fit of logarithmized Eq. 1, as combined with Eqs. P-1 1 into a single expression, to the experimental data provided the following optimized values of the adjustable parameters A. = (1.807 f 0.363) X Do = (5.088 * 0.423) X lop2, DI = (9.493 f 0.765) x I O - ~ , Dl~=(9.306*0.816)~ E=(4.687&0.286) x lo-', F=(7.419+0.443) x lo-', G=2.929f0.031, 9=(5.231+0.347) x lo-' and o=(2 .632f 1 . 4 0 0 ) ~ lo3. As can be seen in the values of the statistical indices (n = 1020, r = 0.960, SD = 0.154, and F = 1485), the fit was satisfactory. In Figure 3, the kinetics of the toxicities for several kojic acid derivatives are plotted. The model describes the experimental data satisfactorily if one considers that (1) the toxicities are given on the linear, not logarithmic scale and (2) the lines are calculated from Eqs. 1, 9-1 1 using the properties of the compounds. The satisfactory fit can be seen also in the plot of calculated and experimental toxicities (Figure 4). The optimization of the parameters AIE, AlI, Bo, BIE, BI I and DII does not improve the fit and the parameters were set as B,= BIE = 1 (in accord with the model for nonionizable kojic acid derivatives [ to] ) and A I E = A I I = B I I = D I I = O . The optimization of DII(DII =(2.028 f 1.568) x lo3) resulted in negligible changes of other adjustable parameters (except for w = (1.254 0.947) x lo5) and a small improvement in the statistical indices (r = 0.963, SD = 0.149).

I I

1 2 3 4

log T

Figure 4. Calculated vs. experimental toxicities ( T = l/c50, c50 is in mol L-', Table 2) of the nonionizable (0) and ionizable (0) kojic acid derivatives (Table 1) with the identity line plotted.

The results can be interpreted in the light of the model properties as follows. The transport of the tested compounds is fast in comparison with the duration of the experiment and the kinetics of biological activity can, therefore, be described by a monoexpo- nential function. The compounds attain readily pseudo-equilibrium distribution, characterized by the volume of distribution v d (Eq. 9). The accumulation in the membranes and binding to proteins of ionized species is not significant (AlE = AII = 0). Ionization influences the distribution mainly in the extracellular aqueous phase (BI1 =O). The elimination rate constant kel is, for the studied set of derivatives, positively influenced by the size of the substituent in the position R2 and by ionization mainly in the extracellular aqueous phase (Dl1= 0, although its optimization contributes slightly to the improvement of the fit). The drug- receptor association constant depends on hydrophobicity in a non- linear manner: it increases linearly with growing lo@ and later levels off. The binding of the studied compounds is also enhanced by the size of the substituent in the position R2 and is about w =(2.632f 1.400) x lo3 times stronger for the ionized species than for the nonionized species.

Although the presented interpretation must be considered as indicative and further studies are needed to confirm its conclu- sions. We hope that the presented results do illustrate the usefulness of the model-based approach to the construction of QSTAR for our understanding of chemico-biological interactions.

Acknowledgement

The work was supported by the Slovak Grant Agency and the Fulbright Commission.

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Received on November 6th, 1996; accepted on April 16th, 1997