quantitative structure-time-activity relationships (qstar): growth inhibition of escherichia coli by...

Quant. Struct.-Act. Relat. 15, 87-93 (1996) QSTAR: Antibacterial Effects of Kojic Acid Derivatives 87

Quantitative Structure-Time-Activity Relationships (QSTAR): Growth Inhibition of Escherichia coli by Nonionizable Kojic Acid Derivatives Katarina Pirzelovi4, Stefan Balai*, Regina Ujhelyova, Ernest $turd&

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

Miroslav Veverka

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

Michal Uher

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

Julius Brtko

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

Abstract

A semi-empirical model for quantitative structure-time-activity relationships (QSTAR) has been applied to the data on inhibition of Escherichia coli in a batch culture in seven media of different acid- ity (pH 5.6-8.0) by twenty one nonionizable derivatives of kojic acid (5-hydroxy-2-hydroxymethyl-4H-pyrane-4-one). The antibacterial potency of individual derivatives was characterized by the equieffective concentrations causing the 50%-decrease in the specific growth rate in comparison with the untreated control. The QSTAR models satisfactorily describe toxicity of the studied compounds as a model-based non-linear function of hydrophobicity, the size of the substituents in the position 2, and the time of exposure. The dependence of the antibacterial activity on hydrophobicity at a fixed exposure time exhibits a broad maximum: the decrease for hydrophilic compounds is caused by their diminished ability for binding to the receptors and that for hydrophobic compounds is elicited by their lower concentrations in the aqueous phases and their slower inactivation. Inactivation is probabiy enzymatic because its rate depends on the size of the molecules. The size has a positive effect also on the binding to the receptor.

Key words: QSTAR, kinetics, antibacterial activity, kojic acid, 5-hydroxy-2-hydroxymethyl-4H-pyrane-4-one, hydrophobicity

Abbreviations and symbols

a, b, c, const adjustable parameters A, B, C, D, D,, E, F, G terms in the disposition function, adjust-

able parameters At7 A0 absorbance at the time given by the sub-

P exponent from the Collander equation script

* to receive all correspondence

0 VCH Verlagsgesellschaft mbH, D-69469 Weinheim

‘50 concentration (in mol d ~ n - ~ ) of the compound causing 50% decrease in the specific growth rate equieffective concentration eliciting the fraction X of the maximum effect dimethylsulphoxide elimination rate constant drug-receptor association constant 1-octanouwater partition coefficient P calculated by the Crippen method time l/cx, the subscript 0 indicating the initial conditions, and the subscript corr the corrected values (Eq. 10)

1 Introduction

Besides the technological use of the kojic acid (5-hydroxy-2-hydroxymethyl-4H-pyrane-4-one) and its derivatives in food industry and cosmetics, a wide range of potential medical applications is emerg- ing due to their analgesic, antithrombotic and anti-infl ammatory activities [l]. Anti-tumour effects of the derivatives in humans and laboratory animals were also demonstrated [2]. The antibacterial 13-51. antiprotozoal and insecticide effects [6, 71, as well as preservative activity on plants against several fungal diseases [3] are attributed to the chelating ability of the compounds [8]. The exact mechanism of antimicrobial action of kojic acid and its derivatives is not completely understood. There are some indications that kojic acid derivatives could interfere with building the poly- peptide chain in the cell wall formation [5].

As a chemical substance of microbial origin produced by species of the genera Aspergillus and Penicillium [9, lo], kojic acid provides a promising skeleton for development of new biologically active derivatives. A rational approach in this direction could be represented by the use of quantitative structure-time-activity relationships

093 1-877 1/96/0204-0087 $10.00+.25/0

88 Katm'na PirSelova et ni. Quant. Struct.-Act. Relat. I S , 87-93 (1996)

(QSTAR). This communication presents the formulation of model- based description of the kinetics of growth inhibitory activity of kojic acid derivatives against Escherichia coli.

derivation of the right side of Eq.1 in the analytical form, using the optimized values of parameters a, b, and c [13]. All calculations were made on a personal computer using own programs.

2 Materials and Methods 2.2.4 Determiniation of Antibacterial Activity

2. I Chemicals

The kojic acid derivatives (structures in Table 1) were prepared by previously reported methods from kojic acid isolated from the fer- mentation medium of Aspergillus tumarii VIII (for references see

The growth inhibitory activities expressed as log ( U C ~ ~ ) were determined graphically from the dose-response curves fitted by an empirical function as the concentrations of the respective derivatives causing the decrease of the specific growth rate to 50% of that of the untreated control.

[111).

2.3 Partition Coeficients 2.2 Antimicrobial Activity

2.2.1 Microorganism, Media and Cultivation

Bacterial strain Escherichia coli CCM 2260 was used to assay the bacterial growth inhibitory activity of kojic acid derivatives during the cultivation in liquid peptone-broth media (Imuna, hiSskC Mi- chal'any, Slovakia), which were prepared into phosphate-citrate buffers with pH values 5.6-8.0 and the ionic strength 0.5 [12]. To the test-tubes (15 mL) with sterilized medium (5 mL), inoculum (6.5% V N ) and the stock solution (1% V N ) of the tested kojic acid derivative in dimethylsulphoxide (DMSO) were added to give the required concentration. The control tube contained only DMSO (1% V N ) without inhibitor. Inoculum was prepared in 500 mL flasks containing 100 mL of the medium. The liquid peptone broth was inoculated from the peptone-broth slant and cultivated for 27 h at 28 "C on a rotary shaker. Then a portion (10% V N ) of the culture was transferred to the fresh medium and after 15-h-cultivation the bacterial suspension was used for inoculation of the test tubes.

2.2.2 Measurement of Antibacterial Effects

The effects of single doses of kojic acid derivatives (twofold serial dilutions in the concentration scale lo-* to mol. L-') were in- vestigated in the liquid media with the pH values varying in the scale 5.6-8.0. Bacterial growth in the presence of the tested derivatives was measured spectrophotometrically during the cultivation at 28 "C on a rotary shaker (180 rev. min-') until the culture has at- tained the stationary phase. No inhibitory effect of DMSO on the growth of E. coli was detected at the used concentration (1 % V N ) .

2.2.3 Specific Growth Rate Determination

The growth curves obtained by spectrophotometrical measurements were described by Eq. 1 published previously [13]:

MA,/Ao) = uct - a In [b exp (ct) + 11 ( 1 )

where A, is the absorbance of the bacterial suspension at the time of measurement r and A, is the absorbance at the time of inoculation. The values of the adjustable parameters a, b, and c were optimized by nonlinear regression analysis. The specific growth rates at cho- sen times after inoculation (t = 2,4,6, 8,lO h) were calculated from

The partition coefficients P, determined using a kinetic method in the system 1-OctanoVwater, were published previously [ 11 1. For the compounds where sufficient quantities for this experiment were not available, the partition coefficients were estimated as follows. The partition coefficients P, were calculated by the Crippen method [14]. As this method does not take into account the interactions between more distant polar fragments that can be anticipated between the substituents R, and the oxygens of the skeleton, the calculated values of P, were correlated with the experimental values of P as logP=1.136 logP, - 1.828 (n=7, r=0.965, SD=0.340, F = 68) and the missing values of P were estimated from this equation.

2.4 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:l drug-receptor interaction and (2) pro- portional to the fraction of the receptors occupied, kinetics of the biological activity following the single dose can be described as [I51

l/c, = [K (1 -X)/X(APB + B)] exp [-(& + D)r/(APp + B)] (2)

where c, 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 p is the exponent from the Collander equation relating hydrophobicity of the membranes, inert proteins and metabolizing enzymes to that of the reference (usually l-octa- noywater) system [ 161. 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-D can acquire various functional forms depending on the properties of both the drug molecules (e.g. ioni- zation [17]) and the test system (e.g. change in the pH value [18]). The terms A and B express structure-nonspecific interactions and their functional forms can contain only physicochemical properties of the drug molecules. If the tested compounds do not ionize, as it is the case with the kojic acid derivatives, the term A is a constant that can be optimized by non-linear regression analysis and B = 1. In contrast, K, C, and D describe structure-specific properties and

Quant. Struct.-Act. Relat. 15. 87-93 [ 1996) QSTAR: Antibacterial Effects of Kojic Acid Derivatives 89

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. The data on kinetics of biological activity of a series of compounds are complex and a direct application of Eq. 1 with the terms K, C, and D substituted by various possible functional forms could cause problems in the search for a suitable functional form and, conse- quently, with initial estimates in the nonlinear regression analysis. The situation can be simplified by fitting the dependence of biological activity for each compound to the simple monoexponential function of time:

as well as the parameters A and B quantifying the initial pseudo- equilibrium distribution of the compounds in the test biological system. The relation for the elimination rate parameter k,, (Eq. 5) comprises, in addition to A and B, the terms for hydrophobicity-dependent and -independent elimination (C and D, resp.). Eqs. 4 and 5 are easier to apply than the original Eq. 2 and can provide both functional forms for the terms A-D and reasonable initial estimates for the adjustable parameters in Eq. 2. Note that the terms A and B are encountered in both Eqs. 4 and 5 and should be substituted by identical expressions in both cases. If the compounds do not ionize, the term A should have approximately the same optimized value and the term B should be equal to unity in both Eqs. 4 and 5.

T = To exp (- k,,t) (3)

with T=l/c,, the subscript 0 indicating the initial conditions, and k,, as the elimination rate constant. Comparing Eqs. 2 and 3 we get

To = K ( i - X)/X(APp + B) (4)

and

k,, = (Cfp + D)/(A@ + B) (5)

Eq. 4 describes the dependence of the initial toxicity on the partition coefficient P and involves the drug-receptor association constant K

3 Results and Discussion

The structure of the nonionizable kojic acid derivatives, their I-octanol partition coefficients, and the values of the mean initial equieffective concentrations log T, and the elimination rate parameters k,, are summarized in Table 1. The biological data were obtained from the fit o f the logarithmized Eq. 3 to the experimental values of the mean equieffective concentrations measured at the individual exposure times for the media differing in their pH values (Table 2). The time courses of biological activities for all the tested compounds were monoexponential (Figure 1) and the fits of Eq. 3

Table 1. Structure of the studied kojic acid derivatives, their I-octanoVwater partition coefficients P, the indicator variables I ( I = 1 if R2 contains more than six bonds in the longest sequence), the initial toxicities To (= I / C ~ ~ , where cj0 is the concentration in mol L-' causing 50%-decrease in the specific growth rate of Escherichiu coli) and the elimination rate constants k,,.

No. R , Rz log P I log To

1 2 3 4 5 6 7 8 9

I0 1 1 12 13 14 15 16 17 1% 19 20 21

OH CH3 OH (CO)CHCI, OH (CO)CH,CHC12 OH (COI(CO)OC$, OH (CO)C(CHJ, OH (CO)CH&~-~I I )~

OH (CO)CH,O-2,4,6-triCI-PhC OH (CO)CH( CH,)O-2,4-diC1-PhC

OH (CO)CH,O - ~ - N P ) ~

CI CH,OH c1 (C0)Az'

Br (CO)CH,(~-TII)~

S(CH,),CH3 (CO)CH20(2,4-diCl-Ph)C

S(CH,),CH, (CO)CH20(2,4-diC1-Ph)c

OH (C0)-2,4,6-triC1-Phc

OH (C0)(2,5-F~)( 3-CI-Ph)'

CI CH3

Br (CO)CH3

S(CS)N(CH& CH,

S(CH2)?CH3 (CO)CH20(2-CH-,-4-CI-Ph)C

S(2-Py)' (CO)CH20(2-CH,-4-C1-Ph)C

- 0.257 - 0.669" - 1.103" - 1.646

0.705 0.681 1.92 1 1.699" I .863" 1.954= I .092a 0.161

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

- 0.275'

0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 I 0 1 1 I 1

2.609 f 0. I17 2.1 I5 f 0.1 I6 1.978 * 0.056 2.371 f0.158 2.974 f 0.112 3.742*0.132 3.865+0.127 4.071 f0 .131 3.915 f 0.102 3.698f0.135 3.892 f 0.093 3.066 f 0.079 2.596f 0.087 3.086 f 0.080 2.962 f 0.123 4.012 f 0.115 2.879 f 0.081 3.506 + 0.10 I 3.707 f 0.096 3.46410.108 3.724 *0.101

3.530 i 1.602 3.322~k 1.651 2.861 *OX13

2.961 i 0.000 11.66 & 3.716

11.85f 1.910 12.32 z t 1.870 11.99f 1.960 11.83 f 1.590 l 2 . 3 4 i 1.760 12.08f2.160 3.840 =k 1.280 3.720 k 1.271 3.245f 1.180 3.425 i 1.903

3.390 5 1.048 8.301 jt 1.283 8 . 3 1 8 i 1.344 4.9 15 f 1.754 7.864 f 1.238

12.21 * 1.550

a estimated. 2-Th = 2-thienyl. Ph = phenyl. 2-Np = 2-naphtyl. Az = 4-(3-methyl-1,2-oxazol)-yl. 2-Py = 2-pyridyl.

90 Katan'na PirSelovi er ul. Quant. Struct.-Act. Relat. 15. 87-93 (1996)

Table 2. Toxicities of the kojic acid derivatives ( T = where c30 is the concentration in mol L-' causing 50%-decrease in the specific growth rate of Escherichiu coli) in the medium with the given pH value at the given exposure times, their mean and calculated values (Eq. 9 with the optimized values of the parameters for the mean toxicities given in the text).

No. Time (h) log T at pH log T 5.6 6.0 6.6 7.0 7.6 8.0 mean & s.d. calc.

1

2

3

4

5

6

7

8

9

10

11

12

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 4 6 8

2.232 2.166 2.101 2.034 2.172 1.889 1.826 1.774 1.715 1.642 1.921 1.854 1.782 1.771 1.653 2.265 1.965 1.545 - - 3.011 2.943 2.886 2.821 2.763 3.712 3.313 2.997 2.653 2.414 3.811 3.405 3.101 2.854 2.601 3.93 3.623 3.445 3.265 2.954 3.812 3.503 3.197 2.843 2.524 3.593 3.356 3.103 2.800 2.645 3.534 3.321 3.023 2.763 2.568 2.854 2.814 2.732 2.665

2.645 2.554 2.486 2.402 2.336 2.123 2.054 1.986 1.91 1.849 1.953 1.824 - - - 2.151 2.011 1.602 - - 2.823 2.774 2.726 2.678 2.625 3.402 3.124 2.983 2.801 2.612 3.802 3.505 3.245 3.054 2.754 3.805 3.567 3.213 3.021 2.732 3.705 3.451 3.223 2.983 2.732 3.500 3.223 2.956 2.689 2.465 3.689 3.432 3.175 2.934 2.643 2.954 2.901 2.857 2.557

2.680 2.602 2.526 2.447 2.375 2.106 2.065 2.035 1.914 1.858 1.963 1.902 1.845 1.789 1.715 2.012 1.814 1.652 - - 3.042 2.956 2.856 2.764 2.665 3.302 3.145 3.011 2.856 2.634 3.487 3.247 3.022 2.766 2.542 4.000 3.756 3.465 3.221 2.998 3.602 3.412 3.223 2.953 2.743 3.278 3.076 2.832 2.53 1 2.365 3.702 3.431 3.154 2.893 2.634 3.021 2.943 2.855 2.787

2.470 2.400 2.336 2.265 2.198 1.911 1.863 1.801 1.754 1.702 1.723 - - - - 2.167 1.846 1.695 - - 2.812 2.762 2.714 2.667 2.615 3.478 3.200 2.975 2.698 2.489 3.489 3.284 3.103 2.956 2.795 3.623 3.521 3.268 3.100 2.786 3.600 3.324 3.243 3.024 2.783 3.632 3.23 1 3.065 2.789 2.476 3.789 3.476 3.146 2.811 2.545 3.044 2.953 2.865 2.832

2.390 2.346 2.298 2.246 2.197 2.154 2.032 1.928 1.832 1.793 1.723 - - - - 2.014 1.798 1.654 - - 2.793 2.742 2.697 2.65 1 2.6 11 3.632 3.368 3.101 2.873 2.688 3.604 3.302 3.032 2.812 2.563 3.713 3.478 3.265 3.043 2.784 3.802 3.532 3.236 2.954 2.73 1 3.473 3.211 2.987 2.675 2.365 3.452 3.367 3.167 2.934 2.704 3.100 2.98 1 2.848 2.781

2.620 2.535 2.445 2.356 2.265 2.112 2.054 1.998 1.938 1.874 1.953 1.879 1.802 1.756

2.201 2.020 1.862

-

- - 3.021 2.952 2.894 2.842 2.794 3.685 3.398 3.103 2.853 2.565 3.734 3.423 3.182 2.834 2.612 3.943 3.652 3.332 3.065 3.000 3.523 3.310 3.145 3.054 2.793 3.360 3.087 2.990 2.785 2.802 3.573 3.297 3.032 2.765 2.563 2.988 2.883 2.853 2.778

2.506f 0.175 2.434f0.163 2.365 f 0.156 2.292 f 0.148 2.257 f 0.083 2.049f0.117 1.982 fO.108 1.920f0.109 1.844fO.093 1.786 f 0.095 1.873 f 0.117 1.865 * 0.034 1.8 10 f 0.032 1.752 f 0.039 1.684 * 0.044 2.135f0.103 1.909 f 0.101 1.668 f 0.108 - - - - 2.917 10.119 2.855 f0.105 2.796 f 0.092 2.737 f 0.083 2.679 f 0.080 3.535 f 0.166 3.258 f 0.117 3.028 f 0.058 2.789 rt 0.092 2.567f0.101 3.655 f0.149 3.361 f0.099 3.114 f 0.086 2.879&0.106 2.645 f0.105 3.836 f 0.147 3.600 f 0.100 3.331 f0.103 3.119 3~ 0.100 2.876rk0.121 3.674 f0.118 3.422 f 0.091 3.211 f0.036 2.969 f 0.073 2.718 rt0.098 3.473 f 0.135 3.197f0.104 2.989 f 0.094 2.712 f 0.104 2.520f0.172 3.623 f 0.125 3.387zt 0.070 3.116 i 0.069 2.850 f 0.080 2.6 10 f 0.06 1 2.994 f 0.084 2.913 zkO.060 2.835 z t 0.05 1 2.733 f 0.103

2.505 2.439 2.372 2.306 2.240 2.175 2.109 2.042 1.976 1.909 1.779 1.712 1.646 1.579 1.513 1.901 1.592 1.283 0.973 0.664 2.947 2.881 2.816 2.750 2.684 3.593 3.288 2.982 2.676 2.370 3.674 3.414 3.155 2.896 2.636 3.680 3.403 3.125 2.848 2.571 3.676 3.412 3.147 2.882 2.617 3.672 3.416 3.160 2.904 2.648 3.657 3.356 3.055 2.754 2.454 2.760 2.694 2.628 2.561

Quant. Stmct.-Act. Relat. 13. 87-93 (1996) QSTAR: Antibacterial Effects of KOJIC Acid Derivatives 91

Table 2. Continued

No. Time ( h ) log Tat pH log T 5.6 6.0 6.6 7.0 7.6 8.0 mean f s.d. calc.

13

14

15

16

17

18

19

20

21

10 2 $

6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10

4 6 8

I0 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10 2 4 6 8

10

7 ..

2.632 2.553 2.478 2.411 2.367 2.3 12 3.151 3.001 2.865 2.735 2.676 3.000 2.9 I 1 2.83 I 2.745 2.652 3.900 3.578 3.378 2.956 2.72 3.005 2.875 2.762 2.634 2.532 3.402 3.200 3.043 2.8 I I 2.732 3.664 3.468 3.295 3.112 2.924 3.501 3.346 3.201 3.058 2.936 3.702 3.543 3.354 3.176 2.899

2.565 2.423 2.386 2.355 2.296 2.223 3.124 3.023 2.945 2.886 2.8 I3 2.955 2.872 2.804 2.704 2.614 3.834 3.656 3.356 3.110 2.874 2.804 2.725 2.68 I 2.634 2.522 3.552 3.302 3.088 2.932 2.734 3.600 3.417 3.243 3.045 2.891 3.501 3.343 3.122 3.002 2.856 3.497 3.348 3.178 3.038 2.879

2.734 2.689 2.543 2.398 2.243 2.1 19 3.056 2.982 2.92 1 2.883 2.814 2.8 1 2.752 2.687 2.63 1 2.200 3.874 3.621 3.422 2.876 2.920 2.775 2.732 2.654 2.623 2.554 3.198 3.032 2.977 2.765 2.61 I 3.386 3.224 3.076 2.920 2.765 3.389 3.312 3.245 3.165 3.078 3.550 3.395 3.247 3.098 2.938

2.775 2.423 2.387 2.38 I 2.342 2.3 I I 2.924 2.882 2.842 2.806 2.763 2.983 2.924 2.854 2.789 2.725 3.766 3.435 3.23 I 3.012 2.754 2.755 2.700 2.656 2.602 2.564 3.265 3.111 2.932 2.787 2.650 3.555 3.38 I 3.197 3.015 2.846 3.320 3.271 3.194 3.124 3.432 3.710 3.523 3.347 3.167 3.013

2.702 2.465 2.387 2.297 2.241 2.188 2.953 2.873 2.798 2.763 2.698 2.745 2.702 2.667 2.615 2.596 3.587 3.393 3.213 2.987 2.786 2.723 2.657 2.612 2.508 2.467 3.378 3.200 3.087 2.945 2.689 3.480 3.3 I I 3.168 3.024 2.864 3.262 3.189 3.134 3.054 2.958 3.440 3.298 3.154 3.01 I 2.923

2.756 2.613 2.505 2.386 2.301 2.211 3.000 2.963 2.925 2.883 2.842 2.754 2.7 12 2.675 2.622 2.587 3.654 3.467 3.256 2.952 2.854 2.800 2.743 2.723 2.62 I 2.603 3.245 3.118 2.986 2.795 2.632 3.588 3.423 3.278 3. I05 2.987 3.255 3.177 3.076 2.997 2.942 3.490 3.346 3.23 I 3.105 2.965

2.694 f 0.081 2.528 f 0.109 2.448 f 0.070 2.371 fO.041 2.298 f 0.05 I 2.227 f 0.074 3.035 f 0.092 2.954 f 0.063 2.883 f0 .057 2.826 f 0.067 2.768 f 0.068 2.875 * 0. I18 2.812f0.102 2.753 f 0.086 2.684 f 0.073 2.562 i 0.184 3.769rt0.126 3.525 f 0.108 3.309 zk 0.087 2.982 f 0.078 2.818fO.077 2.810 f 0. l o o 2.739 f 0.073 2.68 I f 0.054 2.604 i 0.048 2.540 f 0.046 3.340f0.130 3.161 f0 .094 3.019 f0 .064 2.839 f 0.078 2.675 f 0.052 3.546 f 0.099 3.37 I f 0.089 3.210f0.081 3.037 f 0.070 2.880 f 0.075 3.371 fO.111 3.273 * 0.075 3.162 f 0.062 3.067 f 0.067 3.034 f 0.208 3.565 f 0.115 3.409 f 0.10 I 3.252 f 0.084 3.099 f 0.066 2.936 f 0.048

2.495 2.492 2.426 2.359 2.293 -.-- 7 737 3.014 2.950 2.887 2.824 2.760 2.896 2.830 2.764 2.698 2.632 3 679 3.406 3.133 2.860 2.588 3.005 2.940 2.876 2.8 I I 2.747 3.478 3.360 3.243 3.126 3.009 3 503 3.376 3.248 3.121 2.994 3.212 3.157 3.102 3.047 2.992 3.574 3.41 1 3.248 3.086 2.923

were of satisfying quality (the lowest value of the correlation coefficient was 0.976, the highest standard deviation 0.098).

Here const and E are adjustable parameters. Then Eq. 4 can be re- written:

The initial toxicities To are plotted against the I-octanol/water par- log To = logP - log (APB + B) - log (EP + I ) + F/ + G (7) tition coefficient P in Figure 2. The data can be described by Eq. 4 where the drug-receptor association constant is expressed as the The fit of Eq. 7 to the experimental data (Table 1) provided the function of P and the indicator variable I assuming the value 1 following values of the adjustable parameters: A = (1.339 f. if the substituent in the position 2 has more than six bonds in a 0.435) x E = 1.087f0.189, F=(8.705*0.597) x lo-', direct sequence and the value 0 otherwise: and G=3.102f0.048. As the tested compounds do not ionize

under the physiological conditions, the value of the term B was K = const ( P + /) l(EP + 1) set as B = 1 [15]. The optimization of the parameter p was not (6)

92 Katarina PirSeiovi et nl Quant. Struct.-Act. Relat. 15. 87-93 (1996)

Time (h)

Figure 1. Logarithmized time course of biological activity (mean values for all media differing in their pH values) as described by Eq. 3 for compounds No. 1 (0). 4 (m), 7 (r),12 (v) and 20 (*) (structures in Table 1).

4 l-----l

2

logP Figure 2. Dependence of the initial equieffective concentrations log To on hydrophobicity as described by Eq. 7 with the values of the adjustable parameters given in the text. individual curves correspond to the value of the indicator variable 1=0 and I= 1.

needed and the parameter was set as p = 1. The fit of Eq. 7 to the experimental data is satisfactory as can be seen in Figure 2 as well as from the values of the statistical indices (n=21, r=0.985, SD=O.111, and F=185).

The dependence of the elimination rate parameters k,, on the partition coefficient P is depicted in Figure 3. Again the experimental points are split into two subsets according to the size of the substituent in the position 2. The dependence can be described by the following modification of Eq. 5:

Here I is the same indicator variable as in Eq. 5 . The values of the adjustable parameters were optimized by non-linear regression analysis as: D = (3.093 f 0.247) x D, = (9.556 & 0.757) x loe2, and A=(9.133 52.822) x In accord with the description for the initial toxicities (Eq. 7) the parameters B and p were not optimized and set as B = f! = 1. Again a satisfactory agreement between the model and experimental data has been achieved (n =21,

0.12 0 -

CI r

k v

0.08 - -

T I

0.04 -

0.001 ' " " ' I " ' -2 -1 0 1 2 3 4

logP Figure 3. Dependence of the elimination rate parameter k,, on hydrophobicity as described by Eq. 8 with the values of the adjustable parameters given in the text. Individual curves correspond to the value of indicator variable 1=0 and I = 1.

r =0.985, SD = 0.008, F = 293) as can be seen in Figure 3. Note that the optimized values of the parameter A in Eqs. 7 and 8 have very close values. This fact indicates that both descriptions for different aspects of the kinetics of biological activities (the drug-receptor association constant K and the initial pseudo-equilibrium distribution - Eq. 7, elimination rate - Eq. 8) are consistent and can be used for construction of a more complex QSTAR equation based on Eq. 2. Substitution of Eqs. 7 and 8 into Eq. 2 results in the following QSTAR expression:

log T= log P - log (Up + B) - (D + D,l)r/(APP + B) - log (EP + 1) + FI + G (9)

When Eq. 9 is fit to the mean toxicities (Table 2), the values of the adjustable parameters are optimized as follows: A= (2.309 f 0.759) x D=(3.327&0.984) x lo-', D,=(1.214~0.155) x lo-', E=(7.023& 1.026) x lo-', F=(8.916&0.918) x lo-', and G=2.972 * 0.073. The satisfactory quality of the f i t is, in addition to the standard deviations of the adjustable parameters, illustrated by the values of the statistical indices: n = 103, r=0.966, SD = 0.139, and F = 27 1. In a similar way Eq. 9 can be used for the correlation of all experimental data (Table 2) . Then the following results are obtained: A=(1.831 &0.421) x D= (4.791 f0.626) x D,=(9.851&0.971) x E = (4.870k0.452) x lo-', F=(7.806&0.593) x lo-', G= 2.907 f 0.045, n = 606, r = 0.949, SD = 0.177, and F= 1087. In both cases, using the mean as well as actual toxicities measured in the media with different pH values, fairly similar results have been obtained. The satisfactory quality of the fit and its prediction ability is documented also by the fact that in the cases where no toxicity was reported (derivative no. 4 after 8 and 10 h application - Table 2), the predicted toxicities are much lower thah the highest tested concentrations.

Equation 9 cannot be displayed graphically because it contains three independent variables. In order to get an imagination of its behavior, the experimental toxicities were corrected as:

log T,,,= log T - FI + D,l/(APB i- B) (10)

Quant. Strucr-Act. Relat. / 5 , 87-93 ( 1996)

logP

Figure 4. Antibacterial activity of kojic acid derivatives against Escherichia coli (corrected according to Eq. 10) as a function of hydrophobicity ( logf ) and time. The surface corresponds to Eq. 9 corrected according to Eq. 10 with the values of the adjustable parameters for the mean toxicities.

The corrected toxicities (calculated using Eq. 10 with the values of adjustable parameters for the mean toxicities) are plotted against the partition coefficient P and the exposure time t in Figure 4. The dependence of biological activity on P has a broad maximum. The decrease o f biological activity of hydrophilic compounds is caused by the diminished ability to bind to the receptors that are localized in the aqueous phases as indicated by the form of Eq. 9. The lower biological activity of hydrophobic compounds is connected with their lower concentrations in the intracellular aqueous phases and their slower inactivation. The time course of biological activity is governed by the metabolic inactivation of the compounds. The process is probably enzymatic, because its rate is dependent on the size of the molecules expressed roughly through the indicator variable I. Interestingly, within the limited series tested, the size of the substituent effect has a positive effect on the binding of the compounds both to the receptor and to metabolizing enzymes.

Although further studies are needed, the presented analysis seems to confirm the suitability of our approach to description of subcel- lular pharmacokinetics and its use for formulation of model-based QSTAR for the studied biological effects of nonionizable kojic acid derivatives. We plan to extend the analysis to the same biological activities of ionized kojic acid derivatives in the near future.

QSTAR. Antibacterial Effects of Kojic Acid Derivatives 93

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Acknowledgement

This work was supported by the grants Nos. 1/712/94 and 111435194 from the Slovak Grant Agency.

Received on October 27th. 95; accepted on January 3rd 96

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