quantitative structure-activity relationships (qsar) study of flavonoid derivatives for inhibition...

Quantitative Structure-Activity Relationships (QSAR)Study of Flavonoid Derivatives for Inhibition ofCytochrome P450 1A2

Taesung Moon1, Myung Hwan Chi1, Dong-Hyun Kim1, Chang No Yoon1* and Young-Sang Choi2

1 Bioanalysis and Biotransformation Research Center, Korea Institute of Science and Technology, P.O. Box 131 Cheongryang,

Seoul 130-650, Korea2 Department of Chemistry, Korea University, Seoul 136-761, Korea

Abstract

The quantitative structure-activity relationships (QSAR)

studies on ¯avonoid derivatives as cytochrome P450 1A2

inhibitors were performed using multiple linear regression

analysis (MLR) and neural networks (NN). The results of

MLR and NN show that Hammett constant, the highest

occupied molecular orbital energy (HOMO), the nonoverlap

steric volume, the partial charge of C3 carbon atom, and the

HOMO p coef®cients of C3, C30 and C4

0 carbon atoms of

¯avonoids play an important role in inhibitory activity. The

correlations between the descriptors and the activities were

improved by neural networks although the descriptors of

optimum MLR model were used in the networks, which

implies that the descriptors used in MLR model include

nonlinear relationships. Moreover, neural networks using

descriptors selected by the pruning method gave higher r2

value than neural networks using MLR descriptors.

1 Introduction


were introduced by Hansch and co-workers [1, 2]. In many

works, their methods have been applied to ®nd the relation-

ships between biological activities of chemical compounds

and their physicochemical properties. These relationships are

determined using multiple linear regression which minimizes

the variance between the data and model. However, third and

higher order terms as well as cross-product terms correspond-

ing to the interaction between physicochemical properties are

not used in practice. The equation determined using multiple

linear regression is simple but the lack of high order terms

restricts to ®nding linear relationships.

The neural networks have been focused in the ®eld of pattern

recognition. The most important features of neural networks

are the interconnections of many nodes called neurons, which

enable the parallel and distributed processing in the neural

networks. The interconnections convey information learned

from environments and facilitate content addressable storage

called neuron. To store a particular pattern, the connection

strengths called weights must be modi®ed to memorize the

distinguishable features of the pattern so that the pattern can

be recalled later. The nonlinear feature of neural networks

suggests their potential usefulness in QSAR study. Recently,

neural networks have been applied to ®nd the relationships

between the molecular physicochemical parameters and

biological activities [3±6].

Flavonoids are widely distributed in nature and found in all

parts of edible plants [7]. Based on chemical structures, they

can be broadly classi®ed as ¯avone, ¯avanonol, ¯avonol,

¯avonone, and ¯avan (Figure 1). Many ¯avonoids exhibit

activity on different enzymatic systems. They have been

shown to possess antiin¯ammatory, antiallergeric, antiviral,

antimutagenic, and anticarcinogenic activities [8±11].

Furthermore, some of these compounds were found to have

estrogenic or antiestrogenic activities as well as cytochrome

P450 1A2 inhibitory activity. Caffeine N3-demethylase

activity is inhibited by the presence of various ¯avonoids.


studies were carried out to obtain further insight into the

relationships between the structure and biological activity of

several ¯avonoid inhibitors for human cytochrome P450

1A2. The neural networks as well as multiple linear regres-

sion analysis were performed to ®nd out the relationships

between them. While there are several neural network

methods, the back propagation algorithm was used in this

study.

* To receive all correspondence

Key words: QSAR, multiple linear regression analysis (MLR),

neural networks (NN), ¯avonoids, cytochrome P450 1A2

Quant. Struct.-Act. Relat., 19 (2000) # WILEY-VCH Verlag GmbH, D-69469 Weinheim 0931-8771/00/0306-0257 $17.50+.50/0 257

Flavonoid Derivatives for Inhibition of Cytochrome P450 1A2 QSAR

2 Methods

2.1 Biological Activity Measurements

The inhibition assays of cytochrome P450 1A2 activities by

¯avonoids were performed by caffeine 3-demethylation

assay using human liver microsome [12]. The inhibitory

activities of ¯avonoids were determined as IC50 (concentra-

tion required to reduce the caffeine 3-demethylation activity

by 50%). The ¯avonoids used in this study and their structur-

al features are shown in Figure 1 and Table 1.

2.2 Molecular Modeling

Molecular structures of all the ¯avonoid derivatives were

constructed using the InsightII molecular modeling package

(MSI Inc.). All the rotable bonds were searched from 0� to

360� in 6� increments in order to obtain low energy struc-

tures. In the cases of neohesperidin and panasenoside, the

rotable bonds were searched in 30� increments because these

molecules have many rotable bonds. The lowest energy

conformer for a given molecule was minimized using the

conjugate gradient and va09a minimizers until maximum

energy derivatives were less than 0.001 kcaly(mol AÊ ). The

minimized structures were then fully geometry optimized

using AM1 model Hamiltonian in MOPAC in order to

compute the values of molecular descriptors which are

dependent on conformation. The following set of descriptors

were used in multiple linear regression analysis and neural

networks; (1) Hammett constant of B ring, (2) molecular

volume, (3) nonoverlap steric volume between each analogue

and reference molecule (¯avone), (4) connolly surface area,

(5) ratio of molecular volume to surface area (VolyArea), (6)

largest principal moments of inertia, (7) total dipole moment,

(8) highest occupied molecular orbital energy, HOMO, (9)

lowest unoccupied molecular orbital energy, LUMO, (10)

partial charges of C3, C5, C7, C30, C4

0, and C50 carbon atoms,

(11) HOMO p coef®cients of C3, C5, C7, C30, C4

0, and C50

carbon atoms, and (12) the difference between HOMO and

LUMO.

Table 1. The structures and IC50 values for ¯avonoid derivatives on caffeine N3-demethylationactivity by human hepatic microsomes [12].

Flavonoids Structure IC50 (M)

Flavone Chrysin 5,7-Dihydroxy¯avone 2.0610ÿ7

Apigenin 4 0,5,7-Trihydroxy¯avone 1.35610ÿ6

Luteolin 3 0,4 0,5,7-Tetrahydroxy¯avone 1.34610ÿ5

Flavonol Galangin 3,5,7-Trihydroxy¯avone 3.06610ÿ6

Quercetin 3 0,4 0,3,5,7-Pentahydroxy¯avone 1.69610ÿ4

Avicularin Quercetin 3-O-ararbinofuranose 3.77610ÿ4

Quercitrin Quercetin 3-O-Rha 2.24610ÿ4

Myricetin 3 0,4 0,5 0,3,5,7-Hexahydroxy¯avone 1.85610ÿ4

Fisetin 3 0,4 0,3,7-Tetrahydroxy¯avone 2.37610ÿ4

Morin 2 0,4 0,3,5,7-Pentahydroxy¯avone 9.46610ÿ6

Kaempferol 4 0,3,5,7-Tetrahydroxy¯avone 7.34610ÿ5

Panasenoside Kaempferol 3-O-Gal-Glu 3.68610ÿ4

Populnin Kaempferol 7-O-Rha 3.27610ÿ4

Flavanone Hesperetin 3 0,5,7-Trihydroxy¯avanone 2.72610ÿ4

Neohesperidin Hesperetin 7-O-neohesperidoside 5.05610ÿ4

Prunin Naringenin 7-O-Glu 2.73610ÿ4

Hesperetin-5-glucoside Hesperetin 5-O-Glu > 6610ÿ4

Naringenin 4 0,5,7-Trihydroxy¯avanone 1.82610ÿ4

Flavan (-)Epigallocatechin(EGC) 3 0,4 0,5 0,3,5,7-Hexahydroxy¯avan 1.05610ÿ4

Figure 1. Structure and numbering of ¯avonoid derivatives.

QSAR T. Moon, M.H. Chi, D.-H. Kim, C.N. Yoon and Y.-S. Choi

258 Quant. Struct.-Act. Relat., 19 (2000)

All conformational searches and molecular mechanics cal-

culations were carried out using Discover2.97 package (MSI

Inc.) with CVFF (Consistent Valence Force Field) imple-

mented on SGI Indigo2 (R4400) workstation.

2.3 QSAR Analysis

2.3.1 Selection of Training Set and Multiple Linear

Regression Analysis

In order to ensure reliability of our model, the data set was

divided into the training and test sets. The least-squares

estimate is b� (X 0X)ÿ1X 0y in the linear model

y � Xb� e �1�

where y is an N61 vector of independent variables, X is an

N6k matrix of dependent variables, b is the k61 vector of

coef®cients to be estimated, and e is an N61 vector of error

terms. Several criteria have been used for selection of the best

subset. One of the most popular criteria is the maximization

of jX 0Xj which is used in D-optimal design. In this work, the

stepwise addition method was applied for the D-optimal

design of Mitchell [13] for selection of training set. The

subsets having high jX 0Xj were listed in the order of

decreasing jX 0Xj. Then, one sample was added to the subsets

and the new subsets were listed again. This procedure was

repeated to reach a given number of members in the training

set. The number of training set members was set to 14 taking

into consideration of the ratio of the training to test sets. Prior

to the D-optimal design, the crossvalidation was performed

in order to ®nd out the optimum descriptors. Up to ten

descriptors, all the possible combinations of descriptors were

used in the crossvalidation to ®nd out the best regression

model and four descriptors were obtained ®nally. The multi-

collinearity among descriptors was identi®ed using variance

in¯ation factor (VIF) [14]. The VIF for the ith regression

coef®cient expressed as

VIF � 1

1ÿ r2i

�2�

is the coef®cient produced by regressing the descriptor xi

against the other descriptors, the xj (j 6� i). The models of

which VIF is greater than 10 were not considered. The

predictivity of the model is quantitated in terms of r2 which

is de®ned as

r2 � 1:0ÿP �ypred ÿ yactual�2P �yactual ÿ ymean�2

�3�

where ypred, yactual, and ymean are predicted, actual, and mean

values of the target property, respectively.

2.3.2 Neural Networks

Arti®cial neural networks consist of layers of which the

outputs are connected to the other neurons. While there are

many different arti®cial neural network architectures, the

most popular network used in QSAR is multi-layer feed-

forward network [15]. In this type of network the neurons are

arranged into groups called layers; an input layer, an output

layer and various number of hidden layers. The number of

neurons and layers depends on the number of descriptors in

the data set, the number of compounds and the type of output.

In this study, the back propagation neural network (BPN) [16,

17] was applied for the learning phase. The number of layers

is arbitrary and generally consists of n layers. The value of a

neuron Oj at the nth layer may be expressed

Oj �1

eÿayj�4�

yj � �P

j Wijxi� � yj �5�

where xi is one of the values of the neurons at the n±1 layer,

Wij is the connection weight to neuron j from neuron i, and yj

is a bias term. The training is carried out until a mean square

error (MSE) becomes small enough. The MSE is

MSE �P �tj ÿ Oj�2

�no: of compds:� no: of output units� �6�

where tj and Oj are the desired output and calculated output,

respectively. The calculated output was obtained by aver-

aging neural network predictions over several independent

networks in order to avoid the local minimum [18]. The

connection weights are iteratively changed to minimize MSE

as follows

W 0ij � Wij ÿ Z@MSE

@Wij

�7�

where W 0ij is the weight after iteration, MSE is a mean square

error, Z is a momentum. The values of input layer are rescaled

to have values between circa 0.1 and 1.0 by the scaling

equation

x 0ij �xij ÿ xmin � 0:1

xmax ÿ xmin � 0:1�8�

where xij is the value of nth descriptor, xmin and xmax are its

minimum and maximum values.


Quant. Struct.-Act. Relat., 19 (2000) 259

2.3.3 Pruning Method for Descriptor Selection

The importance of neurons in hidden or input layers was

estimated according to sensitivity [18±19].

Si �P wji

maxa jwjaj

!2

�Sj �9�

where maxa is the maximum weight of all weights ending at

neuron j and Sj is a sensitivity in the upper layer. The neuron

having the greatest value Si gives the most important in¯u-

ence on all other neurons in the next layer. So the sensitivities

of neurons in input and hidden layers were calculated and the

neurons with the small sensitivities were deleted. The prun-

ing was carried out iteratively to achieve a given number of

neurons which have small mean square error (MSE) accord-

ing the following procedure [20] ; (1) choose a large size

network and determine the number of neurons to be pruned to

step, (2) training the network, (3) compute neuron sensitivity

for every N-epochs, (4) delete the neurons with low sensi-

tivity, and (5) if stopping criterion is not met, go to step (2).

The sensitivities of output layer neurons are set to 1. All the

sensitivities in a layer are normalized to a maximum value

of 1.

3 Results and Discussion

3.1 Multiple Linear Regression Analysis

Table 2 shows the 14 training set members selected using D-

optimal design. Prior to training set selection, the four

descriptors were obtained by crossvalidation. Hesperetin-5-

glucoside was not used in the selection of training set

members because of its unde®ned IC50 value of

46� 10ÿ4 (Table 1). The high crossvalidated r2 value of

0.719 was achieved using four descriptors of Hammett

constant (Sig), the highest occupied molecular orbital energy

(HOMO), the HOMO p coef®cient of C3 carbon atom (Cp3),

and the HOMO p coef®cient of C30 carbon atom (Cp3

0). The

optimum MLR model is as follows

ÿlog�IC50� � 2:289�Sig� ÿ 2:295�HOMO� ÿ 2:580�Cp3��1:223� ��0:597� ��0:575��2:761�Cp 03� ÿ 15:795 �10��0:942� ��5:426�

This result suggests that the activity depends linearly on

Hammett constant, the highest occupied molecular orbital

energy (HOMO), the HOMO p coef®cients of C3 and C30

carbon atoms (Cp3 and Cp30). Since Hammett constant, the

partial charge, and HOMO p coef®cient are mainly depen-

dent on the substituents, the substituents of C3 and C30 carbon

atoms have an in¯uence on the activity. However, it is not

always possible to discuss about the effect of individual term

according to its coef®cient since the coef®cient results from

the combination of all descriptors. In our MLR model, the

individual descriptors of Sig, HOMO, Cp3, and Cp30 gave

low r2 values of 0.448, 0.055, 0.249, and 0.017, respectively,

so it is impossible to discuss about the effect of individual

descriptor according to its coef®cient.

3.2 Neural Networks

The neural networks (NN) were carried out using two kinds

of descriptor sets; (1) descriptors used in multiple linear

regression analysis (MLR) and (2) descriptors selected using

pruning method. The pruning was performed using one input

layer - one hidden layer - one output layer neural network

architecture. The learning rate and momentum were set to 0.7

and 0.3, respectively. The network was not allowed to run

more than 10000 epochs since full network training takes lots

of computation time. In order to avoid the local minimum, the

neuron sensitivity was obtained by averaging the sensitivities

over 10 independent networks. The 4-4-1 (an input layer with

four neurons, a hidden layer with four neurons, and an output

layer with one neuron) network architecture was ®nally

determined starting from the 23-23-1 one. The selected

descriptors were the nonoverlap steric volume (Steric), the

partial charge of C3 carbon atom (C3), the HOMO p coef®-

cients of C3 and C40 carbon atoms (Cp3 and Cp4

0) (Table 3).

The nonoverlap steric volume between each ¯avon deriva-

Table 2. The descriptors used in multiple linear regressionanalysis.

Compounds Sig(a) HOMO(b) Cp3(c) Cp3

0(d)

Training Set

Chrysin 0.00 ÿ9.267 ÿ0.457 ÿ0.076

Galangin 0.00 ÿ8.812 ÿ0.482 ÿ0.090

Morin ÿ0.25 ÿ8.839 ÿ0.445 ÿ0.000

Luteolin ÿ0.25 ÿ9.096 0.221 0.176

Naringenin ÿ0.37 ÿ9.282 0.131 ÿ0.027

Quercetin ÿ0.25 ÿ8.590 ÿ0.387 ÿ0.267

Myricetin ÿ0.13 ÿ8.613 ÿ0.360 ÿ0.205

EGC ÿ0.13 ÿ8.726 ÿ0.088 0.135

Hesperetin ÿ0.15 ÿ8.892 0.086 ÿ0.237

Prunin ÿ0.37 ÿ9.187 0.352 0.057

Populnin ÿ0.37 ÿ8.648 ÿ0.096 ÿ0.089

Avicularin ÿ0.25 ÿ8.841 ÿ0.383 ÿ0.267

Quercitrin ÿ0.25 ÿ9.003 0.318 0.208

Panasenoside ÿ0.25 ÿ9.250 0.445 ÿ0.012

Test Set

Kaempferol ÿ0.37 ÿ8.643 ÿ0.452 ÿ0.179

Apigenin ÿ0.37 ÿ9.102 ÿ0.464 ÿ0.206

Neohesperidin ÿ0.15 ÿ9.025 0.142 ÿ0.197

Fisetin ÿ0.25 ÿ8.980 0.177 0.069

Hesperetin 5-glucoside ÿ0.15 ÿ8.833 0.033 ÿ0.196

(a)Sig�Hammett constant(b)HOMO� highest occupied molecular orbital energy(c)Cp3�HOMO p coef®cient of C3 carbon atom(d)Cp3

0 �HOMO p coef®cient of C30 carbon atom



tive and the shape reference molecule (¯avon) depends on the

size of the substituents, so the size of the substituents has an

in¯uence on the activity. The HOMO p coef®cient of C3

atom is also selected in MLR, which implies the substitution

of C3 carbon atom plays an important role in inhibitory

activity. The full BPN was then performed with the 4-4-1

network architecture. The calculated output was obtained by

averaging neural network predictions over 50 independent

networks in order to avoid the local minimum. The experi-

mental and calculated ÿlog(IC50) values of training set in

multiple linear regressions analysis (MLR) and neural net-

works (NN) are shown in Table 4, in which the training set

shows good correlations between the descriptors and the

activities in NN. The r2 values of MLR, NN1 (NN using MLR

descriptors), and NN2 (NN using descriptors selected by

pruning) in training set are 0.867, 0.947, and 0.984, respec-

tively. Although the descriptors of optimum MLR model

were used as inputs of neural networks, the correlations

between the descriptors and the activities were improved

by neural networks. These results show that the descriptors

used in MLR model include nonlinear relationships. More-

over, neural networks (NN2) using descriptors selected by

the pruning method gave higher r2 value than neural networks

(NN1) using MLR descriptors. From the results, it is implied

that the descriptor selection method based on linearity (i.e.

multiple linear regression or crossvalidation) is not suf®cient

Table 3. The descriptors selected by pruning method.

Compounds Steric(a) C3(b) Cp3

(c) Cp40(d)

Training Set

Chrysin 13.01 ÿ0.287 ÿ0.457 ÿ0.200

Galangin 24.17 ÿ0.086 ÿ0.482 ÿ0.251

Morin 58.29 ÿ0.069 ÿ0.445 ÿ0.049

Luteolin 44.63 ÿ0.270 0.221 0.183

Naringenin 66.91 ÿ0.241 0.131 ÿ0.030

Quercetin 36.83 ÿ0.084 ÿ0.387 ÿ0.339

Myricetin 65.53 ÿ0.080 ÿ0.360 ÿ0.383

EGC 82.78 0.013 ÿ0.088 0.249

Hesperetin 84.24 ÿ0.232 0.086 ÿ0.233

Prunin 164.16 ÿ0.264 0.352 0.090

Populnin 137.70 ÿ0.091 ÿ0.096 ÿ0.141

Avicularin 130.19 ÿ0.079 ÿ0.383 ÿ0.315

Quercitrin 166.89 ÿ0.086 0.318 0.230

Panasenoside 280.29 ÿ0.034 0.445 0.007

Test Set

Kaempferol 29.97 ÿ0.091 ÿ0.452 ÿ0.287

Apigenin 20.06 ÿ0.293 ÿ0.464 ÿ0.300

Neohesperidin 292.82 ÿ0.272 0.142 ÿ0.207

Fisetin 52.92 ÿ0.070 0.177 0.068

Hesperetin 5-glucoside 196.07 ÿ0.230 0.033 ÿ0.195

(a)Steric� nonoverlap steric volume(b)C3� partial charge of C3 carbon atom(c)Cp3�HOMO p coef®cient of C3 carbon atom(d)Cp4

0 �HOMO p coef®cient of C40 carbon atom

Table 4. Experimental versus calculated 7 log(IC50) values in multiple linear regression analysis(MLR) and neural networks (NN1 and NN2).

MLR(a) NN1(b) NN2(c)

ÿlog(IC50) ÿlog(IC50) residual ÿlog(IC50) residual ÿlog(IC50) residual

Compounds (exp) (calc) (calc) (calc)

Training Set

Chrysin 6.70 6.439 ÿ0.261 6.494 ÿ0.206 6.673 ÿ0.027

Galangin 5.51 5.421 ÿ0.089 5.531 0.021 5.297 ÿ0.213

Morin 5.02 4.938 ÿ0.082 5.097 0.077 5.137 0.117

Luteolin 4.87 4.296 ÿ0.574 4.420 ÿ0.450 4.853 ÿ0.017

Naringenin 3.74 4.060 0.320 4.153 0.413 3.809 0.069

Quercetin 3.77 3.480 ÿ0.290 3.466 ÿ0.304 4.058 0.288

Myricetin 3.73 3.969 0.239 3.514 ÿ0.216 3.653 ÿ0.077

EGC 3.97 4.466 0.496 4.011 0.041 3.898 ÿ0.072

Hesperetin 3.57 3.315 ÿ0.255 3.467 ÿ0.103 3.551 ÿ0.019

Prunin 3.56 3.504 ÿ0.056 3.628 0.068 3.485 ÿ0.075

Populnin 3.49 3.020 ÿ0.471 3.459 ÿ0.031 3.494 0.004

Avicularin 3.42 4.046 0.626 3.594 0.174 3.520 0.100

Quercitrin 3.65 3.921 0.271 3.823 0.173 3.477 ÿ0.173

Panasenoside 3.43 3.553 0.123 3.606 0.176 3.466 0.036

Test Set

Kaempferol 4.13 3.678 ÿ0.452 3.505 ÿ0.625 4.750 0.620

Apigenin 5.87 4.688 ÿ1.182 4.839 ÿ1.031 6.556 0.686

Neohesperidin 3.30 3.586 0.286 3.508 0.208 3.467 0.167

Fisetin 3.63 3.848 0.218 3.677 0.047 3.640 0.010

Hesperetin 5-glucoside 3.22 3.429 0.209 3.474 0.254 3.473 0.253

(a)MLR�multiple linear regression analysis(b)NN1� neural networks using MLR descriptors(c)NN2� neural networks using descriptors selected by pruning method



for nonlinear ®tting (i.e. neural networks). The test set also

shows good predictivity. The predictive r2 values are 0.626,

0.671, and 0.800 in MLR, NN1, and NN2, respectively.

Statistics of MLR, NN1, and NN2 are summarized in Table 5.

The weight values of NN1 are listed in Table 6. In order to

compare the weight values of NN with the regression

coef®cients of MLR, the MLR was carried out using the

input values which are rescaled to have values between circa

0.1 and 1.0. The regression coef®cients of Sig, HOMO, Cp3,

and Cp30 are 0.196,ÿ0.271,ÿ0.395, and 0.237, respectively.

Since the signs of weights between hidden and output units

are all positive, the signs of weights between input and

hidden units can decide the signs of overall weight. The

weight values of Sig and Cp30 between input and hidden

layers are all positive and those of HOMO and Cp3 are all

negative. These results show good agreement with MLR in

which the regression coef®cients of Sig and Cp30 are positive

and those of HOMO and Cp3 are negative. The total weights

of descriptors were calculated by the following equation

Wtot �P

i Wij �Wjk �11�

where Wtot is the total weight of input descriptor i, Wij is the

weight between input and hidden units, and Wjk is the weight

between hidden and output units. The Wtots of Sig, HOMO,

Cp3, and Cp30 are 8.509, ÿ22.338, ÿ24.240, and 18.663,

respectively. The signs of Wtot and regression coef®cient are

the same. The Wtots and regression coef®cients of Sig and

Cp30 are positive and those of HOMO and Cp3

0 are negative.

The order of magnitude of Wtots and regression coef®cients is

also same (Cp34HOMO4Cp304Sig), which shows good

agreement between Wtots and regression coef®cients.

4 Conclusions

In this study the multiple linear regression analysis and

neural networks were carried out in order to obtain the

information about the inhibitory activity on cytochrome

P450 1A2. The D-optimal design and pruning method were

tried for selection of training set and descriptors, respec-

tively. The MLR, NN1, and NN2 showed good correlations

between the descriptors and the activities in training set (r2

values of 0.867, 0.947, and 0.984, respectively). The correla-

tions were improved by neural networks, although the

descriptors of optimum MLR model were used as inputs of

neural networks. These results imply that the descriptors used

in MLR model include nonlinear relationships. The weight

values of NN1 showed good agreement with the regression

coef®cients of MLR. Moreover, neural networks (NN2)

using descriptors selected by the pruning method gave higher

r2 value than neural networks (NN1) using MLR descriptors,

which suggests that the descriptor selection method based on

linearity is not suf®cient for nonlinear ®tting.

References

[1] Hansch, C., Maloney, P.P., Fujita, T., and Muir, R.M.,Correlation of biological activity of phenoxyacetic acids withHammett substitution constants and partition coef®cients,Nature 194, 178±180 (1962).

[2] Hansch, C., A quantitative approach to biochemical structure-activity relationships, Acc. Chem. Res. 2, 232±239 (1969).

[3] Andrea, T. A., and Kalayeh, H., Applications of Neuralnetworks in quantitative structure-activity relationships ofdihydrofolate reductase inhibitors, J. Med. Chem. 34, 2824±2836 (1991).

[4] Aoyama, T., Suzuki, Y., and Ichikawa, H., Neural networksapplied to quantitative structure-activity relationship analy-sis, J. Med. Chem. 33, 2583±2590 (1990).

Table 6. The weight values of NN1(a).

input hidden output weight

unit unit unit value

[between input and hidden units]

Vol 1st 2.396

Vol 2nd 2.497

Vol 3rd 2.399

Vol 4th 2.501

C3 1st ÿ6.334

C3 2nd ÿ6.428

C3 3rd ÿ6.323

C3 4th ÿ6.433

Cp3 1st ÿ6.914

Cp3 2nd ÿ6.812

Cp3 3rd ÿ6.912

Cp3 4th ÿ6.809

Cp50 1st 5.330

Cp50 2nd 5.227

Cp50 3rd 5.326

Cp50 4th 5.218

[between hidden and output units]

1st 1st 1.418

2nd 1st 0.414

3rd 1st 1.345

4th 1st 0.341

(a)NN1� neural networks using MLR descriptors

Table 5. Statistics of multiple linear regression analysis (MLR)and neural networks (NN1 and NN2).

Training Set Test Set

r2 s r2 s

MLR(a) 0.867 0.346 0.626 0.596

NN1(b) 0.946 0.219 0.671 0.559

NN2(c) 0.984 0.121 0.800 0.453

(a)MLR�multiple linear regressions(b)NN1� neural networks using MLR descriptors(c)NN2� neural networks using descriptors selected by pruning method



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Received on October 1, 1999; accepted on December 17, 1999



quantitative structure-activity relationships (qsar) study of flavonoid derivatives for inhibition...

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