Prediction of micelle–water partition coefficient from the theoretical derived molecular descriptors

Journal of Colloid and Interface Science 314 (2007) 665–672 www.elsevier.com/locate/jcis

Prediction of micelle–water partition coefficient from the theoretical derived molecular descriptors M.H. Fatemi ∗ , F. Karimian Department of Chemistry, University of Mazandaran, Babolsar, Iran Received 24 February 2007; accepted 8 June 2007 Available online 29 June 2007

Abstract The micelle–water partition coefficients of 81 organic compounds in SDS solution were predicted by quantitative structure–property relationship method. The multiple linear regression (MLR) and artificial neural network (ANN) techniques were used to build linear and nonlinear model, respectively. In this work the proposed QSPR models, both by MLR and ANN, contain identical descriptors which are zero order of Kier–Hall index, count of Hydrogen donors site [Zefirovs PC], average valency of a C atom, atomic charge weighted by partial positively charged surface area and minimum one electron reaction index for a C atom. The MLR model gave a root mean square (RMS) of 0.166, 0.25, and 0.289 for training, prediction and test sets, respectively, whereas ANN gave an RMS error of 0.06, 0.21, and 0.20 for training, prediction, and test sets, respectively. Comparison the results of these two methods reveals that those obtained by the ANN model are much better. © 2007 Elsevier Inc. All rights reserved. Keywords: Micelle–water partition coefficient; Multiple linear regressions; Artificial neural network; Quantitative structure–property relationship; Theoretical molecular descriptor

1. Introduction

distinct polarities and degree of hydrophobicity. The micelle– water partition coefficient, Kmw can be represented as follow:

When a surfactant is added to water in minute quantities, such that the total surfactant concentration is below the critical micelle concentration (CMC), each surfactant molecule moves about essentially free in solution and the solution behaves as a strong electrolyte. As more surfactant is added, and the concentration exceeds the CMC, the monomers tend to aggregate forming the micelles [1]. These micellar solutions are microscopically heterogeneous, being composed of amphiphilic micellar aggregate and the bulk surrounding solvent which contains surfactants whose concentration is approximately equal to the CMC. The solute can be preferentially solubilized into or onto the micellar assembly, a process which is dynamic and characterized by various rate constants. In fact, one of the most fundamental properties of aqueous micellar solutions is their ability to solubilize a wide variety of organic solutes with quite

[C]mc , (1) [C]w where [C]mc and [C]w are the concentration of solubilized considered compound in micelles and water (mol/L), respectively. There is considerable interest in the interaction between organic solutes and micellar structures for modifying chemical reactions as a model for understanding of even more complex phenomena such as those occurring in biological systems. Like wise the transfer of solute from one phase to another can be used to predict the solubilities of small molecules and anaesthetic drugs in biological membranes [2]. Additionally successful determination of micelle–water partition coefficient could greatly facilitate method development, and optimization of some separation methods such as micellar electrokinetic chromatography (MEKC) and micellar liquid chromatography (MLC). Finally the ability to quickly, accurately, and unambiguously evaluation the partition coefficients of a wide variety of solutes between micelle and water is of great importance in

* Corresponding author. Fax: +98 112 5242002.

E-mail address: [email protected] (M.H. Fatemi). 0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2007.06.047

Kmw =

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M.H. Fatemi, F. Karimian / Journal of Colloid and Interface Science 314 (2007) 665–672

the fields of micellar catalyst [3,4], tertiary oil recovery [5], enzyme and membrane modeling [3,4], and so forth. Various soft and hard methods were used for determination of Kmw . Micellar electrokinetic chromatography and micellar liquid chromatography are some examples of hard method. In these methods a surfactant is added to the mobile phase above the CMC, therefore the resultant micelles act as a pseudostationary phase and solute are separated by differential partitioning between micellar phase and mobile phase (and also stationary phase in MLC) [6]. In spite of the demonstrated success of these methods, the process can be very laborious if many parameters are involved, because numerous experimental points are necessary to derive the parameters of the hard model. Over the last decade, increased attention has been paid to the applications of “soft” models in chemistry. Soft models can be defined as approaches in which an explicit mathematical model is neither formulated nor used [7]. Methods used to calculate/predict Kmw value based on the soft model can be classified into three categories. One approach is to build the linear relationships between micelle–water and octanol–water partition coefficient as belows [8,9]: log Kmw = p log Pow + B,

(2)

where log Pow is the octanol–water partition coefficient and B is the constant of equation. The advantage of such approach is the availability of a very large database for log Pow that is the most widely used descriptor for solute hydrophobicity. A limitation of this equation is the existence of congeneric behavior (i.e., existence of different lines for various groups of solutes) for certain micellar systems (most notably, sodium dodecyl sulfate (SDS)) [8]. The second type method is the linear solvation energy relationships (LSER) which is represented by the following equation:   log Kmw = vVx + rR + sπ ∗ + a (3) α+b β + c.   The Vx , R, π ∗ , β, and α terms are the solute descriptors, while the system coefficients v, r, s, b, and a are related to the interactive properties of the pseudophase. The LSER have been extensively investigated for a variety of pseudo-phases in MEKC [10–12]. The use of LSER for estimation of log Kmw is limited  to thosesolutes whose descriptor values (i.e., Vx , R, π ∗ , β, and α) are known. The third method to calculate/predict Kmw is based on the additivity principles that assume partition coefficients of solutes which can be determined from the sum of constituent functional groups or molecular fragments, taking into account correction terms for various intramolecular effects and interactions such as resonance, hydrogen bonding interactions between neighboring groups, steric effects, and others. This approach can be divided into group contribution approach [13] and the fragmental constant approach [14]. Once the substituent constants are determined, the Kmw for a given solute can be predicted from the constituent groups without any prior experiments. Since in this method a plenty of training solute is needed to determine many group or fragment constants for the micellar systems and the experimental determination of the micelle water partition coefficients by

classical methods for a set of training solute initially is very difficult, therefore the application of this method is limited. In addition, the fatal shortcoming of this approach is difficult to generalize the built model to new compounds because every groups/fragments in new compounds must occur in the training solute and it is impossible to know every group or fragment constants. An alternative would be to develop methods for calculation of micelle–water partition coefficients from theoretical derived molecular descriptors. The prime example of such an approach is quantitative structure–property relationship (QSPR) which provides a promising method for the estimation of compound’s behavior based on the descriptors derived solely from their molecular structure to fit experimental data. This approach has become very useful in the prediction of physical and chemical properties [15,16]. The advantage of this approach over other methods lies in the fact that it requires only the knowledge of chemical structure and is not dependent on the experimental properties. This study can develop a method for the prediction of the property of new compounds that have not been synthesized or found [17]. The QSPR model was constructed by using multiple linear regression (MLR), artificial neural network (ANN) or support vector machine (SVM) techniques [18–22]. QSPR methods have been applied for the calculation of micelle–water partition coefficient of peptides and other compounds from their structural descriptors [23,24]. Huanxiang and coworkers constructed a QSPR model for the calculation of Kmw for some organic compounds by MLR technique using five molecular descriptors. The statistical parameters of their model are R 2 = 0.94, F = 350, and S = 0.141. Descriptors which were used in their model are: Kier–Hall index (order 3) (KHI3), count of Hdonor sites [Zefirovs PC] (NHAS), FNSA-3 fractional PNSA (PNSA-3/TMSA) [Quantum-Chemical PC] (FNSA3), molecular volume (MV), and PPSA-3 atomic charge weighted PPSA [Zefirovs PC] (PPSA-3). In this investigation, the calculated descriptors from structure were used lonely to predict the micelle– water partition coefficients of 81 neutral solutes between bulk aqueous and SDS micelles by using the ANN and QSPR methods. 2. Methods 2.1. Data set The micelle–water partition coefficient Kmw of 81 organic compounds were taken from Ref. [25], that were used as a data set. These compounds were: alcohols, amines, ketones, aldehydes, esters and eters and are shown in Table 1. The Kmw of these compounds were obtained in 4 mM of SDS solutions, under the same conditions. The values of Kmw ranged between 1.27 to 3.93 for 4-aminophenol and 2,3,5,6-tetrachloroaniline, respectively. The data set was randomly divided into three groups including training, prediction and test set, which consists of 49, 16, and 16 molecules, respectively. The training set was used for model generation, prediction set was used for monitoring the extent of overtraining and test set was used for evaluation of the prediction power for obtained model.

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Table 1 The data set and corresponding observed and ANN predicted values of the micelle–water partition coefficient No.

Name

K(mw) exp

K(mw)ANN

K(mw)MLR

(KANN− Kexp )

Training set 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 36 37 38 39 40 41 42 43 44 45 46 47 48 49

p-Anisidine 1-Nitronaphthalene 4-Iodophenol 4-Isopropylphenol 4-Aminophenol 4-Bromophenol 4-Fluoroacetophenone 4-Bromobenzaldehyde 2-Methylnaphthalene 3-Methylphenol 3-Amino-o-cresol 2,3,5,6-Tetrachloroaniline 2-Chloronitrobenzene Phenazine 4-Nitrotoluene Carbazole 1-Fluoro-4-iodobenzene 4-Propoxyphenol 4-Amino-o-cresol 1,4-Acetylbenzene Quinaldine Methyl-2-methylbenzoate 2,7-Dimethylquinoline 4-Bromoacetophenone 1,3,5-Trichlorobenzene 4-Acetylphenol 4-Bromoaniline 1-Ethyl-4-iodobenzene 4-Propylphenol 1,4-Diethylbenzene 3-Bromophenol 4-Ethoxyphenol 4-Chlorophenol 4-Chloroaniline 4-Methoxyphenol p-Tolunitrile 4-Butoxyphenol 4-Chloroanisole 1,4-Dimethoxybenzene p-Aminobenzophenone Dimethylamine Ethoxybenzene 4-Iodoacetophenone 2-Amino-p-cresol Butyrophenone 4-Bromonitrobenzene 4-Methylphenol 4-Diiodobenzene 1-Chloro-4-iodobenzene

1.94 3.23 2.71 2.80 1.27 2.47 2.24 2.66 3.51 2.04 1.62 3.93 2.45 3.21 2.49 3.46 2.91 2.57 1.76 2.29 2.95 2.82 3.22 2.85 3.58 1.96 2.39 3.75 2.91 3.58 2.44 2.09 2.32 2.23 1.62 2.45 3.01 2.75 2.34 3.09 3.30 2.48 3.08 1.89 2.87 2.61 2.08 3.79 3.36

2.09 3.21 2.67 2.98 1.28 2.48 2.32 2.58 3.54 2.07 1.69 3.84 2.48 3.27 2.53 3.44 2.94 2.56 1.74 2.32 2.89 2.81 3.38 2.93 3.54 1.98 2.41 3.76 2.84 3.51 2.44 2.03 2.21 2.27 1.61 2.43 3.06 2.74 2.35 3.06 3.23 2.47 3.05 2.01 2.91 2.60 2.08 3.75 3.40

2.05 3.00 2.57 2.77 1.47 2.48 2.22 2.59 3.35 2.01 1.17 3.70 2.33 3.50 2.44 3.43 2.86 2.62 2.03 2.52 2.86 2.72 3.34 3.09 3.49 1.92 2.51 3.76 2.68 3.60 2.41 2.26 2.10 2.25 1.92 2.56 3.00 2.78 2.59 2.96 3.20 2.49 3.16 2.15 2.92 2.80 2.05 3.83 3.39

0.15 −0.02 −0.04 0.18 0.01 0.01 0.08 −0.08 0.03 0.03 0.07 −0.09 0.03 0.06 0.04 −0.02 0.03 −0.01 −0.02 0.03 −0.06 −0.01 0.16 0.08 −0.04 0.02 0.02 0.01 −0.07 −0.07 0.00 −0.06 −0.11 0.04 −0.01 −0.02 0.05 −0.01 0.01 −0.03 −0.07 −0.01 −0.03 0.12 0.04 −0.01 0.00 −0.04 0.04

Prediction set 50 51 52 53 54 55 56 57 58 59 60

1,4-Benzenedimethanol 4-Fluorophenol 3-Methylphenol 4-Methylbenzyl alcohol 4-Chlorobenzyl alcohol 3,5-Dimethylphenol 4-Chloronitrobenzene 1-Chloro-4-fluorobenzene 4-Chloroacetophenone Ethylbenzoate 4-Bromoanisole

1.45 1.81 2.04 2.12 2.30 2.43 2.46 2.50 2.70 2.86 2.90

1.57 2.04 2.07 2.09 2.56 2.70 2.09 2.35 2.70 2.50 3.20

2.17 1.58 2.02 2.57 2.56 2.51 2.44 2.46 2.72 2.68 3.13

0.12 0.23 0.03 −0.03 0.26 0.27 −0.37 −0.15 0.00 −0.36 0.30 (continued on next page)

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Table 1 (continued) No.

Name

K(mw) exp

K(mw)ANN

K(mw)MLR

(KANN− Kexp )

61 62 63 64 65

o-Dichlorobenzene 4-Bromochlorobenzene Valerophene 1-Bromo-4-iodobenzene Hexanophenone

3.01 3.10 3.27 3.51 3.72

2.83 3.26 3.36 3.71 3.65

2.92 3.30 3.27 3.73 3.60

−0.18 0.16 0.09 0.20 −0.07

Test set 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81

4-Hydroxybenzyl alcohol 2-Amino-m-cresol Phenethyl alcohol 3-Methylbenzyl alcohol 3-Chlorophenol 1,4-Diacetoxybenzene 4-Ethylphenol Propiophenone 1-Bromo-4-fluorobenzene p-Xylene 4-Iodobenzaldehyde p-Dichlorobenzene 4-Bromotoluene 1,4-Dibromobenzene 1-Methylnaphthalene Biphenyl

1.36 1.80 1.97 2.10 2.30 2.39 2.46 2.50 2.66 2.81 2.89 2.95 3.10 3.24 3.47 3.58

1.11 2.23 2.00 2.05 2.29 2.60 2.79 2.79 2.85 2.83 2.70 2.77 3.41 3.63 3.51 3.59

1.71 2.15 2.40 2.43 2.04 3.10 2.36 2.52 2.78 2.94 2.70 2.96 3.30 3.64 3.36 3.34

−0.25 0.43 0.03 −0.05 −0.01 0.21 0.33 0.29 0.19 0.02 −0.19 −0.18 0.31 0.39 0.04 0.01

Table 2 Specification of multiple linear regression model Descriptor

Notation

Coefficient

S.E.

Mean effect

Kier–Hall index order Count of H donor sites Zefirovs PC Average valency of a C atom Atomic charge weighted partial positively charged surface area Minimum one electron reaction index for a C atom Constant

KHI H-donors AVC PPSA-3 MERI

0.487 −0.011 20.026 −0.149 −0.148 −78.680

±0.026 ±0.002 ±3.532 ±0.043 ±0.046 ±13.868

18.672 −7.034 5.670 −3.482 −3.236

2.2. Molecular descriptors One important step in QSPR investigation is the numerical representation of the chemical structure (often called molecular descriptor). The built model performance and accuracy of the results are strongly dependent on the way that descriptor was performed. The software CODESSA, developed by Katritzky group, enables the calculation of a large number of quantitative descriptors based on the molecular structural information [26–28] and codes this chemical information into mathematical form. In this way the structures of compounds were drawn with HyperChem 4.0 program [29] and exported in a file format suitable for MOPAC program [30]. The geometry optimization was performed with the semi empirical quantum method AM1 by MOPAC 6.0 [31]. All geometries had been fully optimized without symmetry restrictions. The HyperChem and MOPAC output files were used by the CODESSA program to calculate five classes of descriptors including: constitutional (number of various types of atoms and bonds, number of rings, molecular weight, etc.), topological (Winner index, Randic indices, Kier–Hall shape indices, etc.), geometrical (moment of inertia, molecular volume, molecular surface area, etc.), electrostatic (minimum and maximum of partial charges, polarity parameters, charged partial surface area descriptors, etc.), and

quantum chemical (reactivity indices, dipole moment, HOMO and LUMO energies, etc.). Some descriptors generated for each compound, encoded similar information about the molecule of interest, therefore, it was desirable to test each descriptor and eliminate those that show high correlation (R > 0.90) with each other. Subsequently the method of stepwise multiple linear regression was performed on the training set to select the most important descriptors and to calculate the coefficients relating the descriptors to micelle–water partition coefficient. The name of descriptors that appear in the best MLR equation and other statistical parameters of this model are shown in Table 2. These descriptors are: zero order of Kier–Hall index (KHI), count of hydrogen donors site [Zefirovs PC] (H-donors), average valency of a C atom (AVC), atomic charge weighted by partial positively charged surface area [Quantum-Chemical PC] (PPSA-3) and minimum one electron reaction index for a C atom (MERI). These descriptors were used as inputs for generated ANN. 2.3. Artificial neural network generation The term “artificial neural network” denotes a computational structure intended to model the properties and behavior of the brain structures, particular self-adaptation, learning and paral-

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lel processing. They are nonlinear mapping structures based on the function of the human brain which are intelligent, thinking machines and working in the same way as the animal brain. Although the concept of ANN analysis has been discovered nearly 50 years ago it is only in the last two decades that application software has been developed to handle practical problems. ANN were developed initially to model biological functions. A detailed description of the theory behind a neural networks have been adequately described elsewhere [32–39]. A complete ANN is composed of a set of nodes and a set of interconnections between them. Each neuron is a processing element (PE) that receives one or more inputs and produces an output signal through a transfer function (activation function). Associated with each connection, there is a weight. Neural networks are based on the principle that a highly interconnected system of simple processing elements can learn complex interrelationships between independent and dependent variables. The behavior and properties of such a net is dependent on the computational elements, in particular the weights and the transfer function, as well as the net topology. Usually the net topology and the transfer function are specified in advance and are kept fixed, so only the weights of the synaptic connections, and the number of neurons in the hidden layer need to be estimated. The error function should be minimized so that the neural network achieves the best performance. Different algorithms have been developed to minimize the error function. The most popular is the so-called back-propagation (BP) algorithm, which belongs to the class of supervised learning techniques. The error at the output layer in a BP neural network propagates backward to the input layer through the hidden layer in the network to obtain the final desired output. The gradient descent method is utilized to calculate the weights of the network and adjust the weights of interconnections to minimize the output error. In this work, multi layered feed forward neural networks were used, which employed the algorithm of back-propagation of errors and a gradient-descent technique, known as “delta rule” [40,41] for the adjustment of the connection weights (further called BP networks). BP networks comprise one input layer, one (or possibly several) hidden layer(s) and an output layer. The number of nodes in the input and output layers are defined by the complexity of the problem being solved. The input layer receives the experimental information and the output layer contains the response sought, for example the migration times, resolution of a defined peak pair, overall resolution, etc. The hidden layer codes the information obtained from the input layer, and delivers it to the output layer. The number of nodes in the hidden layer may be considered as an adjustable parameter [7]. In this work, descriptors that appeared in the selected MLR model were used as inputs for the generated ANN and its output was the Kmw for molecules of interest. The value of each input was divided into its mean value to bring them into the dynamic range of the sigmoid transfer function in the ANN. Commonly neural networks are adjusted, or trained, so that a particular input leads to a specific target output. Before training, the network was optimized for the number of nodes in the hidden layer, learning rates and momentum. Then the network was trained using the training set by back-propagation strategy

669

to optimize the values of the weights and biases. It is known that neural networks can become over-trained. An over-trained network has usually learned perfectly the stimulus pattern which it has be seen (training set), but cannot give accurate predictions for unseen stimuli, and it is no longer able to generalize. There are several methods for overcoming this problem. One of the superior methods is to use an external set to validate the generalization of the network during training [35]. In order to evaluate the performance of ANN, standard error of calibration (SEC) and standard error of prediction (SEP) were used [42]. 3. Results and discussion The data set and corresponding observed and ANN predicted values of the kmw of all molecules studied in this work are shown in Table 1. Table 2 shows the names of descriptors and specification of the obtained MLR model which were constructed by using of stepwise procedure. Detailed explanations about these descriptors were found in the Handbook of Molecular Descriptors [43]. Among different factors affecting the micelle–water partition coefficient of a solute, size of the hydrophobic segment has the most significant effect. As shown in Table 2, the most important descriptor with the highest mean effect (18.672) was zero order Kier–Hall index. This descriptor which usually known as Kier–Hall connectivity indices were calculated from the following equation:  −1/2 K n  m (4) δa χq = , k=1

a=1

k

where k runs over all of the mth-order subgraphs constituted by n atoms (n = m + 1 for acyclic subgraphs); K is the total number of mth-order subgraphs present in the molecular graph and in the case of path subgraphs equal the mth-order path count m P . The product is over the simple vertex degrees δ of all the vertices involved in each graph. The subscript “q” for the connectivity indices refers to the type of molecular subgraph and ch is for chain or ring, pc for path-cluster, c for cluster, and p for path [44]. This topological descriptor represents the size of the hydrophobic segment and contains the group contributions for all nonhydrogen atoms in the molecules. As the number of carbons in a molecule increase the hydrophobicity of molecule increases, therefore the tendency of solute to binding with micelle increases. The positive sign for the mean effect of this descriptor indicates that increasing of the value related to this descriptors increase the value of Kmw . The second descriptor in the model is the count of Hydrogen donor sites, which indicates the Hydrogen donor ability of a molecule. The negative sign of the mean effect (−7.034) for this descriptor reveals that by the addition in number of Hydrogen donor sites for a molecule, the solubility of molecule in aqueous phase increases due to increasing in hydrogen bonding, therefore its Kmw decreases. Average valency of carbon atom is the third descriptor which appeared in the MLR model. This descriptor is a local electronic descriptor obtained by computational chemistry methods and represent the average valency of carbon atoms in a molecule [45]. Molecule with higher value

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of AVC is more hydrophobe, therefore its tendency to micellar media increases, hence the mean effect of this descriptor has positive sign (5.670). Other descriptor in MLR model is the atomic charge weighted partial positively charged surface area which can be defined as follows:    (SAi ) Q+ PPSA-3 = (5) i , A

where SAi is the surface area contributions of the ith positive atom in molecule and Q+ i is partial atomic charge for the ith positive atom. This descriptor is one type of the charged partial surface area (CPSA) descriptor, that encode features responsible for polar interactions between solute and micelle. As can be seen in Table 2, in MLR equation the PPSA-3 has a negative influence on the Kmw . This fact that PPSA-3 encodes the value of the charged surface area of a solute, reveals that the relatively charged solute has lower tendency to micelle due to decreasing in their lipophilicity. The last descriptor in MLR model which has the smallest mean effect (−3.236) was the minimum one electron reaction index for a C atom. The value of this descriptor calculated from the following equation: MERI =

  CiHOMO Cj LUMO ε i∈A j ∈A LUMO

− εHOMO

,

and bias values. To control the over fitting of the network during the training procedure, the values of SEC and SEP were calculated from training and prediction sets, respectively. Results obtained showed that after 8000 iterations, the value of SEP started to increase and over fitting began. To maintain the predictive power of the network at a desirable level, training was stopped at this point. Based upon the high values of iterations two points may arise. First the architecture of the generated ANN was correctly designed and second, the descriptors appeared in the model have been adequately chosen. To evaluate the prediction power of the network, the trained ANN was used to calculate the Kmw of molecules in the test set. Fig. 1 shows the plot of the ANN predicted versus the experimental values for the Kmw of the test set. The residuals of the ANN calculated values of the Kmw are plotted against the experimental values in Fig. 2. The propagation of the residuals on both sides of the zero line indicates that no systematic error exists in the development of the ANN. The average percent of deviation (APD) were calculated for ANN and MLR predicted values of Kmw [46]. The APD for training, predic-

(6)

where the summation are performed over all atomic orbitals i and j at given atom, CiHOMO and Cj LUMO donate the ith and j th atomic orbital coefficient on the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively. This quantum-chemical descriptor denotes the affinity of the molecules in the electronic interactions. As the value of this descriptors increases, the hydrophobicity of solute increases and the value of Kmw decreases. From the above discussion it was concluded that in the constructed MLR model two types of descriptors appeared which are electronic and topological. Topological descriptors (KHI and AVC) have the positive signs for their main effect, which indicate that by increasing the size of molecule its lipophilicity increases, therefore the value of Kmw increases. Electronic descriptors including H-donor, PPSA-3, and MERI, denote the tendency of solute in interaction with aqueous phase and therefore the mean effect of these descriptors has negative sign. The next step was the generation, optimization and training of the artificial neural network. Table 3 shows the architecture and specifications of the optimized ANN’s parameters. After the optimization of the ANN’s parameters the network was trained by using a training set for the adjustment of weights

Fig. 1. Plot of predicted Kmw against the experimental Kmw values.

Table 3 Architecture of the ANN and specifications Number of nodes in the input layer Number of nodes in the hidden layer Number of nodes in output layer Weights learning rate Biases learning rate Momentum Transfer function

5 5 1 0.1 0.5 0.9 Sigmoidal

Fig. 2. Plot of residuals against experimental value of Kmw .

M.H. Fatemi, F. Karimian / Journal of Colloid and Interface Science 314 (2007) 665–672

related to different molecular structural features that can participate in physicochemical process that occur in partitioning of solute between micelle and water.

Table 4 Statistical parameters obtained using the ANN and MLR models ANN R S.E. F

671

MLR

Training

Prediction

Test

Training

Prediction

Test

0.995 0.06 4886.2

0.941 0.21 107.7

0.948 0.20 124.1

0.967 0.16 124.3

0.916 0.25 73.4

0.890 0.29 53.2

tion and test sets in the ANN model are, 1.76, 7, and 7.75 which should be compared with the values of 5.14, 8.44, and 10.94, respectively for the MLR model. Comparison between these vales and also other statistical results of these two models in Table 4 indicate that obtained results using ANN are better than those obtained using MLR model. Kelly et al. calculated the partition coefficient of some neural solutes between bulk aqueous and micelles of SDS by the principles of additivity contributions of constituent functional groups and molecular fragments [25]. They calculate more than 20 functional groups substitution constant from 27 neural aromatic solutes as training set and then predicted the Kmw of the test set using these substituent constants. It was worth noting that the use of this method for estimation of Kmw (or other properties) is limited to those molecules whose have some special substitution which their values for contributions of substitution constants are known. In addition, the fatal shortcoming of this approach is difficult to generalize the built model to new compounds because every groups/fragments in new compounds must occur in the training solute and it is impossible to know every group or fragment constants. While in our presented QSPR method this restriction is not important. In this method the Kmw of solutes can be predicted from the molecular structure descriptors which can be calculated simply from the molecular structure for all molecules. In addition by using this method it is possible to interpret the effect of each molecular descriptor in the partitioning process of solute between water and micelle to better understanding the types and extent of interaction which occurs during the partition process of solute between water and micelle. 4. Conclusions The multiple linear regressions and the feed- forward artificial neural network were used to construct the linear and nonlinear QSPR for the prediction of micelle–water partition coefficient of 81 organic compounds based on the descriptors calculated from the molecular structure lonely. Both the linear and nonlinear models provided the satisfactory results, at the same time, the nonlinear ANN model produced better results with good predictive ability than linear model, so we can conclude that: (1) The proposed linear model could identify and provide some insight into what structural features are related to the binding of solute to micelle. (2) Nonlinear model can describe accurately the relationship between the structural parameter and micelle–water partition coefficient. (3) ANN proved to be a very promising tool in QSPR studies. Finally, descriptors which included in building of these models provide information

Appendix A. Nomenclature micelle–water partition coefficient concentration of solubilized considered compound in micelles [C]w concentration of solubilized considered compound in water [S]mc concentration of surfactant in both monomeric and micellar form Pow octanol–water partition coefficient B constant of equation p slop of equation Vx solute descriptor which is the solute’s McGowan’s volume  β solute descriptor which is the solute’s hydrogen bond acceptor ability/basicity  α solute descriptor which is the solute’s hydrogen bond donor ability/acidity solute descriptor which is the solute’s dipolarity/ π∗ polarizability R solute descriptor which is the solute’s excess molar refraction ν measure of system’s cohesiveness r measure of system’s dependence on interactions with the solute’s n or π electrons s measure of system’s dipolarity/polarizability b measure of system’s hydrogen bond donor ability/ acidity coefficient a measure of system’s hydrogen bond acceptor ability/basicity coefficient c regression constant SAi surface area contributions of the ith positive atom in molecule Q+ partial atomic charge for the ith positive atom i i and j atomic orbitals at given atom CiHOMO donate the ith atomic orbital coefficient on the highest occupied molecular orbital (HOMO) Cj LUMO donate the j th atomic orbital coefficient on the lowest unoccupied molecular orbital (LUMO) Kmw [C]mc

References [1] G.S. Hartley, Aqueous Solution of Paraffin Chain Salts, Herman, Paris, 1936. [2] S. Mall, G. Buckton, T. Gregory, D.A. Rawlins, J. Phys. Chem. 99 (1995) 8356–8361. [3] C.A. Bunton, Prog. Solid State Chem. 8 (1973) 239–281. [4] E.H. Cordes, C. Gitler, Prog. Bioorg. Chem. 2 (1973) 1–53. [5] P.H. Doe, W.H. Wade, R.S. Schechter, J. Colloid Interface Sci. 59 (1977) 525–531. [6] H. Nishii, J. Chromatogr. A 780 (1997) 243–264. [7] J. Havel, M. Breadmore, M. Macka, P.R. Haddad, J. Chromatogr. A 850 (1999) 345–353. [8] M.D. Trone, M.S. Leonard, M.G. Khaledi, Anal. Chem. 72 (2000) 1228– 1235.

672

[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

M.H. Fatemi, F. Karimian / Journal of Colloid and Interface Science 314 (2007) 665–672

Y. Ishihama, Y. Oda, N. Asakawa, Anal. Chem. 68 (1996) 4281–4284. A.A. Agbodjan, H. Bui, M.G. Khaledi, Langmuir 17 (2001) 2893–2899. S.Y. Yang, M.G. Khaledi, J. Chromatogr. A 692 (1995) 301–310. M.D. Trone, M.G. Khaledi, Anal. Chem. 71 (1999) 1270–1277. K.A. Kelly, S.T. Burns, M.G. Khaledi, Anal. Chem. 73 (2001) 6057–6062. S.T. Burns, M.G. Khaledi, Anal. Chem. 76 (2004) 5451–5458. X. Yao, X. Zhang, R. Zhang, M. Liu, Z. Hu, B. Fan, Comput. Chem. 26 (2002) 159–169. V. Tantishaiyakul, J. Pharm. Biomed. Anal. 37 (2005) 411–415. X.J. Yao, Y.W. Wang, X.Y. Zhang, R.S. Zhang, M.C. Lio, Z.D. Hu, B.T. Fan, Chem. Intel. Lab. Syst. 62 (2002) 217–225. J. Ghasemi, S. Saaidpour, S.D. Brown, J. Mol. Struct. 805 (2006) 27–32. M. Shamsipur, B. Hemmateenejad, M. Akhond, H. Sharghi, Talanta 54 (2001) 1113–1120. S. Agatonovic-Kustrin, L.H. Ling, S.Y. Tham, R.G. Alany, J. Pharm. Biomed. Anal. 29 (2002) 103–119. S. Yang, W. Lu, N. Chen, Q. Hu, J. Mol. Struct. 719 (2005) 119–127. V. Vapnik, The Nature of Statistical Learning Theory, Springer-Verlag, New York, 1995. Y. Shen, Prediction of peptide maps in CZE and MEKC systems, thesis, North California State University, 2005. H. Liu, X. Yao, M. Liu, Z. Hu, B. Fan, Anal. Chim. Acta 558 (2006) 86– 93. K.A. Kelly, S.T. Burns, M.G. Khaledi, Anal. Chem. 73 (2001) 6057–6062. A.R. Katritzky, V.S. Lobanov, M. Karelson, Comprehensive Descriptors for Structural and Statistical Analysis, ver. 2, 1994. A.R. Katritzky, V.S. Lobabanov, M. Karelson, Chem. Soc. Rev. 24 (1995) 279–287.

[28] A.R. Katritzky, V.S. Lobabanov, M. Karelson, Pure Appl. Chem. 69 (1997) 245–248. [29] Hyperchem 4.0. Hypercube, 1994. [30] J.P.P. Stewart, MOPAC 6.0, Quantum Chemistry Program Exchange, vol. 455, India University, Bloomington, 1989. [31] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 115 (1993) 5348. [32] M. Jalali-Heravi, M.H. Fatemi, Anal. Chim. Acta 415 (2000) 95–103. [33] M. Jalali-Heravi, M.H. Fatemi, J. Chromatogr. A 915 (2001) 177–183. [34] M. Jalali-Heravi, M.H. Fatemi, J. Chromatogr. A 825 (1998) 161–169. [35] M. Jalali-Heravi, M.H. Fatemi, J. Chromatogr. A 897 (2000) 227–235. [36] M.H. Fatemi, J. Chromatogr. A 955 (2002) 273–280. [37] S. Haykin, Neural Network, Prentice Hall, Englewood Cliffs, NJ, 1994. [38] M.T. Beal, H.B. Hagan, M. Demuth, Neural Network Design, PWS, Boston, 1996. [39] N.K. Bose, P. Liang, Neural Network, Fundamentals, McGraw–Hill, New York, 1996. [40] S.C. Beale, Anal. Chem. 70 (1998) 279–300. [41] U. Buterhorn, U. Pyell, J. Chromatogr. A 772 (1997) 27–38. [42] T.B. Blank, S.T. Brown, Anal. Chem. 65 (1993) 3081–3089. [43] R. Todeschini, V. Consonni, R. Mannhold, H. Kubinyi, H. Timmerman (Eds.), Handbook of Molecular Descriptors, vol. 11, Wiley–VCH, Germany, 2000. [44] L.B. Kier, L.H. Hall, Molecular Connectivity in Structure-Activity Analysis, Research Studies Press–Wiley, Chichester, UK, 1986. [45] M.S. Gopinathan, K. Jug, Theor. Chim. Acta 63 (1983) 497–509. [46] A. Jouban-Garamaleki, M.G. Khaledi, B.J. Clark, J. Chromatogr. A 868 (2000) 277–283.