Scientific paper
Tertiary Structure Prediction of a-Glucosidase and Inhibition Properties of N-(Phenoxydecyl) Phthalimide Derivatives
Maryam Pooyafar and Davood Ajloo*
School of Chemistry, Damghan University, Damghan, Iran
* Corresponding author: E-mail: ajloo@du.ac.ir Tel. +98 (0232)-5233051-6; fax: +98 (0232)-5235713; Zipcode : 3671641167
Received: 11-09-2011
Abstract
Due to increasing of population of diabetic patients, identifying factors for disease control has received much attention. a-glucosidase (EC 3.2.1.20) is an essential enzyme that helps to digestion of carbohydrates such as starch and sugar. Carbohydrates are normally converted into simple sugars, which can be absorbed through the intestine. Therefore, a-glucosidase inhibitors can be used to decrease the blood sugar level. We have studied the effect of inhibition of N-(phe-noxydecyl) phthalimide derivatives by a computer drug-design protocol involving homology modeling, docking simulation and Quantitative Structure Activity Relationship. The homology modeling of a-glucosidase showed a structure very similar to the crystal structure of oligo-1,6-glucosidase from Saccharomyces cerevisiae. Docking results showed the position of inhibitors binding site is close to active site and the carboxyl oxygen in phthalimide is an effective functional group for binding inhibitors to protein. The equation obtained by QSAR showed that, logIC50 decreases and so inhibition property increases when the size, polarity, geometry and number of halogen factors increase.
Keywords: a-Glucosidase, Inhibition, Homology modeling, Docking, Molecular dynamics simulation, QSAR
1. Introduction
Diabetes is one of the most serious, chronic diseases that is developing with the increase in obesity and ageing in the general population. Persistent hyperglycemia in diabetic patients despite appropriate therapeutic measures leads to several complications including retinopathy, nep-hropathy, and neuropathy.1 Some drugs have been developed for diabetes, and the best way to control postprandial plasma glucose level is medication in combination with dietary restriction and an exercise program. One of the therapeutic approaches for decreasing of postprandial hyperglycemia is to retard absorption of glucose by the inhibition of carbohydrate-hydrolysing enzymes, for example a-glucosidase, in the digestive organs.2 Glucosidases are responsible for the catalytic cleavage of glycosidic bond in the digestive process of carbohydrates with specificity depending on the number of monosaccharides, the position of cleavage site, and the configuration of the hy-droxyl groups in the substrate.3 a-glucosidase (EC 3.2.1.20) has taken a special interest of the pharmaceutical
research community because it was shown that the inhibition of its catalytic activity lead to the retardation of glucose absorption and the decrease in postprandial blood glucose level. This indicates that effective a-glucosidase inhibitors may serve as chemotherapeutic agents for clinic use in the treatment of diabetes and obesity. The catalytic role in digesting carbohydrate substrates also makes a-glucosidase a therapeutic target for the other carbohydrate-mediated diseases including cancer, viral infections and hepatitis4 and therefore many efforts have been made to identify new inhibitors for a-glucosidase5-8. On the other hand, traditional and experimental methods that are used in drug design are expensive and time consuming. Quantitative structure-activity relationship (QSAR) information of a-glucosidases has been limited to those of a few bacterial strains only in ligand-free forms.9 The lack of structural information about the nature of the interactions between a-glucosidases and the inhibitors has thus made it a difficult task to discover good lead compounds based on the structure-based inhibitor design. Consequently docking simulation can be a useful tool for elucidating the ob-
served activity of the identified inhibitors and binding modes.10
So far, many studies have been done to investigate the interaction of various inhibitors on the a-glucosidases. In particular, based on pharmacological studies involving thalidomide, it was found that phenylalkyl tetrachloro-phthalimide derivatives exhibited potent a-glucosidase inhibition.11
In this study, we investigated binding mode of N-(phenoxydecyl)phthalimide derivatives to a-glucosidase, by means of a drug-design protocol involving homology modeling, docking simulations, and quantitative structure-activity relationship.10 We chose the a-glucosidase from baker's yeast as the target protein in docking because it had been used widely in biological assays to identify new a-glucosidase inhibitors.
2. Methods and Materials 2.1. Homology Modeling: 3D Structure Prediction Using Computational Methods
Since there is no structural information for a-gluco-sidase from baker's yeast, we carried out homology modeling to obtain its three-dimensional structure. Primary sequence of the protein includes 584 amino acid residues and was taken from the Swiss-Prot protein sequence data bank (http://www.expasy.org/sprotAAccession No. P53341).12 To get a suitable structural template for homology modeling, we searched for the Protein Data Bank (http://www .rcsb.org/pdb/) using BLAST algorithm with the amino acid sequence of the target as input. Oligo-1,6-glucosida-se from Saccharomyces cerevisiae has the highest sequence identity with the target. So, its X-ray crystal structure (PDB ID: 3A47)13 was selected as the template for modeling. The primary structures of model and template share 72% sequence identity. The initial sequence alignment of protein (Uniprot ID: P533411) with structural template (PDB ID: 3A47) was carried out using the ClustalW program with BLOSUM matrices for scoring the alignments. Based on the highest alignment, the structure of a -gluco-sidase from baker's yeast was constructed using the MODELLER 9V814 program. One thousand models were made and the best model was selected based on DOPE score. DOPE (Discrete Optimized Protein Energy) is the total conformational energy of any amino acids which made by MODELLER for all models. The model which has the most negative energy will be the most stable structure and introduced as the best model. This model was validated by a well-established program, PROCHECK15 for the evaluation of Ramachandran plot.
The molecular dynamics simulation was done by Gromacs 3.3.116 to increase the accuracy of the calculated structure and optimization of the final model. Finally, we
investigated Root Mean Square Deviation (RMSD) plot during 20 ns simulation.
2. 2. Docking Simulation
AutoDock 3.05 program was used17 to obtain some energetic and structural insight into the inhibitory mechanisms of the identified inhibitors of a-glucosidase, as well as their binding modes in the active site. The ligands were designed in Hyperchem7 and optimized with AM1 semi-empirical method. Docking simulation was done in three boxes: first box was taken around the whole of protein with dimension 126 x 126 x 126 points and the spacing of 0.703 A. Second box was taken around the active site of protein, with dimension of 52 x 60 x 74 points and spacing of 0.375 A. Finally, after blind docking discussed in the first step, the most populated site was determined and the box with dimension of 52 x 58 x 66 points and the spacing of 0.375 A was located in that site. For each li-gand, 250 docking runs were performed with the initial population of 150 individuals. Maximum number of generations and energy evaluations were set to 27,000 and 2.5 x 105, respectively.
2. 3. Quantitative Structure-Activity Relationship
QSAR studies were applied to predict logIC50 and find the relationship between structure and activity. The ligands were designed by Hyperchem7.0 and then optimized by semi-empirical AM1 method. These ligands were transferred to Dragon-3.0 software and generate 1497 descriptors. All descriptors that had zero values or constant values in the data set were eliminated. The remaining descriptors were used to generate the prediction models using the SPSS 17 software package. Multiple linear regression method (MLR) and principal component analysis (PCA) were used to select descriptors which are responsible for half maximal inhibitory concentration (IC50) parameters of these compounds. PCA involves a mathematical procedure that reduces and classifies descriptors to the new sets of them.
2. 4. Cross-Validation Technique
Since a high-correlation coefficient only indicates how well the equations fit the data, cross-validation procedure was carried out in order to explore the reliability of the proposed models. In this aspect, the well-known "leave-one-out" (LOO) approach was used in which a number of models were developed with one sample ignored each time. Then, the ignored data were predicted by each model and the differences between predicted and observed activity values were evaluated.18
The cross-validation parameters (qc2v and PRESS) are mentioned in the respective equation
(1)
Which SD is standard deviation and PRESS (predictive residual sum of squares) is the sum of the squared differences between the actual and that predicted. A good q2v value should be always smaller than R2. A model is considered to be significant when q2v > 0.3.18
3. Results and Discussion 3. 1. Protein 3D Structure Prediction Using Homology Modeling Method
Figure 1 shows the sequence alignment between a-glucosidase MAL12 from baker's yeast (EC 3.2.1.20) and crystal structure of oligo-1,6-glucosidase from saccha-romyces cerevisiae (3A47), (EC 3.2.1.10). According to this alignment, the sequence identity and the similarity amounts are 72% and 85%, respectively. Judging from such a high sequence homology, a high-quality 3D structure of a-glucosidase can be expected in the homology modeling. It is indeed well known that a homology-mode-led structure of a target protein can be accurate enough to be used in docking studies. Based on the sequence alignment shown in figure 1, structural models of a-glucosida-se were calculated and one that has the lowest value of MODELLER objective function was selected as the final model.
Figure 2 displays the structure of a-glucosidase obtained from the homology modeling in comparison with the X-ray crystal structure of oligo-1,6-glucosidase from saccharomyces that was used as the template. The target and the template possess a very similar structure. The two enzymes also share the catalytic residues that are situated in their respective active sites in a similar fashion. To this way that Asp215, Glu277 and Asp352 residues form the catalytic triad in the template protein while the Asp214, Glu276 and Asp349 form in S. cerevisiae a-glucosidase, respectively. Two more residues, His109 and His348 of oligo-1,6-glucosidase which may be involved in substrate binding are also conserved in a-glucosidase (His111 and His348, respectively). It is because of both enzymes catalyze the hydrolysis of terminal glycosidic bond of carbohydrates. However, a-glucosidase is more extended in
Figure 2: Stereo view of template (A), modeled (B) and both fitted (C) structure of a-glucosidase
template	S- - S AH PETE PK W WK E AT 1" YQIYP AS FKD SNDDGWGDM KGIAS KLE YIKE L GAD ARV'I SPFYDSPQDD
query	M TISDHPE T E PK W WK E AT IYQIYP ASFK D SXND G WGD LKGIT SKLQYIKDL GYT3 AtWYCPFYD SPQQD
template	M G Y D IAN Y £ K V W PT Y GTN E DC'FAL IE KTHKLG MKFITDL VIN HC S SEHEWEKESRSS K.TNPK RD WFF W
query	MGYDISNYEKVWPTYGTNE DCFELIDKTHK1GMKFITDLVINHC STEHE WFKE SRS SKTNPKRDWFF W
template	RPPKGYDAEGK PIPPNN WKSSf FGGSA WTFDEKTQEFYLRLFC STQ PDLNWENE DCRKAIYES A\ 'GY'WX
queiy	RPPKGYDAEGK PIPPNN WK SFFGGS A WTFDETTNEF YLRLFASRQ VDLNWENEDCR RA IF E SAVGF WL
template DHGYDGFRIDVGSLYSKVYGLPDAP\TDKNSTWQSSDP Y'TLNGPRIHEFHQEMNQFI RNR\'KDGREIM
query	DHGVDGFRIDTAGLYSKRPGLPDSPIFDKTSKLQHPNWGSHNGPRIHEYHQEL HR FtvIKNRVKDGREIM
template	T VGEMQH AS DETKRLYT S ASRHE LSELFNFSHTDVGTSP LFR YN LVP FE LKD WKLAL .AELFRYINGTD
queiy	TVGEVAHGSDNA--L\"TS.\ARYE\SE\FSFTHVEYGTSPFFRYXI\PFTLKQ\YKEAIASNFLFKGTD
template	GWSTIYLENHDQPRSITRFGDD SPKN RVISGKLL S VLLS ALTGTLYVYQGQELGQINFKN WPVE KYED
query	.SWATTYiENHDQARSITRFADDSPKYRKISGKLLTLLECSLTGTL^'YQGQEIGQINFKEWPI EKYED
template	VH I RNNY"NAIKEEHGENSEEKiKKFLE.ALAL ISRDHARTPMQWSREEPNAGFSGPSAKPWFYLNDSFRE
query	VDVKNNYE IIKKSFGKNSKEMKDFFKGLALLSRDHSRTPMPWTKDKPNAGFTGPDXKP^TLLNESFEQ
template	GEsYEDE IKDPNSYLNFWKEALK FRKAHKDITVYGYDFEFID LDNKKLFSFTKKYNNKTLFAALNFSS
query	GIN VEQE^DDD S VLNF WKRALQAR KKYKELMIYGYDFQFIDLDSDQIFSFTKEYED KT&F AALNFS ©
template	DATDFKIPNDD SSFKLEFGN YPKKE VD ASSRT LKP WEGRIYISE
Figure 1: Sequence alignment between a-glucosidase (EC.3.2.1.20) and oligo-1,6-glucosidase (3A47A). The identity and the similarity between the corresponding residues are indicated in red and green, respectively. The active sites characterized by blue color.
amino acid packing than oligo-1,6-glucosidase due to the possession of 5 less amino acid residues in the alignment position.
The results of validation with PROCHECK showed 84.5% of residues of 3D structure are located in favorite region.
Figure 3 shows the DOPE (Discrete Optimized Protein Energy) score profile energy of the homology-modeled a-glucosidase in comparison to that of the X-ray structure of oligo-1,6-glucosidase. In this work, molecular dynamics simulations and energy minimization were performed by GROMACS. Figure 4 shows the corresponding Root Mean Square Deviation (RMSD) plot. As can be seen the system has reached stability during 20 ns.
Figure 4: RMSD plot during 20 ns simulation obtained by molecular dynamics
3. 2. Molecular Docking
Docking studies were performed to check the most probable binding site of new N-(phenoxydecyl) phthali-mide drivatives. The chemical structures and the inhibitory activities of these newly identified inhibitors were shown in Tables 1-3.20
In order to survey the correlation between inhibitory activities and binding energy, we made the box that sur-
Table 1: a-Glucosidase inhibitory activity of substituted N-(phe-noxyalkyl) phthalimide derivatives
Compound	n	ICS0(^M)
8a	2	296 ± 4
9a	3	240 ± 40
25a	4 33 ± 3
10a	5	20.2 ± 0.2
11a	6	10.3 ± 0.1
18a	8	6.5 ± 0.2
19a	9	3.04 ± 0.01
20a	10	2.5 ± 0.2
Table 2: a-Glucosidase inhibitory activity of N-(phenoxyalkyl) phthalimide derivatives
Compound	n	Ri	R2		R4	IC5o( ^M )
8a	2	H	H	H	H	296 ± 4
8b	2	H	H	Cl	H	94 ± 4
8e	2	ch3	H	Cl	H	14.8 ± 0.8
8f	2	ch3	H	Cl	ch3	13.0 ± 0.1
9a	3	H	H	H	H	240 ± 40
9b	3	H	H	Cl	H	59.0 ± 0.5
9c	3	Cl	Cl	H	H	15.0 ± 0.8
9d	3	H	Cl	Cl	H	7.55 ± 0.25
9e	3	ch3	H	Cl	H	8.9 ± 0.4
9f	3	ch3	H	Cl	ch3	9.5 ± 0.3
rounded whole of protein, then the position of the most negative docking energies were analyzed and it was found that the major of them locate near the active. We called that site as docking site. Then we put the box in the binding site. Alternative site was active site that we put the box on active site. So we have three cases; whole of protein, active site and binding site.
Figure 5 shows docking sites (Lys155, Phe157, Glu304, Arg312) and active sites (Asp214, Glu276 and Asp349) of ligands to protein as well as position of two sites relative to each other. These results verify that, the li-gands prefer to bind near the active site.
Figure 6 illustrates the calculated binding mode of compounds 20k and 25a (as the samples) in the active site and docking site of a-glucosidase. It is noteworthy that the carboxyl oxygen in phthalimide forms hydrogen bond with Asp349 and Glu276 in both position of active site
rchidue number
Figure 3: Comparison of the DOPE energy profiles for the homo-logy-modeled structure of a-glucosidase (blue) and the X-ray structure of oligo-1,6-glucosidase (red)
Tim tips)
Table 3: a-Glucosidase inhibitory activity of N-(phenoxydecyl) phthalimide derivatives
Compound	Ri	R2	R3	r4 IC	
20a	H	H	H	H	2.5 ± 0.2
20b	H	H	Cl	H	1.2 ± 0.2
20d	H	Cl	Cl	H	1.00 ± 0.01
20f	ch3	H	Cl	ch3	1.34 ± 0.04
20g	Cl	H	Cl	H	1.19 ± 0.11
20h	H	cf3	no2	H	0.83 ± 0.05
20i	H	H	ch3	H	2.10 ± 0.01
20j	H	H	no2	H	0.86 ± 0.03
20k	no2	H	H	H	1.78 ± 0.01
20l	H	no2	H	H	1.075 ± 0.005
20m	ch3	H	H	ch3	3.25 ± 0.02
20n	H	Cl	H	H	1.09 ± 0.08
20o	H	Cl	H	ch3	0.91 ± 0.05
20p	H	H	cf3	H	0.83 ± 0.12
20q	no2	H	Cl	H	0.475 ± 0.05
20r	H	Cl	Cl	no2	0.52 ± 0.02
20s	Cl	H	Cl	no2	0.75 ± 0.01
20t	no2	H	no2	H	0.97 ± 0.04
20u	no2	H	cf3	H	1.31 ± 0.01
20v	ch3	no2	Cl	ch3	3.6 ± 1.5
20w	ch3	H	no2	ch3	1.32 ± 0.12
20x	H	Cl	no2	ch3	0.65 ± 0.01
Figure 5: Position of active site (blue) and docking site (pink) obtained from docking calculation
and binding site. Since, these two residues play an important role in the most inhibitors of a-glucosidase,21 it looks like that the carboxyl oxygen can be an effective functional group for binding of inhibitors to protein and consequently phthalimide and its derivatives could be introduced as new inhibitors. The residues of two ligands mentioned above were listed in Table 4. The most negative free energies obtained by Autodock and predicted logIC50 were presented in Table 5.
Figure 6: Binding mode of 20k and 25a as the samples in the active site (A,B) and docking site(C,D) respectively, pink dotted lines indicate hydrogen bonds.
Table 4: Amino acids residues in the active site and docking site for compounds 20k and 25a. The common parts in two sites were depicted as bold.
	20k	25a
Active site	Phe157, Phe158, Phe177, Thr215, Glu276, Ala 278, His279, Phe 300, Glu304, Arg312, Asp349, Gln350, Asp408, Arg439	Phe158,Phe177, Asp214, Glu276, His279, Phe300, Glu304, Arg312, Asp349, Gln350
Docking site	Phe158, Phe177, Asp214, Glu276, His279, Phe300, Val303, Glu304, Thr307,Ser308,PRO309, Phe311, Arg312, Asp349, Gln350, Arg439	Phe157, Phe158, Phe177, Asp214, His245, Glu276, Ala278, Phe300, Arg439
Correlation between docking energies and log IC50 were obtained and correlation coefficient (R) for three docking cases; whole of enzyme, active site and binding site are equal to 0.290, 0.185 and 0.801. Figure 6 shows correlation between docking energy and logIC50 only for docking site that has better correlation. Thus, we conclude docking site has higher correlation than others. Thus, more tendency for interaction between ligand and enzyme has less logIC50 and more ligand efficiency.
Table 5. The most negative docking free energies and predicted
logIC50
-6
-8
jé u o
O
<
-10
■12
-14
-16
y = 2.0591X - 12.939	
0 801	
• /	■
	
	
A •	
-1
log IC50(exp)
Figure 7: Correlation between docking free energy (AG) and inhibition activities (log IC50) for docking site
3. 3. Quantitative Structure-Activity Relationship
The 1497 molecular properties (descriptors) were calculated for 37 ligands using Dragon-3.0. Logarithm of inhibitory activities was employed as dependent variables to find the relationship between structure and activity. Multiple linear regression analysis (MLR) of molecular descriptors was carried out using the stepwise strategy in the SPSS 17. The best obtained regression equation for the logarithm of inhibitory activities of 37 derivatives by MLR model is:
Com- Whole Active Binding pound enzyme site site
Experimental
logIC50
Predicted logIC50
MLR PCA
8a	-8.46	-8.56	-8.95	2.47	2.49	1.83
8b	-8.59	-8.98	-9.37	1.97	2.03	1.57
8e	-9.51	-9.05	-9.64	1.17	1.25	1.39
8f	-8.57	-9.55	-9.82	1.11	0.89	1.21
9a	-4.58	-9.15	-8.16	2.38	2.20	1.67
9b	-5.01	-9.40	-9.83	1.77	1.67	1.44
9c	-9.09	-9.73	-9.92	1.18	0.96	1.16
9d	-10.43	-9.97	-10.16	0.88	1.19	1.10
9e	-8.93	-9.91	-9.99	0.95	1.01	1.20
9f	-9.62	-10.01	-10.45	0.98	0.82	1.02
25 a	-7.18	-9.49	-9.69	1.52	1.61	1.33
10a	-4.76	-10.06	-9.88	1.30	1.14	1.11
11a	-6.79	-9.92	-10.64	1.01	0.82	0.86
18a	-7.77	-10.21	-11.09	0.81	0.77	0.74
19a	-7.22	-11.31	-10.45	0.48	0.59	0.54
20a	-7.93	-10.92	-9.55	0.40	0.00	0.38
20b	-9.49	-11.41	-13.11	0.08	-0.06	0.033
20d	-9.10	-9.62	-13.38	0.00	0.16	0.02
20f	-7.68	-8.91	-13.45	0.13	-0.15	0.00
20g	-9.93	-10.44	-13.33	0.07	0.11	-0.16
20h	-9.40	-10.16	-14.09	-0.08	-0.01	0.35
20i	-9.43	-10.21	-13.23	0.32	0.14	0.36
20j	-7.53	-11.18	-8.73	-0.07	0.00	0.40
20k	-7.78	-9.68	-13.33	0.25	-0.01	0.34
20l	-9.87	-10.65	-13.25	0.03	0.31	0.16
20m	-10.32	-11.45	-13.93	0.51	0.31	0.16
20n	-6.95	-10.64	-13.4	0.04	-0.10	0.19
20o	-8.81	-11.29	-13.33	-0.04	0.08	0.18
20p	-8.80	-10.57	-12.99	-0.08	-0.07	0.05
20q	-8.55	-10.50	-12.88	-0.32	-0.28	-0.18
20r	-8.15	-10.12	-14.15	-0.28	-0.23	-0.19
20s	-7.79	-10.12	-13.85	-0.12	0.08	0.17
20t	-7.57	-6.12	-13.38	-0.01	0.10	-0.04
20u	-10.47	-12.21	-13.46	0.12	-0.09	-0.27
20v	-9.28	-9.25	-13.49	0.56	0.38	-0.05
20w	-5.78	-5.80	-12.72	0.12	0.08	-0.11
20x	-6.45	-9.08	-13.66	-0.19	-0.05	1.47
(log ics0pred = 18.341 - (0.679 x ICS) - (7.862 x MATSle) - (9.117 x GATSQm) -(2.371 x GATS7e) - (4.763 x MWC09) - (0.070 x MorOAu) - (3.380 x BEHmA)
Where IC5 is belong to topological class, MATS7e, GATS8m and GATS7e to electronegativity, (MWC09) to size, Mor04u to 3D-MORSE and BEHm4 to BCUT descriptors. Now we define in detail some of these descriptors such as; Broto-Moreau Autocorrelation Descriptors (labeled as ATS), Moran Autocorrelation Descriptors (labeled as MATS) Geary Autocorrelation Descriptors (labeled as GATS).
2D Autocorrelation Indices are defined as
ATSdw = rUlUSij(wiwi)
(3)
Where w; and wj are the weights of the atoms i and j, we(m, p, e, v). The symbol for each of the autocorrelation descriptors is followed by two indices d and w, where d and w stands for the lag and weight, respectively. Thus, for example, ATS4m means the Broto-Moreau Autocorrelation descriptor of lag 4 weighted by mass.The lag is defined as the topological distance d between pairs of atoms. The topological distance between a pair of atoms (i, j) is given in the jth entry in the Topological Level Matrix. The lags can have any value from the set of {0, 1, 2, 3, 4, 5, 6, 7, 8}. The weights can be m (relative atomic mass), p (polarizability), e (Sanderson electronegativity) and v (Van der Waals volume). Relative mass is defined as the ratio of atomic mass of an atom to that of carbon. Similarly, the other three weights p, e and v are scaled by the corresponding values for carbon.
MATS7e: Moran Autocorrelation Descriptors are defined as:
MATSdW=(n)(A)/(B),	(4)
Where n is the number of atoms, A and B are
and
B = ZiU(w, - w)2
w; and wj are the weights of the atoms i and j, we(m, p, e, v), w is the mean of w; over the entire molecule, and 8^ is Kronecker delta, that is, 8y = 1 if the ijth entry in the Topological Level Matrix is = d, and 8- = 0 otherwise.22
GATS8m: GATS7e Geary Autocorrelation Descriptors
are definds as

(5)
and
Other variables are defined same as previous equation [18].
MWC09: Self-returning walk counts are defined as:
awe j

= Y? a.
W V
(6)
A walk starting and ending on the same vertex, i.e. closed in itself and called a self-returning walk. In particular, the diagonal elements (i, j) in the kth power matrix Ak denote the number of self-returning walks from the ith atom to itself.
Mor04u:MoRSE descriptors
3D MoRSE descriptors (3D Molecule Representation of Structures based on Electron diffraction) are derived from infrared spectra simulation using a generalized scattering function.23
= Z^zIl^iWiWj sin(sri;)/(sr;;)
where, rij is the Euclidean distance between the atoms i and j, and wi and wj are the weights of the atoms i and j respectively.24
Figure 8A shows correlation between predicted LogIC50 by MLR and experimental LogIC50 for 37 N-(phenoxydecyl)phthalimide derivatives with a regression coefficient of 0.975.
B = £i=i(Wi - w)2
Figure 8: Correlation between predicted LogIC50 by (A) MLR (B) PCA and experimental LogIC50. Training and test sets were shown
by filled and open symbols, respectively.
As we see in the equation (2) we can predict the log-IC50 for different compounds that we know their descriptor values. On the other hand, these descriptors may be not familiar for all chemists and biologists. So we selected some of more common descriptors that can be discussed the biological activity in detail. Table 6 has listed the 99 familiar descriptors among 1497 descriptors as well as their definition and classification. There are different properties such as size, charge, polarity, aromaticity, geometry or shape and hydrophobicity. Bivariate correlations were obtained between each descriptors and logIC50 and correla-
tion coefficients (R) values were listed in the last column of Table 6. Positive and negative values of R indicate direct and inverse correlation between logIC50 and descriptors. Namely positive values show that logIC50 increases with increasing the cited descriptors and negative values show decreases with increasing the descriptor. As table shows, the logIC50 decreases with size, polarity, number of functional group, geometry and hydrophobicty and increases with aromaticty.
Pascale, et al20 reported that the efficacy of the inhibition activity depends on the chain length of the substrate and compound 20a possessing 10 carbons afforded the highest levels of activity. Structure-activity relationship studies indicated a critical role of electron-withdrawing
substituents at the phenoxy group for the activity. In addition derivatives having a chlorine atom along with a strong electron-withdrawing group, such as a nitro group, were the most potent of the series.
Thus, they conclude that inhibition activity increases with number of CH2 group and Cl atoms, and electronegativity of NO2. On the other hand our findings also confirm their results so that the electronegativity in table 6 (descriptor 4 "sum of atomic Sanderson electronegativities scaled on Carbon atom)" has negative correlation. Also increasing number of nitro group (descriptor 90) causes decreasing the logIC50 and increasing biological activity. Number of chlorine (descriptor 24) or halogen atom (25) also has negative correlation with logIC50.
Table 6. Symbol, definition and classification of 99 used descriptors for PCA analysis
NO	Symbol	Definition	Class	R
1	MW	molecular weight	constitutional descriptors	-0.598
2	AMW	average molecular weight	constitutional descriptors	0.370
3	Sv	sum of atomic van der Waals volumes (scaled on Carbon atom)	constitutional descriptors	-0.835
4	Se	sum of atomic Sanderson electronegativities (scaled on Carbon atom	constitutional descriptors	-0.823
5	Sp	sum of atomic polarizabilities (scaled on Carbon atom)	constitutional descriptors	-0.834
6	Ss	sum of Kier-Hall electrotopological states	constitutional descriptors	-0.705
7	Mv	mean atomic van der Waals volume (scaled on Carbon atom)	constitutional descriptors	0.638
8	Me	mean atomic Sanderson electronegativity (scaled on Carbon atom)	constitutional descriptors	0.083
9	Mp	mean atomic polarizability (scaled on Carbon atom)	constitutional descriptors	0.594
10	Ms	mean electrotopological state	constitutional descriptors	-0.101
11	nAT	number of atoms	constitutional descriptors	-0.817
12	nSK	number of non-H atoms	constitutional descriptors	-0.827
13	nBT	number of bonds	constitutional descriptors	-0.817
14	nBO	number of non-H bonds	constitutional descriptors	-0.827
15	nBM	number of multiple bonds	constitutional descriptors	-0.489
16	SCBO	sum of conventional bond orders (H-depleted)	constitutional descriptors	-0.814
17	RBN	number of rotatable bonds	constitutional descriptors	-0.818
18	RBF	rotatable bond fraction	constitutional descriptors	-0.839
19	nDB	number of double bonds	constitutional descriptors	-0.489
20	nH	number of Hydrogen atoms	constitutional descriptors	-0.765
21	nC	number of Carbon atoms	constitutional descriptors	-0.810
22	nN	number of Nitrogen atoms	constitutional descriptors	-0.489
23	nO	number of Oxygen atoms	constitutional descriptors	-0.489
24	nCL	number of Chlorine atoms	constitutional descriptors	-0.103
25	nX	number of halogen atoms	constitutional descriptors	-0.281
26	qpmax	maximum positive charge	charge descriptors	-0.527
27	qnmax	maximum negative charge	charge descriptors	-0.326
28	Qpos	total positive charge	charge descriptors	-0.766
29	Qneg	total negative charge	charge descriptors	-0.765
30	Qtot	total absolute charge (electronic charge index - ECI)	charge descriptors	-0.765
31	Qmean	mean absolute charge (charge polarization)	charge descriptors	0.172
32	Q2	total squared charge	charge descriptors	-0.640
33	RPCG	relative positive charge	charge descriptors	0.399
34	RNCG	relative negative charge	charge descriptors	0.792
35	SPP	subpolarity parameter	charge descriptors	-0.524
36	TE1	topographic electronic descriptor	charge descriptors	-0.783
37	TE2	topographic electronic descriptor (bond resctricted)	charge descriptors	-0.769
38	PCWTe	partial charge weighted topological electronic charge	charge descriptors	-0.776
39	LDip	local dipole index	charge descriptors	-0.067
40	HOMA	Harmonic Oscillator Model of Aromaticity index	aromaticity indices	0.368
41	RCI	Jug RC index	aromaticity indices	0.337
NO	Symbol	Definition	Class	R
42	AROM	aromaticity (trial)	aromaticity indices	0.181
43	HOMT	HOMA total (trial)	aromaticity indices	0.362
44	J3D	3D-Balaban index	geometrical descriptors	-0.116
45	H3D	3D-Harary index	geometrical descriptors	-0.805
46	AGDD	average geometric distance degree	geometrical descriptors	-0.811
47	DDI	D/D index	geometrical descriptors	-0.811
48	ADDD	average distance/distance degree	geometrical descriptors	-0.816
49	G1	gravitational index G1	geometrical descriptors	-0.782
50	G2	gravitational index G2	geometrical descriptors	-0.812
51	RGyr	radius of gyration (mass weighted)	geometrical descriptors	-0.817
52	SPAN	span R	geometrical descriptors	-0.776
53	SPAM	average span R	geometrical descriptors	0.052
54	MEcc	molecular eccentricity	geometrical descriptors	-0.169
55	SPH	Spherosity	geometrical descriptors	-0.344
56	ASP	Asphericity	geometrical descriptors	-0.552
57	FDI	folding degree index	geometrical descriptors	-0.283
58	PJI3	3D Petijean shape index	geometrical descriptors	-0.272
59	L/Bw	length-to-breadth ratio by WHIM	geometrical descriptors	-0.499
60	SEig	absolute eigenvalue sum on geometry matrix	geometrical descriptors	-0.821
61	DISPm	d COMMA2 value / weighted by atomic masses	geometrical descriptors	-0.482
62	QXXm	Qxx COMMA2 value / weighted by atomic masses	geometrical descriptors	-0.483
63	QYYm	Qyy COMMA2 value / weighted by atomic masses	geometrical descriptors	-0.307
64	QZZm	Qzz COMMA2 value / weighted by atomic masses	geometrical descriptors	-0.816
65	DISPv	COMMA2 value / weighted by atomic van der Waals volumes	geometrical descriptors	-0.286
66	QXXv	Qxx COMMA2 value / weighted by atomic van der Waals volumes	geometrical descriptors	-0.538
67	QYYv	Qyy COMMA2 value / weighted by atomic van der Waals volumes	geometrical descriptors	-0.550
68	QZZv	Qzz COMMA2 value / weighted by atomic van der Waals volumes	geometrical descriptors	-0.812
69	DISPe	d COMMA2 value / weighted by atomic Sanderson electronegativities	geometrical descriptors	-0.484
70	QXXe	Qxx COMMA2 value / weighted by atomic Sanderson electronegativities	geometrical descriptors	-0.590
71	QYYe	Qyy COMMA2 value / weighted by atomic Sanderson electronegativities	geometrical descriptors	-0.656
72	QZZe	Qzz COMMA2 value / weighted by atomic Sanderson electronegativities	geometrical descriptors	-0.807
73	DISPp	d COMMA2 value / weighted by atomic polarizabilities	geometrical descriptors	-0.425
74	QXXp	Qxx COMMA2 value / weighted by atomic polarizabilities	geometrical descriptors	-0.539
75	QYYp	Qyy COMMA2 value / weighted by atomic polarizabilities	geometrical descriptors	-0.545
76	QZZp	QCOMMA2 value / weighted by atomic polarizabilities	geometrical descriptors	-0.812
77	G(N..N)	sum of geometrical distances between N..N	geometrical descriptors	-0.469
78	G(N..O)	sum of geometrical distances between N..O	geometrical descriptors	-0.519
79	G(N..F)	sum of geometrical distances between N..F	geometrical descriptors	-0.229
80	G(N..Cl)	sum of geometrical distances between N..Cl	geometrical descriptors	-0.333
81	G(O..O)	sum of geometrical distances between O..O	geometrical descriptors	-0.551
82	G(O..F)	sum of geometrical distances between O..F	geometrical descriptors	-0.229
83	G(O..Cl)	sum of geometrical distances between O..Cl	geometrical descriptors	-0.304
84	G(Cl..Cl)	sum of geometrical distances between Cl..Cl	geometrical descriptors	-0.211
85	nCp	number of total primary C(sp3)	functional groups	-0.099
86	nCs	number of total secondary C(sp3)	functional groups	-0.799
87	nCq	number of total quaternary C(sp3)	functional groups	-0.230
88	nCaH	number of unsubstituted aromatic C(sp2)	functional groups	0.429
89	nCaR	number of substituted aromatic C(sp2)	functional groups	-0.429
90	nNO2Ph	number of nitro groups (aromatic)	functional groups	-0.489
91	nRCX3	number of RCX3	functional groups	-0.230
92	nPhX	number of X-C on aromatic ring	functional groups	-0.103
93	nHAcc	number of acceptor atoms for H-bonds (N O F)	functional groups	-0.505
94	Ui	unsaturation index	empirical descriptors	-0.491
95	Hy	hydrophilic factor	empirical descriptors	-0.112
96	ARR	aromatic ratio	empirical descriptors	0.851
97	MR	Ghose-Crippen molar refractivity	Properties	-0.846
98	PSA	fragment-based polar surface area	Properties	-0.489
99	MLOGP	Moriguchi octanol-water partition coeff. (logP)	Properties	-0.817
Number of CH2 in reference 20 or number of total secondary C(sp3) (descriptor 86) in this study has good and negative correlation with logIC50. So our finding not only is similar to reference 20 but also, it gives a quantitative rather than qualitative interpretation for all results. Also number and variety of descriptors in our study is more than cited reference.
Data reduction by PCA method was done on these 99 descriptors to reduce and classify the descriptors. Table 7 shows the actual factors that were extracted. Phrase "Rotation Sums of Squared Loadings," shows only those factors that met cut-off criterion (eigenvalues greater than 1). SPSS software always extracts as many factors initially as there are variables in the dataset, but the rest of these didn't make the grade. The "% of variance" column tells us how much of the total variability (in all of the variables together) can be accounted for by each of these summary scales or factors. Factor 1 accounts for 42.093% of the variability in all variables, factor 2 accounts for 23.882 and so on.
Finally, the Rotated Component Matrix shows the factor loadings for each variable (Table 8). We went across each row, selected the factor that each variable loaded
most strongly on higher than absolute 0.500 and removed those less than absolute 0.500. Thus missing values in Table 8 related to descriptors having loading number less than absolute 0.5. The first, second, third and fourth columns loaded strongly on factors 1 to 4, which we called size, polarity, geometry and number of halogen, respectively.
Then, by performing MLR on the resulted PCs (Principal component regression, PCR) we can obtain an equation between logIC50 and PCs.
(0.179 x polarity) - (0.136 x geometry) -
(8)
The predicted values of logIC50 by PCA were listed in Table 5. Figure 8B shows correlation between predicted and experimental logIC50 by PCA analyses.
The correlation coefficient (R) for prediction of inhibitory activation was 0.849 by PCA model.
Table 7. Total variance explained by four principal components (PCs)
Component
Initial
Eigenvalues
Extraction Sums of Squared Loadings
Rotation Sums of SquaredLoadings
	Total	% of	Cumulative	Total	% of	Cumulative	Total	% of	Cumulative
		Variance	%		Variance	%		Variance	%
PC1	51.780	52.303	52.303	51.780	52.303	52.303	41.673	42.093	42.093
PC2	14.867	15.017	67.320	14.867	15.017	67.320	23.643	23.882	65.975
PC3	9.114	9.206	76.526	9.114	9.206	76.526	8.790	8.878	74.854
PC4	6.851	6.920	83.446	6.851	6.920	83.446	8.507	8.593	83.446
Table 8. Rotated component matrixof reduced selected descriptors into 4 factors
Symbol PC1	PC2	PC3	PC4
(Size) (polarity) (geometry) (number
of halogen)
MW	0.792
AMW	-0.75
Sv	0.955
Se	0.954
Sp	0.962
Ss	0.603
Mv	-0.909
Me	
Mp	-0.846
Ms	
nAT	0.967
nSK	0.857
nBT	0.967
nBO	0.857
nBM	
Symbol PC1	PC2 PC3	PC4
(Size)	(polarity) (geometry) (number
of halogen)
SCBO 0.828	0.519
RBN 0.958
RBF	0.953
nDB	0.876
nH	0.988
nC	0.98
nN	0.876
0.737	nO nCL		0.876
0.706	nX Qpmax		0.865
0.893	Qnmax		0.765
	Qpos	0.842	0.529
	Qneg	0.841	0.53
	Qtot	0.841	0.529
	Qmean		0.866
0.876	Q2	0.588	0.801
Acta Chim. Slov. 2012, 59, 221-232						
						
Symbol	PC1	PC2 PC3 PC4	Symbol	PC1	PC2 PC3	PC4
	(Size)	(polarity) (geometry) (number of halogen)		(Size)	(polarity) (geometry)	(number of halogen)
RPCG	-0.712	0.527	QXXv		0.898	
RNCG	-0.924		QYYv			
SPP		0.874	QZZv	0.96		
TE1	0.857		DISPe		0.751	
TE2	0.838	0.523	QXXe		0.828	
PCWTe	0.871		QYYe	0.609	0.507	
LDip		0.945	QZZe	0.951		
HOMA			DISPp			0.521
RCI			QXXp		0.911	
AROM			QYYp			
HOMT			QZZp	0.965		
J3D		0.928	G(N..N)		0.867	
H3D	0.962		G(N..O)		0.838	
AGDD	0.971		G(N..F)			
DDI	0.967		G(N..Cl)			0.889
ADDD	0.976		G(O..O)		0.814	
G1	0.619	0.58	G(O..F)			
G2	0.73	0.554	G(O..Cl)			0.905
RGyr	0.957		G(Cl..Cl)			0.802
SPAN	0.969		nCp		0.653	
SPAM		-0.890	nCs	0.97		
MEcc	0.622		nCq			
SPH	0.704		nCaH		-0.581	-0.539
ASP	0.837		nCaR		0.581	0.539
FDI	0.669	-0.612	nNO2Ph		0.876	
PJI3	0.583	-0.532	nRCX3			
L/Bw	0.753		nPhX			0.926
SEig	0.968		nHAcc		0.919	
DISPm		0.649	Ui		0.876	
QXXm		0.756	Hy		0.844	
QYYm		0.619	ARR	-0.89		
QZZm	0.888		MR	0.922		
DISPv			PSA		0.876	
QXXv		0.898	MLOGP	0.907		
In order to investigate of model validity we performed a cross validation. We took some of compounds as test set (8a, 8b, 8f, 9f, 11a, 20f, 20i, 20/, 20o, 20r, 20u and
20x in Table 5) and the reminder as training set. Then using leave-one-out methods we obtained qc2v based on equation (1). These values were inserted in the Fig. 8. As we see the q2v values are higher than 0.3 and lower than R2.
4. Conclusions
The purposes of this study were to survey the inhibition effect of N-(phenoxydecyl) phthalimide derivatives on a-glucosidase enzyme, and finding the key features of responsible a-glucosidase inhibitory activity. It was done by a computer drug-design protocol involving homology modeling for target protein, docking simulation and Quantitative Structure Activity Relationship. Firstly the homology modeled structure of S. cerevisiae a-glucosida-
se was built and used for molecular docking to define the interaction mode of the N-(phenoxydecyl) phthalimide derivatives with the protein. The results showed the important role of carboxyl group in binding of ligands with the active site of protein by formation of hydrogen bonds. Results of MLR on total and selected descriptors, showed a realistic correlation between predicted and experimental values. Experimental data showed that the inhibition activity increases with chain length, number of chlorine and electronegativity, while our results not only confirm the experimental data but also introduced new variables such as aromaticity, hydrophobicity, polarity to investigate the data in detail and quantitative manner. The QSAR studies showed that the inhibition increases (logIC50 decreases) with increasing size, polarity, geometry and number of halogen factors and decreasing of aromaticity. Consecutively, these results revealed that N-(phenoxydecyl) phtha-limide derivatives bind to site near the active site residues and free energy of binding has relatively good correlation with logIC50.
5. Acknowledgement
Financial support of Damghan University is acknowledged.
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Povzetek
Število bolnikov z diabetesom se povečuje, zato je razpozavanje dejavnikov, ki uravnavajo bolezen, zelo pomembno. a-Glukozidaza (EC 3.2.1.20) je esencialni encim, ki sodeluje pri presnovi ogljikovih hidratov, kot je npr. škrob. Ogljikovi hidrati se običajno presnovijo do enostavnih sladkorjev, ki se lahko absorbirajo v tankem črevesu. Zato lahko a-glukozidazne inhibitorje uporabljamo za znižanje ravni krvnega sladkorja. Z računalniškim programom za načrtovanje zdravil, ki vključuje homologno modeliranje, sidranje in QSAR analizo, smo preiskovali učinke inhibicije derivatov N-(fenoksidecil) ftalimida. Homologni model a-glukozidaze kaže na strukturo, ki je zelo podbna kristalni strukturi oli-go-1,6-glukozidaze iz kvasovke Saccharomyces cerevisiae. Rezultati sidranja so pokazali, da je položaj vezavnega mesta na inhibitorju blizu aktivnega mesta in da je karbonilni kisik na ftalimidu učinkovita funkcionalna skupina za vezavo inhibitorja na protein. Enačba, pridobjena s QSAR analizo, pa je pokazala, da se inhibicijske lastnosti derivatov N-(fenoksidecil) ftalimida zmanjšujejo, če se povečuje velikost, polarnost, geometrija in število halogenskih faktorjev.