Human protein tyrosine phosphatase 1B inhibitors: QSAR by genetic function approximation

Figures & data

Table I.  Structures and biological activities of the training set molecules.

No.	R1	R2	R3	Obsd. act.^a	Pred. act.^b
1	H	H	-CH (CH3)2	− 1.340	− 1.360
2	H	H	Cl	− 1.447	− 1.396
3	H	H	Br	− 1.301	− 1.496
4	Br	H	Br	− 1.301	− 1.375
5	H	H	NO2	− 1.959	− 2.091
6	H	H	F	− 1.740	− 1.444
7				− 1.146	− 1.241
8				− 1.398	− 1.251
9	H	H	-C6H4 C6H5	− 0.634	− 0.868
10	H	H		− 0.851	− 0.758
11	H	H		− 0.398	− 0.836
12	Br	H		− 1.041	− 0.715
13	H	H		− 0.987	− 0.765
14	H	H		− 1.041	− 0.911
15	Br	H		− 1.204	− 0.964
16	H	H		− 0.887	− 1.090
17	Br	H		− 0.914	− 1.049
18	H	H		− 0.881	− 0.899
19	Br	H		− 1.00	− 0.963
20	H	H		− 0.792	− 0.840
21	Br	H		− 0.892	− 0.882
22	H	H		− 0.778	− 1.095
23	H	H		− 0.505	− 0.677
24	C6H5	H	H	− 1.204	− 1.125
25	H	H		− 0.0414	− 0.442
26	C6H5	H		0.000	0.083
27	H	H	C6H5CH2	− 1.556	− 1.159
28	C6H5CH2	H	H	− 1.255	− 1.139
29	C6H5CH2	H	C6H5CH2	− 1.114	− 0.859

^a Obsd. act = observed biological activity is defined as log 1/ IC50 against human recombinant PTP 1B enzyme (h-PTP 1B) in μM

^b Pred. act = Predicted biological activity calculated using Equation (7) in Table IV.

Table II.  Structures and observed, predicted activities along with residuals for the test set molecules.

No	R1	R2	R3	Obsd. act^a	Pred. act^b	Residual
1	H	H	H	− 1.863	− 1.463	− 0.400
2	Cl	H	Cl	− 1.398	− 1.325	− 0.073
3	H	CH3	Cl	− 1.255	− 1.349	0.094
4	H	H	C6H5	− 1.146	− 1.162	0.016
5	H	H		− 0.778	− 1.049	0.271
6	C6H5	H	C6H5	− 0.519	− 0.809	0.273
7	C6H5	H	C6H5 C6H4	− 0.301	− 0.511	0.189

^a Obsd. act = observed biological activity is defined as log 1/ IC50 against human recombinant PTP 1B enzyme (h-PTP 1B) in μM

^b Pred. act = Predicted biological activity calculated using Equation (6) in Table IV.

Table III.  Descriptors used in the present study.

No	Descriptor	Type	Descriptor
1	Vm	Spatial	Molecular volume^d
2	Area	Spatial	Molecular surface area^d
3	Density	Spatial	Molecular density^d
4	RadOfGyr	Spatial	Radius of gyration^d
5	PMI–X	Spatial	Principle moment of inertia X–component
6	PMI–Y	Spatial	Principle moment of inertia Y–component
7	PMI–Z	Spatial	Principle moment of inertia Z–component
8	PMI-mag	Spatial	Principle moment of inertia^d
9	MW	Structural	Molecular weight^d
10	RotlBonds	Structural	Number of rotatable bonds^d
11	HbondAcc	Structural	Number of hydrogen bond acceptors^d
12	HbondDon	Structural	Number of hydrogen bond donors^d
13	AlogP98	Thermodynamic	Logarithm of partition coefficient^d
14	MolRef	Thermodynamic	Molar refractivity^d
15	Dipole-mag	Electronic	Dipole moment^d
16	Dipole–X	Electronic	Diploe moment–X–component
17	Dipole–Y	Electronic	Dipole moment–Y–component
18	Dipole–Z	Electronic	Dipole moment–Z–component
19	Charge	Electronic	Sum of partial charges^d
20	Apol	Electronic	Sum of atomic polarizabilities^d
21	HOMO	Electronic	Highest occupied molecular orbital energy
22	LUMO	Electronic	Lowest unoccupied molecular orbital energy
23	Sr	Electronic	Superdelocalizability^d
24	Foct	Thermodynamic	Desolvation free energy for octanol
25	Fh2o	Thermodynamic	Desolvation free energy for water
26	Hf	Thermodynamic	Heat of formation
27	DIFFV	MSA	Difference volume
28	COSV	MSA	Common overlap steric volume
29	Fo	MSA	Common overlap volume ratio
30	NCOSV	MSA	Non-common overlap steric volume
31	Shape RMS	MSA	RMS to shape reference
32	SR Vol	MSA	Volume of shape reference compound

^d default descriptor

Figure 1 Pharmacophore alignment of PTP 1B inhibitors used in the present QSAR study.

Table IV.  Summary of the best equations selected from different GFA models. Equation (7) from Model C was selected to explain the observed PTP 1B inhibitory activity of formylchromone derivatives.

No.	Equation	LOF	r^2		F- value
Model A
1	log (1/IC50) = − 2.172220 + 0.000752 MR − 0.033806 Hbond acceptor + 0.003790 Area	0.077	0.740	0.652	23.733	0.745
2	log (1/IC50) = − 1.958960 + 0.004640 Vm − 0.067095 Hbond acceptor − 0.010514 Dipole-mag	0.075	0.747	0.636	24.661	0.718
3	log (1/IC50) = − 2.144630 + 0.001768 MR +0.000081 Apol − 0.04886 Hbond acceptor	0.076	0.746	0.654	24.414	0.723
Model B
4	log (1/IC50) = − 1.171580 − 0.062104 Sr − 0.112848 Hbond acceptor + 0.000569 PMI-mag	0.073	0.754	0.663	25.511	0.724
5	log (1/IC50) = − 2.112700 + 0.005140 MR − 0.056313 Foct − 0.000367 HOMO	0.068	0.771	0.700	28.100	0.665
6	log (1/IC50) = − 1.260340 + 0.000047 Hf − 0.099213 Hbond acceptor + 0.000516 PMI-mag	0.074	0.751	0.659	25.113	0.671
Model C
7	log (1/IC50) = − 2.056111 + 0.001121COSV − 0.007113 Sr − 0.055721 Foct	0.070	0.766	0.689	27.245	0.785
8	log (1/IC50) = − 2.057600 − 0.055482 Foct +0.00392 Dipole-mag + 0.001127 COSV	0.070	0.766	0.662	27.233	0.778
9	log (1/IC50) = − 2.068400 − 0.054748 Foct +0.001144 COSV + 0.026906 Shape RMS	0.069	0.767	0.677	27.371	0.785
10	log (1/IC50) = − 2.296100 + 0.001377 COSV − 0.054131 Foct − 0.057383 Hbond acceptor	0.067	0.774	0.685	28.602	0.772
11	log (1/IC50) = − 2.033400 + 0.000035 Hf +0.000988 COSV − 0.053871 Foct	0.069	0.768	0.691	27.600	0.751

Figure 2 A graph of actual versus predicted activities of training set molecules using Equation (7) of Model C.

Figure 3 A graph of actual versus predicted activities of test set molecules using Equation (7) of Model C.

Table V.  Results of randomized r² for Equation (7) (Model C).

Confidence level	Trials			SD^a	SD^b	r^2 < ^c	r^2 < ^d
95%	19	0.766	0.098	5.336	0.208	19	0
98%	49	0.766	0.261	3.975	0.204	49	0

^a Number of standard deviations of the mean value of r² of all random trials to the non-random r² value

^b Standard deviation of the r² values of all random trials from the mean value of r²

^c Number of r² values from random trials that are less than the r² value for the non-random trial

^d Number of r² values from random trials that are greater than the r² value for the non-random trial.