The system of self-consistent models based on quasi-SMILES as a tool to predict the potential of nano-inhibitors of human lung carcinoma cell line A549 for different experimental conditions

Figures & data

Table 1. Percentage of identical distribution of samples into the active/passive training sets, calibration set, and validation set.

	Split 1	Split 2	Split 3	Split 4	Split 5
Split 1	0	40.6	46.0	40.2	37.9
Split 2	43.5	0	36.8	42.8	33.2
Split 3	43.8	43.5	0	39.6	40.4
Split 4	51.6	40.8	36.8	0	41.1
Split 5	40.2	41.1	39.2	38.5	0

Matrix Element[i,j], i>j the identity for the active training sets. Matrix Element[i,j], i<j the identity for the validation sets.

$\mathrm{Identity} \left(\mathrm{\%}\right)=\frac{N_{ij}}{0.5\times (N_i+N_j)}\times 100.$

N_ij is the number of quasi-SMILES that are distributed into the same set for both ith. split and jth split (set = active training set or passive training set or calibration set or validation set). N_i is the total number of substances that are distributed into the set for ith split. N_j is the total number of substances that are distributed into the set for jth split.

Figure 1. The general scheme of building up quasi-SMILES.

Figure 2. The graphical representation of the model was obtained for split #1 by the CORAL program interface. Red and green colors show the statistical characteristics of hidden correlations for active and passive training sets.

Table 2. The statistical quality of models for splits #1–#5 observed in the cases of the Monte Carlo optimization with different target functions calculated with Equation (4)(4) $${TF}_1=r_{AT}+r_{PT}-\left|r_{AT}-r_{PT}\right|\times 0.1$$(4) and Equation (5)(5) $${TF}_2={TF}_1+{\mathit{IIC}}_{ }\times 0.5$$(5) .

Split	Target function	Set	n^a	R^2	CCC	IIC	Q^2	RMSE	MAE	F
1	TF1	Active training	92	0.5989	0.7491	0.6221	0.5772	24.8	20.4	134
		Passive training	97	0.5142	0.7043	0.6703	0.4838	25.9	21.2	101
		Calibration	92	0.1720	0.2262	0.2789	0.1248	38.8	32.5	19
		Validation	96	0.2702				33.5	28.9
2		Active training	95	0.5680	0.7245	0.5481	0.5412	21.0	16.6	122
		Passive training	91	0.6022	0.7355	0.4788	0.5820	29.0	22.6	135
		Calibration	94	0.1552	0.2133	0.2416	0.1100	31.6	25.6	17
		Validation	97	0.1549				32.6	27.0
3		Active training	95	0.5889	0.7413	0.7514	0.5689	23.7	20.2	133
		Passive training	94	0.5888	0.7124	0.5347	0.5670	24.5	20.9	132
		Calibration	92	0.0497	0.1699	0.2057	0	28.2	23.7	5
		Validation	96	0.2437				27.8	24.2
4		Active training	92	0.5025	0.6688	0.6787	0.4757	24.2	20.3	91
		Passive training	98	0.6097	0.6618	0.5156	0.5886	27.4	24.1	150
		Calibration	93	0.1022	0.1854	0.2251	0.0411	25.7	22.0	10
		Validation	94	0.3487				22.5	18.9
5		Active training	98	0.5341	0.6963	0.5040	0.5105	24.1	20.4	110
		Passive training	95	0.5645	0.6597	0.7030	0.5419	27.3	24.5	121
		Calibration	91	0.2440	0.4712	0.4139	0.1959	20.6	16.9	29
		Validation	93	0.3430				21.1	17.3
1	TF2	Active training	92	0.3910	0.5622	0.5253	0.3620	30.5	27.7	58
		Passive training	97	0.3983	0.5606	0.5660	0.3642	28.6	25.8	63
		Calibration	92	0.6400	0.7844	0.7999	0.6062	11.0	9.07	160
		Validation	96	0.6611				11.6	9.23
2		Active training	95	0.3202	0.4851	0.5093	0.2856	26.3	23.1	44
		Passive training	91	0.5153	0.5334	0.4602	0.4932	33.4	29.3	95
		Calibration	94	0.6834	0.8006	0.8267	0.6624	8.54	6.78	199
		Validation	97	0.5728				9.39	7.86
3		Active training	95	0.3969	0.5683	0.5436	0.3695	28.7	25.0	61
		Passive training	94	0.4179	0.5320	0.4621	0.3851	29.3	25.7	66
		Calibration	92	0.5264	0.6868	0.7255	0.4814	12.8	10.2	100
		Validation	96	0.6796				11.6	9.18
4		Active training	92	0.3637	0.5334	0.5066	0.3300	27.4	24.0	51
		Passive training	98	0.4482	0.5157	0.4907	0.4209	31.9	28.6	78
		Calibration	93	0.5952	0.6671	0.7715	0.5618	11.1	9.20	134
		Validation	94	0.6603				10.3	8.59
5		Active training	98	0.3885	0.5596	0.5292	0.3595	27.6	23.6	61
		Passive training	95	0.4232	0.5440	0.5507	0.3941	30.4	26.0	68
		Calibration	91	0.5386	0.7315	0.7339	0.5017	12.5	10.1	104
		Validation	93	0.5134				12.4	9.89

a n: the number of quasi-SMILES in a set; R²: the determination coefficient; CCC: concordance correlation coefficient; IIC: index of ideality of correlation; Q²: cross-validated R²; RMSE: root mean squared error; MAE: mean absolute error; F: Fisher’s F-ratio.

Table 3. Fragments of quasi-SMILES are promoters of increase/decrease inhibition of human lung carcinoma cell line A549.

APP,Sk,SSk,qSk	CWs Run 1	CWs Run 2	CWs Run 3	Na	Np	Nc	Statistical defect, dk
[NoDop]…..	0.24666	1.04451	1.19031	48	63	86	0.0031
(O..═)..2.2.	0.90088	1.54215	1.46468	16	15	31	0.0035
[Ag]……..	2.24721	0.85776	1.92846	15	11	15	0.0000
[do6,25]….	2.36345	1.06771	1.56749	15	12	9	0.0027
[do0,01]….	2.71251	1.59610	2.12650	12	9	10	0.0010
[do12,50]…	2.08471	1.60590	2.11192	11	11	16	0.0020
[do25,00]…	2.85563	1.65641	2.34717	11	8	15	0.0017
[SOCIT]…..	2.39803	1.09635	2.37297	9	13	18	0.0036
[PVP]…….	0.28446	0.58024	0.68047	8	10	6	0.0016
[Ce]……..	1.72872	1.00184	1.31621	5	2	2	0.0047
[Fe]……..	0.82665	0.49958	0.58206	5	14	14	0.0051
(………..	0.33099	0.07855	0.78283	3	1	5	0.0027
C…(…….	0.93386	0.93735	0.95397	3	1	5	0.0027
[Au(25%)]…	0.58743	1.55060	1.73304	3	0	1	0.0054
[Citrate]…	1.24923	0.53949	2.00244	3	0	2	0.0022
[do100,00]..	–0.12733	–0.56522	–0.57266	21	19	3	0.0082
[do50,00]…	–0.47533	–0.24178	–0.97419	16	17	11	0.0020
[Cl(3%)]….	–0.81813	–0.21497	–0.07199	4	0	1	0.0065
[Co(2%)]….	–0.22639	–0.16728	–0.25761	4	2	0	1.0000
C…C…….	–0.36947	–0.69105	–0.42154	3	1	5	0.0027
[COOH]……	–0.35344	–0.35271	–0.52850	3	1	7	0.0043
[di149,00]..	–1.20930	–0.13487	–0.54397	3	3	0	1.0000
[di164,70]..	–0.20162	–0.41797	–0.21815	3	3	0	1.0000
[bPEI]……	–1.26530	–0.44992	–0.96465	2	3	1	0.0036
[di1968,00].	–1.46506	–0.90406	–0.52725	2	4	0	1.0000
[di28,55]…	–1.24826	–0.56019	–1.15220	2	3	1	0.0036
(O..═)..3.2.	–1.26318	–0.81951	–0.22331	1	4	2	0.0036
[Cr]……..	–1.14221	–0.79011	–1.33245	1	1	1	0.0000
[di1159,00].	–0.76851	–0.46016	–1.29132	1	1	1	0.0000

Na, Np, and Nc are the numbers of quasi-SMILES that contain the code in the active training, passive training sets, and calibration set, respectively.

Table 4. The statistical characteristics of the models for the lists of quasi-SMILES that were unknown when developing the corresponding model (i.e., quasi-SMILES which are absent in the active training, passive training, and calibration sets used to develop corresponding models).

	Split 1	Split 2	Split 3	Split 4	Split 5
Model1		n = 42, $R_{\mathit{VLD}}^2=0.69, \mathit{MAE}=6.6$^a	n = 42, $R_{\mathit{VLD}}^2=0.77, \mathit{MAE}=7.2$	n = 49, $R_{\mathit{VLD}}^2=0.67, \mathit{MAE}=7.9$	n = 38, $R_{\mathit{VLD}}^2=0.62, \mathit{MAE}=7.6$
Model2	n = 42, $R_{\mathit{VLD}}^2=0.72, \mathit{MAE}=9.0$		n = 42, $R_{\mathit{VLD}}^2=0.63, \mathit{MAE}=8.0$	n = 39, $R_{\mathit{VLD}}^2=0.46, \mathit{MAE}=7.5$	n = 39, $R_{\mathit{VLD}}^2=0.65, \mathit{MAE}=8.7$
Model3	n = 42, $R_{\mathit{VLD}}^2=0.81,$ MAE = 8.4	n = 42, $R_{\mathit{VLD}}^2=0.72, \mathit{MAE}=7.8$		n = 35, $R_{\mathit{VLD}}^2=0.69, \mathit{MAE}=8.6$	n = 37, $R_{\mathit{VLD}}^2=0.61, \mathit{MAE}=8.3$
Model4	n = 49, $R_{\mathit{VLD}}^2=0.67, \mathit{MAE}=9.0$	n = 39, $R_{\mathit{VLD}}^2=0.54, \mathit{MAE}=7.1$	n = 35, $R_{\mathit{VLD}}^2=0.65, \mathit{MAE}=7.8$		n = 36, $R_{\mathit{VLD}}^2=0.69, \mathit{MAE}=8.1$
Model5	n = 38, $R_{\mathit{VLD}}^2=0.57, \mathit{MAE}=8.3$	n = 39, $R_{\mathit{VLD}}^2=0.46, \mathit{MAE}=7.2$	n = 37, $R_{\mathit{VLD}}^2=0.54, \mathit{MAE}=7.7$	n = 36, $R_{\mathit{VLD}}^2=0.72, \mathit{MAE}=8.8$

a n: the number of quasi-SMILES in the validation set of defined splits that are not involved in the active training, passive training, and calibration sets applied to build the corresponding model. R²_VLD: determination coefficient for quasi-SMILES selected by the above limitations. MAE: mean absolute error for indicated lists of quasi-SMILES.

Data availability statement

The data used in this work and developed models are freely available Supplementary materials section.