Prediction of n-Octanol/Water Partition Coefficients (Kow) for Pesticides Using a Multiple Linear Regression-Based QSPR Model ^†

Abstract

This study developed a QSPR model to predict the n-octanol/water partition coefficient (log Kow) of 56 pesticides. Molecular descriptors were calculated using Dragon software. A genetic algorithm and variable subset selection identified key descriptors. The model, built by multiple linear regression, showed strong performance (R² = 0.9322, Q²_LOO = 0.9089, Q²_ext = 0.9277). The dataset was split using the Kennard-Stone algorithm to ensure representative sampling. Internal and external validations confirmed robustness and predictive power. This model offers a reliable tool for estimating log Kow, supporting environmental risk assessment and the evaluation of pesticide behavior and toxicity.

1. Introduction

Pesticides are unique among chemicals because they are intentionally introduced into the environment to manage pests and protect crops and industrial goods. However, their effects are not limited to target species; they also impact non-target organisms and ecosystems. Frequent use can reduce biodiversity [1]. Many pesticides are persistent, remaining in soil or leaching into water bodies, which leads to widespread contamination. Due to their chemical nature, they can bioaccumulate in living organisms and affect human health through food chains. The environmental risks of intensive pesticide use are well documented and significant [2].

Quantitative structure–activity relationships (QSARs) offer a way to predict chemical toxicity based on molecular structure, even before synthesis. These models are especially useful when experimental data are scarce [1,2]. QSPR/QSAR methods rely on the idea that molecular properties are linked to specific structural features, called descriptors [3]. These computational tools can forecast chemical behavior, identify key structural elements, and reduce the need for experimental testing, making them cost- and time-effective in areas like drug development [4].

Physicochemical properties—such as vapor pressure, solubility, and partition coefficients—are central to understanding how organic compounds behave in the environment [5]. Among these, the n-octanol/water partition coefficient (Kow) is crucial. A high log Kow suggests a higher potential for bioaccumulation in organisms. This parameter is also used to infer systemic action and environmental fate of compounds [6]. In QSAR models, log Kow is often employed as a descriptor of toxicity [7,8,9]. The partition coefficient is defined as the ratio of equilibrium concentrations of a substance in a biphasic system like octanol and water [10], with octanol mimicking biological lipids [11].

This study aimed to develop QSAR models for predicting the acute toxicity of pesticides and to construct a statistical model for estimating their log Kow. Using multiple linear regression (MLR), the model identifies which molecular descriptors significantly influence variation in log Kow across the pesticide dataset.

2. Materials and Method

2.1. Experimental Data

This study used a dataset of 56 pesticides obtained from the published work of Patil [12]. The partition coefficient values were converted to log Kow to minimize data variability. The dataset was split into two subsets: 42 compounds for training and 14 for external validation.

2.2. Descriptors Generation

The molecular structures of all compounds were built using HyperChem (version 6.02) [13] and initially optimized via the MM+ force field with the Polak–Ribiere algorithm. Final geometries corresponding to the lowest energy conformers were obtained using the semi-empirical PM3 method at the restricted Hartree–Fock level, without configuration interaction, applying a gradient norm threshold of 0.001 kcal·Å⁻¹·mol⁻¹. These optimized structures were used to calculate 1664 molecular descriptors with Dragon software (version 5.4) [14]. Additionally, quantum chemical descriptors—including HOMO, LUMO, the HOMO–LUMO gap (ΔHL), and ionization potential-were computed using the PM3 method in HyperChem and considered during descriptor selection for model development.

3. Results and Discussion

The dataset of 56 compounds was partitioned into two subsets using the Kennard–Stone algorithm implemented in CADEX: a calibration set of 42 compounds and a validation set of 14, as shown in

Table 1. The data set and the corresponding observed and predicted values of log (Kow) by MLR for the training and test sets.

ID	Object	Status	Log KowExp	Log KowCalc	Log KowPred
1	aa Aldicarb	Training	1.1300	1.6633	1.7055
2	ac Azinphos-ethyl	Training	3.400	3.8846	3.9365
3	ad Azinphos-methyl	Training	2.6900	3.1298	3.1679
4	af Bromophos-ethyl	Training	5.6800	4.6503	4.5145
5	ah Carbofuran	Training	1.6300	2.4009	2.4373
6	ak Chlordimeform	Training	2.8900	3.1089	3.1360
7	al Chlorfenvinphos	Training	3.8100	3.7036	3.6872
8	am Chlorpyrifos	Training	4.9600	4.2289	4.1797
9	aq Dichlorvos	Training	1.4700	0.7627	0.6021
10	as Disulfoton	Training	4.0200	4.0222	4.0225
11	at Disulfoton-sulfone	Training	1.8700	1.8826	1.8843
12	au Disulfoton-sulfoxide	Training	1.7300	2.7337	2.8112
13	av Ethion	Training	5.0700	5.0293	5.0176
14	ax Fenitrothion	Training	3.400	3.0789	3.0405
15	ay Fensulfothion	Training	2.2300	2.9470	2.9820
16	az Fensulfothion-sulfide	Training	4.1600	4.3343	4.3540
17	bb Fensulfothion-sulfoxide	Training	2.5900	1.0347	0.8113
18	bd Fenofos	Training	3.8900	3.9289	3.9362
19	bf Isofenphos	Training	4.1200	4.3999	4.4441
20	bg Leptophos	Training	5.8800	5.4460	5.3194
21	bh Malathion	Training	2.8400	2.4827	2.3990
22	bi Methidathion	Training	2.4200	2.4721	2.4771
23	bk Paraoxon	Training	1.9800	1.9711	1.9700
24	bl Parathion	Training	3.7600	3.4904	3.4617
25	bm Parathion-amino	Training	2.6000	3.5076	3.5685
26	bn Parathion-methyl	Training	2.9400	2.7758	2.7507
27	bo Phorate	Training	3.8300	3.7061	3.6934
28	bp Phorate sulfoxide	Training	1.7700	2.3529	2.3898
29	bq Phorate sulfone	Training	1.9800	1.5262	1.4635
30	br Phosalone	Training	4.3800	4.0743	4.0489
31	bs Phosmet	Training	2.7800	2.4588	2.4096
32	bt Phoxim	Training	4.3900	3.9275	3.8851
33	bu Pirimiphos ethyl	Training	4.8500	4.7015	4.6813
34	bv Pirimiphos methyl	Training	4.2000	3.9870	3.9580
35	bw Propoxur	Training	1.5500	2.1930	2.2259
36	bx Ronnel	Training	4.8100	3.7066	3.6269
37	by Temephos	Training	5.9500	6.4691	6.6715
38	bz Terbufos	Training	4.4800	4.2510	4.1733
39	cb Terbufos-sulfoxide	Training	2.4800	2.9511	3.0095
40	cc Terbufos sulfone	Training	2.2100	2.1428	2.1249
41	cd Triazophos	Training	3.5500	4.2176	4.2735
42	ce Trichlorfon	Training	0.4300	1.0645	1.1735
43	ab Aminocarb	Test	1.7300	-	2.3518
44	ae Bromophos	Test	4.8800	-	3.9279
45	ag Carbaryl	Test	2.3100	-	2.5399
46	ai Carbophenothion	Test	5.1200	-	5.1524
47	aj Carbophenothion-methyl	Test	4.8200	-	4.4169
48	an Chlorpyrifos-methyl	Test	4.3000	-	3.4384
49	ao Diazinon	Test	3.8100	-	4.1168
50	ap Dicapthon	Test	3.6200	-	3.1335
51	ar Dimethoate	Test	0.7700	-	1.6071
52	aw Fenamiphos	Test	3.2300	-	3.6289
53	bc Fenthion	Test	4.0900	-	3.9071
54	be Iodofos	Test	5.1600	-	4.3957
55	bj Methomyl	Test	0.1300	-	0.8981
56	cf Trichloronat	Test	5.2200	-	4.4896

. The objective was to select a reduced set of descriptors that best account for the variation in the dependent variable (log Kow). Descriptor selection was performed using genetic algorithms provided in the Mobydigs software (version 1.1) [15].

The application of the GA–VSS led to several effective models for predicting the Kow of pesticide chemicals based on various sets of molecular descriptors. The best model, derived from the 56 pesticide compounds, demonstrated high predictive accuracy and was established using the following regression equation:

log Kow = 1.63 + 0.301 × Polarizability − 0.798 × O-058 − 0.230 × nHAcc − 4.55 × E1u

(1)

Equation (1) incorporates four distinct categories of molecular descriptors, summarized in

Table 2. Description of the selected descriptors by GA.

Descriptors	Class	Signification
Polarizability	Hyperchem descriptor	Polarizability defined as the dipole moment of a molecule induced by an electric field of unit intensity.
O-058	Atom-centered fragments	Defined hydrophobicity.
nHAcc	Functional group counts	Total number of Ns, Os and Fs in the molecule, excluding N with a formal positive charge, higher oxidation states and the pyrrolyl form of N.
E1u	WHIM descriptors	1st component accessibility directional WHIM index/unweighted.

. The model’s performance was assessed using predictive metrics such as Q²_LOO and Q²_LMO, along with the coefficient of determination (R²) to evaluate the goodness of fit. Additionally, the standard deviation of prediction error (SDEP) and the standard deviation of calculation error (SDEC) within the applicability domain are reported.

As shown in

Table 3. Results and statistical parameters of GA-MLR.

R2	Q2LOO	Q2EXT	SDEC	SDEP	SDEPEXT	F	s
93.22	90.89	92.77	0.450	0.520	0.546	92.4052	0.511

, the fitting and validation metrics are consistently high, confirming the model’s strong predictive performance. The selected descriptors effectively capture the variation in the partition coefficient. The R² value reflects a well-fitted model, and the small difference between R² and Q²_LOO indicates strong internal robustness, further supported by a high Fisher statistic. The close values of SDEC and SDEP suggest that the model’s predictive ability is consistent with its fitting accuracy. External validation results, including Q²_ext and SDEP_ext, demonstrate the model’s reliability in predicting data not used during its training phase.

The R² value reflects the model’s fitting quality, while the small difference between R² and Q²_LOO indicates strong robustness, reinforced by a high Fisher statistic. The similarity between SDEC and SDEP suggests that the model’s predictive accuracy is consistent with its calibration performance. External validation metrics, including Q²_ext and SDEP_ext, confirm the model’s reliability in predicting the behavior of compounds outside the training set.

The symmetrical distribution of errors around the zero line indicates that the model does not exhibit systematic bias. Figure 1 presents the Q² and R² coefficients, comparing the real model (black dot) with the randomized models (red circles). The Q² values of the randomized models are consistently below 20, and in many cases negative, confirming that the developed model is based on real structure–property relationships rather than random chance.

4. Conclusions

In this study, the QSPR approach was employed to correlate the log Kow values of 56 pesticides with theoretical molecular descriptors selected using a genetic algorithm. Multiple linear regression was applied to identify linear relationships between the descriptors (independent variables) and log Kow (dependent variable). The resulting model demonstrated optimal performance in terms of goodness of fit, internal and external validation, and predictive accuracy.