Atmospheric Environment 37 (2003) 3115–3124

.

Predicting the NO3 radical tropospheric degradability oforganic pollutants by theoretical molecular descriptors

P. Gramatica*, P. Pilutti, E. Papa

Department of Structural and Functional Biology, QSAR and Environmental Chemistry, Research Unit, University of Insubria,

via Dunant 3, 21100 Varese, Italy

Received 6 January 2003; received in revised form 12 March 2003; accepted 21 March 2003

Abstract

The rate constant for the nighttime degradation of 114 heterogeneous organic compounds, through reaction with

nitrate radicals in the troposphere, is predicted here by quantitative structure–activity relationships modelling. The

multiple linear regression approach is based on a variety of theoretical molecular descriptors, selected by the genetic

algorithms-variable subset selection procedure. The proposed model, calculated on a limited subset of compounds

selected by a D-optimal experimental design and checked for reliability and robustness, has good predictivity, verified

by internal (Q2LMO ¼ 89:6%) and ‘‘external’’ validation (Q2

EXT ¼ 95:7%). The model applicability domain was always

verified by the leverage approach in order to propose reliable predicted data. The average root-mean square error for

the prediction of log kNO3 was 0.57, similar to (and even smaller than) the typical experimental error range.

r 2003 Elsevier Science Ltd. All rights reserved.

Keywords: QSAR; Theoretical molecular descriptors; External validation; Prediction; Nitrate radical degradation

1. Introduction

The troposphere is the atmospheric layer into which

large numbers of chemicals of both anthropogenic and

biogenic origin are emitted, by either direct emission or

volatilisation from soils and aquatic systems. Such

chemicals are removed by physical processes (wet and

dry depositions), chemical degradation processes such as

photolysis, and by reaction with reactive atmospheric

compounds like OH radicals and ozone during the

daytime and NO3 radicals at night (G .usten, 1997). These

night-time NO3 free radical reactions are secondary, but

relevant degradative processes that remove trace gases

and organic pollutants from the troposphere, supple-

menting the more relevant daytime removal initiated by

OH radical reactions (Atkinson, 2000).

It is also to be noted that nitro-substituted com-

pounds occur as industrial products in a wide

range of use patterns, and as secondary pollutants from

reactions with hydroxyl radicals (OH�) and nitrate

radicals ðNO�3 Þ in an atmosphere under natural NOx

conditions; thus such compounds form an im-

portant class of pollutant chemicals. The presence of

various nitro-substituted chemicals in environmental

samples is a legitimate cause for concern because some

(nitro-arenes, nitro-PAH and their amino derivatives)

are known to be toxic (Wang et al., 2002) and

carcinogenic (Tejada et al., 1986), thus, there is a need

to identify and quantify these compounds to assess their

potential health hazard and their impact on the

environment. In the past two decades considerable

effort has been put into locating the source and

occurrence of these reaction products, studying their

chemical and physical properties, investigating their

mutagenic and carcinogenic activity (Jinhui and Lee,

2000), and developing new analytical methods for their

identification and quantification.

ARTICLE IN PRESS

*Corresponding author. Fax: +39-0332-421554.

E-mail address: paola.gramatica@uninsubria.it

(P. Gramatica).

URL: http://dipbsf.uninsubria.it/qsar.

1352-2310/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved.

doi:10.1016/S1352-2310(03)00293-0

The measurement of rate constants in the gas phase is

limited due to the difficulty of the necessary experiments

(many industrial organic chemicals have very low

volatility) that are, furthermore, both costly and time-

consuming. Thus, reliable risk assessment calls for

prediction methods that allow a quick estimation of

the abiotic degradability of chemicals. This need is

particularly urgent in view of the growing number of

organic compounds of anthropogenic origin, and such

methods could lead to the development of new safer

organic chemicals. One of the most successful ap-

proaches to the prediction of chemical properties,

starting only from molecular structure information, is

quantitative structure–activity/property relationships

modeling (QSAR/QSPR).

Some QSAR studies on predicting oxidation rate

constants with OH and NO3 radicals have been

published recently (Sabljic and G .usten, 1990; M .uller

and Klein, 1991; Klamt, 1996; Medven et al., 1996;

Bakken and Jurs, 1999; Gramatica et al., 1999; G .usten,

1999) but, while good models for OH� rate constants are

proposed for various chemical classes, the modelling of

reactivity with NO3 radicals is more problematic. All the

published QSAR models were obtained on separate

training sets for aliphatic and aromatic compounds: the

rate constants of aliphatic chemicals with NO3 radicals

were predicted successfully (Sabljic and G .usten, 1990;

M .uller and Klein, 1991; Gramatica et al., 1999),

however the models for aromatic compounds do not

appear to be so satisfactory, often being only local

models built on very small training sets and, conse-

quently, without any reasonable applicability for data

prediction.

This paper proposes a new QSAR model for

predicting oxidation rate constants (kNO3) for a hetero-

geneous set containing both aliphatic and aromatic

compounds (114 chemicals), based on theoretical

molecular descriptors. In order to fill the data gaps

and produce reliable predicted data, applicable to the

risk assessment of large groups of heterogeneous

chemicals, the model prediction performances and the

chemical domain are considered of primary importance

(Tropsha et al., 2003): thus, internal and ‘‘external’’

validation procedures and the leverage approach have

been applied. The molecular descriptors selected in the

model encode the structural features of the chemicals

related to reactivity with NO3 radicals.

2. Methods

2.1. Experimental data

The experimental data shown in Table 1 are the

degradation rate constants, due to NO3 radicals, of 114

heterogeneous organic compounds reported in the

literature (Atkinson, 1991; EPI Suite, 2001). The

selected data pertain to reactions at 25�C and

101.3 kPa; all the rate constants, reported in cm3 s�1

molecule�1, have been transformed to logarithmic units

and multiplied by �1 to obtain positive values.

2.2. Molecular descriptors

The molecular descriptors for the given compounds

were mainly calculated using DRAGON software

(Todeschini et al., 2002a) on the minimal energy

conformations determined by the MM+ method

(HYPERCHEM, 1995). A total of 1.150 molecular

descriptors of differing types were used to describe

compound chemical diversity. The descriptor typology

is: (a) 0D-47 constitutional (atom and group counts); (b)

1D-121 functional groups, (c) 1D-120 atom centred

fragments, (d) 1D-3 empirical; (e) 2D-262 topological,

(f) 2D-64 BCUTs, (g) 2D-21 Galvez Indices from the

adjacency matrix, (h) 2D-21 walk counts, (i) 2D-96

various autocorrelations from the molecular graph, (l)

3D-41 Randic molecular profiles from the geometry

matrix; (m) 3D-58 geometrical, (n) 3D-99 WHIMs

(Todeschini and Gramatica, 1997a, b) and (o) 197

recently proposed GETAWAY descriptors (Consonni

et al., 2002). The meaning of these molecular descrip-

tors, and the calculation procedure, is summarized in the

software DRAGON (free download from the web,

Todeschini et al., 2002a), and is explained in detail with

the related literature references in the Handbook of

Molecular Descriptors by Todeschini and Consonni

(2000). In addition, in order to provide energy informa-

tion, five quantum-chemical descriptors (highest occu-

pied molecular orbital (HOMO), lowest unoccupied

molecular orbital (LUMO) energies, HOMO–LUMO

gap, ionisation potential and heat of formation),

calculated by the semi-empirical molecular orbital

program MOPAC (PM3 Hamiltonian for geometry

optimisation) (CHEM 3D, 1997) are always added as

electronic descriptors. The values of the selected

descriptors for the studied compounds are reported in

Table 1.

Constant values and descriptors found to be corre-

lated pair-wise were excluded in a pre-reduction step

(one of any two descriptors with a K correlation greater

than 0.95 was removed to reduce redundant informa-

tion), thus 393 molecular descriptors underwent sub-

sequent variable selection.

2.3. Chemometric methods

Data exploration by principal component analysis of

molecular descriptors was performed on autoscaled data

by the SCAN (1995).

To have compounds for ‘‘external’’ validation, the

available set of 114 chemicals was split into a training set

ARTICLE IN PRESSP. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–31243116

ARTICLE IN PRESS

Table 1

List of studied chemicals (test set in bold), experimental, predicted -log kNO3; residuals (r) and descriptor values

ID Chemicals CAS �log kNO3exp. �log kNO3

pred. r HOMO nBnz MATS1m

1 Formaldehyde 50-00-0 15.23 16.30 1.07 �10.63 0 0.96

2 Methanol 67-56-1 15.68 15.99 0.31 �11.14 0 0.88

3 2-Propanol 67-63-0 14.64 15.44 0.80 �11.04 0 0.87

4 Ethane 74-84-0 17.10 16.59 �0.51 �11.98 0 0.81

5 Ethene 74-85-1 15.91 14.62 �1.29 �10.64 0 0.87

6 Ethyne 74-86-2 16.29 16.89 0.60 �11.01 0 0.94

7 Chloromethane 74-87-3 16.51 16.26 �0.25 �10.48 0 0.97

8 Methanethiol 74-93-1 12.00 11.72 �0.28 �9.21 0 0.90

9 1-Propyne 74-99-7 15.76 15.94 0.18 �10.89 0 0.91

10 1-Chloroethene 75-01-4 15.37 14.83 �0.54 �9.84 0 0.98

11 Acetaldehyde 75-07-0 14.61 15.79 1.18 �10.70 0 0.92

12 Ethanethiol 75-08-1 11.92 11.62 �0.30 �9.25 0 0.89

13 Dichloromethane 75-09-2 17.30 17.33 0.03 �10.58 0 1.01

14 Dimethyl sulfide 75-18-3 12.00 10.85 �1.15 �8.88 0 0.90

15 2-Methylpropane 75-28-5 16.01 15.99 �0.02 �11.59 0 0.83

16 1,1-Dichloroethene 75-35-4 14.91 15.30 0.39 �9.74 0 1.01

17 2-Methylbutane 78-78-4 15.80 15.85 0.05 �11.50 0 0.83

18 2-Methyl-1,3-butadiene 78-79-5 12.23 11.65 �0.58 �9.31 0 0.88

19 1,1,2-Trichloroethene 79-01-6 15.55 14.77 �0.78 �9.38 0 1.03

20 2,3-Dimethylbutane 79-29-8 15.39 15.43 0.04 �11.30 0 0.84

21 Camphene 79-92-5 12.18 12.84 0.66 �9.92 0 0.87

22 a-Pinene 80-56-8 11.24 11.35 0.11 �9.30 0 0.87

23 b-Caryophyllene 87-44-5 10.72 11.75 1.03 �9.45 0 0.87

24 1,2-Dimethylbenzene 95-47-6 15.42 15.32 �0.10 �9.29 1 0.90

25 1,2,4-Trimethylbenzene 95-63-6 14.74 14.71 �0.03 �9.08 1 0.89

26 3-Methylpentane 96-14-0 15.69 15.78 0.09 �11.45 0 0.84

27 a-Phellandrene 99-83-2 10.07 10.35 0.28 �8.85 0 0.88

28 c-Terpinene 99-85-4 10.53 10.72 0.19 �9.00 0 0.88

29 a-Terpinene 99-86-5 9.74 9.80 0.06 �8.62 0 0.88

30 1,4-Methylisopropylbenzene 99-87-6 15.00 15.03 0.03 �9.26 1 0.89

31 Methoxybenzene 100-66-3 15.68 15.34 �0.34 �9.11 1 0.92

32 1,3,5-Trimethylbenzene 108-67-8 15.10 15.15 0.05 �9.27 1 0.89

33 Ethyl propionate 105-37-3 16.46 16.95 0.49 �11.36 0 0.90

34 1,4-Dimethylbenzene 106-42-3 15.34 15.07 �0.27 �9.18 1 0.90

35 n-Butane 106-97-8 16.18 15.42 �0.76 �11.35 0 0.83

36 1-Butene 106-98-9 13.91 13.17 �0.74 �10.15 0 0.86

37 1,3-Butadiene 106-99-0 13.01 12.21 �0.80 �9.47 0 0.89

38 1-Butyne 107-00-6 15.34 15.32 �0.02 �10.77 0 0.89

39 Acrolein 107-02-8 14.96 16.07 1.11 �10.69 0 0.94

40 3-Chloro-1-propene 107-05-1 15.27 15.28 0.01 �10.23 0 0.95

41 Methyl formate 107-31-3 17.52 17.20 �0.32 �11.15 0 0.94

42 2-Methylpentane 107-83-5 15.69 15.30 �0.39 �11.25 0 0.84

43 2,4-Dimethylpentane 108-08-7 15.84 15.34 �0.50 �11.25 0 0.84

44 1,3-Dimethylbenzene 108-38-3 15.63 15.37 �0.26 �9.31 1 0.90

45 1,3,5-Trimethylbenzene 108-67-8 15.10 15.15 0.05 �9.27 1 0.89

46 Methylbenzene 108-88-3 16.18 15.84 �0.34 �9.44 1 0.91

47 1-Propylacetate 109-60-4 16.30 16.68 0.38 �11.25 0 0.90

48 n-Pentane 109-66-0 16.09 15.37 �0.72 �11.30 0 0.83

49 Ethyl formate 109-94-4 16.70 16.89 0.19 �11.16 0 0.92

50 Pyrrole 109-97-7 10.34 11.41 1.07 �8.93 0 0.92

51 Tetrahydrofuran 109-99-9 14.31 13.90 �0.41 �10.27 0 0.88

52 Furan 110-00-9 11.84 12.89 1.05 �9.38 0 0.94

53 Thiophene 110-02-1 13.41 13.45 0.04 �9.54 0 0.95

54 n-Hexane 110-54-3 15.98 15.36 �0.62 �11.28 0 0.84

55 Propyl formate 110-74-7 16.27 16.65 0.38 �11.16 0 0.91

56 Cyclohexane 110-82-7 15.87 15.68 �0.19 �11.29 0 0.85

57 Cyclohexene 110-83-8 12.28 12.06 �0.22 �9.59 0 0.87

P. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–3124 3117

ARTICLE IN PRESS

Table 1 (continued)

ID Chemicals CAS �log kNO3exp. �log kNO3

pred. r HOMO nBnz MATS1m

58 Pyridine 110-86-1 15.82 14.53 �1.29 �10.10 0 0.93

59 n-Octane 111-65-9 15.74 15.43 �0.31 �11.27 0 0.84

60 n-Nonane 111-84-2 15.62 15.46 �0.16 �11.28 0 0.84

61 1-Propene 115-07-1 14.13 13.15 �0.98 �10.11 0 0.86

62 Dimethyl ether 115-10-6 14.52 14.74 0.22 �10.69 0 0.87

63 2-Methyl-1-propene 115-11-7 12.50 12.34 �0.16 �9.80 0 0.86

64 Tetralin 119-64-2 14.06 15.23 1.17 �9.25 1 0.90

65 Bicyclo(2,2,1)-2,5-heptadiene 121-46-0 11.99 12.84 0.85 �9.66 0 0.90

66 N,N-Dimetyl-aniline 121-69-7 15.70 15.11 �0.59 �9.18 1 0.90

67 Myrcene 123-35-3 10.98 11.58 0.60 �9.32 0 0.88

68 Crotonaldehyde 123-73-9 14.29 15.18 0.89 �10.48 0 0.92

69 n-Decane 124-18-5 15.59 15.48 �0.11 �11.28 0 0.84

70 b-Pinene 127-91-3 11.63 12.32 0.69 �9.70 0 0.87

71 Ethyl acetate 141-78-6 16.85 16.85 0.00 �11.24 0 0.91

72 Cyclopentene 142-29-0 12.33 11.98 �0.35 �9.53 0 0.88

73 n-Heptane 142-82-5 15.86 15.39 �0.47 �11.27 0 0.84

74 cis-1,2-Dichloroethene 156-59-2 15.86 14.69 �1.17 �9.49 0 1.01

75 trans-1,2-Dichloroethene 156-60-5 15.97 14.75 �1.22 �9.52 0 1.01

76 Azulene 275-51-4 9.41 9.84 0.43 �8.17 0 0.93

77 Diethyl sulfide 352-93-2 11.38 10.50 �0.88 �8.86 0 0.88

78 2,2,3-Trimethylbutane 464-06-2 15.65 15.54 �0.11 �11.33 0 0.84

79 Longifolene 475-20-7 12.17 12.58 0.41 �9.82 0 0.87

80 1,4-Benzodioxan 493-09-4 15.22 15.39 0.17 �9.02 1 0.93

81 Bicyclo(2,2,1)-2-heptene 498-66-8 12.61 12.74 0.13 �9.78 0 0.88

82 2-Butyne 503-17-3 13.17 14.31 1.14 �10.35 0 0.89

83 2-Methyl-2-butene 513-35-9 11.02 11.31 0.29 �9.39 0 0.86

84 2,3-Dimethyl-1,3-butadiene 513-81-5 11.64 11.34 �0.30 �9.23 0 0.88

85 1,2,3-Trimethylbenzene 526-73-8 14.73 15.12 0.39 �9.25 1 0.89

86 2,2,4-Trimethylpentane 540-84-1 16.13 15.35 �0.78 �11.24 0 0.84

87 1,3,5-Cycloheptatriene 544-25-2 11.92 11.26 �0.66 �8.95 0 0.91

88 Methyl propionate 554-12-1 16.48 16.67 0.19 �11.17 0 0.91

89 2-Carene 554-61-0 10.73 11.22 0.49 �9.24 0 0.87

90 2,3-Dimethyl-2-butene 563-79-1 10.24 10.69 0.45 �9.15 0 0.86

91 Terpinolene 586-62-9 10.02 10.96 0.94 �9.10 0 0.88

92 cis-2-Butene 590-18-1 12.46 12.00 �0.46 �9.66 0 0.86

93 1-Methylcyclohexene 591-49-1 10.77 11.36 0.59 �9.33 0 0.87

94 1,3-Cyclohexadiene 592-57-4 10.91 10.91 0.00 �8.92 0 0.89

95 1,3-Ethylmethylbenzene 620-14-4 15.36 15.36 0.00 �9.35 1 0.89

96 1,4-Ethylmethylbenzene 622-96-8 15.21 15.11 �0.10 �9.25 1 0.89

97 trans-2-Butene 624-64-6 12.42 11.99 �0.43 �9.66 0 0.86

98 1-Pentyne 627-19-0 15.12 15.12 0.00 �10.76 0 0.88

99 1,4-Cyclohexadiene 628-41-1 12.27 11.56 �0.71 �9.19 0 0.89

100 Cycloheptene 628-92-2 12.32 12.30 �0.02 �9.73 0 0.87

101 1-Hexyne 693-02-7 14.80 14.80 0.00 �10.68 0 0.88

102 Bicyclo(2,2,2)-2-octene 931-64-6 12.84 12.94 0.10 �9.91 0 0.88

103 cis-1,3-Pentadiene 1574-41-0 11.85 11.34 �0.51 �9.18 0 0.88

104 trans-1,3-Pentadiene 2004-70-8 11.80 11.31 �0.49 �9.17 0 0.88

105 cis-Ocimene 3338-55-4 10.62 10.66 0.04 �8.94 0 0.88

106 Sabinene 3387-41-5 11.00 12.18 1.18 �9.64 0 0.87

107 trans-Ocimene 3779-61-1 10.98 10.91 �0.07 �9.05 0 0.88

108 1,3-Cycloheptadiene 4054-38-0 11.19 11.70 0.51 �9.31 0 0.89

109 trans-trans-2,4-Hexadiene 5194-51-4 10.80 10.59 �0.21 �8.92 0 0.88

110 Limonene 5989-27-5 10.95 11.48 0.53 �9.32 0 0.88

111 a-Humulene 6753-98-6 10.46 11.51 1.05 �9.33 0 0.88

112 3-Carene 13466-78-9 11.09 11.43 0.34 �9.33 0 0.87

113 Ocimene 13877-91-3 10.66 10.73 0.07 �8.97 0 0.88

114 Crotonaldehyde 4170-30-3 14.29 15.18 0.89 �10.48 0 0.92

P. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–31243118

and an ‘‘external’’ validation set. The training set

selection was performed by the package DOLPHIN

(Todeschini and Mauri, 2002) using a D-optimal

experimental design (Marengo and Todeschini, 1992).

Multiple linear regression analysis and variable

selection were performed by the software Moby Digs

(Todeschini et al., 2002b) using the ordinary least-

squares regression (OLS) method; the genetic algo-

rithms-variable subset selection (GA-VSS) method

(Leardi et al., 1992) was applied to the input set of

molecular descriptors in order to set out the most

relevant variables in modelling the response of the

training set chemicals.

All the calculations were performed by maximising

the cross-validated R2 (Q2; leave-one-out), applying the

QUIK rule (Todeschini et al., 1999); the acceptable

models are only those with a global correlation of

[X þ y] block (KXY ) greater than the global correlation

of the X block (KXX ) variable, X being the molecular

descriptors and y the response variable. The collinearity

in the original set of molecular descriptors results in

many similar models that more or less yield the same

predictive power (in MOBY-DIGS software 100 models

of different dimensionality). Therefore, when there were

models of similar performance those with higher

DKðKXY � KXX Þ were selected, and, on these, stronger

validation proceeded via the leave-many-out validation

(Q2LMO) and response permutation testing (Y -scram-

bling). Standard deviation error in prediction (SDEP),

standard deviation error in calculation (SDEC), stan-

dard error of estimate (s), the F -value of the Fisher, the

inter-correlation of the selected descriptors (KXX ) and

the correlation of the X block with response (KXY ) are

also reported, together with the coefficient of determina-

tion (R2).

The predictive power of the regression model devel-

oped on the selected training set is estimated on the

predictions of validation set chemicals, by the external

Q2 that is defined (Shi et al., 2001):

Q2ext ¼ 1 �

Ptesti¼1ðyi � #yiÞ

2

Ptesti¼1ðyi � %ytrÞ

2;

where yi and #yi are respectively the measured and

predicted (over the validation set) values of the

dependent variable, and %ytr the averaged value of the

dependent variable for the training set; the summations

cover all the compounds in the validation set.

The presence of outliers (i.e. compounds with cross-

validated standardized residuals greater than two

standard deviation units), and chemicals very influential

in determining model parameters (i.e. compounds with

high leverage value (h) (Atkinson, 1985) greater than

3p0=n; where p0 is the number of model variables plus

one, and n the number of the objects used to calculate

the model) were verified by the Williams plot (SCAN,

1995).

3. Results and discussion

This work proposes a new QSAR model of the

reaction rate constant of nitrate radical (kNO3) for an

heterogeneous set containing both aliphatic and aro-

matic chemicals, without separating these two classes as

in previous modelling approaches.

In order to find a relationship between kNO3 and the

structural features of the chemicals, we calculated a wide

set of theoretical molecular descriptors, using the

software DRAGON (Todeschini et al., 2002a) for the

studied chemicals. Information regarding the energetics

of the studied reaction was also taken into account by

adding five quantum-chemical descriptors from among

those most commonly used (HOMO, LUMO, HOMO-

LUMO gap, ionisation potential and heat of formation).

The great advantage of theoretical descriptors is that

they are also calculable homogeneously for not yet

synthesised chemicals. As modelling input variables, we

used many different types of molecular descriptors; this

was to give us the possibility of capturing all the relevant

structural features really related to response.

The ultimate objective of developing models for the

prediction of degradation rate constants is to obtain

knowledge of the reactivity with NO3 radical of

substances not yet tested or for which reliable experi-

mental data are not available. Prediction reliability can

only be achieved through regression models that have

been validated both internally and externally (Tropsha

et al., 2003). The effective predictive capability of a

model is evaluated by an ‘‘external’’ validation proce-

dure, i.e. by comparing the predictions made for

molecules excluded from the model generation step with

their actual experimental activity. To have compounds

for use in external validation, the available set of 114

chemicals was split into a training set and an ‘‘external’’

validation set. The best splitting of the data set was

realised by the experimental design procedure, using the

software DOLPHIN of Todeschini and Mauri (2002).

Experimental Design (here D-optimal design, Marengo

and Todeschini, 1992) provides a strategy for selecting

the most dissimilar molecular structures in a data set,

taking into account the complete structural information

and also the response value. This guarantees that the

chemical composition of the training set is representative

of the structural diversity of the validation set and that

the entire range of response is represented.

Two different splittings were performed using 393

molecular descriptors and response: (a) 67% of the

chemicals in the training set (77 chemicals) and 33% in

the validation set (37 chemicals), and (b) 50% of the

chemicals in each set. Fig. 1 shows the principal

ARTICLE IN PRESSP. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–3124 3119

components analysis of the data set, represented by the

molecular descriptors and split as in (a). In this view of

the first two principal components, explaining 38.2% of

the structural variance, the data set appears split into

two representative sets thus confirming the efficiency of

the applied experimental design in the splitting: in fact

the training set consists of representatives of the more

dissimilar structures.

Note that the validation chemicals are all included in

the chemical domain of the training set. In the data set

b-caryophyllene (23), longifolene (79) and a-humulene

(111) appear to be the most structurally diverse

chemicals, and are correctly included in the training

set. Regression models deriving from such chemicals can

have a wider range of applicability with regard to

chemical domain.

Fig. 2 shows the response histogram in the training

and validation sets, highlighting that the entire range of

response is covered in both sets in a way that is quite

well balanced.

The range of the response in the training set is 9.41–

17.52 log unit ( %y ¼ 14:02), while the range of validation

set response is 9.74–16.85 log unit ( %y ¼ 13:37).

Given the correlation of all the calculated descriptors,

and the impossibility of performing multilinear regres-

sion, a variable selection procedure was needed to select

the predictive variables. Genetic algorithms were applied

to select, from among all the calculated descriptors, only

the best combinations of those descriptors most relevant

to the obtaining of models with the highest predictive

power of the nitrate radical rate constant. Genetic

Algorithms, a powerful tool applied in recent years to

optimise many decisional problems (Davis, 1991;

Devillers, 1996) were initially proposed by Leardi et al.

(1992) as a strategy for variable subset selection in

multivariate analysis. This strategy is now widely and

successfully applied (in various modified versions,

depending on the way of performing reproduction,

crossover, mutation, etc.) in QSAR approaches (Rogers

and Hopfinger, 1994; Kubinyi, 1994; Todeschini and

Gramatica, 1997a, b; Gramatica and Papa, 2003;

Gramatica et al., 1998, 1999, 2000, 2002, 2003) in which

a high number of molecular descriptors are used as X-

variables.

The application of Genetic Algorithms to the set of

393 molecular descriptors for each chemical, and the

related response, yielded a population of regression

models, ordered according to their decreasing predictive

performance, verified by Q2 with particular attention to

the collinearity of the selected molecular descriptors. In

fact, to avoid multicollinearity without, or with ‘‘appar-

ent’’, prediction power (chance correlation), the regres-

sions were calculated only for variable subsets with an

acceptable multivariate correlation with response, by

applying the QUIK rule (Q Under Influence of K)

(Todeschini et al., 1999).

In addition, attention must be paid to the danger of

overfitting and the possibility of overestimating model

predictivity by Q2 (Shao, 1993; Golbraikh and Tropsha,

2002). For this reason, the predictivity stability of the

models must be verified using the leave-many-out (Q2LMO)

procedure (repeated 5000 times with 25–50% of

randomly selected objects left out from the training set

at each step and then predicted by the model) as is

strongly recommended for QSAR modelling (Wold and

Eriksson, 1995; Shi et al., 2001). The robustness of the

proposed models and their predictivity is guaranteed by

the stability of the Q2LMO; even when 50% of the training

compounds are randomly left out. Good predictive

properties are also an indication that chance correlation

among the molecular descriptors and the studied

response has been avoided.

Proposed models are also checked for reliability and

robustness by permutation testing: new models are

recalculated for randomly reordered response (Y scram-

bling). Evidence that the proposed model is well

founded, and not just the result of chance correlation,

is provided by obtaining new models on the set with

randomised response that have significantly lower R2

and Q2 than the original model. Thus our proposed

QSAR model was subjected to the Y scrambling

procedure to verify that this condition had been

achieved.

Finally, for a stronger evaluation of model applic-

ability to new chemicals not used in the training set,

‘‘external’’ validation (verified by Q2EXT) is performed:

the regression model, developed on the selected training

set, is applied to predict the rate constant for the

molecules remaining in the study and included in the

validation set.

The best predictive model obtained from the first

splitting is:

�log kðNO3Þ ¼ � 28:7 � 2:40HOMO þ 3:41nBnz

þ 20:41MATS1m;

nðtrainingÞ ¼ 77; nðvalidationÞ ¼ 37;

R2 ¼ 91:2%; Q2 ¼ 90:3%;

Q2LMOð50%Þ ¼ 89:6%; Q2

ext ¼ 95:7%;

s ¼ 0:650; F ¼ 253:3; SDEP ¼ 0:666;

SDEC ¼ 0:633; Kxx ¼ 23:2%; Kxy ¼ 34:4%:

The regression line of the above-proposed model is

reported in Fig. 3 and the data predicted by this model

are reported in Table 1.

Ethene (5), pyridine (58), tetralin (64), cis- and trans-

1,2-dichloroethene (74 and 75) are the outliers in this

model (highlighted in Fig. 3), while there are no

influential chemicals with high leverage value. There

could be two explanations for the outliers, either (a) the

ARTICLE IN PRESSP. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–31243120

experimental data were wrong, in some cases for

experimental difficulties due to low vapour pressure or

(b) the descriptors in the model failed to capture some

relevant structural feature present in these molecules and

absent in others. At this stage it is impossible to verify

either statement.

As no chemical in the validation set is an outlier or

influential, the data predicted by the model can be

considered reliable, also for chemicals not participating

in the model construction.

The root-mean squared (RMS) error for this model is

0.663 log units for the training set chemicals and

ARTICLE IN PRESS

PC1

PC

2

1

2

3

4

5

6

7

89

10

1112

13

14

15

16

17

18

19

20

2122

23 2425

26

27

282930

3132

33

34

35

363738

3940

41

4243

444546

47

48

49

50

51

52

53

54

55 56

57

58

59

60

61

62

63

64 65

66

67

68

69

70

71

72

73

74

75

76

7778

79 80

81

82

83

84

85

86

87

88

89

90

91

92

93

9495

96

97

98

99100

101

102

103104

105

106

107

108

109

110111

112

113

114

-20

-15

-10

-5

0

5

10

15

20

25

-35 -25 -15 -5 5 15 25

Training setTest set

Fig. 1. Principal component analysis of the structural descriptors (EV%=38.2%) for the data set chemicals splitted in training (�) and

test set (n) by experimental design (Marengo and Todeschini, 1992).

N o

f obs

serv

atio

ns

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

<= 9 (10,11] (12,13] (14,15] (16,17] > 18

Training setTest set

Fig. 2. Distribution of the response in the training and test chemicals.

P. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–3124 3121

0.483 log units for the validation set; the mean RMS is

0.573, similar to (and even smaller than) the typical

experimental error range for such types of measures.

Note that the validation set chemicals are better

predicted, probably because the structural variability of

this set is smaller than the training set, owing to the

algorithm of the D-optimal experimental design adopted

for the original set splitting. Thus by carrying out such

splitting the prediction power of the proposed model can

be overestimated.

In the above equation the descriptors are reported in

decreasing order of significance, as indicated in Table 2

where the meaning of the molecular descriptors, selected

by Genetic Algorithms as the most predictive for

degradation with nitrate radicals, is reported. In fact,

since the molecular descriptors do not have equal

variance (i.e. they are not autoscaled), their relative

importance in the model is better measured by the

standardized regression coefficients (i.e. the coefficients

multiplied by the standard deviation of the correspond-

ing predictor).

The molecular descriptors selected by Genetic Algo-

rithms in this model are all highly informative of the

different aspects of the studied reaction. The best

descriptor is the energy of the highest occupied

molecular orbital (HOMO); this descriptor is a measure

of the nucleophilicity of a molecule: more reactive

chemicals have high HOMO energy values. The

information related to the dimension and shape of the

molecules is encoded by a 2D-autocorrelation descriptor

MATS1m, weighted by atomic masses (Moran, 1950),

while the number of aromatic rings (nBnz) is probably

selected in the model to encode for the different

reactivity of aliphatic and aromatic chemicals in relation

to the attack sites for nitrate radicals.

A model, based on the same descriptors and with

similar predictive performance (Q2EXT ¼ 94:8%), was

also obtained by the 50% splitting of the original data

set, demonstrating the validity and reproducibility of

Genetic Algorithms selection for this particular combi-

nation of structural information, being relevant to

studied response prediction.

4. Conclusion

The obtaining of knowledge of organic pollutant

nighttime degradability by NO3 radicals is severely

ARTICLE IN PRESS

-logk(NO3) experimental

-lo

gk(

NO

3) p

red

icte

d

9

10

11

12

13

14

15

16

17

18

8.5 10.5 12.5 14.5 16.5 18.5

Training setTest set

5

58

6474

75

Fig. 3. Regression line for the model; the log k(NO3) values for training and test set chemicals are differently highlighted, the outliers

and influential chemicals are numbered.

Table 2

List of molecular descriptors selected by Genetic Algorithm,

meaning and standardized coefficients

Symbol Description Std. reg.

coeff.

HOMO Energy of the highest

occupied molecular orbital

�1.01

nBnz Number of aromatic rings 0.49

MATS1m 2D-(Moran) autocorrelation

weighted by atomic masses

0.45

P. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–31243122

hindered by the difficulty encountered in producing

experimental data for tropospheric reactions. Thus the

use of data predicted by QSAR models could overcome

this problem. ‘‘Ideal’’ QSAR models would be applic-

able throughout the chemical world, and would use

independent variables that are easily and homoge-

neously calculable for each chemical. Nevertheless, such

models must always be verified for prediction perfor-

mance. This paper proposes a new QSAR model based

on theoretical molecular descriptors that take into

account the different features of chemical structures

related to reactivity with nitrate radicals. The model is

validated for its predictivity on an ‘‘external’’ validation

set obtained by splitting the original data set by

experimental design. The possibility of having molecular

descriptors available for all chemicals (even those not yet

synthesized), the high prediction performance of a

model applicable to a wide typology of aromatic and

aliphatic chemicals, and the possibility of verifying the

chemical domain of applicability by the leverage

approach, makes this a useful model for producing

reliable, estimated NO3 radical rate constants when

experimental parameters are not available.

Acknowledgements

We wish to thank Prof. R. Todeschini for the software

for the molecular descriptor calculation and modeling,

and the University of Insubria for a fellowship granted

to Pamela Pilutti.

References

Atkinson, A.C., 1985. Plots, Transformations and Regression.

Clarendon Press, Oxford, pp. 282.

Atkinson, R., 1991. Kinetics and mechanisms of the gas-phase

reactions of the NO3 radical with organic compounds.

Journal of Physical and Chemical Reference Data 20, 459–

507.

Atkinson, R., 2000. Atmospheric chemistry of VOCs and NOx.

Atmospheric Environment 34, 2063–2101.

Bakken, G., Jurs, P., 1999. Prediction of hydroxyl radical rate

constants from molecular structure. Journal of Chemical

Information and Computer Sciences 39, 1064–1075.

CHEM 3D, 1997. Cambridge Soft, MA, USA.

Consonni, V., Todeschini, R., Pavan, M., 2002. Structure/

response correlation and similarity/diversity analysis by

GETAWAY descriptors. Part 1. Theory of the novel 3D

molecular descriptors. Journal of Chemical Information and

Computer Sciences 42, 693–705.

Davis, L., 1991. Handbook of Genetic Algorithms. Van

Nostrand Reinhold, New York, USA.

Devillers, J., 1996. Genetic Algorithms in Molecular Modelling.

Academic Press, London.

EPI Suite, 2001.Ver.3.10. Environmental Protection Agency,

USA.

Golbraikh, A., Tropsha, A., 2002. Beware of q2! Journal of

Molecular Graphics and Modelling 20, 269–276.

Gramatica, P., Navas, N., Todeschini, R., 1998. 3D-Modelling

and prediction by WHIM Descriptors. Part 9. Chromato-

graphic relative retention time and physico-chemical proper-

ties of polychlorinated biphenyls (PCBs). Chemometrics

and Intelligent Laboratory System 40, 53–63.

Gramatica, P., Consonni, V., Todeschini, R., 1999. QSAR

study on the tropospheric degradation of organic com-

pounds. Chemosphere 38, 1371–1378.

Gramatica, P., Corradi, M., Consonni, V., 2000. Modelling and

prediction of soil sorption coefficients of non-ionic organic

pesticides by different sets of molecular descriptors. Chemo-

sphere 41, 763–777.

Gramatica, P., Pilutti, P., Papa, E., 2002. Ranking of volatile

organic compounds for tropospheric degradability by

oxidants: a QSPR approach. SAR and QSAR in Environ-

mental Research 13 (7–8), 743–753.

Gramatica, P., Papa, E., 2003. QSAR modelling of bioconcen-

tration factor by theoretical molecular descriptors. Quanti-

tative Structure-Activity Relationships 22, 374–385.

Gramatica, P., Pilutti, P., Papa, E., 2003. QSAR prediction of

ozone tropospheric degradation. Quantitative Structure-

Activity Relationships 22, 364–373.

G .usten, H., 1997. Degradation of atmospheric pollutants by

tropospheric free radical reactions. In: Minisci, F. (Ed.),

Free Radicals in Biology and Environment. Kluwer

Academic Publishers, Dordrecht, Boston, London,

pp. 387–408.

G .usten, H., 1999. Predicting the abiotic degradability of

organic pollutants in the troposphere. Chemosphere 38

(6), 1361–1370.

HYPERCHEM, 1995. Rel. 4 for Windows. Autodesk, Inc.,

Sausalito, CA, USA.

Jinhui, X., Lee, F.S.C., 2000. Quantification of nitrated

polynuclear aromatic hydrocarbons in atmospheric parti-

culate matter. Analytica Chimica Acta 416, 111–115.

Klamt, A., 1996. Estimation of gas-phase hydroxyl radical rate

constants of oxygenated compounds based on molecular

orbital calculations. Chemosphere 32 (4), 717–726.

Kubinyi, H., 1994. Variable selection in QSAR studies. II. A

highly efficient combination of systematic search and

evolution. Quantitative Structure-Activity Relationships

13, 393–401.

Leardi, R., Boggia, R., Terrile, M., 1992. Genetic algorithms as

a strategy for feature selection. Journal of Chemometrics 6,

267–281.

Marengo, E., Todeschini, R., 1992. A new algorithm for

optimal distance—based experimental design. Chemo-

metrics and Intelligent Laboratory System 16, 37–44.

Medven, Z., G .usten, H., Sabljic, A., 1996. Comparative QSAR

study on hydroxyl radical reactivity with unsaturated

hydrocarbons: PLS versus MLR. Journal of Chemometrics

10, 135–147.

Moran, P.A.P., 1950. Notes on continuous stochastic phenom-

ena. Biometrika 37, 17–23.

M .uller, M., Klein, W., 1991. Estimating atmospheric degrada-

tion processes by SARs. The Science of the Total Environ-

ment 109, 261–273.

Rogers, D., Hopfinger, A.J., 1994. Application of genetic

function approximation to quantitative structure–activity

ARTICLE IN PRESSP. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–3124 3123

relationships and quantitative structure–property relation-

ships. Journal of Chemical Information and Computer

Sciences 34, 854–866.

Sabljic, A., G .usten, H., 1990. Predicting the nighttime NO3

radical reactivity in the troposphere. Atmospheric Environ-

ment 24A, 73–78.

SCAN—Software for Chemometric Analysis, 1995. Rel. 1.1 for

Windows. Minitab, USA.

Shao, J., 1993. Linear model selection by cross-validation.

Journal of the American Statistical Association 88, 486–494.

Shi, L.M., Fang, H., Tong, W., Wu, J., Perkins, R., Blair,

R.M., Branham, W.S., Dial, S.L., Moland, C.L., Sheehan,

D.M., 2001. QSAR models using a large diverse set of

estrogens. Journal of Chemical Information and Computer

Science 41, 186–195.

Tejada, S.B., Zweidinger, R.B., Sigsby, J.E., 1986. Fluorescence

detection and identification of nitro derivatives of poly-

nuclear aromatic hydrocarbons by on-column catalytic

reduction to aromatic amines. Analytical Chemistry 58

(8), 1827–1834.

Todeschini, R., Consonni, V., 2000. Handbook of Molecular

Descriptors. Wiley-VCH, Weinheim, Germany, p. 667.

Todeschini, R., Gramatica, P., 1997a. The WHIM theory: new

3D molecular descriptors for QSAR in environmental

modelling. SAR and QSAR in Environmental Research 7,

89–115.

Todeschini, R., Gramatica, P., 1997b. 3D-Modelling and

prediction by WHIM descriptors. Part 6. Applications of

WHIM descriptors in QSAR studies. Quantitative Struc-

ture-Activity Relationships 16, 120–125.

Todeschini, R., Mauri, A., 2002. DOLPHIN-software for

optimal distance-based experimental design. Ver. 2.0 for

Windows. Talete srl, Milan, Italy.

Todeschini, R., Maiocchi, A., Consonni, V., 1999. The K

correlation index: theory development and its application in

chemometrics. Chemometrics and Intelligent Laboratory

System 46, 13–29.

Todeschini, R., Consonni, V., Pavan, M., 2002a. DRAGON-

software for the calculation of molecular descriptors. Ver.

2.1 for Windows. Free download available at: http://

www.disat.unimib/chm.

Todeschini, R., Consonni, V., Pavan, M., 2002b. MOBY DIGS-

software for multilinear regression analysis and variable

subset selection by genetic algorithm. Ver. 1.2 for Windows.

Talete srl, Milan, Italy.

Tropsha, A., Gramatica, P., Gombar, V.K., 2003. The

importance of being earnest: validation is the absolute

essential for successful application and interpretation of

QSPR models. Quantitative Structure-Activity Relation-

ships 22, 69–77.

Wang, X., Yin, C., Wang, L., 2002. Structure–activity relation-

ships and response-surface analysis of nitroaromatics

toxicity to the yeast (Saccharomyces cerevisiae). Chemo-

sphere 46, 1045–1051.

Wold, S., Eriksson, L., 1995. Chemometric Methods in

Molecular Design. VCH, Germany, pp. 309–318.

ARTICLE IN PRESSP. Gramatica et al. / Atmospheric Environment 37 (2003) 3115–31243124