REGULAR PAPERS
QSPR Modeling Of The Octanol/Water Partition Coefficient Of Alcohols By Means Of Optimization Of Correlation Weights Of Local Graph Invariants
Duchowicz1, P.R.; Castro1, E. A.; Toropov2, A. A.; Nesterova2, A. I.; Nabiev2, O. M.
1 INIFTA,
Departamento de Química, Facultad de Ciencias Exactas, UNLP,
Suc. 4, C.C. 16, La
Plata 1900, Argentina
FAX:
+54 221 425 4642; direccion@inifta.unlp.edu.ar
2 Uzbekistan Academy of Sciences, Algorithm-Engineering Institute, F.
Khodjaev Street
25,
100125 Tashkent, Uzbekistan
Received November 10, 2003. In final form February 23, 2004
Dedicated
to Prof. Pedro J. Aymonino on the occasion of his 75th birthday
Abstract
A particular approach based on the concept
of flexible topological descriptors,the so called “Optimization of Correlation
Weights of Local Graph Invariants”,is applied to model the octanol/water
partition coefficient of a representative setof 62 alcohols. Predictions are
quite satisfactory and the numerical data improve previous results based on the
application of a novel atomic-level-based AI topological descriptor. Some
possible further extensions of the method are pointed out.
Resumen
Se aplica una aproximación particular basada en el
concepto de descriptores topológicos flexibles, la denominada “Optimización de
los Pesos de Correlación de Invariantes de Grafos Locales” al modelado del
coeficiente de partición octanol/agua para un conjunto representativos de 2
alcoholes. Las predicciones son bastante satisfactorias y los resultados
numéricos constituyen una mejora en resultados previos basados en la
aplicación de un nuevo descriptor topológico, el denominado descriptor de
nivel atómico de base AI. Finalmente, se destacan algunas posibles extensiones
del método.
Introduction
The
progress in computer technology during the last 25 years has enabled the
performance of ever more precise quantum mechanical calculations related to
structure and interactions of chemical compounds. However, the qualitative
models relating electronic structure to molecular geometry have not progressed
at the same pace. There is a continuing need in chemistry for simple concepts
and qualitatively clear pictures that be also quantitatively comparable to ab
initio quantum chemical calculations. Topological methods, and, more
specifically, graph theory as s fixed-point topology, provide in principle a
chance to fill this gap [1] . With more than 100 years of application to
chemistry, graph theory has proven to be of vital importance as the most
natural language of chemistry. The explosive development of chemical graph
theory during the last 30 years has increasingly overlapped with quantum
chemistry. Besides contributing to the solution of various problems in theoretical
chemistry, this development indicates that topology is an underlying principle
that explains the success of quantum mechanics an goes beyond it, thus
promising to bear more fruit in the future.
Most
applications of data analysis involve attempts to fit a model, usually
quantitative, to a set of experimental measurements or observations. The
reasons for fitting such models are varied. For
example, the model may be purely empirical and be required in order to make
predictions for new experiments. On the other hand, the model may be based on
some theory or law, and an evaluation of the fit of the data to the model may
be used to give insight into the process underlying the observations made. In
some cases the ability to fit a model to a set of data successfully may provide
the inspiration to formulate some new hypothesis. The type of model which may
be fitted to any set of data depends not only on the nature of the data but
also on the intended use of the model. In many applications a model is meant to
be used predictively, but the predictions need not necessarily be quantitative
[2] .
The
majority of molecular discoveries today are the result of an iterative,
three-phase cycle of design, synthesis and test. Analysis of the results from
one iteration provides information and knowledge that enables the next cycle to
be initiated and further improvements to be achieved. A common feature of this
analysis stage is the construction of some form of model which enables the
observed activity or properties to be related to the molecular structure. Many
types of models are possible, with mathematical and statistical models being
particularly common. Such models are often referred to as Quantitative
Structure-Activity Relationships (QSAR) or Quantitative Structure-Property
Relationships (QSPR).
The
basic principle of QSAR/QSPR theory is the mathematical relationship
p = f(s) | (1) |
where p is any
biological activity or physicochemical property, s is a set of variables
associated to the molecular structure (they are called molecular descriptors)
and f is an arbitrary function. Molecular descriptors are numerical values that
characterize properties of molecules. For example, they may represent the
physicochemical properties of a molecule or they may be values that are derived
by applying algorithmic techniques to the molecular structure. Many different
molecular descriptors have been described and used for a wide variety of
purposes. They vary in the complexity of the information they encode and in the
time required to calculate them.
The
biochemical interactions in the living cell occur in both aqueous and
hydrophobic media (i.e. coupling to an active site of an enzyme,
transport through a biomembrane) [3] . In addition, other pharmaco-kinetic
properties are related to the difference in solubility of bioactive molecules
in aqueous and organic solvents. Hence, it is important to account properly for
the solute interactions in both aqueous and organic media. The partition of
chemical compounds between organic and aqueous phases is often modeled by the
octanol/water partition coefficient (log P) [4] , because it is assumed that
octanol may reflect lipid tissues in living organisms. Log P has been
successfully related to bioconcentration factor, soil and sediment sorbtion
partition coefficients and to toxicities of organic chemicals towards aquatic
organisms. Direct measurement of P by means of the shake-flask procedure yields
only reliable data for chemicals with log P less than 4-5 [5] . P of more
hydrophobic substances can be measured either by the generator-column-method or
by the slow-stirring technique. In addition to these direct approaches to the
determination of P, several other methods were employed: (1) calculation based
on molecular fragments additivity [6,7] , (2) correlation with capacity factors
on reversed-phase HPLC, (3) correlation with molecular descriptors (volume,
surface area, molar refraction, parachor, molecular weight) [8] , and (4)
correlation with molar volume and solvachromic parameters.
The partitioning
of a hydrophobic solute between octanol and water is due to the difference
between the interactions that the solute is experiencing in water versus
octanol. Hence, the relationship between water solubility and P [6] has been
studied extensively over the last two decades [9] . Examples of such correlation
have been published for halogenated benzene, aromatic hydrocarbons, aldehydes,
esters and alcohols. However, due to experimental difficulties, few accurate
data for compounds with log P greater than 6 have been reported, which limits
the use of such correlation for prediction purposes.
In a
series of rather recent studies, Ren [10-12] derived a new atom-type AI
topological indices from the adjacency matrix and distance matrix of a graph to
model six properties of alkanes. Further, high quality models were developed to
correlate four physical properties of a small data of alcohols and three
physical properties of a mixed set of compounds containing alkanes and alcohols
with their structures. The atom-type AI indices offer the possibility of
understanding the role of individual groups in molecules. In a latter paper,
Ren [13] have illustrated the application of the novel AI indices to a wide
range of physical properties and especially biological activities that depend
on the strength of intermolecular interactions such as hydrogen bonding
interactions of –OH moieties in molecules. The author calculated the
octanol/water partition for 62 alcohols via a multiple linear regression to
develop the structure-property model based on the modified Xu (Xum)
and AI indices. The best two-parameter model show that although Xum makes a major contribution to octanol/water partition, which indicates the
additive behavior of the property, other atomic groups, especially –OH groups,
are also important factors influencing the values of this property.
Since
there are other alternatives to predict log P within the frame of the QSPR
theory, we have deemed sensible to look for ways to improve these predictions.
An interesting and very promising option is the approach based upon the
correlation weights of local graph invariants [14-16] , which has proved to be a
quite suitable tool to calculate thermodynamic properties for a wide variety of
molecular species [17-22] .
The
paper is organized as follows: the next section deals with the presentation of
the method and the mathematical algorithm applied in this study. Then, we
display the set of alcohols together with available experimental data and
previous theoretical prediction of partition coefficient plus the results
derived from the present approach and they are discussed in a comparative
fashion. Finally, we analyze the main conclusions derived from this study and
point out some possible further extensions of this calculation method.
Method
Molecular
descriptors employed in QSPR theory can be divided into two broad categories:
fixes variable descriptors. Fixed descriptors are molecular invariants that can
be numerically computed once a molecule is selected. This is the case with the
great majority of proposed hundreds pf descriptors. Variable descriptors
involve one or more variables, the values of which are selected during the
regression process. Hence, a variable descriptor can either be a function of a
single variable or function of several variables.
In contrast to the
traditional molecular indices, which one can calculate after selecting a set
of compounds to be studied and then proceed with statistical analysis, the
variable indices are initially non-numerical. Therefore, they cannot be
calculated in advance for the set of compounds. Instead, one starts with an
arbitrary set of values for the yet undetermined variables and, in an iterative
procedure, varies these initial values seeking values that will produce the
smallest standard error of the property under consideration. It is clear that
the use of variable (they are also called flexible) descriptors can only
improve correlations over the use of simple indices because, if all the
variables took on a zero value (which is very unlikely), we would obtain the
results that coincide with the results based on the traditional molecular
indices.
Among
the several existing options to employ flexible molecular descriptors, the
optimization of Correlation Weights of Local Graph Invariants (OCWLI) has shown
to be a suitable possibility to employ in QSPR theory and results have been
very encouraging [14-22] . The method has been described in detail in the
current literature so that we do not deem necessary to repeat it here. The
interested reader can consult the pertinent bibliography [14-22] .
Regarding
the choice of the f function in relationship (1), we have pointed out that it
is arbitrary. The simplest mathematical structure is the linear one, i.e.
p = A + Bs, | (2) |
where A and B
are two numerical coefficients to be determined by a standard least square
criterion and s stands for a single molecular descriptor. In this work we have
resorted to this linear relationship since it provides good enough results, so
that the employment of other more complex formulae would not improved
significantly the final fittings. Mathematical software employed here is the
well known MATHEMATICA® computer program [23] .
The
total molecular set of 62 alcohols is the same as that employed by Ren [13] . We
have employed two numerical approaches: a) The calculations were made on the
complete set, and b) The calculations were made in two subsets. In this second
case, we have divided the complete set into two subsets for calculations: a training
set and a test set comprising 31 alcohols each one. In order to test whether
the choice of molecules in each set influences the final results, we have
performed several choices, and we have seen they furnish practically the same
results, so that we report data for a representative partition. Obviously,
results for the second set are true predictions.
Results And Discussion
In Table 1 we present the main statistical characteristics of the OCWLI models.
Table 1. Statistical characteristics of the OCWLI models
Test set | Complete set | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
|
LIs denotes local LFFG invariants
NLIs denotes the number of parameters of the OCW
EC0, EC1, EC2 are Morgan extended connectivity indices [24] of zero, first and second order, respectively.
The models under consideration to calculate octanol/water partition coefficients are:
log P = A DCW(a,ECX) + B (3)
DCW(a,ECX) = ∑ [ CW(a)
CW(ECX) ] (4)
In Tables 2-4 we display the CW data for the three probes.
Table 2. Numerical values of the CWs on DCW(a,EC0)
LHFG invariant |
CWs of probe 1 |
CWs of probe 2 |
CWs of probe 3 |
C |
2.393 |
2.599 |
2.393 |
H |
2.351 |
2.488 |
2.295 |
O |
3.261 |
2.351 |
2.433 |
0001 |
2.487 |
2.613 |
2.874 |
0002 |
2.730 |
2.591 |
3.011 |
0004 |
2.426 |
2.334 |
2.426 |
Table 3. Numerical values of the CWs on DCW(a,EC1)
LHFG invariant |
CWs of probe 1 |
CWs of probe 2 |
CWs of probe 3 |
C |
2.091 |
2.048 |
2.281 |
H |
1.114 |
0.587 |
0.500 |
O |
6.192 |
5.108 |
6.192 |
0002 |
6.192 |
6.811 |
6.192 |
0004 |
0.525 |
0.997 |
0.637 |
0005 |
6.192 |
5.108 |
7.430 |
0007 |
0.912 |
0.775 |
0.812 |
0008 |
1.851 |
1.771 |
1.418 |
0010 |
1.238 |
1.069 |
1.154 |
0011 |
1.697 |
1.624 |
1.379 |
0013 |
1.353 |
1.175 |
1.336 |
0014 |
0.550 |
0.575 |
0.537 |
0016 |
1.287 |
1.113 |
1.364 |
The final fitting equations based on OCWLI for the octanol/water partition coefficient are the following
log P = 0.03137 DCW(a,ec0) – 2.268 |
(6) |
log P = 0.1422 DCW(a,ec1) – 7.954 |
(7) |
log P = 0.2000 DCW(a,ec2) – 3.127 |
(8) |
Table 4. Numerical values of the CWs on DCW(a,EC2)
LHFG invariant |
CWs of probe 1 |
CWs of probe 2 |
CWs of probe 3 |
C |
0.987 |
1.076 |
1.532 |
H |
0.697 |
0.475 |
0.525 |
O |
2.151 |
1.861 |
2.228 |
0005 |
8.916 |
4.300 |
18.488 |
0007 |
0.912 |
0.887 |
0.825 |
0008 |
1.617 |
1.628 |
1.474 |
0010 |
1.125 |
1.170 |
1.113 |
0011 |
1.603 |
1.360 |
1.362 |
0013 |
1.172 |
1.317 |
1.222 |
0016 |
0.475 |
0.575 |
0.512 |
0020 |
0.637 |
0.812 |
0.662 |
0022 |
1.263 |
1.303 |
1.221 |
0023 |
0.825 |
0.898 |
0.762 |
0025 |
0.991 |
1.069 |
1.016 |
0026 |
0.775 |
0.838 |
0.725 |
0028 |
1.078 |
1.098 |
1.073 |
0029 |
0.898 |
0.875 |
0.787 |
0031 |
0.941 |
1.148 |
0.991 |
0032 |
0.362 |
0.525 |
0.425 |
0034 |
1.805 |
1.717 |
1.591 |
0035 |
1.869 |
1.611 |
1.451 |
Calculations with Eqs. (5) – (7) are displayed in Tables 5 – 10.
Table 5. Log P Model based on DCW(a,EC0) – training set.
n |
Molecule |
DCW |
exp. |
calc. |
exp.-calc. |
1 |
ethanol |
55.595 |
-0.31 |
-0.52 |
0.21 |
2 |
2-propanol |
73.094 |
0.05 |
0.03 |
0.03 |
3 |
2-methyl-1-propanol |
90.594 |
0.65 |
0.57 |
0.08 |
4 |
1-pentanol |
108.093 |
1.40 |
1.12 |
0.28 |
5 |
2-pentanol |
108.093 |
1.14 |
1.12 |
0.02 |
6 |
3-pentanol |
108.093 |
1.14 |
1.12 |
0.02 |
7 |
2-methyl-2-butanol |
108.093 |
0.89 |
1.12 |
-0.23 |
8 |
1-hexanol |
125.592 |
2.03 |
1.67 |
0.36 |
9 |
3-hexanol |
125.592 |
1.61 |
1.67 |
-0.06 |
10 |
2-ethyl-1-butanol |
125.592 |
1.78 |
1.67 |
0.11 |
11 |
4-methyl-2-pentanol |
125.592 |
1.67 |
1.67 |
0.00 |
12 |
3,3-dimethyl-1-butanol |
125.592 |
1.57 |
1.67 |
-0.10 |
13 |
2,2-dimethyl-1-butanol |
125.592 |
1.57 |
1.67 |
-0.10 |
14 |
3,3-dimethyl-2-butanol |
125.592 |
1.19 |
1.67 |
-0.48 |
15 |
1-heptanol |
143.091 |
2.34 |
2.22 |
0.12 |
16 |
3-heptanol |
143.091 |
2.31 |
2.22 |
0.09 |
17 |
2,2-dimethyl-1-pentanol |
143.091 |
2.39 |
2.22 |
0.17 |
18 |
4,4-dimethyl-1-pentanol |
143.091 |
2.39 |
2.22 |
0.17 |
19 |
2,4-dimethyl-1-pentanol |
143.091 |
2.19 |
2.22 |
-0.03 |
20 |
2,4-methyl-2-pentanol |
143.091 |
1.67 |
2.22 |
-0.55 |
21 |
2,4-dimethyl-3-pentanol |
143.091 |
2.31 |
2.22 |
0.09 |
22 |
2,3-dimethyl-3-pentanol |
143.091 |
1.67 |
2.22 |
0.55 |
23 |
2,2-dimethyl-3-pentanol |
143.091 |
2.27 |
2.22 |
0.05 |
24 |
3-nonanol |
178.090 |
3.36 |
3.32 |
0.04 |
25 |
4-nonanol |
178.090 |
3.36 |
3.32 |
0.04 |
26 |
5-nonanol |
178.090 |
3.36 |
3.32 |
0.04 |
27 |
1-decanol |
195.589 |
4.01 |
3.87 |
0.14 |
28 |
1-undecanol |
213.089 |
4.42 |
4.42 |
0.00 |
29 |
1-tetradecanol |
265.586 |
6.11 |
6.06 |
0.05 |
30 |
1-pentadecanol |
283.086 |
6.64 |
6.61 |
0.03 |
31 |
1-hexadecanol |
300.585 |
7.17 |
7.16 |
0.01 |
Average absolute deviation = 0.14
Table 6. Log P Model based on DCW(a,EC0) – test set.
n |
Molecule |
DCW |
exp. |
calc. |
exp.-calc. |
1 |
1-propanol |
73.094 |
0.34 |
0.03 |
0.32 |
2 |
1-butanol |
90.594 |
0.84 |
0.57 |
0.27 |
3 |
2-butanol |
90.594 |
0.61 |
0.57 |
0.04 |
4 |
2-methyl-2-propanol |
90.594 |
0.37 |
0.57 |
-0.20 |
5 |
3-methyl-1-butanol |
108.093 |
1.42 |
1.12 |
0.30 |
6 |
2-methyl-1-butanol |
108.093 |
1.14 |
1.12 |
0.02 |
7 |
3-methyl-2-butanol |
108.093 |
1.14 |
1.12 |
0.02 |
8 |
2,2-dimethyl-1-propanol |
108.093 |
1.36 |
1.12 |
0.24 |
9 |
4-methyl-1-pentanol |
125.592 |
1.78 |
1.67 |
0.11 |
10 |
2-hexanol |
125.592 |
1.61 |
1.67 |
-0.06 |
11 |
2-methyl-1-pentanol |
125.592 |
1.78 |
1.67 |
0.11 |
12 |
2-methyl-2-pentanol |
125.592 |
1.39 |
1.67 |
-0.28 |
13 |
3-methyl-2-pentanol |
125.592 |
1.67 |
1.67 |
0.00 |
14 |
2-methyl-3-pentanol |
125.592 |
1.67 |
1.67 |
0.00 |
15 |
3-methyl-3-pentanol |
125.592 |
1.39 |
1.67 |
-0.28 |
16 |
2,3-dimethyl-2-butanol |
125.592 |
1.17 |
1.67 |
-0.50 |
17 |
4-heptanol |
143.091 |
2.31 |
2.22 |
0.09 |
18 |
5-methyl-2-hexanol |
143.091 |
2.19 |
2.22 |
-0.03 |
19 |
2-methyl-3-hexanol |
143.091 |
2.19 |
2.22 |
-0.03 |
20 |
2-methyl-2-hexanol |
143.091 |
1.84 |
2.22 |
-0.38 |
21 |
3-methyl-3-hexanol |
143.091 |
1.87 |
2.22 |
-0.35 |
22 |
3-ethyl-3-pentanol |
143.091 |
1.87 |
2.22 |
-0.35 |
23 |
2,3-dimethyl-2-pentanol |
143.091 |
2.27 |
2.22 |
0.05 |
24 |
1-octanol |
160.591 |
3.15 |
2.77 |
0.38 |
25 |
2-octanol |
160.591 |
2.84 |
2.77 |
0.07 |
26 |
2-ethyl-1-hexanol |
160.591 |
2.84 |
2.77 |
0.07 |
27 |
1-nonanol |
178.090 |
3.57 |
3.32 |
0.25 |
28 |
2-nonanol |
178.090 |
3.36 |
3.32 |
0.04 |
29 |
2,6-dimethyl-4-heptanol |
178.090 |
3.13 |
3.32 |
-0.19 |
30 |
1-dodecanol |
230.588 |
5.13 |
4.97 |
0.16 |
31 |
1-octadecanol |
335.584 |
8.22 |
8.26 |
-0.04 |
Average absolute deviation = 0.17
Table 7. Log P Model based on DCW(a,EC1) – training set.
n |
Molecule |
DCW |
exp. |
calc |
exp.-calc. |
1 |
ethanol |
53.940 |
-0.31 |
-0.28 |
-0.03 |
2 |
2-propanol |
56.695 |
0.05 |
0.11 |
-0.06 |
3 |
2-methyl-1-propanol |
61.016 |
0.65 |
0.72 |
-0.07 |
4 |
1-pentanol |
65.216 |
1.40 |
1.32 |
0.08 |
5 |
2-pentanol |
64.212 |
1.14 |
1.18 |
-0.04 |
6 |
3-pentanol |
64.212 |
1.14 |
1.18 |
-0.04 |
7 |
2-methyl-2-butanol |
61.132 |
0.89 |
0.74 |
0.15 |
8 |
1-hexanol |
68.974 |
2.03 |
1.85 |
0.18 |
9 |
3-hexanol |
67.970 |
1.61 |
1.71 |
-0.10 |
10 |
2-ethyl-1-butanol |
68.533 |
1.78 |
1.79 |
-0.01 |
11 |
4-methyl-2-pentanol |
67.529 |
1.67 |
1.65 |
0.02 |
12 |
3,3-dimethyl-1-butanol |
67.713 |
1.57 |
1.68 |
-0.11 |
13 |
2,2-dimethyl-1-butanol |
67.713 |
1.57 |
1.68 |
-0.11 |
14 |
3,3-dimethyl-2-butanol |
66.709 |
1.19 |
1.53 |
-0.34 |
15 |
1-heptanol |
72.732 |
2.34 |
2.39 |
-0.05 |
16 |
3-heptanol |
71.729 |
2.31 |
2.25 |
0.06 |
17 |
2,2-dimethyl-1-pentanol |
71.471 |
2.39 |
2.21 |
0.18 |
18 |
4,4-dimethyl-1-pentanol |
71.471 |
2.39 |
2.21 |
0.18 |
19 |
2,4-dimethyl-1-pentanol |
71.850 |
2.19 |
2.26 |
-0.07 |
20 |
2,4-methyl-2-pentanol |
68.207 |
1.67 |
1.75 |
-0.08 |
21 |
2,4-dimethyl-3-pentanol |
70.846 |
2.31 |
2.12 |
0.19 |
22 |
2,3-dimethyl-3-pentanol |
68.207 |
1.67 |
1.75 |
-0.08 |
23 |
2,2-dimethyl-3-pentanol |
70.468 |
2.27 |
2.07 |
0.20 |
24 |
3-nonanol |
79.245 |
3.36 |
3.32 |
0.05 |
25 |
4-nonanol |
79.245 |
3.36 |
3.32 |
0.05 |
26 |
5-nonanol |
79.245 |
3.36 |
3.32 |
0.05 |
27 |
1-decanol |
84.007 |
4.01 |
3.99 |
0.02 |
28 |
1-undecanol |
87.766 |
4.42 |
4.53 |
-0.11 |
29 |
1-tetradecanol |
99.041 |
6.11 |
6.13 |
-0.02 |
30 |
1-pentadecanol |
102.799 |
6.64 |
6.66 |
-0.02 |
31 |
1-hexadecanol |
106.557 |
7.17 |
7.20 |
-0.03 |
Average absolute deviation = 0.09
Table 8. Log P Model based on DCW(a,EC1) – test set.
n |
Molecule |
DCW |
exp. |
calc. |
exp.-calc. |
1 |
1-propanol |
57.699 |
0.34 |
0.25 |
0.09 |
2 |
1-butanol |
61.457 |
0.84 |
0.79 |
0.06 |
3 |
2-butanol |
60.453 |
0.61 |
0.64 |
-0.03 |
4 |
2-methyl-2-propanol |
57.373 |
0.37 |
0.20 |
0.17 |
5 |
3-methyl-1-butanol |
64.774 |
1.42 |
1.26 |
0.16 |
6 |
2-methyl-1-butanol |
64.774 |
1.14 |
1.26 |
-0.12 |
7 |
3-methyl-2-butanol |
63.771 |
1.14 |
1.11 |
0.03 |
8 |
2,2-dimethyl-1-propanol |
63.955 |
1.36 |
1.14 |
0.22 |
9 |
4-methyl-1-pentanol |
68.533 |
1.78 |
1.79 |
-0.01 |
10 |
2-hexanol |
67.970 |
1.61 |
1.71 |
-0.10 |
11 |
2-methyl-1-pentanol |
68.533 |
1.78 |
1.79 |
-0.01 |
12 |
2-methyl-2-pentanol |
64.890 |
1.39 |
1.27 |
0.12 |
13 |
3-methyl-2-pentanol |
67.529 |
1.67 |
1.65 |
0.02 |
14 |
2-methyl-3-pentanol |
67.529 |
1.67 |
1.65 |
0.02 |
15 |
3-methyl-3-pentanol |
64.890 |
1.39 |
1.27 |
0.12 |
16 |
2,3-dimethyl-2-butanol |
64.449 |
1.17 |
1.21 |
-0.04 |
17 |
4-heptanol |
71.729 |
2.31 |
2.25 |
0.06 |
18 |
5-methyl-2-hexanol |
71.287 |
2.19 |
2.18 |
0.01 |
19 |
2-methyl-3-hexanol |
71.287 |
2.19 |
2.18 |
0.01 |
20 |
2-methyl-2-hexanol |
68.649 |
1.84 |
1.81 |
0.03 |
21 |
3-methyl-3-hexanol |
68.649 |
1.87 |
1.81 |
0.06 |
22 |
3-ethyl-3-pentanol |
68.649 |
1.87 |
1.81 |
0.06 |
23 |
2,3-dimethyl-2-pentanol |
68.207 |
2.27 |
1.75 |
0.53 |
24 |
1-octanol |
76.491 |
3.15 |
2.92 |
0.23 |
25 |
2-octanol |
75.487 |
2.84 |
2.78 |
0.06 |
26 |
2-ethyl-1-hexanol |
76.049 |
2.84 |
2.86 |
-0.02 |
27 |
1-nonanol |
80.249 |
3.57 |
3.46 |
0.11 |
28 |
2-nonanol |
79.245 |
3.36 |
3.32 |
0.05 |
29 |
2,6-dimethyl-4-heptanol |
78.363 |
3.13 |
3.19 |
-0.06 |
30 |
1-dodecanol |
91.524 |
5.13 |
5.06 |
0.07 |
31 |
1-octadecanol |
114.074 |
8.22 |
8.27 |
-0.05 |
Average absolute deviation = 0.09
Table 9. Log P Model based on DCW(a,EC2) – training set.
n |
Molecule |
DCW |
exp. |
calc. |
exp.-calc. |
1 |
ethanol |
14.053 |
-0.310 |
-0.32 |
0.01 |
2 |
2-propanol |
16.110 |
0.050 |
0.10 |
-0.05 |
3 |
2-methyl-1-propanol |
19.005 |
0.650 |
0.67 |
-0.02 |
4 |
1-pentanol |
22.368 |
1.400 |
1.35 |
0.05 |
5 |
2-pentanol |
21.493 |
1.140 |
1.17 |
-0.03 |
6 |
3-pentanol |
21.713 |
1.140 |
1.22 |
-0.08 |
7 |
2-methyl-2-butanol |
19.074 |
0.890 |
0.69 |
0.20 |
8 |
1-hexanol |
25.000 |
2.030 |
1.87 |
0.16 |
9 |
3-hexanol |
24.380 |
1.610 |
1.75 |
-0.14 |
10 |
2-ethyl-1-butanol |
24.399 |
1.780 |
1.75 |
0.03 |
11 |
4-methyl-2-pentanol |
22.916 |
1.670 |
1.46 |
0.21 |
12 |
3,3-dimethyl-1-butanol |
23.470 |
1.570 |
1.57 |
0.00 |
13 |
2,2-dimethyl-1-butanol |
23.725 |
1.570 |
1.62 |
-0.05 |
14 |
3,3-dimethyl-2-butanol |
22.202 |
1.190 |
1.31 |
-0.12 |
15 |
1-heptanol |
27.633 |
2.340 |
2.40 |
-0.06 |
16 |
3-heptanol |
27.013 |
2.310 |
2.28 |
0.03 |
17 |
2,2-dimethyl-1-pentanol |
27.124 |
2.390 |
2.30 |
0.09 |
18 |
4,4-dimethyl-1-pentanol |
27.227 |
2.390 |
2.32 |
0.07 |
19 |
2,4-dimethyl-1-pentanol |
27.243 |
2.190 |
2.32 |
-0.13 |
20 |
2,4-methyl-2-pentanol |
24.530 |
1.670 |
1.78 |
-0.11 |
21 |
2,4-dimethyl-3-pentanol |
26.644 |
2.310 |
2.20 |
0.11 |
22 |
2,3-dimethyl-3-pentanol |
24.305 |
1.670 |
1.73 |
-0.06 |
23 |
2,2-dimethyl-3-pentanol |
26.454 |
2.270 |
2.16 |
0.11 |
24 |
3-nonanol |
32.277 |
3.360 |
3.33 |
0.03 |
25 |
4-nonanol |
32.313 |
3.360 |
3.34 |
0.02 |
26 |
5-nonanol |
32.313 |
3.360 |
3.34 |
0.02 |
27 |
1-decanol |
35.529 |
4.010 |
3.98 |
0.03 |
28 |
1-undecanol |
38.161 |
4.420 |
4.51 |
-0.09 |
29 |
1-tetradecanol |
46.058 |
6.110 |
6.09 |
0.03 |
30 |
1-pentadecanol |
48.690 |
6.640 |
6.61 |
0.03 |
31 |
1-hexadecanol |
51.323 |
7.170 |
7.14 |
0.03 |
Average absolute deviation = 0.07
Table 10. Log P Model based on DCW(a,EC2) – test set.
n |
Molecule |
DCW |
exp. |
calc. |
exp.-calc. |
1 |
1-propanol |
17.239 |
0.34 |
0.32 |
0.02 |
2 |
1-butanol |
19.736 |
0.84 |
0.82 |
0.02 |
3 |
2-butanol |
18.826 |
0.61 |
0.64 |
-0.03 |
4 |
2-methyl-2-propanol |
16.017 |
0.37 |
0.08 |
0.29 |
5 |
3-methyl-1-butanol |
21.808 |
1.42 |
1.24 |
0.19 |
6 |
2-methyl-1-butanol |
22.027 |
1.14 |
1.28 |
-0.14 |
7 |
3-methyl-2-butanol |
20.934 |
1.14 |
1.06 |
0.08 |
8 |
2,2-dimethyl-1-propanol |
21.574 |
1.36 |
1.19 |
0.17 |
9 |
4-methyl-1-pentanol |
24.184 |
1.78 |
1.71 |
0.07 |
10 |
2-hexanol |
24.126 |
1.61 |
1.70 |
-0.09 |
11 |
2-methyl-1-pentanol |
24.439 |
1.78 |
1.76 |
0.02 |
12 |
2-methyl-2-pentanol |
21.092 |
1.39 |
1.09 |
0.30 |
13 |
3-methyl-2-pentanol |
23.305 |
1.67 |
1.53 |
0.14 |
14 |
2-methyl-3-pentanol |
23.170 |
1.67 |
1.51 |
0.16 |
15 |
3-methyl-3-pentanol |
21.482 |
1.39 |
1.170 |
0.22 |
16 |
2,3-dimethyl-2-butanol |
19.882 |
1.17 |
0.85 |
0.32 |
17 |
4-heptanol |
27.048 |
2.31 |
2.28 |
0.03 |
18 |
5-methyl-2-hexanol |
25.942 |
2.19 |
2.06 |
0.13 |
19 |
2-methyl-3-hexanol |
25.838 |
2.19 |
2.04 |
0.15 |
20 |
2-methyl-2-hexanol |
23.724 |
1.84 |
1.62 |
0.22 |
21 |
3-methyl-3-hexanol |
23.499 |
1.87 |
1.57 |
0.30 |
22 |
3-ethyl-3-pentanol |
25.905 |
1.87 |
2.05 |
-0.18 |
23 |
2,3-dimethyl-2-pentanol |
24.270 |
2.27 |
1.73 |
0.54 |
24 |
1-octanol |
30.265 |
3.15 |
2.93 |
0.22 |
25 |
2-octanol |
29.390 |
2.84 |
2.75 |
0.09 |
26 |
2-ethyl-1-hexanol |
29.443 |
2.84 |
2.76 |
0.08 |
27 |
1-nonanol |
32.897 |
3.57 |
3.45 |
0.12 |
28 |
2-nonanol |
32.022 |
3.36 |
3.28 |
0.08 |
29 |
2,6-dimethyl-4-heptanol |
29.892 |
3.13 |
2.85 |
0.28 |
30 |
1-dodecanol |
40.794 |
5.13 |
5.03 |
0.10 |
31 |
1-octadecanol |
56.587 |
8.22 |
8.19 |
0.03 |
Average absolute deviation = 0.16
The average absolute deviations for the training and test sets for the different Morgan extended connectivity indices are displayed in Table 11.
Table 11. Average absolute deviations for the different sets.
Descriptor |
Training set |
Test set |
Complete set |
DCW(a,EC0) (a) |
0.17 |
0.14 |
- |
DCW(a,EC1) (a) |
0.09 |
0.09 |
- |
DCW(a,EC2) (a) |
0.16 |
0.07 |
- |
AI, Xum (b) |
- |
- |
0.12 |
(a) Present
calculation
(b)Ref. 13
The
analysis of results presented in Table 11 show several interesting features.
The first one is that statistical parameters are nearly the same for the three
probes corresponding to each Morgan’s index. It means that this approach is
consistent (i.e. final results are not dependent of the particular probe
employed to derive fitting equations). Besides, the overall statistical results
are quite satisfactory for the different sets, although those corresponding to
the training set are the best ones. Specially important are statistical
parameters corresponding to the tests set, since they correspond to real
predictive results, while those associated to the training and complete sets
are just fitting parameters.
Regarding
the behavior of the three Morgan extended indices, the data in Table 1 suggests
that EC1 and EC2 are the best ones and this is confirmed when analyzing the
absolute average deviations displayed in Table 11. In fact, the average
absolute deviations for test sets is 0.09 and 0.07, respectively. These figures
deserve to be compared with that corresponding to the Rens’ results for the
complete set, i.e. 0.12 (see Table 4 in Ref. 13), which show clearly the better
quality of present predictions with regard to those published before. In order
to judge properly these comparisons, one must take into account that Rens’ fitting equation (see Eq. 13 in Ref. 13) depends upon two variables, while
present relationships depend on just one variable. Besides, the comparison of
statistical coefficients also demonstrate the higher quality of the present
equations
Conclusions
We have shown that optimization of correlation weights of local graph invariants are suitable molecular descriptors to model the octanol/water partition coefficients of alcohols. This particular set of flexible topological variables gives quite reliable predictions of this physicochemical property and compares favorably with other recent calculation schemes within the realm of QSPR theory. This finding agrees with other recent similar results for the calculation of other biological activities and physicochemical properties, and it demonstrates the convenience of resorting to variable molecular descriptors for prediction purposes in QSAR/QSPR theory in order to take advantage of this possibility. As stated before, there are other options to improve fitting equations in the regression analysis, such as to employ several variables and/or try different functional algebraic forms for the modeling function f. In this study, it has not been necessary to employ these resources to get optimal results, but they should not be ignored when applying multilinear regression analysis within the realm of QSAR/QSPR theory
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