Pesticides are used today on a planetary-wide scale. The rising need for substances with this
biological activity due to an increasing consumption of agricultural and animal products and to the
development of urban areas makes the chemical industry to constantly investigate new molecules or to
improve the physicochemical characteristics, increase the biological activities and improve the toxicity
profiles of the already known ones. Molecular databases are increasingly accessible for in vitro and in
vivo bioavailability studies. In this context, structure-activity studies, by their in silico - in cerebro
methods, are used to precede in vitro and in vivo studies in plants and experimental animals because
they can indicate trends by statistical methods or biological activity models expressed as mathematical
equations or graphical correlations, so a direction of study can be developed or another can be abandoned,
saving financial resources, time and laboratory animals. Following this line of research the present paper
reviews the Structure-Activity Relationship (SAR) studies and proposes a correlation between a topological
connectivity index and the biological activity or toxicity made as a result of a study performed on 11 molecules
of organophosphate compounds, randomly chosen, with a basic structure including a Phosphorus atom
double bounded to an Oxygen atom or to a Sulfur one and having three other simple covalent bonds with two
alkoxy (-methoxy or -ethoxy) groups and to another functional group different from the alkoxy groups. The
molecules were packed on a cubic structure consisting of three adjacent cubes, respecting a principle of topological
efficiency, that of occupying a minimal space in that cubic structure, a method that was called the Clef
Method. The central topological index selected for correlation was the Wiener index, since it was possible
this way to discuss different adjacencies between the nodes in the graphs corresponding to the organophosphate
compounds molecules packed on the cubic structure; accordingly, "three dimensional" variants of these
connectivity indices could be considered and further used for studying the qualitative-quantitative relationships
for the specific molecule-enzyme interaction complexes, including correlation between the Wiener
weights (nodal specific contributions to the total Wiener index of the molecular graph) and the biochemical
reactivity of some of the atoms. Finally, when passing from SAR to Q(uantitative)-SAR studies, especially by
the present advanced method of the cubic molecule (Clef Method) and its good assessment of the
(neuro)toxicity of the studied molecules and of their inhibitory effect on the target enzyme - acetylcholinesterase,
it can be seen that a predictability of the toxicity and activity of different analogue compounds can
be ensured, facilitating the in vivo experiments or improving the usage of pesticides.
The Wiener index of signed graphs
