Drug Design 2 - Applied Bioinformatics Group
Drug Design 2 - Applied Bioinformatics Group
Drug Design 2 - Applied Bioinformatics Group
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Wiener Index<br />
• In 1947, H. Wiener observed that the boiling<br />
point of alkanes can be predicted based on their<br />
topology<br />
• For n-‐alkanes this is trivial based on chain length<br />
alone, but not for branched alkanes<br />
• For example, different nonanes have boiling<br />
points between 122°C (2,2,4,4-‐tetramethyl-‐<br />
pentane) and 150°C (n-‐nonane)<br />
• Wiener proposed to model the boiling point as<br />
a linear funcDon of two variables, p and w:<br />
T B = a p + b w + c<br />
with constants a, b, c<br />
• Based on this simple model, he could predict<br />
boiling points with an accuracy of about 1 K<br />
Wiener Index<br />
• p is called polarity number, a 1D<br />
descriptor, coun%ng the number of<br />
carbon-‐carbon pairs separated by<br />
exactly three bonds (C—C—C—C)<br />
• W, the path number, is a topological<br />
descriptor and is also called Wiener<br />
index<br />
• w is the sum of lengths of all<br />
pairwise paths in the molecular<br />
graph<br />
• In acyclic alkanes this corresponds to<br />
the product of all atoms to the lem<br />
and to the right of any bond<br />
Wiener Index<br />
T B / °C<br />
250<br />
200<br />
150<br />
100<br />
50<br />
0<br />
4 6 8<br />
Chain Kettenlänge length<br />
10 12<br />
Boiling points of n-alkanes<br />
3<br />
1<br />
2<br />
4<br />
5<br />
D 1,2 = 1, D 3,5 = 3, ...<br />
w = (1·4) + (4·1) + (3·2) + (4·1)<br />
= 18<br />
• There is a large number of generaliza%ons of the Wiener index to<br />
make it applicable for cyclic structures as well<br />
• A widely used defini%on is half the sum of the entries of the<br />
distance matrix of the molecular graph (= sum of all minimal pair-‐<br />
wise paths)<br />
• Wiener index is omen used if the degree of branchedness is<br />
relevant for a property<br />
• It is also relevant for predic%ng pharmacological ac%vi%es, e.g.,<br />
there are models for carboanhydrase II inhibitor ac%vity based on<br />
the Wiener index<br />
4<br />
4<br />
6<br />
4<br />
Saxena, Khadikar, Acta Pharm. 49 (1999) 171-179