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What is Wiener Index

Wiener index is molecular descriptor which is widely used in Structure property activity studies. wiener index  is based on the chemical application of graph theory  thence  counts the number of bonds between pairs of atoms and sums the distance between all pairs by generating a distance matrix. It generates a hydrogen depleted graph/matrix calculating elemental type plus the number of non hydrogen atoms.

Molecular Descriptors are numerical value that characterize properties of a molecule 
1. Physico-chemical properties like log P, Mol. wt.
2. Topological Indexes like Wiener index.

Various Descriptors values are considered, to attain best binding affinity, which can be used for preliminary screening of molecules from a large template libraries.

Distance Matrix

The distance matrix  D = D(G) of a graph G with N vertices is the square N X N symmetric matrix whose elements are defined as-

                          
The elements are calculated in the shortest possible distance. With this matrix Wiener index of a chemical structure can be calculated with the following formula

                                 
 The calculated Wiener indices for some small molecules including cyclic, acyclic, aromatic, multiple bonds and hetero atoms are given below:

Wiener indices of some common chemical molecules.

Wiener Index for Drug Screening
Need for Wiener Index or Novel Molecular Descriptors

1)  Novel descriptors may lead to better regression analysis
2)  Novel or alternative descriptors may be computationally simple, which is important.
     When screening combinatorial libraries which may have 100000 structures or more.
Advantages of Wiener Index
  1. Encode all pairs of atoms in a molecule.
  2. Include the length of shortest bond by bond path between them using shortest path algorithms.
  3. It has fast screening of ligands/molecules as it can be directly calculated from molecular structure, so its use in QSAR models is of immense utility compared to experimentally determined physicochemical parameters that are not always available for a particular molecular structure.

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