The Cramer Steroid Set—A Worked Out Example of MQS

However, the column stochastic similarity matrix [145] appears to be no longer symmetric as is its originating quantum similarity matrix Z. The columns of the stochastic matrix [145], as defined in Eq. [146], can substitute the QOS density function tag elements, which have previously generated them. A new kind of discrete QOS can be constructed in this way. 

This brief mathematical background seems sufficient to prove how the quantum similarity application structure can be well founded on a new set of theoretical concepts, which encompasses basic quantum mechanical ideas. 

It is appropriate to illustrate these concepts with a worked out example of a typical application of molecular quantum similarity ideas. The example addressed here involves the set of globulin bindings steroids used by Cramer et al. ° and subsequently in other studies to develop QSAR models. This dataset has also been used by chemists in molecular quantum similarity studies and to develop quantum QSAR models. ° °  

The plain numbers refer to QSSA alignment, the ones in italics to TGSA alignments. Numerical data reprinted with permission from Bultinck et al. Copyright 2003 American Chemical Society. 

As shown, in some extreme cases, differences up to nearly 25% occur, which is naturally an appreciable amount. Moreover, the difference between the TGSA and QSSA alignments is not constant, and consequently, the similarity ordering of the pairs of molecules differs. Both approaches have their limitations and their merits. Whereas QSSA (and MaxiSim) gives higher MQSM values, TGSA often gives results in better accordance with chemical intuition. It is therefore up to users to carefully decide which approach is best suited for their needs. 

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