Design with Inverse-QSAR

The forward QSAR procedure defines an equation or a set of equations that relates a variable of interest (dependent variable) with independent variables. The dependent variable is normally an activity/property of interest (binding affinity, normal boiling point, IC50, etc.), whereas the independent variables are related to the structure of the substance. Developing a QSAR 

Anyone reading this chapter has, undoubtedly, solved an inverse-type problem in one form or another. The key to efficient solution lies in the restriction of the solution space. If constraints are composed such that the solution space is limited, a brute-force technique (try all candidates) can guarantee a solution. In the field of molecular design, however, the solution space comes from all compounds that can be reasonably made from the various atoms in the Periodic Table. Hence, we need a way to limit this solution space to arrive at candidate solutions efficiently. We will describe some of these techniques. 

As mentioned earlier, Kier and Hall published a series of papers in the early 1990s that described the inverse QSAR methodology with chi indices. The QSARs they developed had a maximum of four descriptors. Example applications included the inverse design of alkanes from molar volume and the identification of isonarcotic agents.  

Simultaneous with the work from Kier and Hall, Zefirov et al. developed a similar technique with the count of paths. The QSARs they used were given for three Kappa-shape descriptors and they considered three functional groups, namely, alkanes, alcohols, and small oxygen-containing compounds. 

In 2001, Bruggemann et al. demonstrated Hasse diagrams combined with a similarity measure in the generation of solutions to the inverse problem involving toxicity of algae. Their method is based on partial ordered sets and does not assume a particular model for the QSAR. 

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In this work, we focus on reviewing inverse molecular design based on hypersurfaces of molecular properties molecular structures that are constructed through direct calculations of molecular properties from variable Hamiltonians (for representing diiferent chemical structures). Alternatively, analogous hypersurfaces relating property and structure have been constructed based on statistical models for molecular properties with respect to sets of chosen molecular descriptors (for molecular structures or properties). Such hypersurfaces are used extensively for the inverse design based on quantitive structure activity relationship (QSAR). We refer interested readers to literature " on inverse QSAR, which is not the focus of this review. 

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