Quantitative structure-activity relationships inverse QSAR

The fundamental assumption of SAR and QSAR (Structure-Activity Relationships and Quantitative Structure-Activity Relationships) is that the activity of a compound is related to its structural and/or physicochemical properties. In a classic article Corwin Hansch formulated Eq. (15) as a linear frcc-cncrgy related model for the biological activity (e.g.. toxicity) of a group of congeneric chemicals [37, in which the inverse of C, the concentration effect of the toxicant, is related to a hy-drophobidty term, FI, an electronic term, a (the Hammett substituent constant). Stcric terms can be added to this equation (typically Taft s steric parameter, E,). 

In 1868 two Scottish scientists, Crum Brown and Fraser [4] recognized that a relation exists between the physiological action of a substance and its chemical composition and constitution. That recognition was in effect the birth of the science that has come to be known as quantitative structure-activity relationship (QSAR) studies a QSAR is a mathematical equation that relates a biological or other property to structural and/or physicochemical properties of a series of (usually) related compounds. Shortly afterwards, Richardson [5] showed that the narcotic effect of primary aliphatic alcohols varied with their molecular weight, and in 1893 Richet [6] observed that the toxicities of a variety of simple polar chemicals such as alcohols, ethers, and ketones were inversely correlated with their aqueous solubilities. Probably the best known of the very early work in the field was that of Overton [7] and Meyer [8], who found that the narcotic effect of simple chemicals increased with their oil-water partition coefficient and postulated that this reflected the partitioning of a chemical between the aqueous exobiophase and a lipophilic receptor. This, as it turned out, was most prescient, for about 70% of published QSARs contain a term relating to partition coefficient [9]. 

Another example is Quantitative Structure-Activity Relationships (QSAR) in which the first block contains measurements or calculated values of compounds and the second block contains measured biological activities. Here the purpose is to predict activities of new compounds using (simple) measurements or calculated values of that new compound and the model. Sometimes, the reverse is also sought given a certain desired activity, what should a compound look like This is known as the inverse problem and is considerably more complicated than predicting activity. 

AP, that result from the application of particular transformations, AS, and hence provide an inverse quantitative structure-activity relationship (QSAR) approach to lead optimization [19]. Another difference is that, given an appropriate source of data, they can model not only biological activity, the principal focus of the bioisosterism approaches, but also any chemical, physicochemical, or ADMETproperty that needs to be optimized. 

The water solubilities are an indirect, and inversely proportional, measurement of hpophflicity. As alkyl chain length increases, the water solubility decreases (increase in lipohilicity) and the toxicity increases. With AE, the lipohilicity can be altered by both alkyl chain length and EO number. Quantitative structure activity relationship (QSAR) models have... 

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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