Quantum Molecular Similarity: Theory and Applications to the Evaluation of Molecular Properties, Biological Activities and Toxicity

Modelling Toxicity using Molecular Quantum Similarity Measures

“…In other words, the exposed protocol consists of an unbiased and universal procedure based on a theoretical relationship [85] and potentially capable to model different biological responses without introducing further information that the provided by MQSM.…”

“…Once established the theoretical basis of MQS, this technique was considered as a valid tool to generate QSAR/QSPR descriptors. The first work in this field is due to Martín [69], which was later used and developed by many other researchers [70 -83], which finally rendered into a theoretical protocol for the application of similarity measures in the QSAR/QSPR field [84,85]. This methodology has been successfully applied in our research group for the construction of correlation models into the pharmacological [86 -94] and toxicity evaluation [95 -99] frameworks.…”

About the prediction of molecular properties using the fundamental Quantum QSPR (QQSPR) equation†

“…This condition, if the computed similarities are not faulty, constitute a metric matrix of the U-m space, subtended by the U-m QSM columns. Thus, provided that the U-m discrete representations with respect to the core set are linearly independent, the inverse of A is guaranteed to exist, as it will be positive definite; moreover, implying the quadratic error (30) is a minimum at the value jx Opt 1 i given by equation (31). One can easily estimate the unknown parameterised U-m property vector jp 1 i, submitted to the quadratic error restriction, after defining the auxiliary matrix:…”

“…The optimal coefficient value (23) produces a minimum of the quadratic error, being the second order coefficient of the quadratic error polynomial (22), associated to the positive definite Euclidian norm of the U-m discrete representation with respect the core set density tags, that is: z j z h i > 0. Such a quadratic error restriction is equivalent to constructing the difference vector (21) with elements as small as possible.…”

Molecular Quantum Similarity: Theory and Applications

“…53 However, it has been not until recently that the mathematical and physical foundations of QS have been developed in a series of publications. 5,[8][9][10]65,68,[148][149][181][182][183][184][185][186] In those articles, several new theoretical definitions, related to old concepts, were described. The first idea described was the so-called tagged set concept.…”