Abstract
Data on ligand–target (LT) interactions has played a growing role in drug research for several decades. Even though the amount of data has grown significantly in size and coverage during this period, most datasets remain difficult to analyze because of their extreme sparsity, as there is no activity data whatsoever for many LT pairs. Even within clusters of data there tends to be a lack of data completeness, making the analysis of LT datasets problematic. The current effort extends earlier works on the development of set-theoretic formalisms for treating thresholded LT datasets. Unlike many approaches that do not address pairs of unknown interaction, the current work specifically takes account of their presence in addition to that of active and inactive pairs. Because a given LT pair can be in any one of three states, the binary logic of classical set-theoretic methods does not strictly apply. The current work develops a formalism, based on ternary set-theoretic relations, for treating thresholded LT datasets. It also describes an extension of the concept of data completeness, which is typically applied to sets of ligands and targets, to the local data completeness of individual ligands and targets. The set-theoretic formalism is applied to the analysis of simple and joint polypharmacologies based on LT activity profiles, and it is shown that null pairs provide a means for determining bounds to these values. The methodology is applied to a dataset of protein kinase inhibitors as an illustration of the method. Although not dealt with here, work is currently underway on a more refined treatment of activity values that is based on increasing the number of activity classes.
Highlights
Accepted: 3 December 2021Data on ligand–target (LT) interactions has played a growing role in drug research over the last several decades
Such datasets provide information that can be used for the determination of pharmacological properties such as polypharmacologies
If there is no need to distinguish between them, the term polypharmacology, without any modifying adjective, will be employed.), which are of interest in a number of phases of drug research [1,2]
Summary
Data on ligand–target (LT) interactions has played a growing role in drug research over the last several decades. Because publicly available datasets are usually comprised of data obtained from multiple sources, the data in these datasets tend to be of uneven quality, and to be quite sparse and inhomogeneously distributed, appearing much like ‘Islands of data floating on a largely empty sea’ In such instances, determining activity values computationally is a non-trivial task. A problem arises in the case of LT pairs for which neither experimentally nor computationally determined values exist Such null pairs represent a degree of uncertainty with respect to the activity or inactivity of a given pair.
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