Biological Activity, Physical Properties, and Toxicity: A Number Counting and Reactivity-Based Analysis

Introduction

Ever since the advent of quantification of various biological activities of compounds in the mid-19^th century, quantitative structure–activity relationship (QSAR) has been showing increasing applications in the field of biological sciences, pharmaceuticals, and computational chemistry. Following the works of Cros (1863), Curm-Brown and Fraser (1868), Richardson (1869), Richet (1893), Meyer (1899), and Overton (1901), Hammett (1935, 1937) made his well-known contribution of representing the electronic effects on reaction mechanisms in terms of electronic substituent (σ) and reaction (ρ) constants. The work of Hansch (1962, 1964), using n-octanol/water partition coefficient (logP) basically gave QSAR a huge boost, opening up the domains of drug design and toxicity prediction to a whole new direction. logP has been in use in this context ever since. Though logP, describing the hydrophobicity of a compound, directly correlates to a compounds’ physicochemical properties, its calculation is time-consuming and tedious. With the development of various SAR techniques, the search for new descriptors have also been developing (Todeschini & Consonni, 2008; Roy et al., 2015; Tandon et al., 2019; Muratov et al., 2020). Quantum chemical descriptors (Parr, 1983; Parr & Yang, 1989; Chermette, 1999; Geerlings et al., 2003), especially conceptual density functional theory (CDFT) based reactivity/selectivity descriptors (Thanikaivelan et al., 2000; Parthasarathi et al., 2003; Vijayaraj et al., 2009), have proved to be quite reliable in analyzing and quantifying toxic behaviour and various biological activities (Parthasarathi et al., 2004; Roy et al., 2006, 2007). Determining the appropriate descriptor for the study of a particular property/activity is a difficult job. The goal is to use as simple and easily computable descriptor as possible.

The number of atoms in a compound can serve as a simple yet effective descriptor in QSAR studies. Randic and Basak (2001) estimated the toxic behavior of aliphatic ethers in terms of this descriptor. It originated from the idea that number of atoms is related to the logP of a compound as the former directly influences the molecular weight and hence the latter. The efficiency of logP as a descriptor is no secret and hence the studies that followed (Chattaraj et al., 2007; Roy et al., 2007; Giri et al., 2008; Carbó-Dorca et al., 2009; Roy et al., 2009;), explored the possibility of using number of atoms as a descriptor with which additional descriptors might be added to improve the robustness of the model. The CDFT based global electrophilicity index has time and again proved to be a reasonably good descriptor for analyzing biological activity and toxicity (Parthasarathi et al., 2004; Roy et al., 2006, 2007). Its use as an additional descriptor also significantly improves the model efficiency as exemplified in the works done by Giri et al. (2008), Chattaraj et al. (2007), and Roy et al. (2007). CDFT based reactivity and selectivity indices provide useful insights into the reactivity and site selectivity of the studied systems, and thus makes it easier to analyze the chemical interactions and generate more efficient QSAR models. Charge transfer is another parameter that can be considered as a predictor in electrophilic and nucleophilic interactions when they are predominantly present (Roy et al., 2006).