Differential shannon entropy as a sensitive measure of differences in database variability of molecular descriptors

A method termed Differential Shannon Entropy (DSE) is introduced to compare differences in information content and variance of molecular descriptors between compound databases. The analysis is based on histograms recording the individual and grouped distributions of molecular descriptors and calculation of Shannon entropy (SE), a formalism originally applied to digital communication. We have recently shown that SE values reflect the nonparametric variability of descriptor settings. Now the analysis has been advanced to assess differences in information content of 143 molecular descriptors in databases containing synthetic compounds, natural products, or drug-like molecules. The DSE metric captures the degree to which descriptor distributions complement or duplicate information contained in molecular databases. In our analysis, we observe significant differences for a number of descriptors and rank them according to their associated DSE values. Using DSE calculations, relative information content of different types of descriptors can be quantified, even if differences are subtle.