A biosynthetically informed distance measure to compare secondary metabolite profiles

Secondary metabolite profiles are one of the most diverse phenotypes of organisms and can consist of a large number of compounds originating from a limited number of biosynthetic pathways. The statistical treatment of such profiles often is complicated due to their diversity as well as the intra- and interspecific variability in the quantitative and qualitative composition of secondary metabolites. Most importantly, the assumption of independence of the presence/absence and the quantity of compounds is violated due to the shared biosynthetic origin of many compounds. Therefore, I propose a biosynthetically informed pairwise distance measure that fully considers the biosynthesis of the compounds and thus quantifies the similarity in the enzymatic equipment of two samples. The biosynthetic similarity of compounds is calculated based on the proportion of shared enzymes that are required for their biosynthesis. Using this information (provided as dendrogram structure) and the quantitative composition of the samples, generalized UniFrac distances are calculated measuring that fraction of the dendrogram (i.e., the branch lengths) that is unique to either of the samples but not shared by both samples. To allow a straightforward cross-platform application of the approach, I provide functions for the statistical software R and sample data sets. A hypothetical and a real world example show the feasibility of the biosynthetically informed distances d_A,B and highlight the differences to conventional distance measures. The advantages of this approach and potential fields of application are discussed.