A graph-theory method to establish serological relationships within a bacterial taxon, with example from Porphyromonas gingivalis

This paper develops a rationale for transforming serological data obtained by indirect immunofluorescence (IF) into a meaningful character-state matrix, and uses this matrix for numerical phylogenetic analysis. Typically, immunofluorescence data come in square asymmetrical matrices; columns correspond to strains used for adsorption and rows to strains used in the IF test. Such matrices can be decomposed into a symmetric and a skew-symmetric part. We first show that all pertinent biological information needed to reconstruct a phylogeny lies in the skew-symmetric component. Then we show how to transform the skew-symmetric matrix into a character-state tree, and how to obtain a binary character-state matrix from it. The character-state matrices obtained for different hyperimmune serum antibodies are assembled into a total character-state matrix, on which phylogenetic analysis is conducted. The data that motivated this methodological development concern Porphyromonas gingivalis, a major pathogen in adult periodontitis. Various proposals have been put forward in the literature, concerning the number of major serogroups found in this taxon. Six human and two animal strains of P. gingivalis were subjected to serotyping and to the phylogenetic analysis described above. Using a test of statistical significance recently developed to compare independently-obtained phylogenetic trees, or to compare hypotheses to trees, we show that our results best fit the hypothesis that there are three groups of serotypes, one animal and two human. Alternate hypotheses are not, or less strongly supported by our data. The algorithms developed to implement the new phylogenetic analysis method are presented in appendices.