Inferring bacterial genome flux while considering truncated genes

Abstract

Bacterial gene content variation during the course of evolution has been widely acknowledged and its pattern has been actively modeled in recent years. Gene truncation or gene pseudogenization also plays an important role in shaping bacterial genome content. Truncated genes could also arise from small-scale lateral gene transfer events. Unfortunately, the information of truncated genes has not been considered in any existing mathematical models on gene content variation. In this study, we developed a model to incorporate truncated genes. Maximum-likelihood estimates (MLEs) of the new model reveal fast rates of gene insertions/deletions on recent branches, suggesting a fast turnover of many recently transferred genes. The estimates also suggest that many truncated genes are in the process of being eliminated from the genome. Furthermore, we demonstrate that the ignorance of truncated genes in the estimation does not lead to a systematic bias but rather has a more complicated effect. Analysis using the new model not only provides more accurate estimates on gene gains/losses (or insertions/deletions), but also reduces any concern of a systematic bias from applying simplified models to bacterial genome evolution. Although not a primary purpose, the model incorporating truncated genes could be potentially used for phylogeny reconstruction using gene family content.

Figure 1.—

(A–D) Phylogenies with varied levels of divergence. Clade names and strain abbreviations are as in Table 1. Horizontal scale bar indicates genome size.

Figure 2.—

Association between estimated parameters and phylogenetic divergence in each group. Three maximum-likelihood estimates (MLEs), μ, π_a, and α_Γ, are estimated under the M₀ + π model using different cutoff thresholds in BLASTP/TBLASTN searches. Solid symbols represent MLEs using a criterion of E-value ≤10⁻²⁰ and match length ≥85%, while open symbols represent MLEs using a criterion of E-value ≤10⁻¹⁰ and match length ≥70%. The four groups are sorted from the least diverse group (Escherichia) on the left to the most diverse group (Bacillaceae) on the right. Although shown along with three estimates, tree length is not an estimate from the gene insertion/deletion model. Indeed, it is the sum of branch lengths based on nucleotide substitution and used as an indicator for the degree of divergence in the clade.

Figure 3.—

Estimated parameters of the instantaneous rate matrix in each clade. As described in methods, α was fixed to be 1, and β and γ were estimated under the M₀ + π model.

Figure 4.—

Rate parameters estimated on a five-taxon phylogeny. Rates on external branches are μ₁, and rates on internal branches are μ₂.

Figure 5.—

Comparison of MLEs with (solid symbols) or without (open symbols) considering truncated genes in the model. MLEs were estimated under the M₀ + π model. When not considering truncated genes, truncated genes were entirely classified as absent (top half) or present (bottom half).