# Family-specific scaling laws in bacterial genomes

## TL;DR

This study reveals that individual protein domain families in bacterial genomes follow specific scaling laws with genome size, indicating complex functional and evolutionary relationships beyond current annotations.

## Contribution

It systematically characterizes family-specific scaling laws and introduces a heterogeneity score, deepening understanding of protein family evolution in bacterial genomes.

## Key findings

- Protein families follow distinct scaling laws with genome size.
- Functionally similar families often share similar scaling behaviors.
- Heterogeneity score reveals diverse scaling patterns within categories.

## Abstract

Among several quantitative invariants found in evolutionary genomics, one of the most striking is the scaling of the overall abundance of proteins, or protein domains, sharing a specific functional annotation across genomes of given size. The size of these functional categories change, on average, as power-laws in the total number of protein-coding genes. Here, we show that such regularities are not restricted to the overall behavior of high-level functional categories, but also exist systematically at the level of single evolutionary families of protein domains. Specifically, the number of proteins within each family follows family-specific scaling laws with genome size. Functionally similar sets of families tend to follow similar scaling laws, but this is not always the case. To understand this systematically, we provide a comprehensive classification of families based on their scaling properties. Additionally, we develop a quantitative score for the heterogeneity of the scaling of families belonging to a given category or predefined group. Under the common reasonable assumption that selection is driven solely or mainly by biological function, these findings point to fine-tuned and interdependent functional roles of specific protein domains, beyond our current functional annotations. This analysis provides a deeper view on the links between evolutionary expansion of protein families and the functional constraints shaping the gene repertoire of bacterial genomes.