Evolutionary tinkering enriches the hierarchical and nested structures in amino acid sequences

Genetic information often exhibits hierarchical and nested relationships, achieved through the reuse of repetitive subsequences such as duplicons and transposable elements, a concept termed "evolutionary tinkering"by François Jacob. Current bioinformatics tools often struggle to capture these, particularly the nested, relationships. To address this, we utilized ladderpath, an approach within the broader category of algorithmic information theory, introducing two key measures: order rate η for characterizing sequence pattern repetitions and regularities, and ladderpath-complexity κ for assessing hierarchical and nested richness. Our analysis of amino acid sequences revealed that humans have more sequences with higher κ values, and proteins with many intrinsically disordered regions exhibit increased η values. Additionally, it was found that extremely long sequences with low η are rare. We hypothesize that this arises from varied duplication and mutation frequencies across different evolutionary stages, which in turn suggests a zigzag pattern for the evolution of protein complexity. This is supported by simulations and studies of protein families such as ubiquitin and NBPF, implying species-specific or environment-influenced protein elongation strategies. The ladderpath approach offers a quantitative lens to understand evolutionary tinkering and reuse, shedding light on the generative aspects of biological structures.