Growth: Molecular accretion, growth and innovation

Accretion brings together disparate parts to form bigger wholes. In doing so, it provides opportunities for growth and innovation. This process occurs pervasively in nature at widely different timeframes. In biological evolution, component parts are added to growing macromolecules, which also interact and merge with other growing molecules to form molecular complexes and higher levels of molecular and cellular organization. Here we study accretion by focusing on protein structural domains that make up proteomes. Phylogenomic reconstruction generates phylogenetic trees and chronologies of structural domains, which can be used to describe proteome growth. We find that the interface between evolutionary models, trees, and data supports Leibniz's principle of spatiotemporal continuity. The growth of macromolecular systems complies with mathematical universals, such as the Zipf and Heaps laws. Finally, sequential S-shaped logistic wavelets that model growth and diffusion of innovations describe processes of diversification. Remarkably, pairs of wavelets induce biphasic patterns that help model protein evolution. It appears fine-grained structural elaborations in growing funnels of diversification give rise to coarsegrained innovations that tailor the generation of structural modules and biological complexity.