Scarcity of scale-free topology is universal across biochemical networks

Biochemical reactions underlie all living processes. Like many biological and technological systems, their complex web of interactions is difficult to fully capture and quantify with simple mathematical objects. Nonetheless, a huge volume of research has suggested many real-world biological and technological systems – including biochemical systems – can be described rather simply as ‘scale-free’ networks, characterized by a power-law degree distribution. More recently, rigorous statistical analyses across a variety of systems have upended this view, suggesting truly scale-free networks may be rare. We provide a first application of these newer methods across two distinct levels of biological organization: analyzing a large ensemble of biochemical networks generated from the reactions encoded in 785 ecosystem-level metagenomes and 1082 individual-level genomes (representing all three domains of life). Our results confirm only a few percent of individual and ecosystem-level biochemical networks meet the criteria necessary to be anything more than super-weakly scale-free. Leveraging the simultaneous analysis of the multiple coarse-grained projections of biochemistry, we perform distinguishability tests across properties of individual and ecosystem-level biochemical networks to determine whether or not they share common structure, indicative of common generative mechanisms across levels. Our results indicate there is no sharp transition in the organization of biochemistry across distinct levels of the biological hierarchy - a result that holds across different network projections. This suggests the existence of common organizing principles operating across different levels of organization in biochemical networks, independent of the project chosen.