Scarcity of scale-free topology is universal across biochemical networks

Abstract

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. Author SummaryFully characterizing living systems requires rigorous analysis of the complex webs of interactions governing living processes. Here we apply statistical approaches to analyze a large data set of biochemical networks across two levels of organization: individuals and ecosystems. We find that independent of level of organization, the standard scale-free model is not a good description of the data. Interestingly, there is no sharp transition in the shape of degree distributions for biochemical networks when comparing those of individuals to ecosystems. This suggests the existence of common organizing principles operating across different levels of biochemical organization that are revealed across different network projections.