Researchers in Japan have identified a new principle explaining why living organisms' growth slows even with abundant nutrients. The global constraint principle integrates classic biological laws to reveal sequential limitations in cellular processes. Verified through E. coli simulations, it could enhance crop yields and biomanufacturing.
A team including Tetsuhiro S. Hatakeyama from the Earth-Life Science Institute (ELSI) at the Institute of Science Tokyo and Jumpei F. Yamagishi from RIKEN has discovered the global constraint principle for microbial growth. This framework mathematically describes the law of diminishing returns, where growth rates increase with nutrients but eventually plateau due to interconnected cellular constraints.
Since the 1940s, the Monod equation has modeled microbial growth as limited by a single nutrient, while Liebig's law of the minimum highlights the scarcest resource as the bottleneck. Hatakeyama and Yamagishi's work unites these, proposing a terraced barrel model where new limiting factors—like enzyme production, cell volume, or membrane space—emerge sequentially as nutrients become plentiful.
"The shape of growth curves emerges directly from the physics of resource allocation inside cells, rather than depending on any particular biochemical reaction," explains Hatakeyama. He compares it to Liebig's barrel analogy: "In our model, the barrel staves spread out in steps, each step representing a new limiting factor that becomes active as the cell grows faster."
Using constraint-based modeling, the researchers simulated Escherichia coli, incorporating protein usage, intracellular crowding, and membrane limits. The models predicted growth slowdowns with added nutrients and matched lab experiments on oxygen and nitrogen effects.
Published in Proceedings of the National Academy of Sciences (2025; 122 (40)), the principle offers a unified view of growth across life forms. "Our work lays the groundwork for universal laws of growth," says Yamagishi. Applications include optimizing biotechnology, improving agriculture, and modeling ecosystem responses to environmental changes.