Scientists Just Rewrote an 80-Year-Old Law of Biology

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Here’s what you’ll learn when you read this story:

• Similar to the “law of diminishing returns in economics,” biology inevitably experiences a leveling off of microbial growth at some point, even as available nutrients rise.

• A new study reformulates an 80-year-old equation for calculating microbial growth by combining it with Leibig’s Law of Minimums, which describes how plant growth can be limited by resources.

• According to the researchers, this lays the groundwork for “universal laws of growth” that could be a huge boon to industries or green technologies that rely on microbial production.

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Although life takes a massive variety of forms, shapes, and sizes, all the different versions rely on the same fundamentals (nutrients, energy, and cellular machinery) to keep on living. Scientists have also long known that biology experiences a process in which cellular growth slows as nutrient levels rise—very similar to what economists call the “law of diminishing returns,” which states that adding a variable input will increase productivity sharply before eventually plateauing.

Typically, scientists have tried to understand this biological limit through singular nutrients or biochemical reactions. Their primary method of describing the system has long been what’s known as the “Monod equation” (named after Nobel Prize-winning chemist Jacques Monod), which describes how microbes grow in response to a limiting nutrient, or the nutrient that inhibits further growth. But in a new study, two Japanese scientists—Jumpei Yamagishi from the University of Tokyo and Tetsuhiro Hatakeyama from the Institute of Science Tokyo—attempt to expand on this idea by taking a more complex, holistic picture of microbial growth that they call the “global constraint principle.” The results were published in the journal Proceedings of the National Academy of Sciences (PNAS).

According to Yamagishi and Hatakeyama, the Monod equation only captures one part of a much broader system that actually encompasses thousands of chemical processes. To fill in this bigger picture, the authors marry Monod’s equation with the idea of Liebig’s Law of the Minimum, which describes how resources like phosphorus and nitrogen can limit plant growth. This idea is sometimes described like a barrel—the shortest plank (technically called a ‘stave’) of a barrel is the limiting factor in how high the water level can rise.

However, the research duo put a twist on this metaphor, creating what they call a “terraced barrel.” Here, limiting factors take effect sequentially, which helps explain why everything—from microbes to humans—experiences this leveling off.

“The shape of growth curves emerges directly from the physics of resource allocation inside cells, rather than depending on any particular biochemical reaction,”Hatakeyama said in a press statement. “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.”

To test this theory, scientists worked with a computer model of the bacterium E. coli to analyze how the organism uses proteins, how they’re packed spatially, and what the capacities of their membranes are. “Our work lays the groundwork for universal laws of growth,” Yamagishi said in a press statement. “By understanding the limits that apply to all living systems, we can better predict how cells, ecosystems, and even entire biospheres respond to changing environments.”

Of course, accurately identifying limiting nutrients can give a big boost to industries that rely on microbial production—whether for creating probiotics, biofertilizers, or even super-enzymes that can munch on discarded plastic. The web of life is vast and complicated, but when you get down to the cellular level, nature’s beautiful simplicity is laid bare.

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