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Global constraint principle for microbial growth laws.

Jumpei F Yamagishi1,2, Tetsuhiro S Hatakeyama3

  • 1Center for Biosystems Dynamics Research, RIKEN, Kobe 650-0047, Japan.

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|October 3, 2025
PubMed
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The global constraint principle explains microbial growth by considering multiple intracellular resources, moving beyond single-nutrient limitations. This new model integrates Monod and Liebig

Keywords:
cellular growthconvex optimizationdual problemmetabolismresource allocation

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Area of Science:

  • Microbial physiology
  • Systems biology
  • Biophysics

Background:

  • The Monod equation describes microbial growth based on a single substrate, but its mechanistic basis is debated due to complex cellular resource allocation.
  • Existing models struggle to explain growth limitations arising from multiple intracellular resources and coordination of metabolic reactions.

Purpose of the Study:

  • To propose and validate the global constraint principle for cellular growth, explaining resource allocation dynamics.
  • To integrate classical phenomenological growth laws (Monod and Liebig) into a unified theory.

Main Methods:

  • Developed a general framework based on constraint-based modeling and its dual formulations.
  • Mathematically proved general properties of microbial growth kinetics under nutrient availability.
  • Performed numerical simulations using genome-scale *Escherichia coli* models incorporating proteome allocation, molecular crowding, and membrane capacity constraints.

Main Results:

  • Demonstrated that microbial growth kinetics are generally monotonically increasing and concave with respect to nutrient availability.
  • Simulations reproduced multiphasic growth patterns consistent with the global constraint principle.
  • The principle captures dependence on multiple nutrients, generalizing Liebig's law of the minimum into a landscape of diminishing returns.

Conclusions:

  • The global constraint principle offers a comprehensive theory of cellular growth, unifying Monod's and Liebig's laws.
  • It explains how increasing availability of one nutrient leads to limitations by others, driving resource allocation shifts.
  • This principle provides a more mechanistically grounded understanding of microbial growth dynamics.