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Structural conditions on complex networks for the Michaelis-Menten input-output response.

Felix Wong1,2, Annwesha Dutta3, Debashish Chowdhury3

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Proceedings of the National Academy of Sciences of the United States of America
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PubMed
Summary

The Michaelis-Menten (MM) formula, describing enzyme kinetics, applies broadly due to specific graph structures. This study reveals general conditions for its wide applicability in biological systems.

Keywords:
Michaelis–Menten formulacomplex networkinput–output responselinear frameworknonequilibrium

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Area of Science:

  • Biochemistry
  • Systems Biology
  • Enzyme Kinetics

Background:

  • The Michaelis-Menten (MM) formula is a cornerstone in enzyme kinetics, relating reaction rate to substrate concentration.
  • Its hyperbolic relationship, derived from a three-reaction network, is observed across diverse biological processes.
  • Previous explanations for its ubiquity relied on restrictive structural or parametric assumptions.

Purpose of the Study:

  • To derive general structural conditions for the emergence of the Michaelis-Menten formula.
  • To explain the formula's widespread applicability beyond its original context.
  • To provide a unified framework for understanding MM kinetics in various biological systems.

Main Methods:

  • Utilizing a graph-based linear framework for timescale separation.
  • Analyzing network structures to identify conditions for MM formula derivation.
  • Investigating systems at and away from thermodynamic equilibrium.

Main Results:

  • Identified general structural conditions for the MM formula, involving graph partitioning and input variable placement.
  • Demonstrated that arbitrary parameter values are permissible, explaining the formula's ubiquity.
  • Derived a necessary and sufficient condition for systems at thermodynamic equilibrium.

Conclusions:

  • The ubiquity of the Michaelis-Menten formula is explained by general graph structural properties, not just regular network structures.
  • The findings accommodate a broader range of biological systems, including those with irreversible reactions.
  • This work provides a more general theoretical foundation for Michaelis-Menten kinetics in biological research.