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Luis A Cisneros-Ake1, Juan C Gonzalez-Rodriguez2, Laura R González-Ramírez3

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Summary

This study models the glycolytic process using Sel'kov's equations to understand oscillations and pattern formation. Researchers identified conditions for limit cycles, spiral waves, and 2D patterns like spots and stripes in glycolysis.

Keywords:
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Area of Science:

  • Biochemistry
  • Chemical Kinetics
  • Theoretical Biology

Background:

  • The glycolytic process is fundamental to cellular energy production.
  • Sel'kov's equations model key enzymatic reactions, like phosphofructokinase, within glycolysis.
  • Understanding oscillations and pattern formation is crucial for cellular dynamics.

Purpose of the Study:

  • To investigate single-frequency oscillations and pattern formation in a reduced glycolytic model.
  • To establish conditions for limit cycles and their average radius using averaging theory.
  • To analytically and numerically determine parameter regimes for pattern formation, including spots, stripes, and spiral waves.

Main Methods:

  • Utilized averaging theory to analyze kinetic reaction equations.
  • Performed analytical derivations for limit cycle existence and pattern formation conditions.
  • Employed numerical simulations to validate findings and explore parameter spaces for spiral waves.
  • Investigated Hopf bifurcations to characterize reaction dynamics.

Main Results:

  • Established conditions for limit cycles and their average radius in glycolytic equations.
  • Identified parameter conditions for unstable nonlinear modes leading to 2D patterns (spots, stripes).
  • Confirmed the existence of Hopf bifurcations, generating glycolytic rotating spiral waves.
  • Determined parameter regions for spiral wave existence and stability, noting loss of stability with suppressed source rate.

Conclusions:

  • The study provides analytical and numerical insights into pattern formation in glycolysis.
  • Model findings align with in vitro experimental observations of spatiotemporal glycolytic activity.
  • Results suggest plausible biological implications for cellular dynamics and energy metabolism.