Turing Instabilities and Rotating Spiral Waves in Glycolytic Processes.

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.