Glycolytic Wave Patterns in a Simple Reaction-diffusion System with Inhomogeneous Influx: Dynamic Transitions

Area of Science:

• Biochemistry
• Chemical Kinetics
• Nonlinear Dynamics

Background:

• Glycolytic oscillations are fundamental biological processes.
• Reaction-diffusion systems model spatio-temporal patterns in biological systems.
• The Selkov model describes a simplified glycolytic oscillator.

Purpose of the Study:

• To investigate pattern formation in glycolytic waves under inhomogeneous chemostatted conditions.
• To analyze the influence of diffusion amplitude and symmetry on spatial dynamics.
• To understand transitions between periodic, quasiperiodic, and chaotic patterns.

Main Methods:

• Utilized a Selkov reaction-diffusion framework.
• Performed systematic numerical simulations.
• Developed an analytical formulation of the amplitude equation.
• Connected Complex Ginzburg-Landau and Lambda-omega representations.

Main Results:

• Inhomogeneous chemostatted species profiles generate diverse spatio-temporal patterns.
• Diffusion amplitude and symmetry significantly dictate pattern formation and transitions.
• Observed periodic, quasiperiodic, and chaotic dynamics, including wave propagation direction changes.
• Analytical formulation provided insights into phase dynamics.

Conclusions:

• Inhomogeneous chemostatted species are crucial for generating complex patterns in glycolytic waves.
• The study elucidates the role of diffusion parameters in controlling biological pattern formation.
• Findings align with experimental results and offer insights into biological information processing.