Dissipative structures for an allosteric model. Application to glycolytic oscillations.

Area of Science:

• Biochemistry
• Chemical Kinetics
• Theoretical Biology

Background:

• Enzyme kinetics and allosteric regulation are crucial for metabolic control.
• Product activation in enzyme systems can lead to complex dynamic behaviors.
• Understanding metabolic oscillations is key to deciphering cellular regulation.

Purpose of the Study:

• To analyze an allosteric monosubstrate enzyme model with product activation.
• To identify conditions leading to temporal (limit cycle) or spatial (dissipative structures) instabilities.
• To investigate the role of substrate activation in generating sustained oscillations.

Main Methods:

• Development of an allosteric model for an open monosubstrate enzyme reaction.
• Mathematical analysis to determine conditions for system instabilities.
• Numerical simulations to explore limit cycle behavior and parameter dependencies.
• Application of the model to phosphofructokinase and glycolytic oscillations.

Main Results:

• The model predicts instabilities leading to organized states in time or space.
• Sustained oscillations in substrate and product concentrations were observed numerically.
• Oscillations are favored by substrate activation and occur for realistic kinetic parameters.
• The model qualitatively and quantitatively matches experimental data for glycolytic self-oscillations.

Conclusions:

• Allosteric enzymes activated by product can exhibit complex dynamics, including sustained oscillations.
• Substrate activation plays a significant role in promoting these oscillations.
• The model provides a framework for understanding glycolytic oscillations mediated by enzymes like phosphofructokinase.