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Transitions between oscillatory modes in a glycolytic model system.
1Max-Planck-Institut für Ernährungsphysiologie, Rheinlanddamm 201, 4600 Dortmund, Federal Republic of Germany.
Summary
This study analyzes a glycolytic model with phosphofructokinase and pyruvate kinase enzymes. It reveals complex dynamics, including chaotic patterns and self-sustained switching between states, controllable by substrate pulses.
Area of Science:
- Biochemistry and Systems Biology
- Enzyme Kinetics and Metabolic Modeling
Background:
- Glycolysis is a fundamental metabolic pathway.
- Understanding enzyme dynamics is crucial for metabolic control.
- Previous models often simplify enzyme interactions and dynamic behaviors.
Purpose of the Study:
- To analyze a glycolytic model system with phosphofructokinase and pyruvate kinase under periodic substrate addition.
- To investigate complex dynamic behaviors including periodic, quasiperiodic, and chaotic attractors.
- To explore hysteresis, coexisting attractors, and triggered/autonomous switching phenomena.
Main Methods:
- Utilized detailed rate laws for Escherichia coli phosphofructokinase (EC 2.7.1.11) and pyruvate kinase (EC 2.7.1.40).
- Employed numerical solutions to analyze metabolite concentrations and system dynamics.
- Visualized multi-metabolite concentrations within a trapezium representation.
- Investigated system responses to slow changes in bifurcation parameters and short substrate pulses.
Main Results:
- Identified a rich variety of time patterns, including periodic, quasiperiodic, and chaotic attractors.
- Observed complex hysteresis loops upon slow variation of bifurcation parameters like input amplitude.
- Discovered up to four coexisting attractors in phase space.
- Demonstrated switching between coexisting attractors via substrate pulses, including autonomous, self-sustained (intermittent) switching.
- Showed that the time between self-sustained switchings is externally tunable by input amplitude.
Conclusions:
- The analyzed glycolytic model exhibits complex, non-linear dynamics and multi-stability.
- Periodic substrate addition can induce diverse temporal patterns, including chaos.
- The system's ability to switch between states, both triggered and autonomous, highlights intricate metabolic control mechanisms.
- The findings have implications for understanding metabolic regulation and oscillations in biological systems.