Oscillations and multiple steady states in active membrane transport models

Area of Science:

• Biophysics
• Biochemistry
• Systems Biology

Background:

• Active membrane transport is crucial for cellular function.
• Understanding the dynamic behavior of transport models is key to elucidating cellular processes.

Purpose of the Study:

• Investigate the dynamic behavior of non-linear extensions of the six-state alternating access model for active membrane transport.
• Analyze the stability of steady states and identify conditions leading to self-oscillations and multiple steady states.

Main Methods:

• Stoichiometric network analysis to study steady-state stability.
• Bifurcation analysis using standard numerical methods.
• Modeling of extended six-state models including autocatalysis, monomer-dimer cycle competition, and complex formation.

Main Results:

• The basic six-state model has a single, globally asymptotically stable steady state.
• Introducing an autocatalytic step or monomer-dimer cycle competition leads to self-oscillations.
• Complex formation alone did not alter steady states, but combined with autocatalysis, it yielded self-oscillations and multiple steady states.

Conclusions:

• Active membrane transport systems can exhibit oscillations with sufficient steps and coupling to autocatalytic reactions or monomer-dimer cycles.
• Autocatalysis can be a simplified representation of more realistic monomer-dimer cycle competition in biological systems.
• Self-regulation via multiple steady states is predicted for models combining autocatalysis and complex formation.