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Minimal model for Ca(2+)-dependent oscillations in excitable cells.

M Colding-Jørgensen1, H O Madsen, B Bodholdt

  • 1Department of General Physiology and Biophysics, Panum Institute, Copenhagen, Denmark.

Journal of Theoretical Biology
|June 7, 1992
PubMed
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This study presents a minimal model of calcium oscillations, revealing how ion exchange dynamics control cellular excitability. Key parameters, like the calcium pump rate, dictate transitions between stable and oscillatory states.

Area of Science:

  • Biophysics
  • Computational Biology
  • Cellular Physiology

Background:

  • Cellular oscillations are crucial for various biological processes.
  • Understanding the minimal mechanisms driving these oscillations is essential for cellular control.
  • Calcium ions play a pivotal role in regulating cellular functions and signaling pathways.

Purpose of the Study:

  • To develop a simplified mathematical model for calcium-controlled oscillations.
  • To investigate the dynamic behaviors arising from ion exchange across the plasma membrane.
  • To identify key parameters governing the transition between different cellular states.

Main Methods:

  • A minimal biophysical model incorporating calcium and potassium ion fluxes was developed.
  • The model simulates ion leakage and extrusion across the plasma membrane.

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  • Mathematical analysis was used to explore parameter-dependent state transitions.

    • Main Results:

    • The model exhibits five distinct states: non-excitable stability, single-spike excitability, slow oscillations, reverse-spike excitability, and another stable state.
    • The rate constant of the calcium pump significantly influences the model's switching behavior.
    • Intracellular calcium concentration dynamics are the sole source of time dependence.

    Conclusions:

    • A minimal model can recapitulate complex calcium-controlled oscillatory behaviors.
    • The calcium pump's rate is a critical determinant of cellular excitability states.
    • This model provides insights into the fundamental mechanisms of cellular rhythmicity.