Nonlinear Model of Calcium Excitations in Biomembranes

  • S. I. Braichenko Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics
  • A. N. Vasilev Taras Shevchenko National University of Kyiv, Faculty of Physics, Chair of Theoretical Physics
Keywords: calcium, spark, biomembrane, diffusion


A model is proposed to describe the calcium redistribution in biological substances. The model takes into consideration that calcium can be located inside or outside a cell. Calcium is redistributed due to its transport from the cell volume into the outer space and backward. The model makes allowance for the calcium diffusion into the outer space. It is shown that there are two modes of functioning of the system. In one of them, the initial perturbation of the calcium concentration in the extracellular space monotonically vanishes in time. In the other mode, this perturbation first grows, but afterward decreases to the zero value. The calcium concentration in the intracellular space is shown to be a critical parameter that governs the system operation mode.


  1. D.M. Bers. Cardiac excitation-contraction coupling. Nature 415, 198 (2002).

  2. M.J. Berridge, P. Lipp, M.D. Bootman. The versatility and universality of calcium signalling. Natl. Rev. Mol. Cell Biol. 1, 11 (2000).

  3. M.J. Berridge, M.D. Bootman, P. Lipp. Calcium – a life and death signal. Nature 395, 645 (1998).

  4. D.M. Bers. Calcium cycling and signaling in cardiac myocytes. Annu. Rev. Physiol. 70, 23 (2008).

  5. C.J. Fearnley, H.L. Roderick, M.D. Bootman. Calcium signaling in cardiac myocytes. Cold Spring Harb. Perspect. Biol. 3, a004242 (2011).

  6. G. Williams, A. Chikando, H. Tuan, E. Sobie, W. Lederer, M. Jafri. Dynamics of calcium sparks and calcium leak in the heart. Biophys. J. 101, 1287 (2011).

  7. M. Nivala, C.Y. Ko, M. Nivala, J.N. Weiss, Z. Qu. Criticality in intracellular calcium signaling in cardiac myocytes. Biophys. J. 102, 2433 (2012).

  8. B.D. Stuyvers, P.A. Boyden, H.J. ter Keurs. Calcium waves: Physiological relevance in cardiac function. Circulat. Res. 86, 1016 (2000).

  9. A.A. Kort, M.C. Capogrossi, E.G. Lakatta. Frequency, amplitude, and propagation velocity of spontaneous Ca++-dependent contractile waves in intact rat cardiac muscle and isolated myocytes. Circulat. Res. 57, 844 (1985).

  10. H. Cheng, W.J. Lederer, M.B. Cannell. Calcium sparks: Elementary events underlying excitation-contraction coupling in heart muscle. Science 262, 740 (1993).
How to Cite
Braichenko, S., & Vasilev, A. (2018). Nonlinear Model of Calcium Excitations in Biomembranes. Ukrainian Journal of Physics, 63(4), 327.
Physics of liquids and liquid systems, biophysics and medical physics