Electrical Rhythmicity and Excitability in Cell Membranes

  • Arthur T. Winfree
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 12)


Every cell has a plasma membrane. The plasma membrane is a thin film, less than a hundred angstroms thick, which maintains a difference between inside and outside by gate-keeping the passage of molecules and ions. Every cellular membrane is freely permeable to some substances (e.g., water) and essentially impermeable to others (e.g., proteins and certain ions). Nerve cells and some secretory cells are distinguished from most other kinds of cell chiefly in that the selective permeability of their plasma membranes depends sharply on an electric field. All cells experience an electric potential difference between inside and outside, ultimately because amino acids bear an ionic charge and, once polymerized inside the cell, they can’t get out.1 This potential difference is typically about one-tenth of a volt, so the thin plasma membrane is stressed by an electric field in the order of 10 million volts/m. In nerve cells, molecular anatomy within the plasma membrane is believed to readjust when this field is reduced to less than a certain threshold. With its selective permeability altered, the membrane passes certain ions that it had formerly restrained, resulting in a further decrease in the field maintained, and a self-catalyzing breakdown of membrane potential quickly ensues. But things are so arranged that a recovery promptly follows in which electrical imbalance is restored.


Slow Wave Refractory Period Excitable Medium Spiral Wave Spreading Depression 
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  1. 1.
    This potential difference would persist without expenditure of energy were the membrane perfectly impermeable to select ions. But it leaks a little, so the observed voltage must also be maintained by sodium-potassium ATPase pumping ions across the membrane.Google Scholar
  2. 2.
    Added in proof (1979): data from Jalife seem to provide this for the first time, using sinus node of the kitten.Google Scholar
  3. 3.
    Added in proof (1979): this has already appeared in Guttman et al. (1980) who incidentally point out that Teorell (1971 Appendix 3) observed a singular annihilating pulse in his 2-variable model of a sensory pacemaker (his Figures 10e, 12h, 16c). Both these cases, as well as Best’s computations, expedite location of the phase singularity by adjusting parameters to make the neuroelectric steady-state locally an attractor. Jalife and Antzelevitch (1979) using kitten sinus node also demonstrated annihilation by a critically timed singular stimulus.Google Scholar
  4. 4.
    Similar measurements have emerged in the literature of the female cycle and of the cell cycle. Cycles without ovulation seem to occur in the menstrual rhythm, without upsetting its quasi-regularity (Chapter 23). According to Kauffman and Wille (1975), the mitotic cycle in Physarum can be suppressed without suppressing a timer that brings about the next mitosis one or two or three cycles later, roughly on schedule. If these observations are to be taken at face value, they suggest that the action potential, ovulation and mitosis are caused by a covert timer (see, for example, Both et al., 1976) but do not in turn affect it unless they just happen to affect it in such a manner that the time to the next event is the same either way.Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of ArizonaTucsonUSA

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