Journal of Mathematical Biology

, Volume 8, Issue 2, pp 197–214 | Cite as

Excitation of paramecium

A model analysis
  • C. Hook
  • E. Hildebrand


In a model analysis the excitation mechanism of Paramecium is simulated. The model is based on a specific Ca channel mechanism located in the ciliary part of the membrane. The Ca2+ permeability depends on transmembrane voltage and the binding of cations to channel subunits. Renormalization of intraciliary [Ca2+] following excitation is mediated by active Ca2+ extrusion and diffusion between cilia and cell body. Including the kinetic equations of a. K+ transport system we get a complete description of ionic fluxes and current-voltage relations. The electric responses to injected current pulses of different duration can be simulated as well as voltage-clamp measurements, after introduction of an electrogenic Ca2+ transport system. Allowing Ba2+ to substitute for Ca2+ with slightly different permeability and binding rates, the features of all-or-none action potentials and repetitive firing are reflected by the model. Simulation of membrane responses to varying external [K+] and [Ca2+] leads us to require some additional, slowly changing mechanism to account for processes like slow inactivation and recovery. The possible existence of negative surface charges is discussed.

Key words

Cilia Membrane Ca channels Action potential Ion competition Electrogenic pump 


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Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • C. Hook
    • 1
  • E. Hildebrand
    • 2
  1. 1.Institut für Theoretische PhysikRheinisch-Westfälische Technische HochschuleAachen
  2. 2.Institut fur NeurobiologieJülichFederal Republic of Germany

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