  The behaviour of a system of ion channels formed across the cell membrane is
presented. The infinite number of channels with an infinite coupling is
introduced first as a reference point for the detailed derivation of the
thermal-equilibrium probability distribution and the classification of the
phase transitions. Fluctuations in a finite system are discussed next. We
propose a new, step-like model of the ion channel switching, for which we
provide the analytical results. The relation of this model to experiment is
also provided. Finally, the master equation for the finite channel-number
membrane is analysed numerically with the help of an exact-diagonalization
technique. In particular, the decay-time of a metastable solution is estimated.
The results do not agree with those obtained perturbationally, the difference
is explained by the proposed frozen-diffusion approach.
