  By use of a stochastic generalization of the Hodgkin-Huxley model we
investigate both the phenomena of stochastic resonance (SR) and coherence
resonance (CR) in variable size patches of an excitable cell membrane. Our
focus is on the challenge how internal noise stemming from individual ion
channels does affect collective properties of the whole ensemble. We
investigate both an unperturbed situation with no applied stimuli and one in
which the membrane is stimulated externally by a periodic signal and additional
external noise. For the nondriven case, we demonstrate the existence of an
optimal size of the membrane patch for which the internal noise causes a most
regular spike activity. This phenomenon shall be termed intrinsic CR. In
presence of an applied periodic stimulus we demonstrate that the
signal-to-noise ratio (SNR) exhibits SR vs. decreasing patch size, or vs.
increasing internal noise strength, respectively. Moreover, we demonstrate that
conventional SR vs. the external noise intensity occurs only for sufficiently
large membrane patches, when the intensity of internal noise is below its
optimal level. Thus, biological SR seemingly is rooted in the collective
properties of large ion channel ensembles rather than in the individual
stochastic dynamics of single ion channels.
