12 Membrane Clusters of Ion Channels: Size Effects for Stochastic Resonance

By use of a stochastic generalization of the Hodgkin-Huxley model we investigate the phenomenon of Stochastic Resonance (SR) for a distribution of ion channels within a cluster of variable size. In the presence of a periodic stimulus we demonstrate intrinsic SR vs. decreasing patch size, or, put differently, vs. increasing internal noise strength. SR with external noise occurs only for large cluster sizes which possess suboptimal internal noise levels. In particular, SR in biology thus seemingly is rooted in the collective properties of optimally selected ion channel assemblies. Moreover, upon investigating the signal-to-noise ratio (SNR) for sub-threshold sinusoidal driving vs. driving frequency we encounter also a stochastic resonance behavior which reflects the existence of a random internal limit cycle. The occurrence of intrinsic SR in a combination with the conventional frequency resonance may be of importance for the frequency tuning in biological signal processing.