Abstract. 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.
IntroductionMuch attention is presently given to the behavior of complex networks with the particular focus being on so termed scale-free networks, which are believed to present many complex phenomena in nature [1,2,3,4,5,6,7]. Such networks naturally also occur in biological settings. In this spirit we focus here on the constructive role of noise on voltage gated, globally connected assemblies of ion channels. If the distribution of such ion channels consists of at least two types, excitable behavior becomes possible which in turn rules the transduction of biological information. The transduction of signals in presence of ambient, internal noise then likely makes use of a cooperative behavior between nonlinearity and noise, known under the label of Stochastic Resonance [8].During the last decade, the effect of Stochastic Resonance (SR) -a cooperative phenomenon wherein the addition of external noise improves the detection and transduction of signals in nonlinear systems (for comprehensive surveys and relevant further references, see in [8,9]) -has been studied experimentally and theoretically in various biological systems [10,11,12,13,14]. For example, SR has been experimentally demonstrated within the mechanoreceptive system in crayfish [10], in the cricket cercal sensory system [11], for human tactile sensation [12], visual perception [13], and response behavior of the arterial baroreflex system of humans [14]. The importance of this SR-phenomenon for sensory biology is by now well established; yet, it is presently not known to which minimal R. Pastor-Satorras, M. Rubi, A. Diaz-Guilera (Eds.): LNP 625, pp. [195][196][197][198][199][200][201][202][203][204][205][206] 2003.