We consider here a simple example of stimulated sensory neurons operating under the influence of their own internal noise: the hair mechanoreceptor of the crayfish stimulated by a weak, periodic, hydrodynamic signal. Action potential spike trains from the sensory neuron are recorded and assembled into two objects for analysis: the interspike interval histogram (ISIH) and the cycle histogram of the spike density. A time transformation is carried out on the ISIH's in order to test the hypothesis that the spike train is basically random and that the probability of coherent spike generation is related to the instantaneous stimulus amplitude. Moreover it is shown that the physiological spike train data can be qualitatively mimicked by an electronic Fitzhugh-Nagumo model, operated in the subcritical mode, driven by noise and a weak periodic signal. A discussion of how the Fitzhugh-Nagumo model is properly operated to mimic noisy data from sensory neurons is included.

A simple phenomenon called stochastic resonance (SR), well known in nonlinear statistical physics, offers an explanation of how random fluctuations can enhance the detectability and/or the coherence of a weak signal in certain nonlinear dynamical systems. It is interesting to speculate that SR may play a role in the remarkable sensitivity exhibited by numerous biological sensory systems: systems which are themselves often inherently noisy and which, moreover, must usually operate in a noisy environment. A distinction is thus drawn between the external, or environmental, noise and the internal noise inherent in the sensory neurons themselves and distinguished by the randomness in time intervals between action potential spikes. We report the results of experiments with the internal noise, the intensity of which is varied by controlling the temperature of the preparation during the experiment. The useful range of temperatures could be extended by acclimating individual crayfish to a low or high temperature environment for many weeks prior to the experiment. Our results indicate that noise plays a significant role in signal transduction efficiency, increasing the signal-to-noise (SNR) ratio exponentially with noise intensity up to a maximum. Increasing the temperature beyond this maximum results in reduced SNRs and sharply reduced internal noise levels. The results of shifts in the data due to acclimation temperature can be removed by plotting the data versus the noise level, indicating that the noise may be a universal quantity in the dynamics of biological neurons.

We describe a new realization of stochastic resonance, applicable to a broad class of systems, based on an underlying excitable dynamics with deterministic reinjection. A simple but general theory of such ``single-trigger'' systems is compared with analog simulations of the Fitzhugh-Nagumo model, as well as experimental data obtained from stimulated sensory neurons in the crayfish.

Stochastic Resonance (SR) is a statistical process occurring only in nonlinear dynamical systems whereby a subthreshold coherent stimulus or signal can be enhanced by noise. The signal alone is too weak to cause a state change of the system. State changes are the carriers of information through the system. In the presence of random noise, however, the system can change state, more‐or‐less randomly, but with some degree of coherence with the signal. A measure of this coherence at the output shows a maximum at an optimal value of the noise intensity as the signature of SR. SR is the object of recent and continued experimental and theoretical research in statistical physics. While SR has been demonstrated in a variety of physical systems, it has not yet been discovered in any naturally occurring system. This paper was stimulated by the idea that the sensory nervous system might be an appropriate setting for a search for naturally occurring SR. The detection of weak stimuli, often in the presence of noise, is, after all, the first business of the sensory system. Moreover, the system is evolved, which admits the possibility that the process of natural selection might have resulted in an optimization with respect to the (inevitable) noise. This paper describes an experiment designed to observe SR in the mechanoreceptor cells of the crayfish Procambarus clarkii, shown on the left in Fig. 1, using external noise plus a weak coherent signal as the stimulus.

In this paper we discuss the noise driven dynamics of an array of Schmitt Triggers (ST’s) subject to a weak signal. The signal is subthreshold, that is, when applied without noise, it cannot cause state changes in the ST’s. Each ST is subject to a Gaussian noise which is uncorrelated with that of its neighbors. In this realization, the ST’s are not coupled but rather take their signal input from a common bus. Their outputs are summed to reproduce the input signal. Possible VLSI applications, and the motivation for this experiment are discussed.

Annals of the New York Academy of SciencesVolume 706, Issue 1 p. 26-41 Stochastic Resonance in an Electronic FitzHugh-Nagumo Modela FRANK MOSS, FRANK MOSS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121 Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorJOHN K. DOUGLASS, JOHN K. DOUGLASS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorLON WILKENS, LON WILKENS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorDAVID PIERSON, DAVID PIERSON Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorELENI PANTAZELOU, ELENI PANTAZELOU Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this author FRANK MOSS, FRANK MOSS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121 Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorJOHN K. DOUGLASS, JOHN K. DOUGLASS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorLON WILKENS, LON WILKENS Department of Biology University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorDAVID PIERSON, DAVID PIERSON Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this authorELENI PANTAZELOU, ELENI PANTAZELOU Department of Physics University of Missouri at St. Louis St. Louis, Missouri 63121Search for more papers by this author First published: December 1993 https://doi.org/10.1111/j.1749-6632.1993.tb24679.xCitations: 51 a This work was supported by Office of Naval Research Grant Nos. N00014-90-J-1327 and N00014-92-J-1235. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume706, Issue1Stochastic Processes in AstrophysicsDecember 1993Pages 26-41 RelatedInformation

We consider a system of globally coupled bistable systems under the influence of noise and periodic modulations. The hopping process between the stable states is described by a nonlinear master equation. We observe an unusually large amplification of the periodic modulations for certain values of the noise strength due to collective dynamics of the coupled bistable elements.