Noise in dynamical systems is usually considered a nuisance. But in certain nonlinear systems, including electronic circuits and biological sensory apparatus, the presence of noise can in fact enhance the detection of weak signals. This phenomenon, called stochastic resonance, may find useful application in physical, technological and biomedical contexts.

Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs

IN linear information theory, electrical engineering and neurobiology, random noise has traditionally been viewed as a detriment to information transmission. Stochastic resonance (SR) is a nonlinear, statistical dynamics whereby information flow in a multistate system is enhanced by the presence of optimized, random noise1–4. A major consequence of SR for signal reception is that it makes possible substantial improvements in the detection of weak periodic signals. Although SR has recently been demonstrated in several artificial physical systems5,6, it may also occur naturally, and an intriguing possibility is that biological systems have evolved the capability to exploit SR by optimizing endogenous sources of noise. Sensory systems are an obvious place to look for SR, as they excel at detecting weak signals in a noisy environment. Here we demonstrate SR using external noise applied to crayfish mechanoreceptor cells. Our results show that individual neurons can provide a physiological substrate for SR in sensory systems.

Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance

STOCHASTIC resonance1‡-4 (SR) is a phenomenon wherein the response of a nonlinear system to a weak periodic input signal is optimized by the presence of a particular, non-zero level of noise5 ‡-7. SR has been proposed as a means for improving signal detection in a wide variety of systems, including superconducting quantum interference devices8, and may be used in some natural systems such as sensory neurons9‡-15. But for SR to be effective in a singleunit system (such as a sensory neuron or a single ion channel), the optimal intensity of the noise must be adjusted as the nature of the signal to be detected changes15. This has been thought to impose a limitation on the practical and natural uses of SR. Here we show that the ability of a summing network of excitable units to detect a range of weak (sub-threshold) signals (either periodic or aperiodic) can be optimized by a fixed level of noise, irrespective of the nature of the input signal. We also show that this noise does not significantly degrade the ability of the network to detect suprathreshold signals. Thus, large nonlinear networks do not suffer from the limitations of SR in single units, and might be able to use a single noise level, such as that provided by the intrinsic noise of the individual components, to enhance the system's sensitivity to weak inputs. This suggests a functional role for neuronal noise14,16‡-18 in sensory systems.

Stochastic resonance without tuning

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations— e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being ''suboptimal''. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significant- ly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the ''neural code''. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neurosci- entists and biologists, both computational and experi- mental, to embrace a very broad definition of stochastic resonance in terms of signal-processing ''noise benefits'', and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

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What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

SENSORY systems are often required to detect a small amplitude signal embedded in broadband background noise. Traditionally, ambient noise is regarded as detrimental to encoding accuracy. Recently, however, a phenomenon known as stochastic resonance has been described in which, for systems with a nonlinear threshold, increasing the input noise level can actually improve the output signal-to-noise ratio over a limited range of signal and noise strengths. Previous theoretical and experimental studies of stochastic resonance in physical1–7and biological6–10 systems have dealt exclusively with single-frequency sine stimuli embedded in a broadband noise background. In the past year it has been shown in a theoretical and modelling study that stochastic resonance can be observed with broadband signals11,12. Here we demonstrate that broadband stochastic resonance is manifest in the peripheral layers of neural processing in a simple sensory system, and that it plays a role over a wide range of biologically relevant stimulus parameters. Further, we quantify the functional significance of the phenomenon within the context of signal processing, using information theory.

F. Heslot

Papers

Stochastic resonance in a bistable system