Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.

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Spiking Neuron Models: Single Neurons, Populations, Plasticity

Evolutionary games on graphs

Noise — random disturbances of signals — poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

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Noise in the nervous system.

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

http://people.physik.hu-berlin.de/~lindner/PDF/physreport.pdf

Effects of noise in excitable systems

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 Resonance in an Electronic FitzHugh‐Nagumo Modela

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.

Temperature dependence and the role of internal noise in signal transduction efficiency of crayfish mechanoreceptors

Directional selectivities of mechanoreceptors that innervate filiform hairs on the crayfish tailfan were investigated with unidirectional, sinusoidal, water-motion stimuli. These recordings provide the first representative sample from filiform hair sensilla on the entire tailfan. The filiform hair receptors exhibit unimodal directional selectivity patterns that were well fitted by a cardioid function with a half-width of 122°. The preferred directions correspond to the major axis of hair motion, and are perpendicular to the orientation of lateral branches on the main hair shaft. Pooled plots of preferred directions demonstrate quadrimodal patterns on the telson and endopods which are associated with hair location, and a bimodal pattern on the exopods. For each appendage, the combination of the overall pattern of preferred directions with “coarse coding” of direction by individual receptors provides sensitivity to a full 0–360° range of water motion and the potential to discriminate the direction of water motion throughout this range. The results demonstrate several similarities to the wind-sensitive cercal receptor system in orthopteroid insects, and suggest that crustacean filiform hair receptors provide a sufficient sensory basis for behavioral orientation to water currents and shorelines.

Directional selectivities of near-field filiform hair mechanoreceptors on the crayfish tailfan (Crustacea: Decapoda)

We present several relatively simple procedures for studying the physiology of near-field mechanoreceptors in crustaceans which extend previous measures of sensitivity. The advantages include the quantitative analysis of range fractionation and directionality of receptors and interneurons in the sensory hierarchy of the central nervous system (CNS), based on a stimulus paradigm that is reproducible and easy to use. The technical considerations for quantitative fluid-coupled stimulation addressed by this paper are the complexity of dipole flow fields, reflected interference from traveling waves, and the underlying stimulus wave form. The techniques described here offer corresponding advantages for physiological experiments using other aquatic organisms. In electrophysiological experiments, crustacean preparations are typically placed in an experimental chamber filled with water or saline solution. For studies on near-field sensory receptors, i.e. those responding to flow fields in the aquatic medium, a dipole or vibrating sphere is frequently used to generate stimulus waves (Tautz et al. 1981; Wiese and Wollnik, 1983; Ebina and Wiese, 1984; Hatt, 1986; Heinisch and Wiese, 1987; Tautz, 1987; Wiese and Marschall, 1990; Killian and Page, 1992b). A dipole stimulator is easily constructed by attaching a spherical probe to an electromechanical device such as a loudspeaker, pen motor or piezo crystal. A periodic signal fed to the transducer generates the oscillating dipole movements. With the sphere immersed in the bathing medium, dipole flow fields are generated (see Kalmijn, 1988, for further discussion of dipole sources), whereas dipole oscillations introduced at the air­saline interface generate traveling surface waves. Numerous additional devices and techniques have been used to stimulate crustacean receptors. Several involve wave motion introduced from one end of the chamber by diaphragms or paddles (Laverack, 1962b, 1963; Flood and Wilkens, 1978), by cylindrical dippers (Wilkens and Larimer, 1972; Wiese et al. 1976; Wiese and Schultz, 1982; Reichert et al. 1983) or by water drops (Laverack, 1962b; Strandburg and Krasne, 1985). Another form of fluid-coupled stimulation involves small jets of saline (Laverack, 1963; Tautz, 1990; Schmitz, 1992). In other studies, receptor hairs have been stimulated directly by using a stylus in place of the dipole, e.g. a needle or glass capillary in contact with the hair (Laverack, 1962a; Killian and Page, 1992a; Yen et al. 1992; Nagayama and Sato, 1993) or a miniature wire loop or capillary tube placed over the hair shaft (Mellon, 1963; Wiese, 1976; Tautz et al. 1981; Killian and Page, 1992b).

John K. Douglass

Papers

Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance

Stochastic Resonance in an Electronic FitzHugh‐Nagumo Modela

Temperature dependence and the role of internal noise in signal transduction efficiency of crayfish mechanoreceptors

Directional selectivities of near-field filiform hair mechanoreceptors on the crayfish tailfan (Crustacea: Decapoda)

A stimulus paradigm for analysis of near-field hydrodynamic sensitivity in crustaceans