Towards the brain-computer's code?

A review of methods for identifying stochastic resonance in simulations of single neuron models

Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed on real neural systems. Despite the ubiquity of biophysical sources of stochastic noise in the nervous system, however, it has not yet been established whether neuronal computation mechanisms involved in performance of specific functions such as perception or learning might exploit such noise as an integral component, such that removal of the noise would diminish performance of these functions. In this paper we revisit the methods used to demonstrate stochastic resonance in models of single neurons. This includes a previously unreported observation in a multicompartmental model of a CA1-pyramidal cell. We also discuss, as a contrast to these classical studies, a form of 'stochastic facilitation', known as inverse stochastic resonance. We draw on the reviewed examples to argue why new approaches to studying 'stochastic facilitation' in neural systems need to be developed.

Synchronization and array-enhanced resonances in delayed coupled neuronal network with channel noise

This paper studies the combined effect of transmission delay and channel fluctuations on population behaviors of an excitatory Erdös-Rényi neuronal network. First, it is found that the network reaches a perfect spatial temporal coherence at a suitable membrane size. Such a coherence resonance is stimulus-free and is array-enhanced. Second, the presence of transmission delay can induce intermittent changes of the population dynamics. Besides, two resonant peaks of the population firing rate are observed as delay changes: one is at τd≈7ms for all membrane areas, which reflects the resonance between the delayed interaction and the intrinsic period of channel kinetics; the other occurs when the transmission delay equals to the mean inter-spike intervals of the population firings in the absence of delay, which reflects the resonance between the delayed interaction and the firing period of the non-delayed system. Third, concerning the impact of network topology and population size, it is found that decreasing the connection probability does not change the range of transmission delay but broadens the range of synaptic coupling that supports population neurons to generate action potentials synchronously and temporally coherently. Furthermore, there exists a critical connection probability that distinguishes the population dynamics into an asynchronous and synchronous state. All the results we obtained are based on networks of size N = 500, which are shown to be robust to further increasing the population size.

What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology

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 significantly 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 neuroscientists and biologists, both computational and experimental, 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.

Adaptive Stochastic Resonance in Noisy Neurons Based on Mutual Information

Noise can improve how memoryless neurons process signals and maximize their throughput information. Such favorable use of noise is the so-called "stochastic resonance" or SR effect at the level of threshold neurons and continuous neurons. This paper presents theoretical and simulation evidence that 1) lone noisy threshold and continuous neurons exhibit the SR effect in terms of the mutual information between random input and output sequences, 2) a new statistically robust learning law can find this entropy-optimal noise level, and 3) the adaptive SR effect is robust against highly impulsive noise with infinite variance. Histograms estimate the relevant probability density functions at each learning iteration. A theorem shows that almost all noise probability density functions produce some SR effect in threshold neurons even if the noise is impulsive and has infinite variance. The optimal noise level in threshold neurons also behaves nonlinearly as the input signal amplitude increases. Simulations further show that the SR effect persists for several sigmoidal neurons and for Gaussian radial-basis-function neurons.

Cochlear nerve acoustic envelope response detection is improved by the addition of random-phased tonal stimuli

We test Lowenstein's dc bias hypothesis as an alternative mechanism for the phenomenon sometimes called 'stochastic resonance'. Probe stimuli consisting of paired phase-locked tones at frequencies f(1) and f(2) (where f(2)-f(1)=800 Hz, f(1)>4.5 kHz) and at equal intensity were used to generate synchronous 800 Hz cochlear nerve activity (envelope responses). When a background tone of the same intensity, with a frequency halfway between f(1) and f(2), is presented simultaneously with the probe stimulus, the envelope response amplitude typically decreases. Consistent with Lowenstein's hypothesis, however, when the intensities of the probe and background tone are near the detection threshold of the envelope response (approximately 0-20 dB sound pressure level), the simultaneous presence of the background tone often increases the amplitude of the envelope response. At these same intensity levels, when the background tone precedes the probe stimulus, it decreases the amplitude of the response to the probe stimulus. The effects of simultaneous presentation of the probe and the background tone are frequency-dependent, becoming less pronounced or reversing as the frequency of the background tone departs from those of the probe stimuli.

Neural ensemble coding and statistical periodicity: speculations on the operation of the mind's eye

Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would not be encoded by the periodicity, but rather by the spatio-temporal distributions of neural activity. Statistical periodicity is discussed in relation to the temporal binding hypothesis and to the occurrence of multistability in neural systems.

The effects of extrasynaptic substance P on nociceptive neurons in laminae I and II in rat lumbar spinal dorsal horn

Inflammation of the skin induces release and extrasynaptic spread of neuropeptides such as substance P mainly in spinal laminae I and II and causes changes in discharge properties of nociceptive neurons in spinal dorsal horn. To evaluate the role of extrasynaptic substance P we have superfused the spinal cord at recording segment with artificial cerebrospinal fluid or with substance P. A total of 102 multireceptive neurons responding to both noxious and innocuous skin stimulation were recorded in laminae I or II of lumbar spinal dorsal horn in pentobarbital anaesthetized rats. During superfusion with substance P (10 or 100 microM) significant increases of background activities (from 2.2 +/- 0.6 to 8.4 +/- 3.2 imp./s, mean +/- S.E.M.), enlargement of cutaneous receptive fields (from 359.9 +/- 60.4 to 465.5 +/- 77.3 mm2) and enhanced responses to mechanical (from 89.1 +/- 22.7 to 147.0 +/- 27.5 imp./5 s) but not thermal noxious skin stimuli were observed in the 22 neurons tested. Noxious heat-evoked responses and C-fibre-evoked responses were changed in both directions. In 50 other neurons, the coefficients of dispersion of interspike intervals, which is an indicator of burst-like discharges, were significantly reduced (from 60.4 +/- 5.5 to 52.7 +/- 5.3) after application of substance P. Substance P induced oscillations in background activities in 13 of 40 non-rhythmic neurons and depressed oscillations in 2 of 11 neurons. Cross-correlations of discharges of pairs simultaneously recorded neurons were flat (n = 4), or had a central peak (n = 19) or a central trough (n = 2) and were not changed qualitatively by extrasynaptic substance P. Thus, extrasynaptic substance P can modify not only discharge patterns in the spinal dorsal horn.

Oscillation and noise determine signal transduction in shark multimodal sensory cells

Oscillating membrane potentials that generate rhythmic impulse patterns are considered to be of particular significance for neuronal information processing. In contrast, noise is usually seen as a disturbance which limits the accuracy of information transfer. We show here, however, that noise in combination with intrinsic oscillations can provide neurons with particular encoding properties, a discovery we made when recording from single electro-sensory afferents of a fish. The temporal sequence of the impulse trains indicates oscillations that operate near the spike-triggering threshold. The oscillation frequency determines the basic rhythm of impulse generation, but whether or not an impulse is actually triggered essentially depends on superimposed noise. The probability of impulse generation can be altered considerably by minor modifications of oscillation baseline and amplitude, which may underlie the exquisite sensitivity of these receptors to thermal and electrical stimuli. Additionally, thermal, but not electrical, stimuli alter the oscillation frequency, allowing dual sensory messages to be conveyed in a single spike train. These findings demonstrate novel properties of sensory transduction which may be relevant for neuronal signalling in general.