Resonances and noise in a stochastic Hindmarsh-Rose model of thalamic neurons

Thalamic neurons exhibit subthreshold resonance when stimulated with small sine wave signals of varying frequency and stochastic resonance when noise is added to these signals. We study a stochastic Hindmarsh-Rose model using Monte-Carlo simulations to investigate how noise, in conjunction with subthreshold resonance, leads to a preferred frequency in the firing pattern. The resulting stochastic resonance (SR) exhibits a preferred firing frequency that is approximately exponential in its dependence on the noise amplitude. In similar experiments, frequency dependent SR is found in the reliability of detection of alpha-function inputs under noise, which are more realistic inputs for neurons. A mathematical analysis of the equations reveals that the frequency preference arises from the dynamics of the slow variable. Noise can then transfer the resonance over the firing threshold because of the proximity of the fast subsystem to a Hopf bifurcation point. Our results may have implications for the behavior of thalamic neurons in a network, with noise switching the membrane potential between different resonance modes.     

Slope-Based Stochastic Resonance: How Noise Enables Phasic Neurons to Encode Slow Signals

Fundamental properties of phasic firing neurons are usually characterized in a noise-free condition. In the absence of noise, phasic neurons exhibit Class 3 excitability, which is a lack of repetitive firing to steady current injections. For time-varying inputs, phasic neurons are band-pass filters or slope detectors, because they do not respond to inputs containing exclusively low frequencies or shallow slopes. However, we show that in noisy conditions, response properties of phasic neuron models are distinctly altered. Noise enables a phasic model to encode low-frequency inputs that are outside of the response range of the associated deterministic model. Interestingly, this seemingly stochastic-resonance (SR) like effect differs significantly from the classical SR behavior of spiking systems in both the signal-to-noise ratio and the temporal response pattern. Instead of being most sensitive to the peak of a subthreshold signal, as is typical in a classical SR system, phasic models are most sensitive to the signal''s rising and falling phases where the slopes are steep. This finding is consistent with the fact that there is not an absolute input threshold in terms of amplitude; rather, a response threshold is more properly defined as a stimulus slope/frequency. We call the encoding of low-frequency signals with noise by phasic models a slope-based SR, because noise can lower or diminish the slope threshold for ramp stimuli. We demonstrate here similar behaviors in three mechanistic models with Class 3 excitability in the presence of slow-varying noise and we suggest that the slope-based SR is a fundamental behavior associated with general phasic properties rather than with a particular biological mechanism.     

Stochastic resonance in the LIF models with input or threshold noise

In this paper, two stochastic versions of the LIF neural model are considered: one with the noise signal applied to the firing threshold, the other having it added to the input current. Then, adopting a discontinuous stepwise noise whose innovations are uncorrelated and gaussian distributed, the behaviours of the two models pertaining to the stochastic resonance (SR) are analysed and compared. Furthermore, it is shown that introducing a suitable time correlation into the noise signal brings us from the first model to the second one.     

The mechanism for stochastic resonance enhancement of mammalian auditory information processing

Background  

In a mammalian auditory system, when intrinsic noise is added to a subthreshold signal, not only can the resulting noisy signal be detected, but also the information carried by the signal can be completely recovered. Such a phenomenon is called stochastic resonance (SR). Current analysis of SR commonly employs the energies of the subthreshold signal and intrinsic noise. However, it is difficult to explain SR when the energy addition of the signal and noise is not enough to lift the subthreshold signal over the threshold. Therefore, information modulation has been hypothesized to play a role in some forms of SR in sensory systems. Information modulation, however, seems an unlikely mechanism for mammalian audition, since it requires significant a priori knowledge of the characteristics of the signal.     

Enhancement of information transmission of sub-threshold signals applied to distal positions of dendritic trees in hippocampal CA1 neuron models with stochastic resonance

Stochastic resonance (SR) has been shown to enhance the signal-to-noise ratio and detection of low level signals in neurons. It is not yet clear how this effect of SR plays an important role in the information processing of neural networks. The objective of this article is to test the hypothesis that information transmission can be enhanced with SR when sub-threshold signals are applied to distal positions of the dendrites of hippocampal CA1 neuron models. In the computer simulation, random sub-threshold signals were presented repeatedly to a distal position of the main apical branch, while the homogeneous Poisson shot noise was applied as a background noise to the mid-point of a basal dendrite in the CA1 neuron model consisting of the soma with one sodium, one calcium, and five potassium channels. From spike firing times recorded at the soma, the mutual information and information rate of the spike trains were estimated. The simulation results obtained showed a typical resonance curve of SR, and that as the activity (intensity) of sub-threshold signals increased, the maximum value of the information rate tended to increased and eventually SR disappeared. It is concluded that SR can play a key role in enhancing the information transmission of sub-threshold stimuli applied to distal positions on the dendritic trees.     

Frequency switching in a two-compartmental model of the dopaminergic neuron

Mid-brain dopaminergic (DA) neurons display two functionally distinct modes of electrical activity: low- and high-frequency firing. The high-frequency firing is linked to important behavioral events in vivo. However, it cannot be elicited by standard manipulations in vitro. We had suggested a two-compartmental model of the DA cell that united data on firing frequencies under different experimental conditions. We now analyze dynamics of this model. The analysis was possible due to introduction of timescale separation among variables. We formulate the requirements for low and high frequencies. We found that the modulation of the SK current gating controls the frequency rise under applied depolarization. This provides a new mechanism that limits the frequency in the control conditions and allows high-frequency responses to depolarization if the SK current gating is downregulated. The mechanism is based on changing Ca^2 + balance and can also be achieved by direct modulation of the balance. Interestingly, such changes do not affect the high-frequency oscillations under NMDA. Therefore, altering Ca^2 + balance allows combining the high-frequency response to NMDA activation with the inability of other treatments to effectively elevate the frequency. We conclude that manipulations affecting Ca^2 + balance are most effective in controlling the frequency range. This modeling prediction gives a clue to the mechanism of the high-frequency firing in the DA neuron in vivo and in vitro.     

Intrinsic gain modulation and adaptive neural coding

In many cases, the computation of a neural system can be reduced to a receptive field, or a set of linear filters, and a thresholding function, or gain curve, which determines the firing probability; this is known as a linear/nonlinear model. In some forms of sensory adaptation, these linear filters and gain curve adjust very rapidly to changes in the variance of a randomly varying driving input. An apparently similar but previously unrelated issue is the observation of gain control by background noise in cortical neurons: the slope of the firing rate versus current (f-I) curve changes with the variance of background random input. Here, we show a direct correspondence between these two observations by relating variance-dependent changes in the gain of f-I curves to characteristics of the changing empirical linear/nonlinear model obtained by sampling. In the case that the underlying system is fixed, we derive relationships relating the change of the gain with respect to both mean and variance with the receptive fields derived from reverse correlation on a white noise stimulus. Using two conductance-based model neurons that display distinct gain modulation properties through a simple change in parameters, we show that coding properties of both these models quantitatively satisfy the predicted relationships. Our results describe how both variance-dependent gain modulation and adaptive neural computation result from intrinsic nonlinearity.     

Ubiquitous crossmodal Stochastic Resonance in humans: auditory noise facilitates tactile, visual and proprioceptive sensations

Background

Stochastic resonance is a nonlinear phenomenon whereby the addition of noise can improve the detection of weak stimuli. An optimal amount of added noise results in the maximum enhancement, whereas further increases in noise intensity only degrade detection or information content. The phenomenon does not occur in linear systems, where the addition of noise to either the system or the stimulus only degrades the signal quality. Stochastic Resonance (SR) has been extensively studied in different physical systems. It has been extended to human sensory systems where it can be classified as unimodal, central, behavioral and recently crossmodal. However what has not been explored is the extension of this crossmodal SR in humans. For instance, if under the same auditory noise conditions the crossmodal SR persists among different sensory systems.

Methodology/Principal Findings

Using physiological and psychophysical techniques we demonstrate that the same auditory noise can enhance the sensitivity of tactile, visual and propioceptive system responses to weak signals. Specifically, we show that the effective auditory noise significantly increased tactile sensations of the finger, decreased luminance and contrast visual thresholds and significantly changed EMG recordings of the leg muscles during posture maintenance.

Conclusions/Significance

We conclude that crossmodal SR is a ubiquitous phenomenon in humans that can be interpreted within an energy and frequency model of multisensory neurons spontaneous activity. Initially the energy and frequency content of the multisensory neurons'' activity (supplied by the weak signals) is not enough to be detected but when the auditory noise enters the brain, it generates a general activation among multisensory neurons of different regions, modifying their original activity. The result is an integrated activation that promotes sensitivity transitions and the signals are then perceived. A physiologically plausible model for crossmodal stochastic resonance is presented.     

线性整合放电模型的相干共振

研究了神经递质以随机点序列释放和电压门控离子通道噪声共同作用下,线性整合放电模型的相干共振现象。基于分形布朗运动和改进的欧拉方法,得到了神经元膜电压分布和神经元放电峰峰间隔的信噪比。结果表明,神经元放电的峰峰间隔是神经递质的达到强度、离子通道噪声强度的非单调函数。适当的神经递质到达强度和离子通道噪声强度使峰峰间隔的信噪比出现最大值,即出现相干共振现象。     

Inhibitory synchrony as a mechanism for attentional gain modulation

Recordings from area V4 of monkeys have revealed that when the focus of attention is on a visual stimulus within the receptive field of a cortical neuron, two distinct changes can occur: The firing rate of the neuron can change and there can be an increase in the coherence between spikes and the local field potential (LFP) in the gamma-frequency range (30-50 Hz). The hypothesis explored here is that these observed effects of attention could be a consequence of changes in the synchrony of local interneuron networks. We performed computer simulations of a Hodgkin-Huxley type neuron driven by a constant depolarizing current, I, representing visual stimulation and a modulatory inhibitory input representing the effects of attention via local interneuron networks. We observed that the neuron's firing rate and the coherence of its output spike train with the synaptic inputs was modulated by the degree of synchrony of the inhibitory inputs. When inhibitory synchrony increased, the coherence of spiking model neurons with the synaptic input increased, but the firing rate either increased or remained the same. The mean number of synchronous inhibitory inputs was a key determinant of the shape of the firing rate versus current (f-I) curves. For a large number of inhibitory inputs (approximately 50), the f-I curve saturated for large I and an increase in input synchrony resulted in a shift of sensitivity-the model neuron responded to weaker inputs I. For a small number (approximately 10), the f-I curves were non-saturating and an increase in input synchrony led to an increase in the gain of the response-the firing rate in response to the same input was multiplied by an approximately constant factor. The firing rate modulation with inhibitory synchrony was highest when the input network oscillated in the gamma frequency range. Thus, the observed changes in firing rate and coherence of neurons in the visual cortex could be controlled by top-down inputs that regulated the coherence in the activity of a local inhibitory network discharging at gamma frequencies.     

Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency—a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in “hot spots” of dendrites, spines or axons.     

Contrast enhancement: a physiological effect of striatal dopamine?

Dopamine functions as an important neuromodulator in the dorsal striatum and ventral striatum/nucleus accumbens. Evidence is accumulating for the idea that striatal neurons compete with each other for control over the animals motor resources, and that dopamine plays an important modulatory role that allows a particular subset of neurons, encoding a specific behavior, to predominate in this competition. One means by which dopamine could facilitate selection among competing neurons is to enhance the contrast between stronger and weaker excitations (or to increase the signal to noise ratio among neurons, where the firing of the most excited neurons is assumed to transmit signal and the firing of the least excited to transmit noise). Here, we review the electrophysiological evidence for this hypothesis and discuss potential cellular mechanisms by which dopamine-mediated contrast enhancement could occur.This work was supported by funds provided by the State of California for medical research on alcohol and substance abuse through the University of California, San Francisco, and by NIH grant DA15676 to GOH.     

Coding of envelope modulation in the auditory nerve and anteroventral cochlear nucleus.

We have investigated responses of the auditory nerve fibres (ANFS) and anteroventral cochlear nucleus (AVCN) units to narrowband 'single-formant' stimuli (SFSS). We found that low and medium spontaneous rate (SR) ANFS maintain greater amplitude modulation (AM) in their responses at high sound levels than do high SR units when sound level is considered in dB SPL. However, this partitioning of high and low SR units disappears if sound level is considered in dB relative to unit threshold. Stimuli with carrier frequencies away from unit best frequency (BF) were found to generate higher AM in responses at high sound levels than that observed even in most low and medium SR units for stimuli with carrier frequencies near BF. AVCN units were shown to have increased modulation depth in their responses when compared with high SR ANFS with similar BFS and to have increased or comparable modulation depth when compared with low SR ANFS. At sound levels where AM almost completely disappears in high SR ANFS, most AVCN units we studied still show significant AM in their responses. Using a dendritic model, we investigated possible mechanisms of enhanced AM in AVCN units, including the convergence of inputs from different SR groups of ANFS and a postsynaptic threshold mechanism in the soma.     

Modeling electromagnetic fields detectability in a HH-like neuronal system: stochastic resonance and window behavior

Noise has already been shown to play a constructive role in neuronal processing and reliability, according to stochastic resonance (SR). Here another issue is addressed, concerning noise role in the detectability of an exogenous signal, here representing an electromagnetic (EM) field. A Hodgkin–Huxley like neuronal model describing a myelinated nerve fiber is proposed and validated, excited with a suprathreshold stimulation. EM field is introduced as an additive voltage input and its detectability in neuronal response is evaluated in terms of the output signal-to-noise ratio. Noise intensities maximizing spiking activity coherence with the exogenous EM signal are clearly shown, indicating a stochastic resonant behavior, strictly connected to the model frequency sensitivity. In this study SR exhibits a window of occurrence in the values of field frequency and intensity, which is a kind of effect long reported in bioelectromagnetic experimental studies. The spatial distribution of the modeled structure also allows to investigate possible effects on action potentials saltatory propagation, which results to be reliable and robust over the presence of an exogenous EM field and biological noise. The proposed approach can be seen as assessing biophysical bases of medical applications funded on electric and magnetic stimulation where the role of noise as a cooperative factor has recently gained growing attention. This work investigates the role of noise as a cooperative factor for the detection of an exogenous electromagnetic field in a compartimental model of a myelinated nerve fiber. The occurrence of stochastic resonance is discussed in relation to neuronal frequency sensitivity.     

The Sign Rule and Beyond: Boundary Effects,Flexibility, and Noise Correlations in Neural Population Codes

Over repeat presentations of the same stimulus, sensory neurons show variable responses. This “noise” is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population''s ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem – neural tuning curves, etc. – held fixed. This work yields unifying insights into the role of noise correlations. These are summarized in the form of theorems, and illustrated with numerical examples involving neurons with diverse tuning curves. Our main contributions are as follows. (1) We generalize previous results to prove a sign rule (SR) — if noise correlations between pairs of neurons have opposite signs vs. their signal correlations, then coding performance will improve compared to the independent case. This holds for three different metrics of coding performance, and for arbitrary tuning curves and levels of heterogeneity. This generality is true for our other results as well. (2) As also pointed out in the literature, the SR does not provide a necessary condition for good coding. We show that a diverse set of correlation structures can improve coding. Many of these violate the SR, as do experimentally observed correlations. There is structure to this diversity: we prove that the optimal correlation structures must lie on boundaries of the possible set of noise correlations. (3) We provide a novel set of necessary and sufficient conditions, under which the coding performance (in the presence of noise) will be as good as it would be if there were no noise present at all.     

Modulation of motor unit firing rates during a complex sinusoidal force task in young and older adults.

This study compared motor unit rate coding and muscular force control in the first dorsal interosseous muscle of older (n = 11, mean 72.3 yr) and young (n = 12, mean 18.7 yr) adults. Rate coding during a sinusoidal isometric force-matching task was evaluated using spectral analysis of the time-varying changes in firing rate. The task required force modulations to match a trajectory comprising the sum of 0.15- and 0.45-Hz sine waves. Based on the amplitude of spectral peaks at 0.15 and 0.45 Hz, the amplitude of force modulation was similar in young and older adults at both frequencies (F = 1.9, P = 0.17). Force modulation gain (FMG) was computed as the ratio of the amplitude of force modulation to the amplitude of firing rate modulation. To account for rate coding differences related to the properties of the motoneuron, recruitment threshold force was used as a covariate in age-group comparisons. At both task frequencies, firing rate was modulated with less amplitude (F = 0 14, P < 0.001) and FMG was greater (F = 0 27, P < 0.001) in the older adults. In its transformation of neural input to mechanical output, muscle is known to act as a low-pass filter. Compared with modulation at 0.15 Hz, less change in force per change in firing rate at 0.45 Hz (lower FMG; F = 0 67, P < 0.001), independent of age group, is consistent with this filtering effect. Our conclusion is that there is a reduced amplitude of firing rate modulation in older adults.     

Phase-Lifetime Spectroscopy of Photocycle Processes: Kinetic Analysis of Amplitude Dispersion Curves

Phase-lifetime spectroscopy has been recently used to obtain kinetic information on biological photocycles. A simple, general method is presented for deriving the amplitude response function for light-driven processes. These amplitude response functions may be used to analyze the experimental data obtained when driving the photosystem with a mechanically chopped, actinic light source. This analysis allows a comparison of kinetic parameters obtained from modulation methods with those obtained by flash techniques. Typically the experimental data consist of the signal amplitude measured at several chopping frequencies of the actinic light. These amplitude dispersion curves will be dependent on the harmonic sensitivity of the phase-sensitive detector used to measure the signal. This harmonic sensitivity is taken into account by performing a Fourier decomposition on the amplitude response function of the system and weighting each harmonic in a fashion appropriate for the specific amplifier under consideration. The resulting response function obtained for two commonly used amplifiers is derived. In addition to simple photocycles, the analysis of photocycle-coupled processes is also considered. This second relaxation process, which is coupled to a photocycle process, could represent the chemiosmotic coupling of a light-driven ion pump to a second ion transport protein. Conditions are established in which the kinetics of the second process can be resolved from the photocycle process.     

Spontaneous frequency of a developmental mutant in Volvox

Two types of mutants, those resistant to the base analog 5-bromo-2′-deoxyuridine (BrdU) and somatic regenerator (SR) mutants, have been analyzed in Volvox carteri. In somatic regenerator mutants, the somatic cells which are normally terminally differentiated dedifferentiate and regenerate gonidia [Sessoms, A., and Huskey, R. J. (1973). Proc. Nat. Acad. Sci. USA70, 1335–1338; Starr, R. C. (1970). Develop. Biol. Suppl.4, 59–100]. The SR phenotype allows recovery of SR mutations arising in somatic cells, since such somatic cells would regenerate gonidia and give rise to mutant clones. Mutants of any phenotype other than SR can only be recovered if the mutation first appears in a gonidium. Since the somatic cells are 100-fold more numerous than reproductive cells (gonidia), we have determined the spontaneous frequency of both somatic regenerator mutants and mutations to BrdU resistance in order to determine if the SR mutation exerts its effect in the gonidium or in the somatic cell. The two frequencies were found to be nearly identical, suggesting that the SR mutation must first appear in a gonidium in order to be expressed.     

Random currents through nerve membranes

The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a onedimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits “1/f ^3/2 noise”. Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.