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.     

双层Hodgkin-Huxley神经元网络中的随机共振

随机共振是一种非零噪声优化系统响应的现象。运用信噪比的评价方式,研究单个Hodgkin-Huxley神经元及其所构建的双层神经元网络中的随机共振,来模拟生物感觉系统中检测微弱信号的随机共振现象。结果表明,单个神经元在阈值下存在噪声优化系统检测性能的随机共振现象,但是最优的噪声强度却随外部信号性质的改变而变化;双层神经元网络不但可以在固定的噪声强度上对一定幅度范围内的阈下信号进行优化检测,而且噪声的存在并没有降低网络对阈上信号的检测能力。     

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.     

Noise-Induced Coherence and Network Oscillations in a Reduced Bursting Model

The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons. PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19     

Electrical Resonance in the θ Frequency Range in Olfactory Amygdala Neurons

The cortical amygdala receives direct olfactory inputs and is thought to participate in processing and learning of biologically relevant olfactory cues. As for other brain structures implicated in learning, the principal neurons of the anterior cortical nucleus (ACo) exhibit intrinsic subthreshold membrane potential oscillations in the θ-frequency range. Here we show that nearly 50% of ACo layer II neurons also display electrical resonance, consisting of selective responsiveness to stimuli of a preferential frequency (2–6 Hz). Their impedance profile resembles an electrical band-pass filter with a peak at the preferred frequency, in contrast to the low-pass filter properties of other neurons. Most ACo resonant neurons displayed frequency preference along the whole subthreshold voltage range. We used pharmacological tools to identify the voltage-dependent conductances implicated in resonance. A hyperpolarization-activated cationic current depending on HCN channels underlies resonance at resting and hyperpolarized potentials; notably, this current also participates in resonance at depolarized subthreshold voltages. KV7/KCNQ K⁺ channels also contribute to resonant behavior at depolarized potentials, but not in all resonant cells. Moreover, resonance was strongly attenuated after blockade of voltage-dependent persistent Na⁺ channels, suggesting an amplifying role. Remarkably, resonant neurons presented a higher firing probability for stimuli of the preferred frequency. To fully understand the mechanisms underlying resonance in these neurons, we developed a comprehensive conductance-based model including the aforementioned and leak conductances, as well as Hodgkin and Huxley-type channels. The model reproduces the resonant impedance profile and our pharmacological results, allowing a quantitative evaluation of the contribution of each conductance to resonance. It also replicates selective spiking at the resonant frequency and allows a prediction of the temperature-dependent shift in resonance frequency. Our results provide a complete characterization of the resonant behavior of olfactory amygdala neurons and shed light on a putative mechanism for network activity coordination in the intact brain.     

Modeling of Nonlinear Chemical Reaction Systems and Two-Parameter Stochastic Resonance

The idea of stochastic resonance (SR) is extended to two-parameter dynamical systems based on the Oregonator model of the Belousov-Zhabotinsky (BZ) reaction. The first case presents the photosensitivity of the reaction, and light flux and a flow rate are the two control parameters. The second case presents the effect of temperature on the oscillatory behaviors, and temperature and a flow rate are the control parameters. Stochastic resonance is demonstrated in the first case in which a signal and noise are applied to the different inputs, respectively. The scenario and novel aspects of SR in two-parameter systems are discussed, and the possibility of the analogous SR in biological systems is also pointed out.     

Do neocortical pyramidal neurons display stochastic resonance?

Neocortical pyramidal neurons in vivo are subject to an intense synaptic background activity that has a significant impact on various electrophysiological properties and dendritic integration. Using detailed biophysical models of a morphologically reconstructed neocortical pyramidal neuron, in which synaptic background activity was simulated according to recent measurements in cat parietal cortex in vivo, we show that the responsiveness of the cell to additional periodic subthreshold stimuli can be significantly enhanced through mechanisms similar to stochastic resonance. We compare several paradigms leading to stochastic resonance-like behavior, such as varying the strength or the correlation in the background activity. A new type of resonance-like behavior was obtained when the correlation was varied, in which case the responsiveness is sensitive to the statistics rather than the strength of the noise. We suggest that this type of resonance may be relevant to information processing in the cerebral cortex.     

Ghost resonance in a pool of heterogeneous neurons

We numerically study the subharmonic response of a heterogeneous pool of neurons to a pair of independent inputs. The neurons are stimulated with periodic pulse trains of frequencies f(1)=2 Hz and f(2)=3 Hz, and with inharmonic pulses whose frequencies f(1) and f(2) are equally shifted an amount Delta f. When both inputs are subthreshold, we find that the neurons respond at a frequency equal to f(2)-f(1) in the harmonic situation (Delta f=0), that increases linearly with Delta f in the inharmonic case. Thus the neurons detect a frequency not present in the input; this effect is termed "ghost resonance". When one of the inputs is slightly suprathreshold the ghost resonance persists, but responses related with the frequency of the suprathreshold input also emerge. This behavior must be taken into account in experimental studies of signal integration and coincidence detection by neuronal pools.     

Exploring spike transfer through the thalamus using hybrid artificial-biological neuronal networks

We use dynamic clamp to construct "hybrid" thalamic circuits by connecting a biological neuron in situ to silicon- or software-generated "neurons" through artificial synapses. The purpose is to explore cellular sensory gating mechanisms that regulate the transfer efficiency of signals during different sleep-wake states. Hybrid technology is applied in vitro to different paradigms such as: (1) simulating interactions between biological thalamocortical neurons, artificial reticular thalamic inhibitory interneurons and a simulated sensory input, (2) grafting an artificial sensory input to a wholly biological thalamic network that generates spontaneous sleep-like oscillations, (3) injecting in thalamocortical neurons a background synaptic bombardment mimicking the activity of corticothalamic inputs. We show that the graded control of the strength of intrathalamic inhibition, combined with the membrane polarization and the fluctuating synaptic noise in thalamocortical neurons, is able to govern functional shifts between different input/output transmission states of the thalamic gate.     

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.     

Comparison of Coding Capabilities of Type I and Type II Neurons

We consider the dependence of information transfer by neurons on the Type I vs. Type II classification of their dynamics. Our computational study is based on Type I and II implementations of the Morris-Lecar model. It mainly concerns neurons, such as those in the auditory or electrosensory system, which encode band-limited amplitude modulations of a periodic carrier signal, and which fire at random cycles yet preferred phases of this carrier. We first show that the Morris-Lecar model with additive broadband noise ("synaptic noise") can exhibit such firing patterns with either Type I or II dynamics, with or without amplitude modulations of the carrier. We then compare the encoding of band-limited random amplitude modulations for both dynamical types. The comparison relies on a parameter calibration that closely matches firing rates for both models across a range of parameters. In the absence of synaptic noise, Type I performs slightly better than Type II, and its performance is optimal for perithreshold signals. However, Type II performs well over a slightly larger range of inputs, and this range lies mostly in the subthreshold region. Further, Type II performs marginally better than Type I when synaptic noise, which yields more realistic baseline firing patterns, is present in both models. These results are discussed in terms of the tuning and phase locking properties of the models with deterministic and stochastic inputs.     

UP States Protect Ongoing Cortical Activity from Thalamic Inputs

Cortical neurons in vitro and in vivo fluctuate spontaneously between two stable membrane potentials: a depolarized UP state and a hyperpolarized DOWN state. UP states temporally correspond with multineuronal firing sequences which may be important for information processing. To examine how thalamic inputs interact with ongoing cortical UP state activity, we used calcium imaging and targeted whole-cell recordings of activated neurons in thalamocortical slices of mouse somatosensory cortex. Whereas thalamic stimulation during DOWN states generated multineuronal, synchronized UP states, identical stimulation during UP states had no effect on the subthreshold membrane dynamics of the vast majority of cells or on ongoing multineuronal temporal patterns. Both thalamocortical and corticocortical PSPs were significantly reduced and neuronal input resistance was significantly decreased during cortical UP states – mechanistically consistent with UP state insensitivity. Our results demonstrate that cortical dynamics during UP states are insensitive to thalamic inputs.     

Improved Detection of Magnetic Signals by a MEMS Sensor Using Stochastic Resonance

We introduce the behavior of the electrical output response of a magnetic field sensor based on microelectromechanical systems (MEMS) technology under different levels of controlled magnetic noise. We explored whether a particular level of magnetic noise applied on the vicinity of the MEMS sensor can improve the detection of subthreshold magnetic fields. We examined the increase in the signal-to-noise ratio (SNR) of such detected magnetic fields as a function of the magnetic noise intensity. The data disclosed an inverted U-like graph between the SNR and the applied magnetic noise. This finding shows that the application of an intermediate level of noise in the environment of a MEMS magnetic field sensor improves its detection capability of subthreshold signals via the stochastic resonance phenomenon.     

Spiking resonances in models with the same slow resonant and fast amplifying currents but different subthreshold dynamic properties

The generation of spiking resonances in neurons (preferred spiking responses to oscillatory inputs) requires the interplay of the intrinsic ionic currents that operate at the subthreshold voltage level and the spiking mechanisms. Combinations of the same types of ionic currents in different parameter regimes may give rise to different types of nonlinearities in the voltage equation (e.g., parabolic- and cubic-like), generating subthreshold (membrane potential) oscillations patterns with different properties. These nonlinearities are not apparent in the model equations, but can be uncovered by plotting the voltage nullclines in the phase-plane diagram. We investigate the spiking resonant properties of conductance-based models that are biophysically equivalent at the subthreshold level (same ionic currents), but dynamically different (parabolic- and cubic-like voltage nullclines). As a case study we consider a model having a persistent sodium and a hyperpolarization-activated (h-) currents, which exhibits subthreshold resonance in the theta frequency band. We unfold the concept of spiking resonance into evoked and output spiking resonance. The former focuses on the input frequencies that are able to generate spikes, while the latter focuses on the output spiking frequencies regardless of the input frequency that generated these spikes. A cell can exhibit one or both types of resonances. We also measure spiking phasonance, which is an extension of subthreshold phasonance (zero-phase-shift response to oscillatory inputs) to the spiking regime. The subthreshold resonant properties of both types of models are communicated to the spiking regime for low enough input amplitudes as the voltage response for the subthreshold resonant frequency band raises above threshold. For higher input amplitudes evoked spiking resonance is no longer present in these models, but output spiking resonance is present primarily in the parabolic-like model due to a cycle skipping mechanism (involving mixed-mode oscillations), while the cubic-like model shows a better 1:1 entrainment. We use dynamical systems tools to explain the underlying mechanisms and the mechanistic differences between the resonance types. Our results demonstrate that the effective time scales that operate at the subthreshold regime to generate intrinsic subthreshold oscillations, mixed-mode oscillations and subthreshold resonance do not necessarily determine the existence of a preferred spiking response to oscillatory inputs in the same frequency band. The results discussed in this paper highlight both the complexity of the suprathreshold responses to oscillatory inputs in neurons having resonant and amplifying currents with different time scales and the fact that the identity of the participating ionic currents is not enough to predict the resulting patterns, but additional dynamic information, captured by the geometric properties of the phase-space diagram, is needed.     

Long-term potentiation in rat hippocampal neurons is accompanied by spatially widespread changes in intrinsic oscillatory dynamics and excitability

Oscillations in neural activity are a prominent feature of many brain states. Individual hippocampal neurons exhibit intrinsic membrane potential oscillations and intrinsic resonance in the theta frequency range. We found that the subthreshold resonance frequency of CA1 pyramidal neurons was location dependent, varying more than 3-fold between the soma and the distal dendrites. Furthermore, activity- and NMDA-receptor-dependent long-term plasticity increased this resonance frequency through changes in h channel properties. The increase in resonance frequency and an associated reduction in excitability were nearly identical in the soma and the first 300 mum of the apical dendrites. These spatially widespread changes accompanying long-term synaptic potentiation also reduced the neuron's ability to elicit spikes evoked through a nonpotentiated synaptic pathway. Our results suggest that the frequency response of these neurons depends on the dendritic location of their inputs and that activity can regulate their response dynamics within an oscillating neural network.     

Resonance and selective communication via bursts in neurons having subthreshold oscillations

Revealing the role of bursts of action potentials is an important step toward understanding how the neurons communicate. The dominant point of view is that bursts are needed to increase the reliability of communication between neurons [Trends Neurosci. 20 (1997) 38]. In this paper we present an alternative but complementary hypothesis. We consider the effect of a short burst on a model postsynaptic cell having damped oscillation of its membrane potential. The oscillation frequency (eigenfrequency) plays a crucial role. Due to the subthreshold membrane resonance and frequency preference, the responses (i.e. voltage oscillations) of such a cell are amplified when the intra-burst frequency equals the cell's eigenfrequency. Responses are negligible, however, if the intra-burst frequency is twice the eigenfrequency. Thus, the same burst could be effective for one cell and ineffective for another depending on their eigenfrequencies. This theoretical observation suggests that, in addition to coping with unreliable synapses, bursts of action potentials may provide effective mechanisms for selective communication between neurons.     

On the role of subthreshold dynamics in neuronal signaling

The role of subthreshold dynamics in neuronal signaling is examined using periodic pulse train stimulation of the Fitzhugh-Nagumo (FN) model of nerve membrane excitability and results from the squid giant axon as an experimental data base. For a broad range of stimulus conditions the first pulse in a pulse train elicited an action potential, whereas all subsequent pulses elicited subthreshold responses, both in the axon and in the FN model. These results are not well described by the Hodgkin and Huxley 1952 model. Various different patterns of subthreshold responses, including chaotic dynamics, can be observed in both systems-the FN model and the axon-depending upon stimulus conditions. For some conditions action potentials are occasionally interspersed among the subthreshold events with randomly occurring interspike intervals. The randomness is directly attributable to the underlying subthreshold chaos-deterministic chaos-rather than to a stochastic noise source. We conclude that this mechanism may contribute to multimodal interspike interval histograms which have been observed from individual neurons throughout the nervous system.     

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.     

Information coding by ensembles of resonant neurons

In the present paper, we propose a novel neural procedure for signal processing and coding based on the subthreshold oscillations and resonance of the neural membrane potential that could be used by real neurons to perform frequency spectra analysis and information coding of incoming signals. Taking into account the biophysical properties of the neural membranes, we note that the subthreshold resonant behaviour they exhibit can be used to analyse incoming signals and represent them in the frequency domain. We study the reliability of the representation of signals depending on the biophysical parameters of the neurons, the fault-tolerance of this coding scheme and its robustness against noise and in the presence of spikes. The principal characteristics of our system are the use of the physical phenomenon of neural resonance (rarely considered in the literature for signal coding); it fits well with the biophysical parameters of most neurons that exhibit subthreshold oscillations; it is compatible with experimental data; and it can be easily integrated in a more general model of information processing and coding that includes communication between neurons based on spikes.     

Noise improves transfer of near-threshold, phase-locked activity of the cochlear nerve: evidence for stochastic resonance?

 Stochastic resonance can be described as improved detection of weak periodic stimuli by a dynamic nonlinear system, resulting from the simultaneous presentation of a restricted dynamic range of low-intensity noise. This property has been reported in simple physical and biological activities. The present study describes data consistent with the interpretation that stochastic resonance can be observed in the response of cochlear neurons. These experiments utilized low levels (−5 to 25 dB SPL) of stimuli and noise (5 to 30 dB SPL). Stimuli consisted of simultaneously presented 8 kHz (F ₁) and 8.8 kHz (F ₂) tone bursts, which generated an 800 Hz F ₂–F ₁ cochlear nerve envelope ensemble response in the gerbil. The mean response threshold was approximately −3 dB SPL. Simultaneous presentation of a low-intensity wideband noise increased the amplitude of this response. This was observed with tonal stimuli having intensities of 0–5 dB SPL; responses to stimulus levels >10 dB were attenuated by noise. Response amplitude was increased by noise levels of 10–15 dB; the amplitude was unaffected by lower levels of noise, and decreased in the presence of higher noise levels. These properties are compatible with those of stochastic resonance. Accepted: 11 March 1999