Detection of subthreshold pulses in neurons with channel noise

The Promise of Stochastic Resonance in Falls Prevention

Multisensory integration is essential for maintenance of motor and cognitive abilities, thereby ensuring normal function and personal autonomy. Balance control is challenged during senescence or in motor disorders, leading to potential falls. Increased uncertainty in sensory signals is caused by a number of factors including noise, defined as a random and persistent disturbance that reduces the clarity of information. Counter-intuitively, noise can be beneficial in some conditions. Stochastic resonance is a mechanism whereby a particular level of noise actually enhances the response of non-linear systems to weak sensory signals. Here we review the effects of stochastic resonance on sensory modalities and systems directly involved in balance control. We highlight its potential for improving sensorimotor performance as well as cognitive and autonomic functions. These promising results demonstrate that stochastic resonance represents a flexible and non-invasive technique that can be applied to different modalities simultaneously. Finally we point out its benefits for a variety of scenarios including in ambulant elderly, skilled movements, sports and to patients with sensorimotor or autonomic dysfunctions.

Efficient Coding and Energy Efficiency Are Promoted by Balanced Excitatory and Inhibitory Synaptic Currents in Neuronal Network

Selective pressure may drive neural systems to process as much information as possible with the lowest energy cost. Recent experiment evidence revealed that the ratio between synaptic excitation and inhibition (E/I) in local cortex is generally maintained at a certain value which may influence the efficiency of energy consumption and information transmission of neural networks. To understand this issue deeply, we constructed a typical recurrent Hodgkin-Huxley network model and studied the general principles that governs the relationship among the E/I synaptic current ratio, the energy cost and total amount of information transmission. We observed in such a network that there exists an optimal E/I synaptic current ratio in the network by which the information transmission achieves the maximum with relatively low energy cost. The coding energy efficiency which is defined as the mutual information divided by the energy cost, achieved the maximum with the balanced synaptic current. Although background noise degrades information transmission and imposes an additional energy cost, we find an optimal noise intensity that yields the largest information transmission and energy efficiency at this optimal E/I synaptic transmission ratio. The maximization of energy efficiency also requires a certain part of energy cost associated with spontaneous spiking and synaptic activities. We further proved this finding with analytical solution based on the response function of bistable neurons, and demonstrated that optimal net synaptic currents are capable of maximizing both the mutual information and energy efficiency. These results revealed that the development of E/I synaptic current balance could lead a cortical network to operate at a highly efficient information transmission rate at a relatively low energy cost. The generality of neuronal models and the recurrent network configuration used here suggest that the existence of an optimal E/I cell ratio for highly efficient energy costs and information maximization is a potential principle for cortical circuit networks.

Frequency-difference-dependent stochastic resonance in neural systems

Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural systems to the weak envelope modulation signal, which is superimposed by two periodic signals with different frequencies. We show that stochastic resonance occurs at the beat frequency in neural systems at the single-neuron as well as the population level. The performance of this frequency-difference-dependent stochastic resonance is influenced by both the beat frequency and the two forcing frequencies. Compared to a single neuron, a population of neurons is more efficient in detecting the information carried by the weak envelope modulation signal at the beat frequency. Furthermore, an appropriate fine-tuning of the excitation-inhibition balance can further optimize the response of a neural ensemble to the superimposed signal. Our results thus introduce and provide insights into the generation and modulation mechanism of the frequency-difference-dependent stochastic resonance in neural systems.

Energy-efficient population coding constrains network size of a neuronal array system

We consider the open issue of how the energy efficiency of the neural information transmission process, in a general neuronal array, constrains the network size, and how well this network size ensures the reliable transmission of neural information in a noisy environment. By direct mathematical analysis, we have obtained general solutions proving that there exists an optimal number of neurons in the network, where the average coding energy cost (defined as energy consumption divided by mutual information) per neuron passes through a global minimum for both subthreshold and superthreshold signals. With increases in background noise intensity, the optimal neuronal number decreases for subthreshold signals and increases for suprathreshold signals. The existence of an optimal number of neurons in an array network reveals a general rule for population coding that states that the neuronal number should be large enough to ensure reliable information transmission that is robust to the noisy environment but small enough to minimize energy cost.

Effect of autaptic activity on the response of a Hodgkin-Huxley neuron

An autapse is a special synapse that connects a neuron to itself. In this study, we investigated the effect of an autapse on the responses of a Hodgkin-Huxley neuron to different forms of external stimuli. When the neuron was subjected to a DC stimulus, the firing frequencies and the interspike interval distributions of the output spike trains showed periodic behaviors as the autaptic delay time increased. When the input was a synaptic pulse-like train with random interspike intervals, we observed low-pass and band-pass filtering behaviors. Moreover, the region over which the output ISIs are distributed and the mean firing frequency display periodic behaviors with increasing autaptic delay time. When specific autaptic parameters were chosen, most of the input ISIs could be filtered, and the response spike trains were nearly regular, even with a highly random input. The background mechanism of these observed dynamics has been analyzed based on the phase response curve method. We also found that the information entropy of the output spike train could be modified by the autapse. These results also suggest that the autapse can serve as a regulator of information response in the nervous system.

Optimal size of stochastic Hodgkin-Huxley neuronal systems for maximal energy efficiency in coding pulse signals

The generation and conduction of action potentials (APs) represents a fundamental means of communication in the nervous system and is a metabolically expensive process. In this paper, we investigate the energy efficiency of neural systems in transferring pulse signals with APs. By analytically solving a bistable neuron model that mimics the AP generation with a particle crossing the barrier of a double well, we find the optimal number of ion channels that maximizes the energy efficiency of a neuron. We also investigate the energy efficiency of a neuron population in which the input pulse signals are represented with synchronized spikes and read out with a downstream coincidence detector neuron. We find an optimal number of neurons in neuron population, as well as the number of ion channels in each neuron that maximizes the energy efficiency. The energy efficiency also depends on the characters of the input signals, e.g., the pulse strength and the interpulse intervals. These results are confirmed by computer simulation of the stochastic Hodgkin-Huxley model with a detailed description of the ion channel random gating. We argue that the tradeoff between signal transmission reliability and energy cost may influence the size of the neural systems when energy use is constrained.

The role of coincidence-detector neurons in the reliability and precision of subthreshold signal detection in noise

Subthreshold signal detection is an important task for animal survival in complex environments, where noise increases both the external signal response and the spontaneous spiking of neurons. The mechanism by which neurons process the coding of signals is not well understood. Here, we propose that coincidence detection, one of the ways to describe the functionality of a single neural cell, can improve the reliability and the precision of signal detection through detection of presynaptic input synchrony. Using a simplified neuronal network model composed of dozens of integrate-and-fire neurons and a single coincidence-detector neuron, we show how the network reads out the subthreshold noisy signals reliably and precisely. We find suitable pairing parameters, the threshold and the detection time window of the coincidence-detector neuron, that optimize the precision and reliability of the neuron. Furthermore, it is observed that the refractory period induces an oscillation in the spontaneous firing, but the neuron can inhibit this activity and improve the reliability and precision further. In the case of intermediate intrinsic states of the input neuron, the network responds to the input more efficiently. These results present the critical link between spiking synchrony and noisy signal transfer, which is utilized in coincidence detection, resulting in enhancement of temporally sensitive coding scheme.

Response of Morris-Lecar neurons to various stimuli

We studied the responses of three classes of Morris-Lecar neurons to sinusoidal inputs and synaptic pulselike stimuli with deterministic and random interspike intervals (ISIs). It was found that the responses of the output frequency of class 1 and 2 neurons showed similar evolution properties by varying input amplitudes and frequencies, whereas class 3 neuron exhibited substantially different properties. Specifically, class 1 and 2 neurons display complicated phase locking (p : q, p > q, denoting output action potentials per input spikes) in low-frequency sinusoidal input area when the input amplitude is above their threshold, but a class 3 neuron does not fire action potentials in this area even if the amplitude is much higher. In the case of the deterministic ISI synaptic injection, all the three classes of neurons oscillate spikes with an arbitrary small frequency. When increasing the input frequency (both sinusoidal and deterministic ISI synaptic inputs), all neurons display 1 : 1 phase locking, whereas the response frequency decreases even fall to zero in the high-frequency input area. When the random ISI synaptic pulselike stimuli are injected into the neurons, one can clearly see the low-pass filter behaviors from the return map. The output ISI distribution depends on the mean ISI of input train as well as the ISI variation. Such different responses of three classes of neurons result from their distinct dynamical mechanisms of action potential initiation. It was suggested that the intrinsic dynamical cellular properties are very important to neuron information processing.

Intrinsic variability of latency to first-spike

The assessment of the variability of neuronal spike timing is fundamental to gain understanding of latency coding. Based on recent mathematical results, we investigate theoretically the impact of channel noise on latency variability. For large numbers of ion channels, we derive the asymptotic distribution of latency, together with an explicit expression for its variance. Consequences in terms of information processing are studied with Fisher information in the Morris-Lecar model. A competition between sensitivity to input and precision is responsible for favoring two distinct regimes of latencies.

Optimal network configuration for maximal coherence resonance in excitable systems

We analyze the coherence resonance phenomenon in an ensemble of noise-driven excitable neurons giving special attention to the role of the interaction topology. The neural architecture is modeled using a spatially embedded network in which we can tune the network organization between scale-free-like with dominating long-range connections and a network with mostly adjacent neurons connected. We found that besides an optimal noise intensity, also an optimal network configuration exists at which the largest average coherence of noise-induced spikes is achieved. Furthermore, we show that long- as well as short-range interactions between neurons should exist in order to achieve the optimal response of the neuronal network.

Noise-gated encoding of slow inputs by auditory brain stem neurons with a low-threshold K+ current

Phasic neurons, which do not fire repetitively to steady depolarization, are found at various stages of the auditory system. Phasic neurons are commonly described as band-pass filters because they do not respond to low-frequency inputs even when the amplitude is large. However, we show that phasic neurons can encode low-frequency inputs when noise is present. With a low-threshold potassium current (I(KLT)), a phasic neuron model responds to rising and falling phases of a subthreshold low-frequency signal with white noise. When the white noise was low-pass filtered, the phasic model also responded to the signal's trough but still not to the peak. In contrast, a tonic neuron model fired mostly to the signal's peak. To test the model predictions, whole cell slice recordings were obtained in the medial (MSO) and lateral (LSO) superior olivary neurons in gerbil from postnatal day 10 (P10) to 22. The phasic MSO neurons with strong I(KLT), mostly from gerbils aged P17 or older, showed firing patterns consistent with the preceding predictions. Moreover, injecting a virtual I(KLT) into weak-phasic MSO and tonic LSO neurons with putative weak or no I(KLT) (from gerbils younger than P17) shifted the neural response from the signal's peak to the rising phase. These findings advance our knowledge about how noise gates the signal pathway and how phasic neurons encode slow envelopes of sounds with high-frequency carriers.

Laboratory experience for teaching sensory physiology

The major challenge in laboratory teaching is the application of abstract concepts in simple and direct practical lessons. However, students rarely have the opportunity to participate in a laboratory that combines practical learning with a realistic research experience. In the Bioengineering Department, we started an experiential laboratory physiology to teach graduated students some aspects of sensorial physiology and exposes them to laboratory skills in instrumentation and physiological measurements. Students were able to analyze and quantify the effects of activation of mechanoreceptors in multifiber afferent discharges using equipment that was not overly sophisticated. In consequence, this practical laboratory helps students to make connections with physiological concepts acquired in theoretical classes and to introduce them to electrophysiological research.