Stochastic resonance of ensemble neurons for transient spike trains: wavelet analysis

Detection of subthreshold pulses in neurons with channel noise

Neurons are subject to various kinds of noise. In addition to synaptic noise, the stochastic opening and closing of ion channels represents an intrinsic source of noise that affects the signal-processing properties of the neuron. We study the response of a stochastic Hodgkin-Huxley neuron to transient input subthreshold pulses. It is found that the average response time decreases but variance increases as the amplitude of channel noise increases. In the case of single-pulse detection, we show that channel noise enables one neuron to detect the subthreshold signals and an optimal membrane area (or channel noise intensity) exists for a single neuron to achieve optimal performance. However, the detection ability of a single neuron is limited by large errors. Here, we test a simple neuronal network that can enhance the pulse-detecting abilities of neurons and find that dozens of neurons can perfectly detect subthreshold pulses. The phenomenon of intrinsic stochastic resonance is also found at both the level of single neurons and the level of networks. At the network level, the detection ability of networks can be optimized for the number of neurons comprising the network.

Stochastic resonance driven by time-modulated neurotransmitter random point trains

Information transmitting by temporally modulated random point trains, such as neurotransmitter quanta and spikes, which are neither additive signal and noise nor diffusion approximated additive signal and noise, is studied. We demonstrate that tuning the input train's average rate can optimize the response of an integrate-and-fire model neuron to a signal modulated point train. The characteristics of this phenomenon and its biological significance are discussed.

Dynamical mean-field theory of noisy spiking neuron ensembles: application to the Hodgkin-Huxley model

A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E 67, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of N-unit neurons, each of which is expressed by coupled K-dimensional differential equations (DEs), are assumed to be subject to spatially correlated white noises. The original KN-dimensional stochastic DEs have been replaced by K(K+2)-dimensional deterministic DEs expressed in terms of means and the second-order moments of local and global variables: the fourth-order contributions are taken into account by the Gaussian decoupling approximation. Our DMA has been applied to an ensemble of Hodgkin-Huxley (HH) neurons (K=4), for which effects of the noise, the coupling strength, and the ensemble size on the response to a single-spike input have been investigated. Numerical results calculated by the DMA theory are in good agreement with those obtained by direct simulations, although the former computation is about a thousand times faster than the latter for a typical HH neuron ensemble with N=100.

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

A semianalytical dynamical mean-field theory has been developed for a study of dynamics of an ensemble of N-unit FitzHugh-Nagumo neurons subject to white noises. Assuming weak noises and the Gaussian distribution of state variables, we have driven equations of motions for moments of local and global variables. Dynamical mean-field approximation (DMA) has replaced original, 2N-dimensional stochastic differential equations (DEs) by eight-dimensional deterministic DEs, whereas the conventional moment method yields N(2N+3)-dimensional deterministic DEs for local variables. We have discussed the dependence of the spike firing precision and the synchronization on the noise intensity, synaptic coupling, and the size of the neuron ensemble. The spike timing precision is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. Results calculated by our DMA theory are in good agreement with those obtained by direct simulations. DMA theory is extended to a large cluster which can be divided into multiple subclusters according to their functions. A model calculation has demonstrated that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy subclusters with feed-forward couplings, as in the synfire chain. We have compared DMA theory with the conventional moment method, showing that the former may be alternatively derived from the latter by a reduction in the number of moments with the mean-field approximation.