Detection of pulses in a colored noise setting

The Space-Clamped Hodgkin-Huxley System with Random Synaptic Input: Inhibition of Spiking by Weak Noise and Analysis with Moment Equations

We consider a classical space-clamped Hodgkin-Huxley model neuron stimulated by synaptic excitation and inhibition with conductances represented by Ornstein-Uhlenbeck processes. Using numerical solutions of the stochastic model system obtained by an Euler method, it is found that with excitation only, there is a critical value of the steady-state excitatory conductance for repetitive spiking without noise, and for values of the conductance near the critical value, small noise has a powerfully inhibitory effect. For a given level of inhibition, there is also a critical value of the steady-state excitatory conductance for repetitive firing, and it is demonstrated that noise in either the excitatory or inhibitory processes or both can powerfully inhibit spiking. Furthermore, near the critical value, inverse stochastic resonance was observed when noise was present only in the inhibitory input process. The system of deterministic differential equations for the approximate first- and second-order moments of the model is derived. They are solved using Runge-Kutta methods, and the solutions are compared with the results obtained by simulation for various sets of parameters, including some with conductances obtained by experiment on pyramidal cells of rat prefrontal cortex. The mean and variance obtained from simulation are in good agreement when there is spiking induced by strong stimulation and relatively small noise or when the voltage is fluctuating at subthreshold levels. In the occasional spike mode sometimes exhibited by spinal motoneurons and cortical pyramidal cells, the assumptions underlying the moment equation approach are not satisfied. The simulation results show that noisy synaptic input of either an excitatory or inhibitory character or both may lead to the suppression of firing in neurons operating near a critical point and this has possible implications for cortical networks. Although suppression of firing is corroborated for the system of moment equations, there seem to be substantial differences between the dynamical properties of the original system of stochastic differential equations and the much larger system of moment equations.

A neuron model of stochastic resonance using rectangular pulse trains

Stochastic resonance (SR) is the enhanced representation of a weak input signal by the addition of an optimal level of broadband noise to a nonlinear (threshold) system. Since its discovery in the 1980s the domain of input signals shown to be applicable to SR has greatly expanded, from strictly periodic inputs to now nearly any aperiodic forcing function. The perturbations (noise) used to generate SR have also expanded, from white noise to now colored noise or vibrational forcing. This study demonstrates that a new class of perturbations can achieve SR, namely, series of stochastically generated biphasic pulse trains. Using these pulse trains as 'noise' we show that a Hodgkin Huxley model neuron exhibits SR behavior when detecting weak input signals. This result is of particular interest to neuroscience because nearly all artificial neural stimulation is implemented with square current or voltage pulses rather than broadband noise, and this new method may facilitate the translation of the performance gains achievable through SR to neural prosthetics.

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.

Array enhancement of stochastic synchronization and signal-to-noise ratio gain in the nonlinear regime of signal transmission

The nonlinear transformation of an external noisy signal by an array of noninteracting elements with internal noise is considered. The array simulates a neuronal system that processes spike trains. It is shown that increasing the number of array elements entails significant extending of the stochastic synchronization region and improvement of the signal-to-noise ratio (SNR). The effects are demonstrated for arrays of triggers, overdamped bistable oscillators, and Fitzhugh-Nagumo systems. The interrelation between SNR improvement and the efficiency of information processing is discussed.

Spiking regularity in a noisy small-world neuronal network

The regularity of spiking oscillations is studied in the networks with different topological structures. The network is composed of coupled Fitz-Hugh-Nagumo neurons driven by colored noise. The investigation illustrates that the spike train in both the regular and the Watts-Strogatz small-world neuronal networks can show the best regularity at a moderate noise intensity, indicating the existence of coherence resonance. Moreover, the temporal coherence of the spike train in the small-world network is superior to that in a regular network due to the increase of the randomness of the network topology. Besides the noise intensity, the spiking regularity can be optimized by tuning the randomness of the network topological structure or by tuning the correlation time of the colored noise. In particular, under the cooperation of the small-world topology and the correlation time, the spike train with good regularity could sustain a large magnitude of the local noise.

Receiver Operating Characteristic (ROC) Analysis for Characterizing Synaptic Efficacy

The role of background synaptic activity in cortical processing has recently received much attention. How do individual neurons extract information when embedded in a noisy background? When examining the impact of a synaptic input on postsynaptic firing, it is important to distinguish a change in overall firing probability from a true change in neuronal sensitivity to a particular input (synaptic efficacy) that corresponds to a change in detection performance. Here we study the impact of background synaptic input on neuronal sensitivity to individual synaptic inputs using receiver operating characteristic (ROC) analysis. We use the area under the ROC curve as a measure of synaptic efficacy, here defined as the ability of a postsynaptic action potential to identify a particular synaptic input event. An advantage of using ROC analysis to measure synaptic efficacy is that it provides a measure that is independent of postsynaptic firing rate. Furthermore, changes in mean excitation or inhibition, although affecting overall firing probability, do not modulate synaptic efficacy when measured in this way. Changes in overall conductance also affect firing probability but not this form of synaptic efficacy. Input noise, here defined as the variance of the input current, does modulate synaptic efficacy, however. This effect persists when the change in input variance is coupled with a change in conductance (as would result from changing background activity).

A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties

The integrate-and-fire neuron model describes the state of a neuron in terms of its membrane potential, which is determined by the synaptic inputs and the injected current that the neuron receives. When the membrane potential reaches a threshold, an action potential (spike) is generated. This review considers the model in which the synaptic input varies periodically and is described by an inhomogeneous Poisson process, with both current and conductance synapses. The focus is on the mathematical methods that allow the output spike distribution to be analyzed, including first passage time methods and the Fokker-Planck equation. Recent interest in the response of neurons to periodic input has in part arisen from the study of stochastic resonance, which is the noise-induced enhancement of the signal-to-noise ratio. Networks of integrate-and-fire neurons behave in a wide variety of ways and have been used to model a variety of neural, physiological, and psychological phenomena. The properties of the integrate-and-fire neuron model with synaptic input described as a temporally homogeneous Poisson process are reviewed in an accompanying paper (Burkitt in Biol Cybern, 2006).

Method for numerical simulation of two-term exponentially correlated colored noise

A method for numerical simulation of two-term exponentially correlated colored noise is proposed. The method is an extension of traditional method for one-term exponentially correlated colored noise. The validity of the algorithm is tested by comparing numerical simulations with analytical results in two physical applications.

Exact numerical simulation of power-law noises

Many simulations of stochastic processes require colored noises: I describe here an exact numerical method to simulate power-law noises: the method can be extended to more general colored noises, and is exact for all time steps, even when they are unevenly spaced [as may often happen for astronomical data; see, e.g., N. R. Lomb, Astrophys. Space Sci. 39, 447 (1976)]. The algorithm has a well-behaved computational complexity, it produces a nearly perfect Gaussian noise, and its computational efficiency depends on the required degree of noise Gaussianity.