Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by Ornstein-Uhlenbeck processes. We derive and solve the Fokker-Planck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in Hodgkin-Huxley-type models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the high-conductance states similar to in vivo conditions. Because the steady-state membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons.

this paper, we show that negative interspike interval (ISI) correlations, i.e., the tendency for long ISIs to be followed by short ISIs (and vice versa), reduce spike count variability, whereas positive ISI correlations increase spike count variability. Together, these effects lead to an optimal spike counting time at which discriminability is maximal

Destexhe. Characterization of synaptic conductances and integrative properties during electrically induced EEG-activated states in neocortical neurons in vivo. J Neurophysiol 94: 2805–2821, 2005. First published July 13, 2005; 10.1152/jn.01313.2004. The activation of the electroencephalogram (EEG) is paralleled with an increase in the firing rate of cortical neurons, but little is known concerning the conductance state of their membrane and its impact on their integrative properties. Here, we combined in vivo intracellular recordings with computational models to investigate EEG-activated states induced by stimulation of the brain stem ascending arousal system. Electrical stimulation of the pedonculopontine tegmental (PPT) nucleus produced long-lasting (�20 s) periods of desynchronized EEG activity similar to the EEG of awake animals. Intracellularly, PPT stimulation locked the membrane into a depolarized state, similar to the up-states seen during deep anesthesia. During these EEG-activated states, however, the input

Neurons possess multiple voltage-dependent conductances specific for their function. To investigate how low-threshold outward currents improve the detection of small signals in a noisy background, we recorded from gerbil medial superior olivary (MSO) neurons in vitro. MSO neurons responded phasically, with a single spike to a step current injection. When bathed in dendrotoxin (DTX), most cells switched to tonic firing, suggesting that low-threshold potassium currents (I KLT) participated in shaping these phasic responses. Neurons were stimulated with a computer-generated steady barrage of random inputs, mimicking weak synaptic conductance transients (the “noise”), together with a larger but still subthreshold postsynaptic conductance, EPSG (the “signal”). DTX reduced the signal-to-noise ratio (SNR), defined as the ratio of probability to fire in response to the EPSG and the probability to fire spontaneously in response to noise. The reduction was mainly attrib-Because of the temporal cues present in sound signals, the auditory nervous system provides a good opportunity to explore how multiple membrane currents influence signal integration (Trussell, 1999). The preservation of precise temporal information is crucial for coding and decoding, especially below �2 kHz in mammals. Correspondingly, brainstem auditory neurons have very fast decaying synaptic currents (Raman and Trussell, 1992; Gardner et al., 1999) and fast low-threshold potassium currents

The high variability of cortical sensory responses is often assumed to impose a major constraint on efficient computation. In the auditory cortex, however, response variability can be very low. We have used in vivo whole-cell patch clamp methods to study the trialto-trial variability of the subthreshold fluctuations in membrane potential underlying tone-evoked responses in the auditory cortex of anesthetized rats. Using methods adapted from classical quantal analysis, we partitioned this subthreshold variability into a private component (which includes synaptic, thermal and other sources local to the recorded cell) and a shared component arising from network interactions. Here we report that this private component is remarkably small, usually about 1-3 mV, as quantified by the variance divided by the mean of the ensemble of tone-evoked response heights. The shared component can be much larger, and shows more heterogeneity across the population, ranging from about 0-10 mV. The remarkable fact that, at least five synapses from the auditory periphery, this variability remains so small raises the possibility that the intervening neural circuitry is organized so as to prevent private noise from accumulating as neural signals propagate to the cortex.

Voltage-gated ion channels in neuronal membranes uctuate randomly between dierent conformational states due to thermal agitation. Fluctuations between conducting and non-conducting states give rise to noisy membrane currents and sub-threshold voltage uctuations and may contribute to variability in spike timing. Here we study sub-threshold voltage uctuations due to active voltage-gated Na + and K + channels as predicted by two commonly used kinetic schemes: the Mainen et al. (MJHS) kinetic scheme, which has been used to model dendritic channels in cortical neurons, and the classical Hodgkin-Huxley (HH) kinetic scheme for the squid giant axon. We compute the magnitudes, amplitude distributions, and power spectral densities of the voltage noise in isopotential membrane patches predicted by these kinetic schemes. For both schemes, noise magnitudes increase rapidly with depolarization from rest. Noise is larger for smaller patch areas but is smaller for increased model temp...

Encoding synaptic inputs as a train of action potentials is a fundamental function of nerve cells. Although spike trains recorded in vivo have been shown to be highly variable, it is unclear whether variability in spike timing represents faithful encoding of temporally varying synaptic inputs or noise inherent in the spike encoding mechanism. It has been reported that spike timing variability is more pronounced for constant, unvarying inputs than for inputs with rich temporal structure. This could have significant implications for the nature of neural coding, particularly if precise timing of spikes and temporal synchrony between neurons is used to represent information in the nervous system. To study the potential functional role of spike timing variability, we estimate the fraction of spike timing variability which conveys information about the input for two types of noisy spike encoders---an integrate and fire model with randomly chosen thresholds and a model of a patch of neuronal...

The position of a localized region of active neurons (a "bump") has been proposed to encode information for working memory, the head direction system, and feature selectivity in the visual system. Stationary bumps are ordinarily stable, but including spike frequency adaptation in the neural dynamics causes a stationary bump to become unstable to a moving bump through a supercritical pitchfork bifurcation in bump speed. Adding spatiotemporal noise to the network supporting the bump can cause the average speed of the bump to decrease to almost zero, reversing the effect of the adaptation and "restabilizing" the bump. This restabilizing occurs for noise levels lower than those required to break up the bump. The restabilizing can be understood by examining the effects of noise on the normal form of the pitchfork bifurcation where the variable involved in the bifurcation is bump speed. This noisy normal form can be further simplified to a persistent random walk in which the probability of changing direction is related to the noise level through an Arrhenius-type rate. The probability density function of position for the continuous-time version of this random walk satis es the telegrapher's equation, and the closed-form solution of this PDE allows us to find expressions for the mean and variance of the average speed of the particle (the bump) undergoing the random walk. This noise-induced stabilization is a novel example in which moderate amounts of noise have a beneficial effect on a system, specifically, stabilizing a spatiotemporal pattern.

The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

The basal ganglia (BG) have long been implicated in both motor function and dysfunction. It has been proposed that the BG form a centralized action selection circuit, resolving conflict between multiple neural systems competing for access to the final common motor pathway. We present a new spiking neuron model of the BG circuitry to test this proposal, incorporating all major features and many physiologically plausible details. We include the following: effects of dopamine in the subthalamic nucleus (STN) and globus pallidus (GP), transmission delays between neurons, and specific distributions of synaptic inputs over dendrites. All main parameters were derived from experimental studies. We find that the BG circuitry supports motor program selection and switching, which deteriorates under dopamine-depleted and dopamine-excessive conditions in a manner consistent with some pathologies associated with those dopamine states. We also validated the model against data describing oscillatory properties of BG. We find that the same model displayed detailed features of both �-band (30–80 Hz) and slow (�1 Hz) oscillatory phenomena reported by Brown et al. (2002) and Magill et al. (2001), respectively. Only the parameters required to mimic experimental conditions (e.g., anesthetic) or manipulations (e.g., lesions) were changed. From the results, we derive the following novel predictions about the STN–GP feedback loop: (1) the loop is functionally decoupled by tonic dopamine under normal conditions and recoupled by dopamine depletion; (2) the loop does not show pacemaking activity under normal conditions in vivo (but does after combined dopamine depletion and cortical lesion); (3) the loop has a resonant frequency in the �-band. Key words: neural network; action selection; dopamine; oscillations; subthalamic nucleus; globus pallidus