In model networks of E-cells and I-cells (excitatory and inhibitory neurons) , synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions --- homogeneity in relevant network parameters, and all-to-all connectivity for instance --- this mechanism can yield perfect synchronization.

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.

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike-train data in important ways, but they are not very easy to apply to the analysis of spike-train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this article we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying 1 stimulus. We found that while lack of fit of a Poisson model to LIF spike-train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of either the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time the m-IMI model provides a better fit to the LIF data than the TRRP, while when the variance of the stimulus varies across time the TRRP provides the better fit. 1

The hypothesis that the variability in the discharge of cortical neurons results from balanced excitation and inhibition is analyzed. A method is presented for analyzing the integrate and re neural model with reversal potentials which enables the interspike interval distribution to be calculated in the Gaussian approximation. Results are presented for the perfect integrator model, for which a stable value of the membrane potential in the absence of the spiking mechanism exists. The results show close agreement with numerical simulations for large numbers of small amplitude inputs. The coecient of variation is consistently less than 1.0, as observed in cortical neurons. Key words: Integrate and re neurons, Reversal potentials, Perfect integrator, Interspike interval variability, First-passage time. 1 Introduction The origin of the variability in the discharge of cortical neurons is not well understood. An analysis of the coecient of variation in the spikes generated by an integrate an...

An expression for the mutual information between the phase of a periodic stimulus and the timing of the output spikes generated by the stimulus is given in the low output spiking-rate regime. The mutual information is calculated for the leaky integrate-and-fire neuron in the Gaussian approximation. The mutual information is found to be e#ectively described as a function of the synchronization of the output spikes and their average spiking-rate. The results in the subthreshold input regime shed light upon the role of stochastic resonance in such models.

During intense network activity in vivo, cortical neurons are in a high-conductance state, in which the membrane potential (Vm) is subject to a tremendous fluctuating activity. Clearly, this ‘‘synaptic noise’ ’ contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which high-conductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting Vm fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation—or level of synchrony—among thousands of neurons in the network. Thus, ‘‘probing the network’ ’ through intracellular V m activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.