This study examines the ability of neurons to track temporally varying inputs, namely by investigating how the instantaneous firing rate of a neuron is modulated by a noisy input with a small sinusoidal component with frequency (f). Using numerical simulations of conductance-based neurons and analytical calculations of one-variable nonlinear integrate-and-fire neurons, we characterized the dependence of this modulation on f. For sufficiently high noise, the neuron acts as a low-pass filter. The modulation amplitude is approximately constant for frequencies up to a cutoff frequency, fc, after which it decays. The cutoff frequency increases almost linearly with the firing rate. For higher frequencies, the modulation amplitude decays as C/falpha, where the power alpha depends on the spike initiation mechanism. For conductance-based models, alpha = 1, and the prefactor C depends solely on the average firing rate and a spike "slope factor," which determines the sharpness of the spike initiation. These results are attributable to the fact that near threshold, the sodium activation variable can be approximated by an exponential function. Using this feature, we propose a simplified one-variable model, the "exponential integrate-and-fire neuron," as an approximation of a conductance-based model. We show that this model reproduces the dynamics of a simple conductance-based model extremely well. Our study shows how an intrinsic neuronal property (the characteristics of fast sodium channels) determines the speed with which neurons can track changes in input.

Oscillations are a common feature of odor-evoked and spontaneous activity in the olfactory system in vivo and in vitro and are thought to play an important role in information processing and memory in a variety of brain areas. Theoretical and experimental studies have described several mechanisms by which oscillations can be generated and synchronized. Here, we investigate the hypothesis that correlated noisy inputs are able to generate synchronous oscillations in olfactory bulb mitral cells in vitro. We consider several alternative mechanisms and conclude that olfactory bulb synchronous oscillations are likely to arise because of the response of uncoupled oscillating neurons to aperiodic but correlated inputs. This mechanism has been described theoretically, but we provide the first experimental evidence that such a mechanism may underlie synchronization in real neurons. In physiological experiments, we show that this mechanism can generate gamma-band oscillations in populations of olfactory bulb mitral cells. This mechanism synchronizes oscillatory firing by using shared fast fluctuations in stochastic inputs across neurons, without requiring any synaptic or electrical coupling. We discuss the properties and limitations of synchronization by this mechanism and suggest that it may underlie fast oscillations in many brain areas.

We review and extend recent results on the instantaneous firing rate dynamics of simplified models of spiking neurons in response to noisy current inputs. It has been shown recently that the response of the instantaneous firing rate to small amplitude oscillations in the mean inputs depends in the large frequency limit f on the spike initiation dynamics. A particular simplified model, the exponential integrate-and-fire (EIF) model, has a response that decays as 1/f in the large frequency limit and describes very well the response of conductance-based models with a Hodgkin-Huxley type fast sodium current. Here, we show that the response of the EIF instantaneous firing rate also decays as 1/f in the case of an oscillation in the variance of the inputs for both white and colored noise. We then compute the initial transient response of the firing rate of the EIF model to a step change in its mean inputs and/or in the variance of its inputs. We show that in both cases the response speed is proportional to the neuron stationary firing rate and inversely proportional to a 'spike slope factor' Delta(T) that controls the sharpness of spike initiation: as 1/Delta(T) for a step change in mean inputs, and as 1/Delta(T) (2) for a step change in the variance in the inputs.

The thalamus plays a central role in sleep rhythms in the mammalian brain and, yet, surprisingly little is known about its function and interaction with local cortical oscillations during NREM sleep (NREM). We investigated the neuronal correlates of cortical barrel activity in the two corresponding thalamic nuclei, the ventral posterior medial (VPM), and the posterior medial (Pom) nuclei during natural NREM in mice. Our data reveal (1) distinct modulations of VPM and Pom activity throughout NREM episodes, (2) a thalamic nucleus-specific phase-locking to cortical slow and spindle waves, (3) cell-specific subthreshold spindle oscillations in VPM neurons that only partially overlap with cortical spindles, and (4) that spindle features evolve throughout NREM episodes and vary according to the post-NREM state. Taken together, our results suggest that, during natural sleep, the barrel cortex exerts a leading role in the generation and transfer of slow rhythms to the somatosensory thalamus and reciprocally for spindle oscillations.