Amplification of asynchronous inhibition-mediated synchronization by feedback in recurrent networks.

Synchronization of 30-80 Hz oscillatory activity of the principle neurons in the olfactory bulb (mitral cells) is believed to be important for odor discrimination. Previous theoretical studies of these fast rhythms in other brain areas have proposed that principle neuron synchrony can be mediated by short-latency, rapidly decaying inhibition. This phasic inhibition provides a narrow time window for the principle neurons to fire, thus promoting synchrony. However, in the olfactory bulb, the inhibitory granule cells produce long lasting, small amplitude, asynchronous and aperiodic inhibitory input and thus the narrow time window that is required to synchronize spiking does not exist. Instead, it has been suggested that correlated output of the granule cells could serve to synchronize uncoupled mitral cells through a mechanism called "stochastic synchronization", wherein the synchronization arises through correlation of inputs to two neural oscillators. Almost all work on synchrony due to correlations presumes that the correlation is imposed and fixed. Building on theory and experiments that we and others have developed, we show that increased synchrony in the mitral cells could produce an increase in granule cell activity for those granule cells that share a synchronous group of mitral cells. Common granule cell input increases the input correlation to the mitral cells and hence their synchrony by providing a positive feedback loop in correlation. Thus we demonstrate the emergence and temporal evolution of input correlation in recurrent networks with feedback. We explore several theoretical models of this idea, ranging from spiking models to an analytically tractable model.

Response properties of mouse trigeminal ganglion neurons.

We used controlled whisker deflections to examine the response properties of 208 primary afferent neurons in the trigeminal ganglion of adult mice. Proportions of rapidly adapting (RA, 47%) and slowly adapting (SA, 53%) neurons were equivalent, and most cells had low or no spontaneous activity. We quantified angular tuning and sensitivity to deflection amplitude and velocity. Both RA and SA units fired more frequently to larger deflections and faster deflections, but RA units were more sensitive to differences in velocity whereas SA units were more sensitive to deflection amplitudes. Almost all neurons were tuned for deflection angle, and the average response to the maximally effective direction was more than fourfold greater than the average response in the opposite direction; SA units were more tuned than RA units. Responses of primary afferent whisker-responsive neurons are qualitatively similar to those of the rat. However, average firing rates of both RA and SA neurons in the mouse are less sensitive to differences in deflection velocity, and RA units, unlike those in the rat, display amplitude sensitivity. Subtle observed differences between mice and rats may reflect greater mechanical compliance in mice of the whisker hairs and of the tissue in which they are embedded.

Class-II neurons display a higher degree of stochastic synchronization than class-I neurons.

We describe the relationship between the shape of the phase-resetting curve (PRC) and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated Poisson inputs in addition to inputs from independent sources. We use perturbation methods to derive an expression relating the shape of the PRC to the probability density function (PDF) of the phase difference between the oscillators. We compute various measures of the degree of synchrony and cross correlation from the PDF's and use the same to compare and contrast differently shaped PRCs, with respect to their ability to undergo stochastic synchronization. Since the shape of the PRC depends on underlying dynamical details of the oscillator system, we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators. It is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the PRC (type I or type II). It is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation.