Paradoxical phase response of gamma rhythms facilitates their entrainment in heterogeneous networks.

The synchronization of different γ-rhythms arising in different brain areas has been implicated in various cognitive functions. Here, we focus on the effect of the ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depends on the response of their collective phase to external input. We therefore determine the macroscopic phase-response curve for finite-amplitude perturbations (fmPRC) of ING- and PING-rhythms in all-to-all coupled networks comprised of linear (IF) or quadratic (QIF) integrate-and-fire neurons. For the QIF networks we complement the direct simulations with the adjoint method to determine the infinitesimal macroscopic PRC (imPRC) within the exact mean-field theory. We show that the intrinsic neuronal heterogeneity can qualitatively modify the fmPRC and the imPRC. Both PRCs can be biphasic and change sign (type II), even though the phase-response curve for the individual neurons is strictly non-negative (type I). Thus, for ING rhythms, say, external inhibition to the inhibitory cells can, in fact, advance the collective oscillation of the network, even though the same inhibition would lead to a delay when applied to uncoupled neurons. This paradoxical advance arises when the external inhibition modifies the internal dynamics of the network by reducing the number of spikes of inhibitory neurons; the advance resulting from this disinhibition outweighs the immediate delay caused by the external inhibition. These results explain how intrinsic heterogeneity allows ING- and PING-rhythms to become synchronized with a periodic forcing or another rhythm for a wider range in the mismatch of their frequencies. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled γ-rhythms, which may play a role in neural information transfer via communication through coherence.

Development and binocular matching of orientation selectivity in visual cortex: a computational model.

In mouse visual cortex, right after eye opening binocular cells have different preferred orientations for input from the two eyes. With normal visual experience during a critical period, these preferred orientations evolve and eventually become well matched. To gain insight into the matching process, we developed a computational model of a cortical cell receiving orientation selective inputs via plastic synapses. The model captures the experimentally observed matching of the preferred orientations, the dependence of matching on ocular dominance of the cell, and the relationship between the degree of matching and the resulting monocular orientation selectivity. Moreover, our model puts forward testable predictions: 1) The matching speed increases with initial ocular dominance. 2) While the matching improves more slowly for cells that are more orientation selective, the selectivity increases faster for better matched cells during the matching process. This suggests that matching drives orientation selectivity but not vice versa. 3) There are two main routes to matching: the preferred orientations either drift toward each other or one of the orientations switches suddenly. The latter occurs for cells with large initial mismatch and can render the cells monocular. We expect that these results provide insight more generally into the development of neuronal systems that integrate inputs from multiple sources, including different sensory modalities.NEW & NOTEWORTHY Animals gather information through multiple modalities (vision, audition, touch, etc.). These information streams have to be merged coherently to provide a meaningful representation of the world. Thus, for neurons in visual cortex V1, the orientation selectivities for inputs from the two eyes have to match to enable binocular vision. We analyze the postnatal process underlying this matching using computational modeling. It captures recent experimental results and reveals interdependence between matching, ocular dominance, and orientation selectivity.