Modeling the dynamical neural systems on different timescales

Xu, Xize

doi:https://doi.org/10.21985/n2-cx9d-dt97

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Modeling the dynamical neural systems on different timescales

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With neurons as its primary computational components, the brain operates at multiple timescales. In this thesis, we focus on two timescales: on a relatively slow timescale on the order of hours to days, the brain adapts to the environment it is exposed to and learns its circuitry by altering the connections between neurons through synaptic plasticity; on a relatively fast timescale on the order of tens of milliseconds, collective oscillations or brain rhythms emerge from synaptic interactions within neuronal circuits, which have been suggested to play an important role in routing information across cortical regions.In Chapter 2, we explore how learning in visual cortex is achieved by synaptic plasticity, particularly in a model of binocular matching of orientation selectivity in mouse primary visual cortex (V1). Right after eye-opening, binocular cells in mouse V1 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 develop 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: i) The matching speed increases with initial ocular dominance; ii) 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; iii) there are two main routes to matching: the preferred orientations either drift towards each other or one of the orientations switches suddenly. The latter occurs for cells with large initial mismatch and can render the cells monocular. In Chapter 3, we investigate the synchronization of different gamma rhythms arising in different brain areas, which has been implicated in various cognitive functions. In particular, we focus on the effect of ubiquitous neuronal heterogeneity on the synchronization of ING (interneuronal network gamma) and PING (pyramidal-interneuronal network gamma) rhythms. The synchronization properties of rhythms depend 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 acroscopic PRC (imPRC) within the exact mean-field theory. We show that 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, 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 of frequency mismatches. Our results identify a potential function of neuronal heterogeneity in the synchronization of coupled gamma rhythms, which may play a role in neural information transfer via communication through coherence.

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