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Gamma frequency oscillations (25–140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a “biologically plausible” region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space., Author summary Cortical circuits are characterized by a high degree of structural and dynamical complexity, and this biological reality is reflected in the large number of parameters in even semi-realistic cortical models. A fundamental task of computational neuroscience is to understand how these parameters govern network dynamics. While some neuronal parameters can be measured in vivo, many remain poorly constrained due to limitations of available experimental techniques. Computational models can address this problem by relating difficult-to-measure parameters to observable quantities, but to do so one must overcome two challenges: (1) the computational expense of mapping a high dimensional parameter space, and (2) extracting biological insights from such a map. This study aims to address these challenges in the following ways: First, we propose a parsimonious data-informed algorithm that efficiently predicts spontaneous cortical activity, thereby speeding up the mapping of parameter landscapes. Second, we show that lateral inhibition provides a basis for conceptualizing cortical parameter space, enabling us to begin to make sense of its geometric structure and attendant scaling relations. We illustrate our approach on a biologically realistic model of the monkey primary visual cortex.

Autonomous motivated spatial navigation in animals or robots requires the association between spatial location and value. Hippocampal place cells are involved in goal-directed spatial navigation and the consolidation of spatial memories. Recently, Gauthier and Tank (Neuron 99(1):179-193, 2018. https://doi.org/10.1016/j.neuron.2018.06.008) have identified a subpopulation of hippocampal cells selectively activated in relation to rewarded goals. However, the relationship between these cells' spiking activity and goal representation remains elusive. We analyzed data from experiments in which rats underwent five consecutive tasks in which reward locations and spatial context were manipulated. We found CA1 populations with properties continuously ranging from place cells to reward cells. Specifically, we found typical place cells insensitive to reward locations, reward cells that only fired at correct rewarded feeders in each task regardless of context, and "hybrid cells" that responded to spatial locations and change of reward locations. Reward cells responded mostly to the reward delivery rather than to its expectation. In addition, we found a small group of neurons that transitioned between place and reward cells properties within the 5-task session. We conclude that some pyramidal cells (if not all) integrate both spatial and reward inputs to various degrees. These results provide insights into the integrative coding properties of CA1 pyramidal cells, focusing on their abilities to carry both spatial and reward information in a mixed and plastic manner. This conjunctive coding property prompts a re-thinking of current computational models of spatial navigation in which hippocampal spatial and subcortical value representations are independent.