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Regulation of gamma‐frequency oscillation by feedforward inhibition: A computational modeling study

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Abstract

Throughout the brain, reciprocally connected excitatory and inhibitory neurons interact to produce gamma‐frequency oscillations. The emergent gamma rhythm synchronizes local neural activity and helps to select which cells should fire in each cycle. We previously found that such excitation‐inhibition microcircuits, however, have a potentially significant caveat: the frequency of the gamma oscillation and the level of selection (i.e., the percentage of cells that are allowed to fire) vary with the magnitude of the input signal. In networks with varying levels of brain activity, such a feature may produce undesirable instability on the time and spatial structure of the neural signal with a potential for adversely impacting important neural processing mechanisms. Here we propose that feedforward inhibition solves the latter instability problem of the excitation‐inhibition microcircuit. Using computer simulations, we show that the feedforward inhibitory signal reduces the dependence of both the frequency of population oscillation and the level of selection on the magnitude of the input excitation. Such a mechanism can produce stable gamma oscillations with its frequency determined only by the properties of the feedforward network, as observed in the hippocampus. As feedforward and feedback inhibition motifs commonly appear together in the brain, we hypothesize that their interaction underlies a robust implementation of general computational principles of neural processing involved in several cognitive tasks, including the formation of cell assemblies and the routing of information between brain areas.

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... These classes of interneurons have been implicated in specific computational functions in neural circuits. One important function proposed for feedforward inhibition is "background subtraction, " whereby inhibition grows in proportion to and cancels the average level of input to the circuit, enabling only large fluctuations in inputs above the average level to drive circuit output (Grienberger et al., 2017;Rennó-Costa et al., 2019). Here we ask whether this background subtraction mechanism can support a constant level of output given a wide range in the total number of active inputs. ...
... Feedback inhibition has been proposed to regulate the maximum number of output neurons that respond to the same pattern of input (de Almeida et al., 2009;Stefanelli et al., 2016;Rennó-Costa et al., 2019). This circuit function has been termed "winner-take-all, " or "lateral" inhibition, whereby the neurons receiving the highest level of excitatory input recruit feedback inhibition that suppresses neighboring neurons which are receiving less excitation. ...
... This circuit function has been termed "winner-take-all, " or "lateral" inhibition, whereby the neurons receiving the highest level of excitatory input recruit feedback inhibition that suppresses neighboring neurons which are receiving less excitation. However, previous modeling work has shown that feedback inhibition alone is not able to prevent the number of active output neurons from increasing as the total amount of afferent input grows (Rennó-Costa et al., 2019). Furthermore, it is not clear if the extremely low fraction of active output neurons in circuits with ultrasparse representations like the hippocampal dentate gyrus is sufficient to activate the level of feedback inhibition necessary to support "winner-takeall" competition. ...
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... window (e.g. the ~15 ms duration of a single gamma cycle). This highlights the important roles that inhibitory neurons play in regulating sparsity (how many cells are co-active), selectivity (which cells are active), and rhythmicity (when cells fire) in recurrent networks (Almeida et al., 2009b;Rennó-Costa et al., 2019;Stark et al., 2014;Stefanelli et al., 2016). However, while oscillatory feedback inhibition 95 provides a network mechanism for parsing neuronal sequences into discrete elements, additional mechanisms are still required to ensure that distinct subsets of excitatory neurons are activated in a particular order across successive cycles of a rhythm (Lisman et al., 2005;Ramirez-Villegas et al., 2018). ...
... Specifically, inhibitory feedback connections have been shown to regulate the number of simultaneously active neurons (sparsity) (Stefanelli et al., 2016), and to contribute to the generation of theta and gamma network oscillations (Bezaire et al., 2016;Geisler et 200 al., 2005;Rennó-Costa et al., 2019;Stark et al., 2014;Wang, 2010). Plastic excitatory connections between excitatory neurons have long been implicated in stimulus selectivity and the storage and recall of memories (Almeida et al., 2007;Hopfield, 1982;Lisman and Jensen, 2013). ...
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... Phase shift relative to the local field potential (LFP) provides a mechanism for temporal/phase coding to accompany and complement rate coding in the central nervous system (CNS) (11)(12)(13)(78)(79)(80). Responses to optogenetic stimulation depend on the phase of stimulus activation (81)(82)(83); phase reset is an important aspect of phase determination and network behavior that will be affected by nonstationarity at the cellular scale (84)(85)(86)(87). CNS phase coding has been most thoroughly studied in the context of "phase precession" in hippocampal place cells but has also been seen in entorhinal grid cells (53), as well as in successive theta waves in medial prefrontal cortex (88), and ventral striatum (89). ...
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... The computational model was formed of a network composed of a memory module and a decision-making module, built with associated hippocampal and prefrontal properties. The memory module is modeled as a usual hippocampal layer with a convergent projection from input to memory space, local competition at a memory layer, and stable sparsity (Rennó-Costa et al., 2019. The decision-making module follows standard cortical dynamics (Marcos et al., 2013). ...
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This book travels a colorful journey into the fascinatingly diverse world of interneurons, an important class of highly heterogeneous cells found in all cortical neuronal networks. Interneurons are known to play key roles in many brain functions, from sensory processing to neuronal oscillations linked to learning and memory. This book aims to provide new insights into the striking degree of cellular diversity found in interneuronal microcircuits. The book discusses the history of research into interneuronal variability, the developmental origins of interneuronal diversity, the functional roles of heterogeneity in neuronal circuits, contemporary interneuronal classification systems, and the genetic and homeostatic mechanisms that shape the degree of cell to cell variability within interneuronal populations. It elaborates on new ideas about interneuronal diversity that rest upon recent theoretical and experimental results, with arguments touching upon evolution, animal behavior, and the mathematical theory of small world networks.
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I propose that synchronization affects communication between neuronal groups. Gamma-band (30-90 Hz) synchronization modulates excitation rapidly enough that it escapes the following inhibition and activates postsynaptic neurons effectively. Synchronization also ensures that a presynaptic activation pattern arrives at postsynaptic neurons in a temporally coordinated manner. At a postsynaptic neuron, multiple presynaptic groups converge, e.g., representing different stimuli. If a stimulus is selected by attention, its neuronal representation shows stronger and higher-frequency gamma-band synchronization. Thereby, the attended stimulus representation selectively entrains postsynaptic neurons. The entrainment creates sequences of short excitation and longer inhibition that are coordinated between pre- and postsynaptic groups to transmit the attended representation and shut out competing inputs. The predominantly bottom-up-directed gamma-band influences are controlled by predominantly top-down-directed alpha-beta-band (8-20 Hz) influences. Attention itself samples stimuli at a 7-8 Hz theta rhythm. Thus, several rhythms and their interplay render neuronal communication effective, precise, and selective.
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It remains an outstanding question whether gamma-band oscillations reflect unitary cognitive processes within the same task. EEG/MEG studies do lack the resolution or coverage to address the highly debated question whether single gamma activity patterns are linked with multiple cognitive modules or alternatively each pattern associates with a specific cognitive module, within the same coherent perceptual task. One way to disentangle these issues would be to provide direct identification of their sources, by combining different techniques. Here, we directly examined these questions by performing simultaneous EEG/fMRI using an ambiguous perception paradigm requiring holistic integration. We found that distinct gamma frequency sub-bands reflect different neural substrates and cognitive mechanisms when comparing object perception states vs. no categorical perception. A low gamma sub-band (near 40 Hz) activity was tightly related to the decision making network, and in particular the anterior insula. A high gamma sub-band (∼60 Hz) could be linked to early visual processing regions. The demonstration of a clear functional topography for distinct gamma sub-bands within the same task shows that distinct gamma-band modulations underlie sensory processing and perceptual decision mechanisms. Hum Brain Mapp, 2014. 2014 Wiley Periodicals, Inc.
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Neurons can operate in two distinct ways, depending on the duration of the interval over which they effectively summate incoming synaptic potentials. If this interval is of the order of the mean interspike interval or longer, neurons act effectively as temporal integrators and transmit temporal patterns with only low reliability. If, by contrast, the integration interval is short compared to the interspike interval, neurons act essentially as coincidence detectors, relay preferentially synchronized input, and the temporal structure of their output is a direct function of the input pattern. Recently, interest in this distinction has been revived because experimental and theoretical results suggest that synchronous firing of neurons might play an important role for information processing in the cortex. Here, we argue that coincidence detection, rather than temporal integration, might be a prevalent operation mode of cortical neurons. We base our arguments on established biophysical properties of cortical neurons and on particular features of cortical dynamics.
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Cortical processing reflects the interplay of synaptic excitation and synaptic inhibition. Rapidly accumulating evidence is highlighting the crucial role of inhibition in shaping spontaneous and sensory-evoked cortical activity and thus underscores how a better knowledge of inhibitory circuits is necessary for our understanding of cortical function. We discuss current views of how inhibition regulates the function of cortical neurons and point to a number of important open questions.
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When the brain goes from wakefulness to sleep, cortical neurons begin to undergo slow oscillations in their membrane potential that are synchronized by thalamocortical circuits and reflected in EEG slow waves. To provide a self-consistent account of the transition from wakefulness to sleep and of the generation of sleep slow waves, we have constructed a large-scale computer model that encompasses portions of two visual areas and associated thalamic and reticular thalamic nuclei. Thousands of model neurons, incorporating several intrinsic currents, are interconnected with millions of thalamocortical, corticothalamic, and both intra- and interareal corticocortical connections. In the waking mode, the model exhibits irregular spontaneous firing and selective responses to visual stimuli. In the sleep mode, neuromodulatory changes lead to slow oscillations that closely resemble those observed in vivo and in vitro. A systematic exploration of the effects of intrinsic currents and network parameters on the initiation, maintenance, and termination of slow oscillations shows the following. 1) An increase in potassium leak conductances is sufficient to trigger the transition from wakefulness to sleep. 2) The activation of persistent sodium currents is sufficient to initiate the up-state of the slow oscillation. 3) A combination of intrinsic and synaptic currents is sufficient to maintain the up-state. 4) Depolarization-activated potassium currents and synaptic depression terminate the up-state. 5) Corticocortical connections synchronize the slow oscillation. The model is the first to integrate intrinsic neuronal properties with detailed thalamocortical anatomy and reproduce neural activity patterns in both wakefulness and sleep, thereby providing a powerful tool to investigate the role of sleep in information transmission and plasticity.
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Rate remapping is a recently revealed neural code in which sensory information modulates the firing rate of hippocampal place cells. The mechanism underlying rate remapping is unknown. Its characteristic modulation, however, must arise from the interaction of the two major inputs to the hippocampus, the medial entorhinal cortex (MEC), in which grid cells represent the spatial position of the rat, and the lateral entorhinal cortex (LEC), in which cells represent the sensory properties of the environment. We have used computational methods to elucidate the mechanism by which this interaction produces rate remapping. We show that the convergence of LEC and MEC inputs, in conjunction with a competitive network process mediated by feedback inhibition, can account quantitatively for this phenomenon. The same principle accounts for why different place fields of the same cell vary independently as sensory information is altered. Our results show that rate remapping can be explained in terms of known mechanisms.
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Recent studies suggest that cross-frequency coupling (CFC) might play a functional role in neuronal computation, communication and learning. In particular, the strength of phase-amplitude CFC differs across brain areas in a task-relevant manner, changes quickly in response to sensory, motor and cognitive events, and correlates with performance in learning tasks. Importantly, whereas high-frequency brain activity reflects local domains of cortical processing, low-frequency brain rhythms are dynamically entrained across distributed brain regions by both external sensory input and internal cognitive events. CFC might thus serve as a mechanism to transfer information from large-scale brain networks operating at behavioral timescales to the fast, local cortical processing required for effective computation and synaptic modification, thus integrating functional systems across multiple spatiotemporal scales.
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Granule cells of the dentate gyrus (DG) generally have multiple place fields, whereas CA3 cells, which are second order, have only a single place field. Here, we explore the mechanisms by which the high selectivity of CA3 cells is achieved. Previous work showed that the multiple place fields of DG neurons could be quantitatively accounted for by a model based on the number and strength of grid cell inputs and a competitive network interaction in the DG that is mediated by gamma frequency feedback inhibition. We have now built a model of CA3 based on similar principles. CA3 cells receive input from an average of one active DG cell and from 1,400 cortical grid cells. Based on experimental findings, we have assumed a linear interaction of the two pathways. The results show that simulated CA3 cells generally have a single place field, as observed experimentally. Thus, a two-step process based on simple rules (and that can occur without learning) is able to explain how grid cell inputs to the hippocampus give rise to cells having ultimate spatial selectivity. The CA3 processes that produce a single place depend critically on the competitive network processes and do not require the direct cortical inputs to CA3, which are therefore likely to perform some other unknown function.