Minimal Size of Cell Assemblies Coordinated by Gamma Oscillations

In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25–100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.Collaborative Research in Computational NeuroscienceNational Institutes of Health (U.S.) (grant 1R01 NS067199)National Institutes of Health (U.S.) (grant DMS 0717670)National Institutes of Health (U.S.) (grant 1R01 DA029639)National Institutes of Health (U.S.) (grant 1RC1 MH088182)National Institutes of Health (U.S.) (grant DP2OD002002)Paul G. Allen Family FoundationnGoogle (Firm

Temporal patterns of synchrony in a pyramidal-interneuron gamma (PING) network

Synchronization in neural system plays an important role in many brain functions. Synchronization in the gamma frequency band (30Hz-100Hz) is involved in a variety of cognitive phenomena; abnormalities of the gamma synchronization are found in schizophrenia and autism spectrum disorder. Frequently, the strength of synchronization is not very high and is intermittent even on short time scales (a few cycles of oscillations). That is, the network exhibits intervals of synchronization followed by intervals of desynchronization. Neural circuits dynamics may show different distributions of desynchronization durations even if the synchronization strength is fixed. In this study, we use a conductance-based neural network exhibiting pyramidal-interneuron (PING) gamma rhythm to study the temporal patterning of synchronized neural oscillations. We found that changes in the synaptic strength (as well as changes in the membrane kinetics) can alter the temporal patterning of synchrony. Moreover, we found that the changes in the temporal pattern of synchrony may be independent of the changes in the average synchrony strength. Even though the temporal patterning may vary, there is a tendency for dynamics with short (although potentially numerous) desynchronizations, similar to what was observed in experimental studies of neural activity synchronization in the brain. Recent studies suggested that the short desynchronizations dynamics may facilitate the formation and the break-up of transient neural assemblies. Thus, the results of this study suggest that changes of synaptic strength may alter the temporal patterning of the gamma synchronization as to make the neural networks more efficient in the formation of neural assemblies and the facilitation of cognitive phenomena

Temporal patterns of synchrony in a pyramidal-interneuron gamma (PING) network

Synchronization in neural systems plays an important role in many brain functions. Synchronization in the gamma frequency band (30–100 Hz) is involved in a variety of cognitive phenomena; abnormalities of the gamma synchronization are found in schizophrenia and autism spectrum disorder. Frequently, the strength of synchronization is not high, and synchronization is intermittent even on short time scales (few cycles of oscillations). That is, the network exhibits intervals of synchronization followed by intervals of desynchronization. Neural circuit dynamics may show different distributions of desynchronization durations even if the synchronization strength is fixed. We use a conductance-based neural network exhibiting pyramidal-interneuron gamma rhythm to study the temporal patterning of synchronized neural oscillations. We found that changes in the synaptic strength (as well as changes in the membrane kinetics) can alter the temporal patterning of synchrony. Moreover, we found that the changes in the temporal pattern of synchrony may be independent of the changes in the average synchrony strength. Even though the temporal patterning may vary, there is a tendency for dynamics with short (although potentially numerous) desynchronizations, similar to what was observed in experimental studies of neural synchronization in the brain. Recent studies suggested that the short desynchronizations dynamics may facilitate the formation and the breakup of transient neural assemblies. Thus, the results of this study suggest that changes of synaptic strength may alter the temporal patterning of the gamma synchronization as to make the neural networks more efficient in the formation of neural assemblies and the facilitation of cognitive phenomena

Input-dependent modulation of MEG gamma oscillations reflects gain control in the visual cortex

Gamma-band oscillations arise from the interplay between neural excitation (E) and inhibition (I) and may provide a non-invasive window into the state of cortical circuitry. A bell-shaped modulation of gamma response power by increasing the intensity of sensory input was observed in animals and is thought to reflect neural gain control. Here we sought to find a similar input-output relationship in humans with MEG via modulating the intensity of a visual stimulation by changing the velocity/temporal-frequency of visual motion. In the first experiment, adult participants observed static and moving gratings. The frequency of the MEG gamma response monotonically increased with motion velocity whereas power followed a bell-shape. In the second experiment, on a large group of children and adults, we found that despite drastic developmental changes in frequency and power of gamma oscillations, the relative suppression at high motion velocities was scaled to the same range of values across the life-span. In light of animal and modeling studies, the modulation of gamma power and frequency at high stimulation intensities characterizes the capacity of inhibitory neurons to counterbalance increasing excitation in visual networks. Gamma suppression may thus provide a non-invasive measure of inhibitory-based gain control in the healthy and diseased brain

A biophysical model of striatal microcircuits suggests delta/theta - rhythmically interleaved gamma and beta oscillations mediate periodicity in motor control

First author draf

Uncorrelated bilateral cortical input becomes timed across hippocampal subfields for long waves whereas gamma waves are largely ipsilateral

The role of interhemispheric connections along successive segments of cortico-hippocampal circuits is poorly understood. We aimed to obtain a global picture of spontaneous transfer of activity during non-theta states across several nodes of the bilateral circuit in anesthetized rats. Spatial discrimination techniques applied to bilateral laminar field potentials (FP) across the CA1/Dentate Gyrus provided simultaneous left and right readouts in five FP generators that reflect activity in specific hippocampal afferents and associative pathways. We used a battery of correlation and coherence analyses to extract complementary aspects at different time scales and frequency bands. FP generators exhibited varying bilateral correlation that was high in CA1 and low in the Dentate Gyrus. The submillisecond delays indicate coordination but not support for synaptic dependence of one side on another. The time and frequency characteristics of bilateral coupling were specific to each generator. The Schaffer generator was strongly bilaterally coherent for both sharp waves and gamma waves, although the latter maintained poor amplitude co-variation. The lacunosum-moleculare generator was composed of up to three spatially overlapping activities, and globally maintained high bilateral coherence for long but not short (gamma) waves. These two CA1 generators showed no ipsilateral relationship in any frequency band. In the Dentate Gyrus, strong bilateral coherence was observed only for input from the medial entorhinal areas, while those from the lateral entorhinal areas were largely asymmetric, for both alpha and gamma waves. Granger causality testing showed strong bidirectional relationships between all homonymous bilateral generators except the lateral entorhinal input and a local generator in the Dentate Gyrus. It also revealed few significant relationships between ipsilateral generators, most notably the anticipation of lateral entorhinal cortex toward all others. Thus, with the notable exception of the lateral entorhinal areas, there is a marked interhemispheric coherence primarily for slow envelopes of activity, but not for pulse-like gamma waves, except in the Schafer segment. The results are consistent with essentially different streams of activity entering from and returning to the cortex on each side, with slow waves reflecting times of increased activity exchange between hemispheres and fast waves generally reflecting ipsilateral processing

Heterogeneity in E/I neural network allows entrainment to a wide frequency range

Oscillations and rhythms are measured in the brain through large-scale measures like EEG (electroencephalogram) and LFP (Local Field Potential). Particularly, cortical gamma rhythms (30-90 Hz) found in different brain regions are correlated with different cognitive states. Despite vast differences in the range frequencies in gamma rhythms, the regions communicate to complete high-level tasks. One way in which this takes place is entrainment, where the postsynaptic group phase-lock to the rhythmic input from the presynaptic group (constant phase-shift). Mathematical models of the neurons and the neural networks are proposed to uncover the mechanisms behind experimentally observed phenomena. Most works have used homogeneous models of spiking networks. These simplified models provide a valuable understanding of neural dynamics. However, neural heterogeneity (variation in the neural or network parameters) has been experimentally observed and shown to have a non-trivial effect on many neural processes. Few studies have dealt with the role of different types of neural heterogeneity in the entrainment of a large network, and how it affects the frequency range the neural network entrains to. In this project, we aimed to show how different types of network heterogeneity affect the ability of the networks to entrain to gamma frequencies. We used the Pyramidal-Interneuronal Network Gamma (PING) model, a model consisting of excitatory pyramidal cells (E-cells) and inhibitory interneurons (I-cells) that are synaptically connected and generate gamma oscillations. We show that heterogeneity in the synaptic conductance from excitatory neurons to inhibitory neurons greatly increases the frequency range over which the network can entrain. The mechanism that allows this to happen requires the heterogeneity to 1. Create an I-cell excitability gradient; 2. Introduce input synchrony difference among the I-cells. The entrained I-cell subsets formed under these two conditions are necessary for well-enhanced entrainment as they support the entrainment of the whole network through feedback inhibition. This improvement is shown to be robust in large parameter space

The Effect of Adolescent Alcohol on Dopaminergic and Gabaergic Neurotransmission in the Adult Prefrontal Cortex

The prefrontal cortex (PFC) is thought to play an important role in cognitive processes that are negatively impacted by alcohol exposure. Compared to other brain regions, the neuronal connections of the PFC undergo a critical period of reorganization and refinement during adolescence that coincides with improvements in cognitive control and decision-making. Environmental insults that occur during this period may be particularly damaging to the PFC, resulting in aberrant neurodevelopment along with long-lasting effects on cognitive functioning that negatively impacts decision-making and behavioral control. Experimentation with alcohol typically begins during adolescence when it is often consumed in excessive binge-like episodes resulting in high levels of intoxication followed by a short period of abstinence. This dissertation addresses the hypothesis that binge-like adolescent alcohol (AIE) exposure alters the development of neurotransmitter systems in the prelimbic PFC (PrL-C) and as a result, PFC-dependent cognitive functions are compromised in adulthood. First, the effect of adolescent alcohol abuse on dopaminergic neurotransmission in the adult PrL-C was examined. AIE compromised adult protein expression of the dopamine-related enzymes tyrosine hydroxylase and catechol-O-methyl transferase. Electrophysiology studies revealed a loss of D1 receptor modulation of pyramidal neuron evoked firing in adult layer V PrL-C. The next part of this dissertation focuses on the effect of AIE on development of the PrL-C GABA system. AIE produced marked reductions in GABAA receptor-mediated tonic currents in pyramidal neurons in layer V PrL-C. This effect appears to be largely mediated by developmental alterations specifically in GABAA receptors containing the δ-subunit. The dissertation concludes by assessing the effect of AIE on risky decision-making in adulthood. Furthermore, given the role of GABA in decision-making, exploratory studies sought to enhance tonic GABA currents using the novel δ-GABAA receptor positive allosteric modulator AA29504 and testing the effect of the drug on risk/reward decision-making. The results suggest that AIE did not alter risk/reward decision-making in adulthood. Moreover, AA29504 administration did not alter decision-making on the probabilistic discounting task. Taken together, this dissertation reveals that AIE exposure results in persistent deficits in both dopaminergic and GABAergic neurotransmission in the adult PrL-C that may contribute to deficits in PFC-dependent behavioral control in adulthood

On the interaction of gamma-rhythmic neuronal populations

Local gamma-band (~30-100Hz) oscillations in the brain, produced by feedback inhibition on a characteristic timescale, appear in multiple areas of the brain and are associated with a wide range of cognitive functions. Some regions producing gamma also receive gamma-rhythmic input, and the interaction and coordination of these rhythms has been hypothesized to serve various functional roles. This thesis consists of three stand-alone chapters, each of which considers the response of a gamma-rhythmic neuronal circuit to input in an analytical framework. In the first, we demonstrate that several related models of a gamma-generating circuit under periodic forcing are asymptotically drawn onto an attracting invariant torus due to the convergence of inhibition trajectories at spikes and the convergence of voltage trajectories during sustained inhibition, and therefore display a restricted range of dynamics. In the second, we show that a model of a gamma-generating circuit under forcing by square pulses cannot maintain multiple stably phase-locked solutions. In the third, we show that a separation of time scales of membrane potential dynamics and synaptic decay causes the gamma model to phase align its spiking such that periodic forcing pulses arrive under minimal inhibition. When two of these models are mutually coupled, the same effect causes excitatory pulses from the faster oscillator to arrive at the slower under minimal inhibition, while pulses from the slower to the faster arrive under maximal inhibition. We also show that such a time scale separation allows the model to respond sensitively to input pulse coherence to an extent that is not possible for a simple one-dimensional oscillator. We draw on a wide range of mathematical tools and structures including return maps, saltation matrices, contraction methods, phase response formalism, and singular perturbation theory in order to show that the neuronal mechanism of gamma oscillations is uniquely suited to reliably phase lock across brain regions and facilitate the selective transmission of information

Interacting Mechanisms Driving Synchrony in Neural Networks with Inhibitory Interneurons

Computational neuroscience contributes to our understanding of the brain by applying techniques from fields including mathematics, physics, and computer science to neuroscientific problems that are not amenable to purely biologic study. One area in which this interdisciplinary research is particularly valuable is the proposal and analysis of mechanisms underlying neural network behaviors. Neural synchrony, especially when driven by inhibitory interneurons, is a behavior of particular importance considering this behavior play a role in neural oscillations underlying important brain functions such as memory formation and attention. Typically, these oscillations arise from synchronous firing of a neural population, and thus the study of neural oscillations and neural synchrony are deeply intertwined. Such network behaviors are particularly amenable to computational analysis given the variety of mathematical techniques that are of use in this field. Inhibitory interneurons are thought to drive synchrony in ways described by two computational mechanisms: Interneuron Network Gamma (ING), which describes how an inhibitory network synchronizes itself; and Pyramidal Interneuron Network Gamma (PING), which describes how a population of interneurons inter-connected with a population of excitatory pyramidal cells (an E-I network) synchronizes both populations. As first articulated using simplified interneuron models, these mechanisms find network properties are the primary impetus for synchrony. However, as neurobiologists uncover interneurons exhibiting a vast array of cellular and intra-connectivity properties, our understanding of how interneurons drive oscillations must account for this diversity. This necessitates an investigation of how changing interneuron properties might disrupt the predictions of ING and PING, and whether other mechanisms might interact with or disrupt these network-driven mechanisms. In my dissertation, I broach this topic utilizing the Type I and Type II neuron classifications, which refer to properties derived from the mathematics of coupled oscillators. Classic ING and PING literature typically utilize Type I neurons which always respond to an excitatory perturbation with an advance of the subsequent action potential. However, many interneurons exhibit Type II properties, which respond to some excitatory perturbations with a delay in the subsequent action potential. Interneuronal diversity is also reflected in the strength and density of the synaptic connections between these neurons, which is also explored in this work. My research reveals a variety of ways in which interneuronal diversity alters synchronous oscillations in networks containing inhibitory interneurons and the mechanisms likely driving these dynamics. For example, oscillations in networks of Type II interneurons violate ING predictions and can be explained mechanistically primarily utilizing cellular properties. Additionally, varying the type of both excitatory and inhibitory cells in E-I networks reveals that synchronous excitatory activity arises with different network connectivities for different neuron types, sometimes driven by cellular properties rather than PING. Furthermore, E-I networks respond differently to varied strengths of inhibitory intra-connectivity depending upon interneuron type, sometimes in ways not fully accounted for by PING theory. Taken together, this research reveals that network-driven and cellularly-driven mechanisms promoting oscillatory activity in networks containing inhibitory interneurons interact, and oftentimes compete, in order to dictate the overall network dynamics. These dynamics are more complex than those predicted by the classic ING and PING mechanisms alone. The diverse dynamical properties imparted to oscillating neural networks by changing inhibitory interneuron properties provides some insight into the biological need for such variability.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143981/1/sbrich_1.pd