Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure $M_s$ by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$ is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of $M_s$, we quantitatively characterize the stochastic spiking coherence, and find that $M_s$ reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure $M_s$ may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc

Attentional modulation of firing rate and synchrony in a model cortical network

When attention is directed into the receptive field of a V4 neuron, its contrast response curve is shifted to lower contrast values (Reynolds et al, 2000, Neuron 26:703). Attention also increases the coherence between neurons responding to the same stimulus (Fries et al, 2001, Science 291:1560). We studied how the firing rate and synchrony of a densely interconnected cortical network varied with contrast and how they were modulated by attention. We found that an increased driving current to the excitatory neurons increased the overall firing rate of the network, whereas variation of the driving current to inhibitory neurons modulated the synchrony of the network. We explain the synchrony modulation in terms of a locking phenomenon during which the ratio of excitatory to inhibitory firing rates is approximately constant for a range of driving current values. We explored the hypothesis that contrast is represented primarily as a drive to the excitatory neurons, whereas attention corresponds to a reduction in driving current to the inhibitory neurons. Using this hypothesis, the model reproduces the following experimental observations: (1) the firing rate of the excitatory neurons increases with contrast; (2) for high contrast stimuli, the firing rate saturates and the network synchronizes; (3) attention shifts the contrast response curve to lower contrast values; (4) attention leads to stronger synchronization that starts at a lower value of the contrast compared with the attend-away condition. In addition, it predicts that attention increases the delay between the inhibitory and excitatory synchronous volleys produced by the network, allowing the stimulus to recruit more downstream neurons.Comment: 36 pages, submitted to Journal of Computational Neuroscienc

Driving fast-spiking cells induces gamma rhythm and controls sensory responses,”

Cortical gamma oscillations (20280 Hz) predict increases in focused attention, and failure in gamma regulation is a hallmark of neurological and psychiatric disease. Current theory predicts that gamma oscillations are generated by synchronous activity of fast-spiking inhibitory interneurons, with the resulting rhythmic inhibition producing neural ensemble synchrony by generating a narrow window for effective excitation. We causally tested these hypotheses in barrel cortex in vivo by targeting optogenetic manipulation selectively to fast-spiking interneurons. Here we show that light-driven activation of fast-spiking interneurons at varied frequencies (82200 Hz) selectively amplifies gamma oscillations. In contrast, pyramidal neuron activation amplifies only lower frequency oscillations, a cell-type-specific double dissociation. We found that the timing of a sensory input relative to a gamma cycle determined the amplitude and precision of evoked responses. Our data directly support the fast-spiking-gamma hypothesis and provide the first causal evidence that distinct network activity states can be induced in vivo by cell-type-specific activation. Brain states characterized by rhythmic electrophysiological activity have been studied intensively for more than 80 years Cell-type-specific expression of channelrhodopsin-2 To test directly the hypothesis that FS interneuron activity in an in vivo cortical circuit is sufficient to induce gamma oscillations, we used the light-sensitive bacteriorhodopsin Chlamydomonas reinhardtii channelrhodopsin-2 (ChR2), a cation channel activated by ,470 nm blue ligh

Phasic cholinergic signaling promotes emergence of local gamma rhythms in excitatory–inhibitory networks

Recent experimental results have shown that the detection of cues in behavioral attention tasks relies on transient increases of acetylcholine (ACh) release in frontal cortex and cholinergically driven oscillatory activity in the gamma frequency band (Howe et al. Journal of Neuroscience, 2017, 37, 3215). The cue‐induced gamma rhythmic activity requires stimulation of M1 muscarinic receptors. Using biophysical computational modeling, we show that a network of excitatory (E) and inhibitory (I) neurons that initially displays asynchronous firing can generate transient gamma oscillatory activity in response to simulated brief pulses of ACh. ACh effects are simulated as transient modulation of the conductance of an M‐type K+ current which is blocked by activation of muscarinic receptors and has significant effects on neuronal excitability. The ACh‐induced effects on the M current conductance, gKs, change network dynamics to promote the emergence of network gamma rhythmicity through a Pyramidal‐Interneuronal Network Gamma mechanism. Depending on connectivity strengths between and among E and I cells, gamma activity decays with the simulated gKs transient modulation or is sustained in the network after the gKs transient has completely dissipated. We investigated the sensitivity of the emergent gamma activity to synaptic strengths, external noise and simulated levels of gKs modulation. To address recent experimental findings that cholinergic signaling is likely spatially focused and dynamic, we show that localized gKs modulation can induce transient changes of cellular excitability in local subnetworks, subsequently causing population‐specific gamma oscillations. These results highlight dynamical mechanisms underlying localization of ACh‐driven responses and suggest that spatially localized, cholinergically induced gamma may contribute to selectivity in the processing of competing external stimuli, as occurs in attentional tasks.Recent experiments showed that cholinergic signaling in the prefrontal cortex is fast and spatially localized in the context of attentional behavioral tasks. The cholinergic transients also generated gamma frequency oscillations that contributed to successful attentional performance. Using computational modeling, we show that transient cholinergic modulation of neural excitability induced the emergence of transient synchronous gamma activity from a background of asynchronous firing in excitatory–inhibitory neural networks.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/162747/2/ejn14744.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162747/1/ejn14744_am.pd

The Functional Consequences of Cortical Circuit Abnormalities on Gamma Oscillations in Schizophrenia: Insights from Computational Modeling

Schizophrenia is characterized by cortical circuit abnormalities, which might be reflected in γ-frequency (30–100 Hz) oscillations in the electroencephalogram. Here we used a computational model of cortical circuitry to examine the effects that neural circuit abnormalities might have on γ generation and network excitability. The model network consisted of 1000 leaky integrate-and-fire neurons with realistic connectivity patterns and proportions of neuron types [pyramidal cells (PCs), regular-spiking inhibitory interneurons, and fast-spiking interneurons (FSIs)]. The network produced a γ oscillation when driven by noise input. We simulated reductions in: (1) recurrent excitatory inputs to PCs; (2) both excitatory and inhibitory inputs to PCs; (3) all possible connections between cells; (4) reduced inhibitory output from FSIs; and (5) reduced NMDA input to FSIs. Reducing all types of synaptic connectivity sharply reduced γ power and phase synchrony. Network excitability was reduced when recurrent excitatory connections were deleted, but the network showed disinhibition effects when inhibitory connections were deleted. Reducing FSI output impaired γ generation to a lesser degree than reducing synaptic connectivity, and increased network excitability. Reducing FSI NMDA input also increased network excitability, but increased γ power. The results of this study suggest that a multimodal approach, combining non-invasive neurophysiological and structural measures, might be able to distinguish between different neural circuit abnormalities in schizophrenia patients. Computational modeling may help to bridge the gaps between post-mortem studies, animal models, and experimental data in humans, and facilitate the development of new therapies for schizophrenia and neuropsychiatric disorders in general

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