Synchrony with shunting inhibition in a feedforward inhibitory network

Intrinsic Cellular Properties and Connectivity Density Determine Variable Clustering Patterns in Randomly Connected Inhibitory Neural Networks

The plethora of inhibitory interneurons in the hippocampus and cortex play a pivotal role in generating rhythmic activity by clustering and synchronizing cell firing. Results of our simulations demonstrate that both the intrinsic cellular properties of neurons and the degree of network connectivity affect the characteristics of clustered dynamics exhibited in randomly connected, heterogeneous inhibitory networks. We quantify intrinsic cellular properties by the neuron's current-frequency relation (IF curve) and Phase Response Curve (PRC), a measure of how perturbations given at various phases of a neurons firing cycle affect subsequent spike timing. We analyze network bursting properties of networks of neurons with Type I or Type II properties in both excitability and PRC profile; Type I PRCs strictly show phase advances and IF curves that exhibit frequencies arbitrarily close to zero at firing threshold while Type II PRCs display both phase advances and delays and IF curves that have a non-zero frequency at threshold. Type II neurons whose properties arise with or without an M-type adaptation current are considered. We analyze network dynamics under different levels of cellular heterogeneity and as intrinsic cellular firing frequency and the time scale of decay of synaptic inhibition are varied. Many of the dynamics exhibited by these networks diverge from the predictions of the interneuron network gamma (ING) mechanism, as well as from results in all-to-all connected networks. Our results show that randomly connected networks of Type I neurons synchronize into a single cluster of active neurons while networks of Type II neurons organize into two mutually exclusive clusters segregated by the cells' intrinsic firing frequencies. Networks of Type II neurons containing the adaptation current behave similarly to networks of either Type I or Type II neurons depending on network parameters; however, the adaptation current creates differences in the cluster dynamics compared to those in networks of Type I or Type II neurons. To understand these results, we compute neuronal PRCs calculated with a perturbation matching the profile of the synaptic current in our networks. Differences in profiles of these PRCs across the different neuron types reveal mechanisms underlying the divergent network dynamics.

Emergent gamma synchrony in all-to-all interneuronal networks

We investigate the emergence of in-phase synchronization in a heterogeneous network of coupled inhibitory interneurons in the presence of spike timing dependent plasticity (STDP). Using a simple network of two mutually coupled interneurons (2-MCI), we first study the effects of STDP on in-phase synchronization. We demonstrate that, with STDP, the 2-MCI network can evolve to either a state of stable 1:1 in-phase synchronization or exhibit multiple regimes of higher order synchronization states. We show that the emergence of synchronization induces a structural asymmetry in the 2-MCI network such that the synapses onto the high frequency firing neurons are potentiated, while those onto the low frequency firing neurons are de-potentiated, resulting in the directed flow of information from low frequency firing neurons to high frequency firing neurons. Finally, we demonstrate that the principal findings from our analysis of the 2-MCI network contribute to the emergence of robust synchronization in the Wang-Buzsaki network (Wang and Buzsáki, 1996) of all-to-all coupled inhibitory interneurons (100-MCI) for a significantly larger range of heterogeneity in the intrinsic firing rate of the neurons in the network. We conclude that STDP of inhibitory synapses provide a viable mechanism for robust neural synchronization.

Mechanism for Hypocretin-mediated sleep-to-wake transitions

Current models of sleep/wake regulation posit that Hypocretin (Hcrt)-expressing neurons in the lateral hypothalamus promote and stabilize wakefulness by projecting to subcortical arousal centers. However, the critical downstream effectors of Hcrt neurons are unknown. Here we use optogenetic, pharmacological, and computational tools to investigate the functional connectivity between Hcrt neurons and downstream noradrenergic neurons in the locus coeruleus (LC) during nonrapid eye movement (NREM) sleep. We found that photoinhibiting LC neurons during Hcrt stimulation blocked Hcrt-mediated sleep-to-wake transitions. In contrast, when LC neurons were optically stimulated to increase membrane excitability, concomitant photostimulation of Hcrt neurons significantly increased the probability of sleep-to-wake transitions compared with Hcrt stimulation alone. We also built a conductance-based computational model of Hcrt-LC circuitry that recapitulates our behavioral results using LC neurons as the main effectors of Hcrt signaling. These results establish the Hcrt-LC connection as a critical integrator-effector circuit that regulates NREM sleep/wake behavior during the inactive period. This coupling of distinct neuronal systems can be generalized to other hypothalamic integrator nuclei with downstream effector/output populations in the brain.

Detecting effective connectivity in networks of coupled neuronal oscillators

The application of data-driven time series analysis techniques such as Granger causality, partial directed coherence and phase dynamics modeling to estimate effective connectivity in brain networks has recently gained significant prominence in the neuroscience community. While these techniques have been useful in determining causal interactions among different regions of brain networks, a thorough analysis of the comparative accuracy and robustness of these methods in identifying patterns of effective connectivity among brain networks is still lacking. In this paper, we systematically address this issue within the context of simple networks of coupled spiking neurons. Specifically, we develop a method to assess the ability of various effective connectivity measures to accurately determine the true effective connectivity of a given neuronal network. Our method is based on decision tree classifiers which are trained using several time series features that can be observed solely from experimentally recorded data. We show that the classifiers constructed in this work provide a general framework for determining whether a particular effective connectivity measure is likely to produce incorrect results when applied to a dataset.

Network recruitment to coherent oscillations in a hippocampal computer model

Coherent neural oscillations represent transient synchronization of local neuronal populations in both normal and pathological brain activity. These oscillations occur at or above gamma frequencies (>30 Hz) and often are propagated to neighboring tissue under circumstances that are both normal and abnormal, such as gamma binding or seizures. The mechanisms that generate and propagate these oscillations are poorly understood. In the present study we demonstrate, via a detailed computational model, a mechanism whereby physiological noise and coupling initiate oscillations and then recruit neighboring tissue, in a manner well described by a combination of stochastic resonance and coherence resonance. We develop a novel statistical method to quantify recruitment using several measures of network synchrony. This measurement demonstrates that oscillations spread via preexisting network connections such as interneuronal connections, recurrent synapses, and gap junctions, provided that neighboring cells also receive sufficient inputs in the form of random synaptic noise. "Epileptic" high-frequency oscillations (HFOs), produced by pathologies such as increased synaptic activity and recurrent connections, were superior at recruiting neighboring tissue. "Normal" HFOs, associated with fast firing of inhibitory cells and sparse pyramidal cell firing, tended to suppress surrounding cells and showed very limited ability to recruit. These findings point to synaptic noise and physiological coupling as important targets for understanding the generation and propagation of both normal and pathological HFOs, suggesting potential new diagnostic and therapeutic approaches to human disorders such as epilepsy.

Control of neural synchrony using channelrhodopsin-2: a computational study

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.