Phase-locking patterns underlying effective communication in exact firing rate models of neural networks

Macroscopic oscillations in the brain have been observed to be involved in many cognitive tasks but their role is not completely understood. One of the suggested functions of the oscillations is to dynamically modulate communication between neural circuits. The Communication Through Coherence (CTC) theory establishes that oscillations reflect rhythmic changes in excitability of the neuronal populations. Thus, populations need to be properly phase-locked so that input volleys arrive at the peaks of excitability of the receiving population to communicate effectively. Here, we present a modeling study to explore synchronization between neuronal circuits connected with unidirectional projections. We consider an Excitatory-Inhibitory (E-I) network of quadratic integrate-and-fire neurons modeling a Pyramidal-Interneuronal Network Gamma (PING) rhythm. The network receives an external periodic input from either one or two sources, simulating the inputs from other oscillating neural groups. We use recently developed mean-field models which provide an exact description of the macroscopic activity of the spiking network. This low-dimensional mean field model allows us to use tools from bifurcation theory to identify the phase-locked states between the input and the target population as a function of the amplitude, frequency and coherence of the inputs. We identify the conditions for optimal phaselocking and selective communication. We find that inputs with high coherence can entrain the network for a wider range of frequencies. Besides, faster oscillatory inputs than the intrinsic network gamma cycle show more effective communication than inputs with similar frequency. Our analysis further shows that the entrainment of the network by inputs with higher frequency is more robust to distractors, thus giving them an advantage to entrain the network. Finally, we show that pulsatile inputs can switch between attended inputs in selective attention.

Activity Stabilization in a Population Model of Working Memory by Sinusoidal and Noisy Inputs

According to mechanistic theories of working memory (WM), information is retained as stimulus-dependent persistent spiking activity of cortical neural networks. Yet, how this activity is related to changes in the oscillatory profile observed during WM tasks remains a largely open issue. We explore joint effects of input gamma-band oscillations and noise on the dynamics of several firing rate models of WM. The considered models have a metastable active regime, i.e., they demonstrate long-lasting transient post-stimulus firing rate elevation. We start from a single excitatory-inhibitory circuit and demonstrate that either gamma-band or noise input could stabilize the active regime, thus supporting WM retention. We then consider a system of two circuits with excitatory intercoupling. We find that fast coupling allows for better stabilization by common noise compared to independent noise and stronger amplification of this effect by in-phase gamma inputs compared to anti-phase inputs. Finally, we consider a multi-circuit system comprised of two clusters, each containing a group of circuits receiving a common noise input and a group of circuits receiving independent noise. Each cluster is associated with its own local gamma generator, so all its circuits receive gamma-band input in the same phase. We find that gamma-band input differentially stabilizes the activity of the “common-noise” groups compared to the “independent-noise” groups. If the inter-cluster connections are fast, this effect is more pronounced when the gamma-band input is delivered to the clusters in the same phase rather than in the anti-phase. Assuming that the common noise comes from a large-scale distributed WM representation, our results demonstrate that local gamma oscillations can stabilize the activity of the corresponding parts of this representation, with stronger effect for fast long-range connections and synchronized gamma oscillations.

Firing rate models for gamma oscillations

Gamma oscillations are readily observed in a variety of brain regions during both waking and sleeping states. Computational models of gamma oscillations typically involve simulations of large networks of synaptically coupled spiking units. These networks can exhibit strongly synchronized gamma behavior, whereby neurons fire in near synchrony on every cycle, or weakly modulated gamma behavior, corresponding to stochastic, sparse firing of the individual units on each cycle of the population gamma rhythm. These spiking models offer valuable biophysical descriptions of gamma oscillations; however, because they involve many individual neuronal units they are limited in their ability to communicate general network-level dynamics. Here we demonstrate that few-variable firing rate models with established synaptic timescales can account for both strongly synchronized and weakly modulated gamma oscillations. These models go beyond the classical formulations of rate models by including at least two dynamic variables per population: firing rate and synaptic activation. The models’ flexibility to capture the broad range of gamma behavior depends directly on the timescales that represent recruitment of the excitatory and inhibitory firing rates. In particular, we find that weakly modulated gamma oscillations occur robustly when the recruitment timescale of inhibition is faster than that of excitation. We present our findings by using an extended Wilson-Cowan model and a rate model derived from a network of quadratic integrate-and-fire neurons. These biophysical rate models capture the range of weakly modulated and coherent gamma oscillations observed in spiking network models, while additionally allowing for greater tractability and systems analysis. NEW & NOTEWORTHY Here we develop simple and tractable models of gamma oscillations, a dynamic feature observed throughout much of the brain with significant correlates to behavior and cognitive performance in a variety of experimental contexts. Our models depend on only a few dynamic variables per population, but despite this they qualitatively capture features observed in previous biophysical models of gamma oscillations that involve many individual spiking units.

Nicotinic modulation of hierarchal inhibitory control over prefrontal cortex resting state dynamics: modeling of genetic modification and schizophreniarelated pathology

Nicotinic acetylcholine receptors (nAChRs) strongly modulate the cholinergic drive to a hierarchy of inhibitory neurons in the superficial layers of the PFC, critical to cognitive processes. Genetic deletion of various types of nAChRs, located on specific interneurons, impacts the properties of ultra-slow transitions between high and low activity states (H-states and L-states, respectively), recorded in mice during quiet wakefulness. In addition, recent data indicate that a genetic mutation of the α5 nAChR subunit located on vasoactive intestinal polypeptide (VIP) inhibitory neurons, the rs16969968 single nucleotide polymorphism (α5 SNP), appears to be responsible for “hypofrontality” observed in schizophrenia. Chronic nicotine application to α5 SNP mice restores neural activity to control levels. Using firing rate models of hierarchically organized neural populations, we showed that the change of activity patterns recorded in the genetically modified mice can be explained by a change of activity state stability, differentially modulated by cholinergic inputs to parvalbumin (PV), somatostatin (SOM) or VIP inhibitory populations. A change in amplitude, but not duration of H-states fully account for the lowered pyramidal (PYR) firing rates recorded in α5 SNP mice. We demonstrate that desensitization and upregulation of β2 nAChRs located on SOM interneurons, but not activation of α5 nAChRs located on VIP interneurons, by chronic nicotine application could account for activity normalization recorded in α5 SNP mice. The model implies that subsequent nicotine withdrawal should lead to PYR activity depression more severe than the original hypofrontality caused by SNP mutation.

Modeling fast and slow gamma oscillations with interneurons of different subtype

Experimental and theoretical studies demonstrate that neuronal gamma oscillations crucially depend on interneurons, but current models do not consider the diversity of known interneuron subtypes. Moreover, in CA1 of the hippocampus, experimental evidence indicates the presence of multiple gamma oscillators, two of which may be coordinated by differing interneuron populations. In this article, we show that models of networks with competing interneuron populations with different postsynaptic effects are sufficient to generate, within CA1, distinct oscillatory regimes. We find that strong mutual inhibition between the interneuron populations permits distinct fast and slow gamma states, whereas weak mutual inhibition generates mixed gamma states. We develop idealized firing rate models to illuminate dynamic properties of these competitive gamma networks, and reinforce these concepts with basic spiking models. The models make several explicit predictions about gamma oscillators in CA1. Specifically, interneurons of different subtype phase-lock to different gamma states, and one population of interneurons is silenced and the other active during fast and slow gamma events. Finally, mutual inhibition between interneuron populations is necessary to generate distinct gamma states. Previous experimental studies indicate that fast and slow gamma oscillations reflect different information processing modes, although it is unclear whether these rhythms are intrinsic or imposed. The models outlined demonstrate that basic architectures can locally generate these oscillations, as well as capture other features of fast and slow gamma, including theta-phase preference and spontaneous transitions between gamma states. These models may extend to describe general dynamics in networks with diverse interneuron populations. NEW & NOTEWORTHY The oscillatory coordination of neural signals is crucial to healthy brain function. We have developed an idealized neuronal model that generates distinct fast and slow gamma oscillations, a known feature of the rodent hippocampus. Our work provides a mechanism of this phenomenon, as well as a theoretical framework for future experiments concerning hippocampal gamma. It moreover offers a tractable model of competitive gamma oscillations that is generalizable across the nervous system.