Burst synchronization in two pulse-coupled resonate-and-fire neuron circuits

The present paper addresses burst synchronization in out of phase observed in two pulse-coupled resonate-and-fire neuron (RFN) circuits. The RFN circuit is a silicon spiking neuron that has second-order membrane dynamics and exhibits fast subthreshold oscillation of membrane potential. Due to such dynamics, the behavior of the RFN circuit is sensitive to the timing of stimuli. We investigated the effects of the sensitivity and the mutual interaction on the dynamic behavior of two pulse-coupled RFN circuits, and will demonstrate out of phase burst synchronization and bifurcation phenomena through circuit simulations.Applications in Artificial Intelligence - ApplicationsRed de Universidades con Carreras en Informática (RedUNCI

Burst synchronization in two pulse-coupled resonate-and-fire neuron circuits

The present paper addresses burst synchronization in out of phase observed in two pulse-coupled resonate-and-fire neuron (RFN) circuits. The RFN circuit is a silicon spiking neuron that has second-order membrane dynamics and exhibits fast subthreshold oscillation of membrane potential. Due to such dynamics, the behavior of the RFN circuit is sensitive to the timing of stimuli. We investigated the effects of the sensitivity and the mutual interaction on the dynamic behavior of two pulse-coupled RFN circuits, and will demonstrate out of phase burst synchronization and bifurcation phenomena through circuit simulations.Applications in Artificial Intelligence - ApplicationsRed de Universidades con Carreras en Informática (RedUNCI

Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs

Neurosystems: brain rhythms and cognitive processing

Neuronal rhythms are ubiquitous features of brain dynamics, and are highly correlated with cognitive processing. However, the relationship between the physiological mechanisms producing these rhythms and the functions associated with the rhythms remains mysterious. This article investigates the contributions of rhythms to basic cognitive computations (such as filtering signals by coherence and/or frequency) and to major cognitive functions (such as attention and multi-modal coordination). We offer support to the premise that the physiology underlying brain rhythms plays an essential role in how these rhythms facilitate some cognitive operations.098352 - Wellcome Trust; 5R01NS067199 - NINDS NIH HH

Emergence of Spatio-Temporal Pattern Formation and Information Processing in the Brain.

The spatio-temporal patterns of neuronal activity are thought to underlie cognitive functions, such as our thoughts, perceptions, and emotions. Neurons and glial cells, specifically astrocytes, are interconnected in complex networks, where large-scale dynamical patterns emerge from local chemical and electrical signaling between individual network components. How these emergent patterns form and encode for information is the focus of this dissertation. I investigate how various mechanisms that can coordinate collections of neurons in their patterns of activity can potentially cause the interactions across spatial and temporal scales, which are necessary for emergent macroscopic phenomena to arise. My work explores the coordination of network dynamics through pattern formation and synchrony in both experiments and simulations. I concentrate on two potential mechanisms: astrocyte signaling and neuronal resonance properties. Due to their ability to modulate neurons, we investigate the role of astrocytic networks as a potential source for coordinating neuronal assemblies. In cultured networks, I image patterns of calcium signaling between astrocytes, and reproduce observed properties of the network calcium patterning and perturbations with a simple model that incorporates the mechanisms of astrocyte communication. Understanding the modes of communication in astrocyte networks and how they form spatial temporal patterns of their calcium dynamics is important to understanding their interaction with neuronal networks. We investigate this interaction between networks and how glial cells modulate neuronal dynamics through microelectrode array measurements of neuronal network dynamics. We quantify the spontaneous electrical activity patterns of neurons and show the effect of glia on the neuronal dynamics and synchrony. Through a computational approach I investigate an entirely different theoretical mechanism for coordinating ensembles of neurons. I show in a computational model how biophysical resonance shifts in individual neurons can interact with the network topology to influence pattern formation and separation. I show that sub-threshold neuronal depolarization, potentially from astrocytic modulation among other sources, can shift neurons into and out of resonance with specific bands of existing extracellular oscillations. This can act as a dynamic readout mechanism during information storage and retrieval. Exploring these mechanisms that facilitate emergence are necessary for understanding information processing in the brain.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111493/1/lshtrah_1.pd

Fast oscillations in cortical-striatal networks switch frequency following rewarding events and stimulant drugs

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72155/1/j.1460-9568.2009.06843.x.pd

Low-dimensional models of single neurons: A review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as sub-threshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type

Determining how stable network oscillations arise from neuronal and synaptic mechanisms

Many animal behaviors involve the generation of rhythmic patterns and movements. These rhythmic patterns are commonly mediated by neural networks that produce an oscillatory activity pattern, where different neurons maintain a relative phase relationship. This thesis examines the relationships between the cellular and synaptic properties that give rise to stable activity in the form of phase maintenance, across different frequencies in a well-suited model system, the pyloric network of the crab Cancer borealis. The pyloric network has endogenously oscillating ‘pacemaker’ neurons that inhibit ‘follower’ neurons, which in turn feed back onto the pacemaker neurons. The focus of this thesis was to determine the methods by which phase maintenance is achieved in an oscillatory network. This thesis examines the idea that phase maintenance occurs through the actions of intrinsic properties of isolated neurons or through the dynamics of their synaptic connections or both. A combination of pharmacological and electrophysiological techniques a used to show how identified membrane properties and short-term synaptic plasticity are involved with phase maintenance over a range of biologically relevant oscillation frequencies. To examine whether network stability is due to the characteristic stable activity of the identified pyloric neuron types, the hypothesis that phase maintenance is an inherent property of synaptically-isolated individual neurons in the pyloric network was first tested. A set of parameters were determined (frequency-dependent activity profile) to define the response of each isolated pyloric neuron to sinusoidal input at different frequencies. The parameters that define the activity profile are: burst onset phase, burst end phase, resonance frequency and intra-burst spike frequency. Each pyloric neuron type was found to possess a unique activity profile, indicating that the individual neuron types are tuned to produce a particular activity pattern at different frequencies depending on their role in the network. To elucidate the biophysical properties underlying the frequency-dependent activity profiles of the neurons, the hyperpolarization activated current (Ih) was measured and found to possess frequency-dependent properties. This implies that Ih has a different influence on the activity phase of pyloric neurons at different frequencies. Additionally, it was found that the Ih contribution to the burst onset phase depends on the neuron type: in the pacemaker group neurons (PD) it had no influence on the burst onset phase at any frequency whereas in follower neurons it acted to advance the onset phase in one neuron type (LP) and, paradoxically, to delay it in a different neuron type (PY). The results from this part of the study provided evidence that stability is due in part to the intrinsic neuronal properties but that these intrinsic properties do not fully explain network stability. To address the contribution of pyloric synapses to network stability, the mechanisms by which synapses promote phase maintenance were investigated. An artificial synapse that mimicked the feedforward PD to LP synapse, was used so that the synaptic parameters could be varied in a controlled manner in order to examine the influence of the properties of this synapse on the postsynaptic LP neuron. It was found that a static synapse with fixed parameters (such as strength and peak phase) across frequencies cannot result in a constant activity phase in the LP neuron. However, if the synaptic strength decreases and the peak phase is delayed as a function of frequency, the LP neuron can maintain a constant activity phase across a large range of frequencies. These dynamic changes in the strength and peak phase of the PD to LP synapse are consistent with the short-term plasticity properties previously reported for this synapse. In the pyloric network, the follower neuron LP provides the sole transmitter-mediated feedback to the pacemaker neurons. To understand the role of this synapse in network stability, this synapse was blocked and replaced by an artificial synapse using the dynamic clamp technique. Different parameters of the artificial synapse, including strength, peak phase, duration and onset phase were found to affect the pyloric cycle period. The most effective parameters that influence cycle period were the synaptic duration and its onset phase. Overall this study demonstrated that both the intrinsic properties of individual neurons and the dynamic properties of the synapses are essential in producing stable activity phases in this oscillatory network. The insight obtained from this thesis can provide a general understanding of the contribution of intrinsic properties to neuronal activity phase and how short-term synaptic dynamics can act to promote phase maintenance in oscillatory networks