Intermittent synchronization in a network of bursting neurons

Basal ganglia circuits in Parkinson’s disease constitute a prominent example of neural system of coupled inhibitory and excitatory neurons, which exhibit synchronous activity [1]. The phase-locking of neural activity in this system, as analyzed in experimental data intraoperatively recorded in Parkinsonian patients, exhibits intermittent temporal dynamics [2]. The mechanisms of this intermittent synchronous dynamics make the subject of this study. The conductance-based network models of subthalamo-pallidal circuitry of basal ganglia have being shown to reproduce the intermittent temporal patterns of phase-locking observed in experiments with high fidelity [3]. We start with this network model of synaptically coupled excitatory subthalamic and inhibitory pallidal bursting neurons. We further reduce it to the model of two mutually coupled inhibitory neurons with self-inhibition. This network is presented at Figure ​Figure1.1. While real subthalamic neurons are excitatory, the resulting two-neurons network is adequate simplification of the original circuitry under assumption of high fidelity of responses of inhibitory pallidal cells. While this reduction may be associated with the loss of some other biologically realistic features, it produces a relatively generic circuit, therefore the studied mechanism may be quite general too. Figure 1 The network architecture. Each connection is inhibitory synapse. We used geometric dynamical systems and singular perturbation methods to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently synchronous oscillations are generated by overlapped spiking which crucially depend on the geometry of slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of out-of-phase stable solution and the other slower variable for irregular and intermittent activity pattern. The results of analysis can be traced to particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson’s disease.

We study the propagation of traveling solitary pulses in one-dimensional cortical networks with two types of one-dimensional architectures: networks of excitatory neurons and networks composed of both excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. The velocity and stability of propagating, continuous pulses are calculated analytically. For excitatory-only networks, two continuous pulses with different velocities exist if the synaptic coupling is larger than a minimal value; the pulse with the lower velocity is always unstable. Above a certain critical value of the constant delay, continuous pulses lose stability via a Hopf bifurcation, and lurching pulses with spatio-temporal periodicity emerge. The parameter regime for which lurching occurs is strongly affected by the synaptic footprint (connectivity) shape. Two types of stable propagating pulses are observed in networks of excitatory and inhibitory neurons. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. This work shows that simple models of spiking neurons exhibit a large variety of propagating pulses with various spatio-temporal properties.

Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.

Rapid Target-Specific Remodeling of Fast-Spiking Inhibitory Circuits after Loss of Dopamine

Contents: Preface. Part I: Oscillations in Single Neurons and Local Networks. G. Gross, J.M. Kowalski, B.K. Rhoades, Spontaneous and Evoked Oscillations in Cultured Mammalian Neuronal Networks. D.C. Tam, Detection of Oscillations and Synchronous Firing in Neurons. D.A. Baxter, H.A. Lechner, C.C. Canavier, R.J. Butera, Jr., A.A. DeFraneschi, J.W. Clark, Jr., J.H. Byrne, Coexisting Stable Oscillatory States in Single Cells and Multicellular Neuronal Oscillators. M. Stemmler, M. Usher, C. Koch, Oscillatory Local Field Potentials. G.J. Mpitsos, J.P. Edstrom, Computations Neurons Perform in Networks: Inside Versus Outside and Lessons Learned From a Sixteenth-Century Shoemaker. Part II: Oscillations in Cortical and Cortical/Subcortical Systems. I. Soltesz, The Interplay of Intrinsic and Synaptic Membrane Currents in Delta, Theta and 40-Hz Oscillations. E. Thomas, Dynamics of Low-Frequency Oscillations in a Model Thalamocortical Network. M.E. Jackson, L.J. Cauller, Towards the Function of Reciprocal Corticocortical Connections: Computational Modeling and Electrophysiological Studies. D. Young, An Oscillatory Model of Cortical Neural Processing. G.L. Yuen, Response Synchrony, APG Theory, and Motor Control. Part III: Oscillatory Models in Perception, Memory, and Cognition. D. Horn, I. Opher, Temporal Segmentation and Binding in Oscillatory Neural Systems. A. Grunewald, S. Grossberg, Perceptual Framing and Cortical Synchronization. D. DeMaris, Attention, Depth Gestalts, and Spatially Extended Chaos in the Perception of Ambiguous Figures. G. Borisyuk, R. Borisyuk, Y. Kazanovich, G. Strong, Oscillatory Neural Networks: Modeling Binding and Attention by Synchronization of Neural Activity. B. Baird, T. Troyer, F. Eeckman, Attentional Network Streams of Synchronized 40-Hz Activity in a Cortical Architecture of Coupled Oscillatory Associative Memories. Part IV: Applications of Synchronized and Chaotic Oscillations. G.E. Mobus, P.S. Fisher, Foraging Search at the Edge of Chaos. A.G. Brown, S. Collins, An Oscillatory Associative Memory Analogue Architecture. N.S. Park, D. Robertson, K. Stenning, Symbolic Knowledge Encoding Using a Dynamic Binding Mechanism and an Embedded Inference Mechanism. A. Jagota, X. Wang, Oscillations in Discrete and Continuous Hopfield Networks. S. Wolpert, Modeling Neural Oscillation Using VLSI-Based Neuromimes.

Neural mass signals from in-vivo recordings often show oscillations with frequencies ranging from <1 to 100 Hz. Fast rhythmic activity in the beta and gamma range can be generated by network-based mechanisms such as recurrent synaptic excitation-inhibition loops. Slower oscillations might instead depend on neuronal adaptation currents whose timescales range from tens of milliseconds to seconds. Here we investigate how the dynamics of such adaptation currents contribute to spike rate oscillations and resonance properties in recurrent networks of excitatory and inhibitory neurons. Based on a network of sparsely coupled spiking model neurons with two types of adaptation current and conductance-based synapses with heterogeneous strengths and delays we use a mean-field approach to analyze oscillatory network activity. For constant external input, we find that spike-triggered adaptation currents provide a mechanism to generate slow oscillations over a wide range of adaptation timescales as long as recurrent synaptic excitation is sufficiently strong. Faster rhythms occur when recurrent inhibition is slower than excitation and oscillation frequency increases with the strength of inhibition. Adaptation facilitates such network-based oscillations for fast synaptic inhibition and leads to decreased frequencies. For oscillatory external input, adaptation currents amplify a narrow band of frequencies and cause phase advances for low frequencies in addition to phase delays at higher frequencies. Our results therefore identify the different key roles of neuronal adaptation dynamics for rhythmogenesis and selective signal propagation in recurrent networks.

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics. Specifically, the inhibitory population's activation function in the Wilson-Cowan model is modified to be non-monotonic to reflect that inhibitory neurons enter depolarization block given strong input. We find that a physiological state and a seizure state can coexist, where the seizure state is characterized by high excitatory and low inhibitory firing rate. Bifurcation analysis of the mean field model reveals that a transition to the seizure state may occur via a saddle-node bifurcation or a homoclinic bifurcation. We explain the hysteresis observed in network simulations using these two bifurcation types. We also demonstrate that extracellular potassium concentration affects the depolarization block threshold; the consequent changes in bifurcation structure enable the network to produce the tonic to clonic phase transition observed in biological epileptic networks.

Striatal Plasticity and Basal Ganglia Circuit Function

Parkinson's disease is a movement disorder caused by dopamine depletion in the basal ganglia. Abnormally synchronized neuronal oscillations between 8 and 15 Hz in the basal ganglia are implicated in motor symptoms of Parkinson's disease. However, how these abnormal oscillations are generated and maintained in the dopamine-depleted state is unknown. Based on neural recordings in a primate model of Parkinson's disease and other experimental and computational evidence, we hypothesized that the recurrent circuit between the subthalamic nucleus (STN) and the external segment of the globus pallidus (GPe) generates and maintains parkinsonian oscillations, and that the cortical excitatory input to the STN amplifies them. To investigate this hypothesis through computer simulations, we developed a spiking neuron model of the STN-GPe circuit by incorporating electrophysiological properties of neurons and synapses. A systematic parameter search by computer simulation identified regions in the space of the intrinsic excitability of GPe neurons and synaptic strength from the GPe to the STN that reproduce normal and parkinsonian states. In the parkinsonian state, reduced firing of GPe neurons and increased GPe-STN inhibition trigger burst activities of STN neurons with strong post-inhibitory rebound excitation, which is usually subject to short-term depression. STN neuronal bursts are shaped into the 8–15 Hz, synchronous oscillations via recurrent interactions of STN and GPe neurons. Furthermore, we show that cortical excitatory input to the STN can amplify or suppress pathological STN oscillations depending on their phase and strength, predicting conditions of cortical inputs to the STN for suppressing oscillations.

A neurodynamical approach to scene segmentation of hyperspectral imagery is investigated based on oscillatory correlation theory. A network of relaxation oscillators, which is based on the Locally Excitatory Globally Inhibitory Oscillator Network (LEGION), is extended to process multiband data and it is implemented to perform unsupervised scene segmentation using both spatial and spectral information. The nonlinear dynamical network is capable of achieving segmentation of objects in a scene by the synchronization of oscillators that receive local excitatory inputs from a collection of local neighbors and desynchronization between oscillators corresponding to different objects. The original LEGION model was designed for single-band imagery. The proposed multiband version of LEGION is implemented such that the connections in the oscillator network receive the spectral pixel vectors in the hyperspectral data as excitatory inputs. Euclidean distances between spectra in local neighborhoods are used as the measure of closeness in the network. The ability of the proposed approach to perform natural and urban scene segmentation for geospatial analysis is assessed. Our approach is tested on two hyperspectral datasets with notably different sensor properties and scene content.

Electrical Coupling Mediates Tunable Low-Frequency Oscillations and Resonance in the Cerebellar Golgi Cell Network

Movement disorders such as tremor and akinesia observed in Parkinson's disease have been attributed to dopamine (DA) depletion in the basal ganglia. The changes in subcortical neuronal discharge patterns that follow DA depletion have been a matter of much discussion. Here, we implanted rats with chronic recording electrodes bilaterally in the striatum (CPu) and external globus pallidus (GPe), and induced both acute and repeated DA blockade by administration of high-dose haloperidol. Recordings were made in baseline states, as well as before and after haloperidol injections, which rendered rats akinetic. The immediate physiological effect of pharmacological DA blockade was the development of prominent oscillatory firing in the 6-8 Hz range in both CPu and GPe. Importantly, this oscillatory pattern was not accompanied by consistent changes in the firing rate of either CPu or GPe neurons. Cross-correlation analysis further indicated that neurons within the CPu and GPe fired synchronously after DA blockade. Furthermore, although phase lags between neuronal discharges in the GPe and CPu were uniformly distributed prior to haloperidol administration, CPu significantly lagged GPe discharges after repeated DA blockade. Our results demonstrate that acute DA blockade is sufficient to produce synchronous oscillatory activity across basal ganglia neuron populations, and that prolonged DA blockade results in phase lag changes in pallidostriatal synchrony.

Everyday locomotion and obstacle avoidance requires effective gait adaptation in response to sensory cues. Many studies have shown that efficient motor actions are associated with μ rhythm (8-13 Hz) and β band (13-35 Hz) local field desynchronizations in sensorimotor and parietal cortex, whereas a number of cognitive task studies have reported higher behavioral accuracy to be associated with increases in β band power in prefrontal and sensory cortex. How these two distinct patterns of β band oscillations interplay during gait adaptation, however, has not been established. Here we recorded 108 channel EEG activity from 18 participants (10 males, 22-35 years old) attempting to walk on a treadmill in synchrony with a series of pacing cue tones, and quickly adapting their step rate and length to sudden shifts in pacing cue tempo. Independent component analysis parsed each participant's EEG data into maximally independent component (IC) source processes, which were then grouped across participants into distinct spatial/spectral clusters. Following cue tempo shifts, mean β band power was suppressed for IC sources in central midline and parietal regions, whereas mean β band power increased in IC sources in or near medial prefrontal and dorsolateral prefrontal cortex. In the right dorsolateral prefrontal cortex IC cluster, the β band power increase was stronger during (more effortful) step shortening than during step lengthening. These results thus show that two distinct patterns of β band activity modulation accompany gait adaptations: one likely serving movement initiation and execution; and the other, motor control and inhibition. Understanding brain dynamics supporting gait adaptation is crucial for understanding motor deficits in walking, such as those associated with aging, stroke, and Parkinson's. Only a few electromagnetic brain imaging studies have examined neural correlates of human upright walking. Here, application of independent component analysis to EEG data recorded during treadmill walking allowed us to uncover two distinct β band oscillatory cortical networks that are active during gait adaptation to shifts in the tempo of an auditory pacing cue: (8-13 Hz) μ rhythm and (13-35 Hz) β band power decreases in central and parietal cortex and (14-20 Hz) β band power increases in frontal brain areas. These results provide a fuller framework for electrophysiological studies of cortical gait control and its disorders.

A meshless method for geometric nonlinear analysis of arbitrary polygonal and circular stiffened plates

This paper focuses on large neural networks whose synaptic connectivity matrices are randomly chosen from certain random matrix ensembles. The dynamics of these networks can be characterized by the eigenvalue spectra of their connectivity matrices. In reality, neurons in a network do not necessarily behave in a similar way, but may belong to several different categories. The first study of the spectra of two-component neural networks was carried out by Rajan and Abbott [Phys. Rev. Lett. 97, 188104 (2006)]. In their model, neurons are either "excitatory" or "inhibitory," and strengths of synapses from different types of neurons have Gaussian distributions with different means and variances. A surprising finding by Rajan and Abbott is that the eigenvalue spectra of these types of random synaptic matrices do not depend on the mean values of their elements. In this paper we prove that this is true even for a much more general type of random neural network, where there is a finite number of types of neurons and their synaptic strengths have correlated distributions. Furthermore, using the diagrammatic techniques, we calculate the explicit formula for the spectra of synaptic matrices of multicomponent neural networks.