Collective oscillations in disordered neural networks

We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogenous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N^2, analogously to the scaling found for the `splay state'.Comment: 8.5 Pages, 12 figures, submitted to Physical Review

Pattern formation in oscillatory complex networks consisting of excitable nodes

Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small skeletons for most oscillations. Complicated and seemingly random oscillatory patterns can be viewed as well-organized target waves propagating from center nodes along the shortest paths, and the shortest loops passing through both the center nodes and their driver nodes play the role of oscillation sources. Analyzing simple skeletons we are able to understand and predict various essential properties of the oscillations and effectively modulate the oscillations. These methods and results will give insights into pattern formation in complex networks, and provide suggestive ideas for studying and controlling oscillations in neural networks.Comment: 15 pages, 7 figures, to appear in Phys. Rev.

Temporal decorrelation of collective oscillations in neural networks with local inhibition and long-range excitation

We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations phase-lock with a phase-shift dependent on the strength of local inhibition. Increasing the strength of long-range excitation induces a transition to chaos via period-doubling or quasi-periodic scenarios. In the chaotic regime oscillatory activity undergoes fast temporal decorrelation. The generality of these dynamical properties is assessed in firing-rate models as well as in large networks of conductance-based neurons.Comment: 4 pages, 5 figures. accepted for publication in Physical Review Letter

Chaotic Phase Synchronization in Bursting-neuron Models Driven by a Weak Periodic Force

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1 : 1 phase locking between a single spike and one period of the force and 1 : l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale

Spike sorting for large, dense electrode arrays

Developments in microfabrication technology have enabled the production of neural electrode arrays with hundreds of closely spaced recording sites, and electrodes with thousands of sites are under development. These probes in principle allow the simultaneous recording of very large numbers of neurons. However, use of this technology requires the development of techniques for decoding the spike times of the recorded neurons from the raw data captured from the probes. Here we present a set of tools to solve this problem, implemented in a suite of practical, user-friendly, open-source software. We validate these methods on data from the cortex, hippocampus and thalamus of rat, mouse, macaque and marmoset, demonstrating error rates as low as 5%

Propagation of hippocampal ripples to the neocortex by way of a subiculum-retrosplenial pathway

Bouts of high frequency activity known as sharp wave ripples (SPW-Rs) facilitate communication between the hippocampus and neocortex. However, the paths and mechanisms by which SPW-Rs broadcast their content are not well understood. Due to its anatomical positioning, the granular retrosplenial cortex (gRSC) may be a bridge for this hippocampo-cortical dialogue. Using silicon probe recordings in awake, head-fixed mice, we show the existence of SPW-R analogues in gRSC and demonstrate their coupling to hippocampal SPW-Rs. gRSC neurons reliably distinguished different subclasses of hippocampal SPW-Rs according to ensemble activity patterns in CA1. We demonstrate that this coupling is brain state-dependent, and delineate a topographically-organized anatomical pathway via VGlut2-expressing, bursty neurons in the subiculum. Optogenetic stimulation or inhibition of bursty subicular cells induced or reduced responses in superficial gRSC, respectively. These results identify a specific path and underlying mechanisms by which the hippocampus can convey neuronal content to the neocortex during SPW-Rs

Brain-wide interactions during hippocampal sharp wave ripples

During periods of disengagement from the environment, transient population bursts, known as sharp wave ripples (SPW-Rs), occur sporadically. While numerous experiments have characterized the bidirectional relationship between SPW-Rs and activity in chosen brain areas, the topographic relationship between different segments of the hippocampus and brain-wide target areas has not been studied at high temporal and spatial resolution. Yet, such knowledge is necessary to infer the direction of communication. We analyzed two publicly available datasets with simultaneous high-density silicon probe recordings from across the mouse forebrain. We found that SPW-Rs coincide with a transient brain-wide increase in functional connectivity. In addition, we show that the diversity in SPW-R features, such as their incidence, magnitude, and intrahippocampal topography in the septotemporal axis, are correlated with slower excitability fluctuations in cortical and subcortical areas. Further, variations in SPW-R features correlated with the timing, sign, and magnitude of downstream responses with large-amplitude SPW-Rs followed by transient silence in extrahippocampal structures. Our findings expand on previous results and demonstrate that the activity patterns in extrahippocampal structures depend both on the intrahippocampal topographic origin and magnitude of hippocampal SPW-Rs

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

An Approach for Reliably Investigating Hippocampal Sharp Wave-Ripples In Vitro

Among the various hippocampal network patterns, sharp wave-ripples (SPW-R) are currently the mechanistically least understood. Although accurate information on synaptic interactions between the participating neurons is essential for comprehensive understanding of the network function during complex activities like SPW-R, such knowledge is currently notably scarce. counterpart. We show that slice storage in the interface chamber close to physiological temperature is the required condition to preserve network integrity that is necessary for the generation of SPW-R. Moreover, we demonstrate the utility of our method for studying synaptic and network properties of SPW-R, using electrophysiological and imaging methods that can only be applied in the submerged system.The approach presented here demonstrates a reliable and experimentally simple strategy for studying hippocampal sharp wave-ripples. Given its utility and easy application we expect our model to foster the generation of new insight into the network physiology underlying SPW-R