Minimal Size of Cell Assemblies Coordinated by Gamma Oscillations

In networks of excitatory and inhibitory neurons with mutual synaptic coupling, specific drive to sub-ensembles of cells often leads to gamma-frequency (25–100 Hz) oscillations. When the number of driven cells is too small, however, the synaptic interactions may not be strong or homogeneous enough to support the mechanism underlying the rhythm. Using a combination of computational simulation and mathematical analysis, we study the breakdown of gamma rhythms as the driven ensembles become too small, or the synaptic interactions become too weak and heterogeneous. Heterogeneities in drives or synaptic strengths play an important role in the breakdown of the rhythms; nonetheless, we find that the analysis of homogeneous networks yields insight into the breakdown of rhythms in heterogeneous networks. In particular, if parameter values are such that in a homogeneous network, it takes several gamma cycles to converge to synchrony, then in a similar, but realistically heterogeneous network, synchrony breaks down altogether. This leads to the surprising conclusion that in a network with realistic heterogeneity, gamma rhythms based on the interaction of excitatory and inhibitory cell populations must arise either rapidly, or not at all. For given synaptic strengths and heterogeneities, there is a (soft) lower bound on the possible number of cells in an ensemble oscillating at gamma frequency, based simply on the requirement that synaptic interactions between the two cell populations be strong enough. This observation suggests explanations for recent experimental results concerning the modulation of gamma oscillations in macaque primary visual cortex by varying spatial stimulus size or attention level, and for our own experimental results, reported here, concerning the optogenetic modulation of gamma oscillations in kainate-activated hippocampal slices. We make specific predictions about the behavior of pyramidal cells and fast-spiking interneurons in these experiments.Collaborative Research in Computational NeuroscienceNational Institutes of Health (U.S.) (grant 1R01 NS067199)National Institutes of Health (U.S.) (grant DMS 0717670)National Institutes of Health (U.S.) (grant 1R01 DA029639)National Institutes of Health (U.S.) (grant 1RC1 MH088182)National Institutes of Health (U.S.) (grant DP2OD002002)Paul G. Allen Family FoundationnGoogle (Firm

Emergence of beta/gamma oscillations: ING, PING, and what about RING?

Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. Background: Oscillatory activity in high-beta and gamma bands (20-80Hz) is known to play an important role in cortical processing being linked to cognitive processes and behavior. Beta/gamma oscillations are thought to emerge in local cortical circuits via two mechanisms: the interaction between excitatory principal cells and inhibitory interneurons – the pyramidal-interneuron gamma (PING) [1], and in networks of coupled inhibitory interneurons under tonic excitation – the interneuronal gamma (ING) [2]. Experimental evidence underlines the important role of inhibitory interneurons and especially of the fast spiking (FS) interneurons [3,4]. We show in simulation that an important property of FS neurons, namely the membrane resonance (frequency preference), represents an additional mechanism – the resonance induced gamma (RING), i.e. modulation of oscillatory discharge by resonance. RING promotes frequency stability and enables oscillations in purely excitatory networks. Methods: Local circuits were modeled with small world networks of 80% excitatory and 20% inhibitory neuron populations interconnected in small-world topology by realistic conductance-based synapses. Neuron populations were leaky integrate and fire (LIF) or Izhikevich resonator (RES) neurons. We also tested networks of purely inhibitory and purely excitatory RES neurons. Networks were stimulated with miniature postsynaptic potentials (MINIs) [5] and with low frequency sinusoidal (0.5 Hz) input that mimics the effect of gratings passing trough the visual field. The activity was calibrated to match recordings from cat visual cortex (firing rate, oscillatory activity). Results: Sinusoidal input modulates network oscillation frequency. This effect is most prominent in IF excitatory and IF inhibitory (IF-IF) networks and less prominent (about 4 times) in IF-RES or RES-IF networks where frequency remains relatively stable. The most stable frequency was observed in networks of pure resonators (RES-RES, None-RES, RES-None). Interestingly, purely excitatory RES networks (RES-None) were also able to exhibit oscillations through RING. By contrast purely excitatory or inhibitory IF networks (IF-None, None-IF) were not able to express oscillations under these conditions, matching experimental parameters. Conclusions: In both PING and ING, adding membrane resonance to principal cells or inhibitory interneurons stabilizes network oscillation frequency via the RING mechanism. Notably, in networks of purely excitatory networks, where ING and PING are not defined, oscillations can emerge via the RING mechanism if membrane resonance is expressed. Thus, RING appears as a potentially important mechanism for promoting stable network oscillations

A thermal model for adaptive competition in a market

New continuous and stochastic extensions of the minority game, devised as a fundamental model for a market of competitive agents, are introduced and studied in the context of statistical physics. The new formulation reproduces the key features of the original model, without the need for some of its special assumptions and, most importantly, it demonstrates the crucial role of stochastic decision-making. Furthermore, this formulation provides the exact but novel non-linear equations for the dynamics of the system.Comment: 4 RevTeX pages, 3 EPS figures. Revised versio

Complete synchronization in coupled Type-I neurons

For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory-excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally we report an observation of noise-induced CS between non-identical neurons coupled bidirectionally through random non-zero couplings in an all-to- all way in a large neuronal ensemble.Comment: 24 pages, 9 figure

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

Deterministic Partial Differential Equation Model for Dose Calculation in Electron Radiotherapy

Treatment with high energy ionizing radiation is one of the main methods in modern cancer therapy that is in clinical use. During the last decades, two main approaches to dose calculation were used, Monte Carlo simulations and semi-empirical models based on Fermi-Eyges theory. A third way to dose calculation has only recently attracted attention in the medical physics community. This approach is based on the deterministic kinetic equations of radiative transfer. Starting from these, we derive a macroscopic partial differential equation model for electron transport in tissue. This model involves an angular closure in the phase space. It is exact for the free-streaming and the isotropic regime. We solve it numerically by a newly developed HLLC scheme based on [BerCharDub], that exactly preserves key properties of the analytical solution on the discrete level. Several numerical results for test cases from the medical physics literature are presented.Comment: 20 pages, 7 figure

The response of a classical Hodgkin–Huxley neuron to an inhibitory input pulse

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations