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Register a new userMathematical Analysis and Simulations of the Neural Circuit for Locomotion in Lamprey
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We analyze the dynamics of the neural circuit of the lamprey central pattern generator (CPG). This analysis provides insights into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behaviour regimes (characterized by phase and amplitude relationships between oscillators) of forward/backward swimming, and turning, can be controlled using the neural connection strengths and external inputs.
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In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of the neural activity, as expected, but it can also promote neural reactivation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neurons death). However, the random pruning of the connections is able to reverse the action of inhibition, i.e. in a sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of the neurons (neurons rebirth). Thus the number of firing neurons reveals a minimum at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by the neurons with higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving an analytic mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, the system passes from a perfectly regular evolution to an irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.
The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.
Neural noise sets a limit to information transmission in sensory systems. In several areas, the spiking response (to a repeated stimulus) has shown a higher degree of regularity than predicted by a Poisson process. However, a simple model to explain this low variability is still lacking. Here we introduce a new model, with a correction to Poisson statistics, which can accurately predict the regularity of neural spike trains in response to a repeated stimulus. The model has only two parameters, but can reproduce the observed variability in retinal recordings in various conditions. We show analytically why this approximation can work. In a model of the spike emitting process where a refractory period is assumed, we derive that our simple correction can well approximate the spike train statistics over a broad range of firing rates. Our model can be easily plugged to stimulus processing models, like Linear-nonlinear model or its generalizations, to replace the Poisson spike train hypothesis that is commonly assumed. It estimates the amount of information transmitted much more accurately than Poisson models in retinal recordings. Thanks to its simplicity this model has the potential to explain low variability in other areas.
It is shown that, contrary to the claims in a recent letter by Haldeman and Beggs (PRL, 94, 058101, 2005), the branching ratio in epileptic cortical cultures is smaller than one. In addition, and also in contrast to claims made in that paper, the number of metastable states is not significantly different between cortical cultures in the critical state and cultures made epileptic using picrotoxin.
Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we generalize the EI cortical model introduced in a previous paper (S.Scarpetta et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing effects of noise on the spontaneous activity of the nonlinear system, in order to account for the experimental results of Segev et al.. Analytically we can distinguish different regimes of activity, depending from the model parameters. Using analytical results as a guide line, we perform simulations of the nonlinear stochastic model in two different regimes, B and C. The Power Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI) distributions are computed, and compared with experimental results. In regime B the network shows stochastic resonance phenomena and noise induces aperiodic collective synchronous oscillations that mimic experimental observations at 0.5 mM Ca concentration. In regime C the model shows spontaneous synchronous periodic activity that mimic activity observed at 1 mM Ca concentration and the PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function effects) the PSD shows a broad band peak at low frequency. This feature, observed experimentally, does not find explanation in the previous models. Besides we identify parametric changes (namely increase of noise or decreasing of excitatory connections) that reproduces the fading of periodicity found experimentally at long times, and we identify a way to discriminate between those two possible effects measuring experimentally the low frequency PSD.
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