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Register a new userTransient termination of synaptically sustained spiking by stochastic inputs in a pair of coupled Type 1 neurons
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We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing or oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations, hence destroying the stable limit cycle. Further application of the noise may return the system to spiking activity. In a particular noise range, the transition times between the oscillating and the resting state are strongly asymmetric. We numerically investigate an approximate basin of attraction, A, of the periodic orbit and use Markov process theory to explain the firing behavior in terms of the probability of escape of trajectories from A
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Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal description of neurons with adaptation. We derive an integral equation with colored noise that governs the stochastic dynamics of the population activity in response to time-dependent stimulation and calculate the spectral density in the asynchronous state. We show that systems of coupled populations with adaptation can generate a frequency band in which sensory information is preferentially encoded. The theory is applicable to fully as well as randomly connected networks, and to leaky integrate-and-fire as well as to generalized spiking neurons with adaptation on multiple time scales.
The macroscopic dynamics of large populations of neurons can be mathematically analyzed using low-dimensional firing-rate or neural-mass models. However, these models fail to capture spike synchronization effects of stochastic spiking neurons such as the non-stationary population response to rapidly changing stimuli. Here, we derive low-dimensional firing-rate models for homogeneous populations of general renewal-type neurons, including integrate-and-fire models driven by white noise. Renewal models account for neuronal refractoriness and spike synchronization dynamics. The derivation is based on an eigenmode expansion of the associated refractory density equation, which generalizes previous spectral methods for Fokker-Planck equations to arbitrary renewal models. We find a simple relation between the eigenvalues, which determine the characteristic time scales of the firing rate dynamics, and the Laplace transform of the interspike interval density or the survival function of the renewal process. Analytical expressions for the Laplace transforms are readily available for many renewal models including the leaky integrate-and-fire model. Retaining only the first eigenmode yields already an adequate low-dimensional approximation of the firing-rate dynamics that captures spike synchronization effects and fast transient dynamics at stimulus onset. We explicitly demonstrate the validity of our model for a large homogeneous population of Poisson neurons with absolute refractoriness, and other renewal models that admit an explicit analytical calculation of the eigenvalues. The here presented eigenmode expansion provides a systematic framework for novel firing-rate models in computational neuroscience based on spiking neuron dynamics with refractoriness.
We review different aspects of the simulation of spiking neural networks. We start by reviewing the different types of simulation strategies and algorithms that are currently implemented. We next review the precision of those simulation strategies, in particular in cases where plasticity depends on the exact timing of the spikes. We overview different simulators and simulation environments presently available (restricted to those freely available, open source and documented). For each simulation tool, its advantages and pitfalls are reviewed, with an aim to allow the reader to identify which simulator is appropriate for a given task. Finally, we provide a series of benchmark simulations of different types of networks of spiking neurons, including Hodgkin-Huxley type, integrate-and-fire models, interacting with current-based or conductance-based synapses, using clock-driven or event-driven integration strategies. The same set of models are implemented on the different simulators, and the codes are made available. The ultimate goal of this review is to provide a resource to facilitate identifying the appropriate integration strategy and simulation tool to use for a given modeling problem related to spiking neural networks.
Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent states of the network, but their origin has been not yet clarified. Here, we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50 -- 2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics like finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly simulate a model of a local cortical microcircuit consisting of eight neuron types. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.
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