Spontaneous cortical population activity exhibits a multitude of oscillatory patterns, which often display synchrony during slow-wave sleep or under certain anesthetics and stay asynchronous during quiet wakefulness. The mechanisms behind these cortical states and transitions among them are not completely understood. Here we study spontaneous population activity patterns in random networks of spiking neurons of mixed types modeled by Izhikevich equations. Neurons are coupled by conductance-based synapses subject to synaptic noise. We localize the population activity patterns on the parameter diagram spanned by the relative inhibitory synaptic strength and the magnitude of synaptic noise. In absence of noise, networks display transient activity patterns, either oscillatory or at constant level. The effect of noise is to turn transient patterns into persistent ones: for weak noise, all activity patterns are asynchronous non-oscillatory independently of synaptic strengths; for stronger noise, patterns have oscillatory and synchrony characteristics that depend on the relative inhibitory synaptic strength. In the region of parameter space where inhibitory synaptic strength exceeds the excitatory synaptic strength and for moderate noise magnitudes networks feature intermittent switches between oscillatory and quiescent states with characteristics similar to those of synchronous and asynchronous cortical states, respectively. We explain these oscillatory and quiescent patterns by combining a phenomenological global description of the network state with local descriptions of individual neurons in their partial phase spaces. Our results point to a bridge from events at the molecular scale of synapses to the cellular scale of individual neurons to the collective scale of neuronal populations.Electronic supplementary materialThe online version of this article (10.1007/s10827-018-0688-6) contains supplementary material, which is available to authorized users.

In a neuron with hyperpolarization activated current (I_{h}), the correct input frequency leads to an enhancement of the output response. This behavior is known as resonance and is well described by the neuronal impedance. In a simple neuron model we derive equations for the neuron's resonance and we link its frequency and existence with the biophysical properties of I_{h}. For a small voltage change, the component of the ratio of current change to voltage change (dI/dV) due to the voltage-dependent conductance change (dg/dV) is known as derivative conductance (G_{h}^{Der}). We show that both G_{h}^{Der} and the current activation kinetics (characterized by the activation time constant τ_{h}) are mainly responsible for controlling the frequency and existence of resonance. The increment of both factors (G_{h}^{Der} and τ_{h}) greatly contributes to the appearance of resonance. We also demonstrate that resonance is voltage dependent due to the voltage dependence of G_{h}^{Der}. Our results have important implications and can be used to predict and explain resonance properties of neurons with the I_{h} current.

stimuli and contributes to signal propagation, neural coding, and dynamic stability. It also plays an important role in cognitive processes. In this work, by means of studying intracellular recordings from CA1 neurons in rats and results from numerical simulations, we demonstrate that self-sustained activity presents high variability of patterns, such as low neural firing rates and activity in the form of small-bursts in distinct neurons. In our numerical simulations, we consider random networks composed of coupled, adaptive exponential integrate-and-fire neurons. The neural dynamics in the random networks simulates regular spiking (excitatory) and fast spiking (inhibitory) neurons. We show that both the connection probability and network size are fundamental properties that give rise to self-sustained activity in qualitative agreement with our experimental results. Finally, we provide a more detailed description of self-sustained activity in terms of lifetime distributions, synaptic conductances, and synaptic currents.