Cellular and Network Mechanisms of Slow Oscillatory Activity (<1 Hz) and Wave Propagations in a Cortical Network Model

Abstract

Slow oscillatory activity (<1 Hz) is observed in vivo in the cortex during slow-wave sleep or under anesthesia and in vitro when the bath solution is chosen to more closely mimic cerebrospinal fluid. Here we present a biophysical network model for the slow oscillations observed in vitro that reproduces the single neuron behaviors and collective network firing patterns in control as well as under pharmacological manipulations. The membrane potential of a neuron oscillates slowly (at <1 Hz) between a down state and an up state; the up state is maintained by strong recurrent excitation balanced by inhibition, and the transition to the down state is due to a slow adaptation current (Na(+)-dependent K(+) current). Consistent with in vivo data, the input resistance of a model neuron, on average, is the largest at the end of the down state and the smallest during the initial phase of the up state. An activity wave is initiated by spontaneous spike discharges in a minority of neurons, and propagates across the network at a speed of 3-8 mm/s in control and 20-50 mm/s with inhibition block. Our work suggests that long-range excitatory patchy connections contribute significantly to this wave propagation. Finally, we show with this model that various known physiological effects of neuromodulation can switch the network to tonic firing, thus simulating a transition to the waking state.

Impact of membrane bistability on dynamical response of neuronal populations

“…We tested the predication by using a neuron model with biophysically realistic membrane currents, which includes a noninactivating potassium current controlling the up state and an inward rectifying potassium current stabilizing the down state [3]. We find that the normal- ized frequency response is strongly enhanced with the development of the up state [14].…”

Extreme-value statistics of brain networks: Importance of balanced condition

“…Further analysis of a dynamical model of cortical networks with the balanced condition for various ratios of inhibitory and excitatory neurons reveals a connection between the spectra of connectivity matrix and the dynamical response [13]. Balance between recurrent excitation and inhibition generates stable periods of activity [14]. There have been several discussions on how synaptic matrices in the brain achieve the balanced condition; for instance, it has been demonstrated that the balanced condition in sensory pathways and memory networks is maintained through a plasticity mechanism at inhibitory synapses [15].…”

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

“…In previous work [11], we have followed Compte et al [5] and have interpreted the slow oscillation as a form of phase transition. The depolarized "up" and hyperpolarized "down" states are viewed as stable solutions for the mean membrane potential, with the down-to-up transitions being driven possibly by spontaneous neurotransmitter release [12] or random summation of EPSPs [13], and the up-to-down transition driven possibly by voltage-gated ionic (e.g., K + ) currents [5,6,14], or changes in synaptic weight [6,15].…”

“…In terms of cortical modelling, Compte et al [5] showed that a simple one-dimensional collection of neurons can support a prototypical slow oscillation. Hill and Tononi [6] have carried out simulations with a more comprehensive thalamocortical network that show the importance of cortical-cortical interactions in establishing and maintaining the oscillation.…”

“…The depolarized "up" and hyperpolarized "down" states are viewed as stable solutions for the mean membrane potential, with the down-to-up transitions being driven possibly by spontaneous neurotransmitter release [12] or random summation of EPSPs [13], and the up-to-down transition driven possibly by voltage-gated ionic (e.g., K + ) currents [5,6,14], or changes in synaptic weight [6,15]. Molaee-Ardekani et al, using a broadly similar model, have taken a different view of the phenomenon, interpreting the small slow waves seen in light anaesthesia as small, unstable excursions away from the equilibrium state, and the large slow waves of deep anaesthesia as limit cycles of the bulk behavior of the cortex [16].…”