Temporal synchronization of CA1 pyramidal cells by high-frequency, depressing inhibition, in the presence of intracellular noise

The Sharp Wave-associated Ripple is a high-frequency, extracellular recording observed in the rat hippocampus during periods of immobility. During the ripple, pyramidal cells synchronize over a short period of time despite the fact that these cells have sparse recurrent connections. Additionally, the timing of synchronized pyramidal cell spiking may be critical for encoding information that is passed on to post-hippocampal targets. Both the synchronization and precision of pyramidal cells is believed to be coordinated by inhibition provided by a vast array of interneurons. This dissertation proposes a minimal model consisting of a single interneuron which synapses onto a network of uncoupled pyramidal cells. It is shown that fast decaying, high-frequency, depressing inhibition is capable of rapidly synchronizing the pyramidal cells and modulating spike timing. In addition, these mechanisms are robust in the presence of intracellular noise. The existence and stability of synchronous, periodic solutions using geometric singular perturbation techniques are proven. The effects of synaptic strength, synaptic recovery, and inhibition frequency are discussed. In contrast to prior work, which suggests that the ripple is produced by homogeneous populations of either pyramidal cells or interneurons, the results presented here suggest that cooperation between interneurons and pyramidal cells is necessary for ripple genesis

Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks

We study a model for a network of synaptically coupled, excitable neurons to identify the role of coupling delays in generating different network behaviors. The network consists of two distinct populations, each of which contains one excitatory-inhibitory neuron pair. The two pairs are coupled via delayed synaptic coupling between the excitatory neurons, while each inhibitory neuron is connected only to the corresponding excitatory neuron in the same population. We show that multiple equilibria can exist depending on the strength of the excitatory coupling between the populations. We conduct linear stability analysis of the equilibria and derive necessary conditions for delay-induced Hopf bifurcation. We show that these can induce two qualitatively different phase-locked behaviors, with the type of behavior determined by the sizes of the coupling delays. Numerical bifurcation analysis and simulations supplement and confirm our analytical results. Our work shows that the resting equilibrium point is unaffected by the coupling, thus the network exhibits bistability between a rest state and an oscillatory state. This may help understand how rhythms spontaneously arise in neuronal networks.Natural Sciences and Engineering Research Council of Canada