Slow population activities (SPAs) are population activities in the brain with frequencies of less than 5 Hz. SPAs are prominent in many brain structures including the neocortex and the hippocampus. Examples of SPAs include the neocortical EEG δ waves and the hippocampal large amplitude irregular activities during NREM sleep. These in vivo SPAs are believed to play a fundamental role in brain plasticity. However, despite many experimental attempts to understand SPAs, their mechanisms are still not well understood. It is unclear how the individual neurons can sustain low frequency activities on the network as a whole. In this thesis, we demonstrate that a mathematical and computational perspective is indispensable in understanding slow population phenomena and generating testable hypotheses for future experiments. Our focus is on a hippocampal slice preparation exhibiting spontaneous, inhibitory-based SPAs (hippocampal SPAs). We develop a multi-pronged approach consisting of parameter extraction, simulation, and mathematical analysis to elucidate the mechanisms responsible for hippocampal SPAs. Our results suggest that hippocampal SPAs are an emergent phenomenon. In other words, the network “slowness” is not directly represented by any particular individual element within the network. Instead, the low frequency activities on the network are the result of interactions between synaptic and intrinsic characteristics of individual inhibitory interneurons. Our simulations quantify these characteristics which underlie hippocampal SPAs. Specifically, our simulations predict that individual interneurons should 1) be moderately fast-spiking above threshold before the increase in spike frequency slows down with increasing drive, and 2) be well connected with one another for SPAs to occur. We also predict that excitatory noise levels have a larger influence on hippocampal SPAs than mean excitatory drive. Subsequent mathematical analyses show that the synaptic and intrinsic conditions of individual interneurons as predicted by simulations promote network multi-stability. Hippocampal SPAs occur when the network switches from one network firing state to another. Since many of the parameters we use for simulations are extracted from experiments, our simulation model is likely a reasonable representation of actual biological mechanisms in hippocampal networks.

Slow population activities (SPAs) are population activities in the brain with frequencies of less than 5 Hz. SPAs are prominent in many brain structures including the neocortex and the hippocampus. Examples of SPAs include the neocortical EEG δ waves and the hippocampal large amplitude irregular activities during NREM sleep. These in vivo SPAs are believed to play a fundamental role in brain plasticity. However, despite many experimental attempts to understand SPAs, their mechanisms are still not well understood. It is unclear how the individual neurons can sustain low frequency activities on the network as a whole. In this thesis, we demonstrate that a mathematical and computational perspective is indispensable in understanding slow population phenomena and generating testable hypotheses for future experiments. Our focus is on a hippocampal slice preparation exhibiting spontaneous, inhibitory-based SPAs (hippocampal SPAs). We develop a multi-pronged approach consisting of parameter extraction, simulation, and mathematical analysis to elucidate the mechanisms responsible for hippocampal SPAs. Our results suggest that hippocampal SPAs are an emergent phenomenon. In other words, the network “slowness” is not directly represented by any particular individual element within the network. Instead, the low frequency activities on the network are the result of interactions between synaptic and intrinsic characteristics of individual inhibitory interneurons. Our simulations quantify these characteristics which underlie hippocampal SPAs. Specifically, our simulations predict that individual interneurons should 1) be moderately fast-spiking above threshold before the increase in spike frequency slows down with increasing drive, and 2) be well connected with one another for SPAs to occur. We also predict that excitatory noise levels have a larger influence on hippocampal SPAs than mean excitatory drive. Subsequent mathematical analyses show that the synaptic and intrinsic conditions of individual interneurons as predicted by simulations promote network multi-stability. Hippocampal SPAs occur when the network switches from one network firing state to another. Since many of the parameters we use for simulations are extracted from experiments, our simulation model is likely a reasonable representation of actual biological mechanisms in hippocampal networks.