Dynamics of Hippocampal Circuit described by Hodgkin-Huxley Model

The behavior of neuronal networks in the hippocampus is the topic of many experimental and modeling studies, and yet much of these networks’ structures and functionalities in this part of the brain are not well understood. We can use computational models to reproduce some of the hippocampal behavior seen experimentally and begin to investigate possible underlying mechanisms for the network activity. Many computational neuron model are created today to focus different features of the neuron system. A common computational neuron model used for modeling such networks is the Hodgkin-Huxley (HH) neuron, which can describe the spiking behavior of a single neuron very well. In this work, we will focus on replicating the dynamics of the potential in a single neuron and the interactions in a small network as described in Kopell et al. (2010). Motivated by experimental work, we consider a network of three types of neurons: fast excitatory neurons (decay rate ~2-5 ms), fast inhibitory interneurons (decay rate ~4-10ms), and a slow inhibitory neuron based on the oriens lacunosum-moleculare (O-LM) cell, whose interactions are believed to be responsible for network oscillations measured in the characteristic gamma (30-90 Hz) and theta (4-12 Hz) frequency bands. We investigate parameter regimes for the coupling coefficients, external input, and other parameters, in which our model can qualitatively reproduce behavior seen in other computational models to begin to make links between network properties and network behavior