Dynamics of Integrate-and-Fire Model of Hippocampal Circuit

Student: Ricky He
Mentor: Pamela Pyzza (Department of Mathematics and Computer Science)

The study of the human brain has become increasingly popular in contemporary science and yet the dynamics of neuronal networks within the brain are not well understood. We investigate the dynamics of an idealized neuronal network in the hippocampus, which comprises three types of integrate-and-fire model neurons that interact with each other based on their unique properties. Our model balances some loss of detail for the individual neurons with computational efficiency to investigate the behavior of the entire network. Given various parameter values and connectivity structures, we hope to gain a better understanding of how these properties impact the network dynamics.

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. 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. However, the complexity of this model, compounded by network properties makes network simulations with HH computationally expensive. In this work, we will focus on the network dynamics, rather than individual neuron properties and consider a simpler, more computationally efficient model called the integrate-and-fire (I&F) neuron. 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 spike input, and other parameters, in which our model can qualitatively reproduce the behavior seen in other computational models, as described in Kopell et al. (2010), which employ the HH model. We further consider network dynamics created by various network architectures including all-to-all coupled and sparse network connectivity to begin to make links between network properties and network behavior.