Neuromodulation of Hippocampal Microcircuits: Some Modeling and A Little Math

In this talk I will first give an overview of oscillations in the voltage of neuron assemblies, and models thereof. We use these to study neurons in the hippocampus, a part of the brain thought to be central in learning and memory functions. These neurons are connected via electrochemical synapses, which use neurotransmitter released from the presynaptic neuron to change the voltage of the postsynaptic neuron. Inhibitory neurons cause the voltage of their target to decrease. Oscillations in inhibitory-to-inhibitory (I-I) coupled neurons in the hippocampus have been studied extensively numerically, and with analytic continuation methods. Neuromodulation on short time scales, in the form of presynaptic short-term plasticity (STP), can dynamically alter the connectivity of neurons in such a microcircuit. I will discuss the mechanism of STP, and a model for it parameterized from experimental data for a specific synapse in the hippocampus. The goal of the project is to understand the effect of adding this plasticity to the (I-I) microcircuit, both through numerical simulation and bifurcation analysis of a discrete dynamical system.