Date Thesis Awarded
4-2022
Access Type
Honors Thesis -- Open Access
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Mainak Patel
Committee Members
Leah Shaw
Margaret Saha
Abstract
In systems neuroscience, circuit models of cortical structures can be used to deconstruct mechanisms responsible for spike patterns that generate a variety of behaviors observed in the brain. In particular, mathematical simulations of these circuits can replicate complex dynamical behaviors that mirror not only macroscopically patterns observed in the brain, but also a significant amount of experimentally characterized minutiae. These models are capable of analyzing neural mechanisms by explicitly deconstructing connectivities between populations of neurons in ways that tend to be empirically inaccessible. This work presents two such models; one in the rat somatosensory barrel cortex, responsible for processing sensory information from whiskers, and one in the CA3 subfield of the hippocampus, responsible for, among other higher brain functions, memory storage and retrieval. In the former we model the generation of multiwhisker receptive fields by lateral (as opposed to feedforward) synaptic connections in layer IV of the barrel cortex, and show that this hypothesis can capture a range of experimentally characterized responses. In the latter we study the generation of gamma frequency oscillations in the CA3, in particular examining the shift between two network regimes of oscillations upon activation of NMDA receptors. These models are constructed as networks of coupled ordinary differential equations representing integrate and fire neurons, and simulations are computed via numerical integration by the forward Euler method.
Recommended Citation
Ma, Linda, "Modeling and Analyses of Mechanisms Underlying Network Synaptic Dynamics in Two Neural Circuits" (2022). Undergraduate Honors Theses. William & Mary. Paper 1750.
https://scholarworks.wm.edu/honorstheses/1750
