Excitatory-Inhibitory Balance, Imbalance, and Amplification in Cortical Network Models

Doctoral Dissertation

Abstract

Understanding the relationship between a sensory stimulus and the spiking activity of cortical populations is a central problem in neuroscience. Dense recurrent connectivity in local cortical circuits can lead to counterintuitive response properties, raising the question of whether there are simple arithmetical rules for relating circuits’ connectivity structure to their response properties. One such arithmetic is provided by the mean field theory of balanced networks, which is derived in a limit where excitatory and inhibitory synaptic currents precisely balance on average. However, balanced network theory is not applicable to some biologically relevant connectivity structures. We show that cortical circuits with such structure are susceptible to an amplification mechanism arising when excitatory-inhibitory balance is broken at the level of local subpopulations, but maintained at a global level. This amplification, which can be quantified by a linear correction to the classical mean field theory of balanced networks, explains several response properties observed in cortical recordings and provides fundamental insights into the relationship between connectivity structure and neural responses in cortical circuits.

Attributes

Attribute NameValues
Author Christopher L. Ebsch
Contributor Robert Rosenbaum, Research Director
Degree Level Doctoral Dissertation
Degree Discipline Applied and Computational Mathematics and Statistics
Degree Name Doctor of Philosophy
Banner Code
  • PHD-ACMS

Defense Date
  • 2019-03-29

Submission Date 2019-04-04
Subject
  • Applied Mathematics

  • Mathematical Modeling

  • Neuroscience

Record Visibility and Access Public
Content License
  • All rights reserved

Departments and Units
Catalog Record

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