Caudron, Quentin (2012) Neuronal computation on complex dendritic morphologies. PhD thesis, University of Warwick.

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Abstract

When we think about neural cells, we immediately recall the wealth of electrical
behaviour which, eventually, brings about consciousness. Hidden deep in the
frequencies and timings of action potentials, in subthreshold oscillations, and in
the cooperation of tens of billions of neurons, are synchronicities and emergent behaviours
that result in high-level, system-wide properties such as thought and cognition.
However, neurons are even more remarkable for their elaborate morphologies,
unique among biological cells. The principal, and most striking, component of neuronal
morphologies is the dendritic tree.
Despite comprising the vast majority of the surface area and volume of a
neuron, dendrites are often neglected in many neuron models, due to their sheer
complexity. The vast array of dendritic geometries, combined with heterogeneous
properties of the cell membrane, continue to challenge scientists in predicting neuronal
input-output relationships, even in the case of subthreshold dendritic currents.
In this thesis, we will explore the properties of neuronal dendritic trees, and
how they alter and integrate the electrical signals that diffuse along them. After
an introduction to neural cell biology and membrane biophysics, we will review
Abbott's dendritic path integral in detail, and derive the theoretical convergence
of its infinite sum solution. On certain symmetric structures, closed-form solutions
will be found; for arbitrary geometries, we will propose algorithms using various
heuristics for constructing the solution, and assess their computational convergences
on real neuronal morphologies. We will demonstrate how generating terms for the
path integral solution in an order that optimises convergence is non-trivial, and how a computationally-significant number of terms is required for reasonable accuracy.
We will, however, derive a highly-efficient and accurate algorithm for application to
discretised dendritic trees. Finally, a modular method for constructing a solution in
the Laplace domain will be developed.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QP Physiology
Library of Congress Subject Headings (LCSH):	Neurons, Neural networks (Neurobiology), Dendrites, Computational neuroscience
Official Date:	December 2012
Dates:	Date Event December 2012 Submitted
Institution:	University of Warwick
Theses Department:	Centre for Complexity Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Timofeeva, Yulia
Extent:	viii, 184 leaves : illustrations.
Language:	eng

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