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Mathematical Modeling of Synaptic Transmission at Chemical Synapses

  • Synapses are connections between different nerve cells that form an essential link in neural signal transmission. It is generally distinguished between electrical and chemical synapses, where chemical synapses are more common in the human brain and are also the type we deal with in this work. In chemical synapses, small container-like objects called vesicles fill with neurotransmitter and expel them from the cell during synaptic transmission. This process is vital for communication between neurons. However, to the best of our knowledge no mathematical models that take different filling states of the vesicles into account have been developed before this thesis was written. In this thesis we propose a novel mathematical model for modeling synaptic transmission at chemical synapses which includes the description of vesicles of different filling states. The model consists of a transport equation (for the vesicle growth process) plus three ordinary differential equations (ODEs) and focuses on the presynapse and synaptic cleft. The well-posedness is proved in detail for this partial differential equation (PDE) system. We also propose a few different variations and related models. In particular, an ODE system is derived and a delay differential equation (DDE) system is formulated. We then use nonlinear optimization methods for data fitting to test some of the models on data made available to us by the Animal Physiology group at TU Kaiserslautern.

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Metadaten
Author:Philipp Blandfort
URN (permanent link):urn:nbn:de:hbz:386-kluedo-59604
Advisor:Sven O. Krumke, Christina Surulescu
Document Type:Master's Thesis
Language of publication:English
Publication Date:2020/04/23
Year of Publication:2020
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2020/04/23
Number of page:VI, 92
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):34-XX ORDINARY DIFFERENTIAL EQUATIONS
35-XX PARTIAL DIFFERENTIAL EQUATIONS
92-XX BIOLOGY AND OTHER NATURAL SCIENCES
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell (CC BY-NC 4.0)