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The stochastic modelling of the neuronal membrane potential in response to synaptic input

Kintis, Efthalia (2008) The stochastic modelling of the neuronal membrane potential in response to synaptic input. MSc(R) thesis, University of Glasgow.

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Abstract

A synapse is the term used to describe the connection between the axon of the donor cell and the part of the membrane of the target cell onto which the axon impinges . The arrival of an impulse at the site of the synapse causes the release of a chemical neurotransmitter which then diffuses across a narrow gap and binds onto the receptors of the postsynaptic neuron, altering the behaviour of the membrane and allowing the movement of ions between the intracellular and extracellular regions. These neurotransmitters differ in their strength, timing and their ability to excite or inhibit the postsynaptic neuron. Consequently, these inputs have a significant impact on the electrophysiological properties of the neuron. However synaptic properties are difficult to measure at microscopic level, whereas the stationary distribution of the membrane potential, while easy to measure, incorporates the underlying microscopic properties of synapses. The ion flow across the membrane of the postsynaptic neuron at the synapse is modelled as the product of the membrane conductance and of the potential difference, that is the difference of the membrane potential at the site of the synapse and the reversal potential for the specific ionic species to which the synapse is particularised . Therefore , synaptic behaviour is closely linked to synaptic conductance. Two models of synaptic behaviour are examined, namely the point conductance model proposed by Richardson (2004) and the exponential conductance model proposed by Rudolph and Destexhe (2003,2005). Each article aims to determine the stationary distribution of the membrane potential by solving the underlying equation describing its evolution. The latter work describes the evolution of the membrane potential in terms of the solution of a family of three linked stochastic differential equations (SDEs). In this thesis it is demonstrated that the conclusion of the lengthy analysis of Rudolph and Destexhe (2003, 2005) can be obtained directly from the system of SDEs. Through the use of a spectral procedure based on Hermite Polynomials it is shown that the marginal probability density function of the membrane potential can be estimated to arbitrarily accuracy. The procedure is illustrated for one level of approximation.

Item Type: Thesis (MSc(R))
Qualification Level: Masters
Keywords: stochastic,input, membrane potential,synapse
Subjects: Q Science > QR Microbiology
Q Science > QA Mathematics
Colleges/Schools: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Supervisor's Name: Lindsay, Prof Kenneth
Date of Award: 2008
Depositing User: Ms EFTHALIA KINTIS
Unique ID: glathesis:2008-145
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 26 Mar 2008
Last Modified: 10 Dec 2012 13:16
URI: http://theses.gla.ac.uk/id/eprint/145

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