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

QR Microbiology;QA Mathematics

Kintis, Efthalia ; Lindsay, Kenneth

University:University of Glasgow

Department:School of Mathematics and Statistics

关键词: stochastic,input, membrane potential,synapse;   

Others  :  http://theses.gla.ac.uk/145/1/2008KintisMsc.pdf

来源: University of Glasgow

【 摘 要 】

A synapse is the term used to describe the connection between the axon of thedonor 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 neurotransmitterwhich then diffuses across a narrow gap and binds onto the receptors of thepostsynaptic neuron, altering the behaviour of the membrane and allowing the movementof ions between the intracellular and extracellular regions. These neurotransmitters differin their strength, timing and their ability to excite or inhibit the postsynaptic neuron.Consequently, these inputs have a significant impact on the electrophysiological propertiesof 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 modelledas the product of the membrane conductance and of the potential difference, that is thedifference of the membrane potential at the site of the synapse and the reversal potentialfor the specific ionic species to which the synapse is particularised . Therefore , synapticbehaviour is closely linked to synaptic conductance. Two models of synaptic behaviourare examined, namely the point conductance model proposed by Richardson (2004) andthe exponential conductance model proposed by Rudolph and Destexhe (2003,2005). Eacharticle aims to determine the stationary distribution of the membrane potential by solvingthe underlying equation describing its evolution. The latter work describes the evolutionof the membrane potential in terms of the solution of a family of three linked stochasticdifferential equations (SDEs). In this thesis it is demonstrated that the conclusion of thelengthy analysis of Rudolph and Destexhe (2003, 2005) can be obtained directly from thesystem of SDEs. Through the use of a spectral procedure based on Hermite Polynomialsit is shown that the marginal probability density function of the membrane potentialcan be estimated to arbitrarily accuracy. The procedure is illustrated for one level ofapproximation.