Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron

Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron

Bibliographic Details
Main Author: Bennett, Casey
Language:English
Published: Case Western Reserve University School of Graduate Studies / OhioLINK 2016
Subjects:
Applied Mathematics
Neurosciences
Morris-Lecar
PCPA
SDE
ISI
Simulation
Algorithm
Fast
Speed
Runtime
Phase Response Curve
PRC
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=case1441551744
id ndltd-OhioLink-oai-etd.ohiolink.edu-case1441551744
record_format oai_dc
spelling ndltd-OhioLink-oai-etd.ohiolink.edu-case14415517442021-08-03T06:33:15Z Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron Bennett, Casey Applied Mathematics Neurosciences Morris-Lecar PCPA SDE ISI Simulation Algorithm Fast Speed Runtime Phase Response Curve PRC Using a stochastic version of the Morris-Lecar model neuron, a scaling method is introduced in which the ODE that propagates voltage is invariant, but the underlying Markov chain which controls the discrete channel states converges to progressively simpler stochastic descriptions. The relationship between the underlying stochastic description of channel states can then be directly related to the induced interspike interval (ISI) variability as the system is scaled. Specifically, an exact Markov chain model, a piecewise constant propensity approximation to the exact model, and a Langevin approximation are derived. For large systems the ISI variance is found in terms of channel specific phase response curves. Through the development of powerful numerical implementations on a high performance computing cluster and efficient error estimation techniques, convergence of each model to the others is systematically evaluated, so that given any channel configuration and error tolerance, the fastest method can be easily identified. 2016-01-26 English text Case Western Reserve University School of Graduate Studies / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=case1441551744 http://rave.ohiolink.edu/etdc/view?acc_num=case1441551744 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Applied Mathematics
Neurosciences
Morris-Lecar
PCPA
SDE
ISI
Simulation
Algorithm
Fast
Speed
Runtime
Phase Response Curve
PRC
spellingShingle Applied Mathematics
Neurosciences
Morris-Lecar
PCPA
SDE
ISI
Simulation
Algorithm
Fast
Speed
Runtime
Phase Response Curve
PRC

Bennett, Casey
Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
author Bennett, Casey
author_facet Bennett, Casey
author_sort Bennett, Casey
title Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
title_short Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
title_full Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
title_fullStr Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
title_full_unstemmed Channel Noise and Firing Irregularity in Hybrid Markov Models of the Morris-Lecar Neuron
title_sort channel noise and firing irregularity in hybrid markov models of the morris-lecar neuron
publisher Case Western Reserve University School of Graduate Studies / OhioLINK
publishDate 2016
url http://rave.ohiolink.edu/etdc/view?acc_num=case1441551744
work_keys_str_mv AT bennettcasey channelnoiseandfiringirregularityinhybridmarkovmodelsofthemorrislecarneuron
_version_ 1719438970671071232

Similar Items