The ISI distribution of the stochastic Hodgkin-Huxley neuron
The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential,...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2014-10-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fncom.2014.00111/full |
| _version_ | 1819020576314884096 |
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| author | Peter Forbes Rowat Priscilla E Greenwood |
| author_facet | Peter Forbes Rowat Priscilla E Greenwood |
| author_sort | Peter Forbes Rowat |
| collection | DOAJ |
| description | The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model. |
| first_indexed | 2024-12-21T03:53:24Z |
| format | Article |
| id | doaj.art-e0f84143638b4cb5b91880842d206fbb |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-12-21T03:53:24Z |
| publishDate | 2014-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-e0f84143638b4cb5b91880842d206fbb2022-12-21T19:16:55ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882014-10-01810.3389/fncom.2014.00111102803The ISI distribution of the stochastic Hodgkin-Huxley neuronPeter Forbes Rowat0Priscilla E Greenwood1University California San DiegoUniversity of British ColumbiaThe simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.http://journal.frontiersin.org/Journal/10.3389/fncom.2014.00111/fullstochastic dynamicsHodgkin-HuxleyGillespie AlgorithmISI distributionstochastic differential equationISI histogram |
| spellingShingle | Peter Forbes Rowat Priscilla E Greenwood The ISI distribution of the stochastic Hodgkin-Huxley neuron Frontiers in Computational Neuroscience stochastic dynamics Hodgkin-Huxley Gillespie Algorithm ISI distribution stochastic differential equation ISI histogram |
| title | The ISI distribution of the stochastic Hodgkin-Huxley neuron |
| title_full | The ISI distribution of the stochastic Hodgkin-Huxley neuron |
| title_fullStr | The ISI distribution of the stochastic Hodgkin-Huxley neuron |
| title_full_unstemmed | The ISI distribution of the stochastic Hodgkin-Huxley neuron |
| title_short | The ISI distribution of the stochastic Hodgkin-Huxley neuron |
| title_sort | isi distribution of the stochastic hodgkin huxley neuron |
| topic | stochastic dynamics Hodgkin-Huxley Gillespie Algorithm ISI distribution stochastic differential equation ISI histogram |
| url | http://journal.frontiersin.org/Journal/10.3389/fncom.2014.00111/full |
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