A leaky integrate-and-fire model with adaptation for the generation of a spike train
A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016002 |
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| _version_ | 1832590122925686784 |
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| author | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora |
| author_facet | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora |
| author_sort | Aniello Buonocore |
| collection | DOAJ |
| description | A model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described. |
| format | Article |
| id | doaj-art-6ecc941298904e79b656a358e348eef4 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-6ecc941298904e79b656a358e348eef42025-01-24T02:35:23ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-12-0113348349310.3934/mbe.2016002A leaky integrate-and-fire model with adaptation for the generation of a spike trainAniello Buonocore0Luigia Caputo1Enrica Pirozzi2Maria Francesca Carfora3Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 NapoliDipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, NapoliDipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, NapoliIstituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, NapoliA model is proposed to describe the spike-frequency adaptation observed in many neuronal systems. We assume that adaptation is mainly due to a calcium-activated potassium current, and we consider two coupled stochastic differential equations for which an analytical approach combined with simulation techniques and numerical methods allow to obtain both qualitative and quantitative results about asymptotic mean firing rate, mean calcium concentration and the firing probability density. A related algorithm, based on the Hazard Rate Method, is also devised and described.https://www.aimspress.com/article/doi/10.3934/mbe.2016002hazard rate method.calcium-activated potassium currentfast-slow analysis |
| spellingShingle | Aniello Buonocore Luigia Caputo Enrica Pirozzi Maria Francesca Carfora A leaky integrate-and-fire model with adaptation for the generation of a spike train Mathematical Biosciences and Engineering hazard rate method. calcium-activated potassium current fast-slow analysis |
| title | A leaky integrate-and-fire model with adaptation for the generation of a spike train |
| title_full | A leaky integrate-and-fire model with adaptation for the generation of a spike train |
| title_fullStr | A leaky integrate-and-fire model with adaptation for the generation of a spike train |
| title_full_unstemmed | A leaky integrate-and-fire model with adaptation for the generation of a spike train |
| title_short | A leaky integrate-and-fire model with adaptation for the generation of a spike train |
| title_sort | leaky integrate and fire model with adaptation for the generation of a spike train |
| topic | hazard rate method. calcium-activated potassium current fast-slow analysis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016002 |
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