Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons
We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameter...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Frontiers Media S.A.
2013-12-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00184/full |
| _version_ | 1818274555196604416 |
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| author | Wilten eNicola Sue Ann eCampbell |
| author_facet | Wilten eNicola Sue Ann eCampbell |
| author_sort | Wilten eNicola |
| collection | DOAJ |
| description | We analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons, and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presenceof heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons. |
| first_indexed | 2024-12-12T22:15:43Z |
| format | Article |
| id | doaj.art-83c212191b3f4c7fb14d5772a6da8a3b |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-12-12T22:15:43Z |
| publishDate | 2013-12-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-83c212191b3f4c7fb14d5772a6da8a3b2022-12-22T00:10:04ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882013-12-01710.3389/fncom.2013.0018468703Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire NeuronsWilten eNicola0Sue Ann eCampbell1University of WaterlooUniversity of WaterlooWe analytically derive mean-field models for all-to-all coupled networks of heterogeneous, adapting, two-dimensional integrate and fire neurons. The class of models we consider includes the Izhikevich, adaptive exponential, and quartic integrate and fire models. The heterogeneity in the parameters leads to different moment closure assumptions that can be made in the derivation of the mean-field model from the population density equation for the large network. Three different moment closure assumptions lead to three different mean-field systems. These systems can be used for distinct purposes such as bifurcation analysis of the large networks, prediction of steady state firing rate distributions, parameter estimation for actual neurons, and faster exploration of the parameter space. We use the mean-field systems to analyze adaptation induced bursting under realistic sources of heterogeneity in multiple parameters. Our analysis demonstrates that the presenceof heterogeneity causes the Hopf bifurcation associated with the emergence of bursting to change from sub-critical to super-critical. This is confirmed with numerical simulations of the full network for biologically reasonable parameter values. This change decreases the plausibility of adaptation being the cause of bursting in hippocampal area CA3, an area with a sizable population of heavily coupled, strongly adapting neurons.http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00184/fullHippocampusbifurcation analysisburstingintegrate-and-fire neuronmean-field model |
| spellingShingle | Wilten eNicola Sue Ann eCampbell Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons Frontiers in Computational Neuroscience Hippocampus bifurcation analysis bursting integrate-and-fire neuron mean-field model |
| title | Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons |
| title_full | Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons |
| title_fullStr | Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons |
| title_full_unstemmed | Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons |
| title_short | Mean-Field Models for Heterogeneous Networks of Two-Dimensional Integrate and Fire Neurons |
| title_sort | mean field models for heterogeneous networks of two dimensional integrate and fire neurons |
| topic | Hippocampus bifurcation analysis bursting integrate-and-fire neuron mean-field model |
| url | http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00184/full |
| work_keys_str_mv | AT wiltenenicola meanfieldmodelsforheterogeneousnetworksoftwodimensionalintegrateandfireneurons AT sueannecampbell meanfieldmodelsforheterogeneousnetworksoftwodimensionalintegrateandfireneurons |