An analysis of waves underlying grid cell firing in the medial enthorinal cortex
Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo [2013 Neuronal reboun...
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BioMed Central
2017
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| Online Access: | https://eprints.nottingham.ac.uk/44815/ |
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| author | Bonilla-Quintana, Mayte Wedgwood, Kyle C.A. O'Dea, Reuben D. Coombes, Stephen |
| author_facet | Bonilla-Quintana, Mayte Wedgwood, Kyle C.A. O'Dea, Reuben D. Coombes, Stephen |
| author_sort | Bonilla-Quintana, Mayte |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo [2013 Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex. Phil. Trans. R. Soc. B 369: 20120523] showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the I_h current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in I_h resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the I_h current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions. |
| first_indexed | 2025-11-14T19:56:58Z |
| format | Article |
| id | nottingham-44815 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:56:58Z |
| publishDate | 2017 |
| publisher | BioMed Central |
| recordtype | eprints |
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| spelling | nottingham-448152020-05-04T19:02:17Z https://eprints.nottingham.ac.uk/44815/ An analysis of waves underlying grid cell firing in the medial enthorinal cortex Bonilla-Quintana, Mayte Wedgwood, Kyle C.A. O'Dea, Reuben D. Coombes, Stephen Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an I_h current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo [2013 Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex. Phil. Trans. R. Soc. B 369: 20120523] showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the I_h current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in I_h resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the I_h current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions. BioMed Central 2017-08-25 Article PeerReviewed Bonilla-Quintana, Mayte, Wedgwood, Kyle C.A., O'Dea, Reuben D. and Coombes, Stephen (2017) An analysis of waves underlying grid cell firing in the medial enthorinal cortex. Journal of Mathematical Neuroscience, 7 (9). pp. 1-30. ISSN 2190-8567 Grid cell; Medial enthorhinal cortex; h-current; Rebound spiking; Integrate-and-fire neural field model; Nonsmooth dynamics; Travelling wave; Evans function https://mathematical-neuroscience.springeropen.com/articles/10.1186/s13408-017-0051-7 doi:10.1186/s13408-017-0051-7 doi:10.1186/s13408-017-0051-7 |
| spellingShingle | Grid cell; Medial enthorhinal cortex; h-current; Rebound spiking; Integrate-and-fire neural field model; Nonsmooth dynamics; Travelling wave; Evans function Bonilla-Quintana, Mayte Wedgwood, Kyle C.A. O'Dea, Reuben D. Coombes, Stephen An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title | An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title_full | An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title_fullStr | An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title_full_unstemmed | An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title_short | An analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| title_sort | analysis of waves underlying grid cell firing in the medial enthorinal cortex |
| topic | Grid cell; Medial enthorhinal cortex; h-current; Rebound spiking; Integrate-and-fire neural field model; Nonsmooth dynamics; Travelling wave; Evans function |
| url | https://eprints.nottingham.ac.uk/44815/ https://eprints.nottingham.ac.uk/44815/ https://eprints.nottingham.ac.uk/44815/ |