A path integral approach to the Hodgkin–Huxley model
To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent chan...
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2017
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/154732 |
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I19-R120-10915-1547322023-06-27T20:07:17Z http://sedici.unlp.edu.ar/handle/10915/154732 issn:0378-4371 A path integral approach to the Hodgkin–Huxley model Baravalle, Román Rosso, Osvaldo Aníbal Montani, Fernando Fabián 2017 2023-06-27T18:43:46Z en Física Neuronal model Path integrals Stochastic processes Spiking output Neural coding To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered. Instituto de Física de Líquidos y Sistemas Biológicos Facultad de Ciencias Exactas Consejo Nacional de Investigaciones Científicas y Técnicas Articulo Articulo http://creativecommons.org/licenses/by/4.0/ Creative Commons Attribution 4.0 International (CC BY 4.0) application/pdf 986-999 |
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Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
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SEDICI (UNLP) |
| language |
Inglés |
| topic |
Física Neuronal model Path integrals Stochastic processes Spiking output Neural coding |
| spellingShingle |
Física Neuronal model Path integrals Stochastic processes Spiking output Neural coding Baravalle, Román Rosso, Osvaldo Aníbal Montani, Fernando Fabián A path integral approach to the Hodgkin–Huxley model |
| topic_facet |
Física Neuronal model Path integrals Stochastic processes Spiking output Neural coding |
| description |
To understand how single neurons process sensory information, it is necessary to develop suitable stochastic models to describe the response variability of the recorded spike trains. Spikes in a given neuron are produced by the synergistic action of sodium and potassium of the voltage-dependent channels that open or close the gates. Hodgkin and Huxley (HH) equations describe the ionic mechanisms underlying the initiation and propagation of action potentials, through a set of nonlinear ordinary differential equations that approximate the electrical characteristics of the excitable cell. Path integral provides an adequate approach to compute quantities such as transition probabilities, and any stochastic system can be expressed in terms of this methodology. We use the technique of path integrals to determine the analytical solution driven by a non-Gaussian colored noise when considering the HH equations as a stochastic system. The different neuronal dynamics are investigated by estimating the path integral solutions driven by a non-Gaussian colored noise q. More specifically we take into account the correlational structures of the complex neuronal signals not just by estimating the transition probability associated to the Gaussian approach of the stochastic HH equations, but instead considering much more subtle processes accounting for the non-Gaussian noise that could be induced by the surrounding neural network and by feedforward correlations. This allows us to investigate the underlying dynamics of the neural system when different scenarios of noise correlations are considered. |
| format |
Articulo Articulo |
| author |
Baravalle, Román Rosso, Osvaldo Aníbal Montani, Fernando Fabián |
| author_facet |
Baravalle, Román Rosso, Osvaldo Aníbal Montani, Fernando Fabián |
| author_sort |
Baravalle, Román |
| title |
A path integral approach to the Hodgkin–Huxley model |
| title_short |
A path integral approach to the Hodgkin–Huxley model |
| title_full |
A path integral approach to the Hodgkin–Huxley model |
| title_fullStr |
A path integral approach to the Hodgkin–Huxley model |
| title_full_unstemmed |
A path integral approach to the Hodgkin–Huxley model |
| title_sort |
path integral approach to the hodgkin–huxley model |
| publishDate |
2017 |
| url |
http://sedici.unlp.edu.ar/handle/10915/154732 |
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