1 / 25

Modelling firing nerve cells

Modelling firing nerve cells. A. Lessig. Self-organization in physical systems: rhythms, patterns and chaos. 2010-11-17. Contents. Physiology of nerve cells Structure of a „typical“ neuron Stimulus conduction via action potentials Neurons as excitable system Hodgkin-Huxley model

betrys
Download Presentation

Modelling firing nerve cells

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Modelling firing nerve cells A. Lessig Self-organization in physical systems: rhythms, patterns and chaos 2010-11-17

  2. Contents • Physiology of nerve cells • Structure of a „typical“ neuron • Stimulus conduction via action potentials • Neurons as excitable system • Hodgkin-Huxley model • FitzHugh-Nagumo model • Summary • Literature

  3. Structure Source: Carlson, Niel A. (1992). Foundations of Physiological Psychology. Needham Heights, Massachusetts: Simon & Schuster. pp. 36

  4. Structure Source: „Neurevolution“, http://www.neurevolution.net/page/3/

  5. Resting potential cK+ cNa+ + - Source: „Neurosignaling“, http://www.columbia.edu/cu/psychology/courses/1010/mangels/neuro/neurosignaling/neurosignaling.html

  6. Resting potential Nernst equation:

  7. Action potential gNa = max gK = max Source: „Action potential“, openwetware.org/images/thumb/a/a6/Action-potential.png

  8. Action potential

  9. Hodgkin-Huxley model Source: Cross, M. & Greenside, H. (2009). Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge: Cambridge University Press. pp. 405

  10. Hodgkin-Huxley model

  11. Hodgkin-Huxley model

  12. Hodgkin-Huxley model Source: A. L. Hodgkin, A. F. Huxley: A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve.Journal of Physiology. 117, 1952, pp. 530

  13. FitzHugh-Nagumo model Nullclines:

  14. FitzHugh-Nagumo model fixed point u* ≈ -1.51 v* ≈ -1.07 a = -1.3 b = 0.2 Source: Cross, M. & Greenside, H. (2009). Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge: Cambridge University Press. pp. 416

  15. FitzHugh-Nagumo model Linear stability analysis: fixed point

  16. FitzHugh-Nagumo model Linear stability analysis: Source: Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos. New York: Perseus Books Publishing, LLC. pp. 137

  17. FitzHugh-Nagumo model Linear stability analysis:

  18. FitzHugh-Nagumo model

  19. FitzHugh-Nagumo model weak stimulus strong stimulus Source: „ Das FitzHugh-Nagumo Modell einer Nervenzelle“, http://www.math.uni-hamburg.de/home/gunesch/Vorlesung/SoSe2007/Sem_DS_ODE/Vortrag/Brouwer.pdf

  20. FitzHugh-Nagumo model Source: „ FitzHugh-Nagumo model“, http://www.scholarpedia.org/article/FitzHugh-Nagumo_model

  21. FitzHugh-Nagumo model Source: „ Das FitzHugh-Nagumo Modell einer Nervenzelle“, http://www.math.uni-hamburg.de/home/gunesch/Vorlesung/SoSe2007/Sem_DS_ODE/Vortrag/Brouwer.pdf

  22. FitzHugh-Nagumo model Source: „ Das FitzHugh-Nagumo Modell einer Nervenzelle“, http://www.math.uni-hamburg.de/home/gunesch/Vorlesung/SoSe2007/Sem_DS_ODE/Vortrag/Brouwer.pdf

  23. FitzHugh-Nagumo model Source: „ Das FitzHugh-Nagumo Modell einer Nervenzelle“, http://www.math.uni-hamburg.de/home/gunesch/Vorlesung/SoSe2007/Sem_DS_ODE/Vortrag/Brouwer.pdf

  24. Summary • stimulus conduction via action potentials • neurons are classic excitable systems: sufficient perturbations cause large and amplified response • 4-D Hodgkin-Huxley model very close to physiology • reduced version of Hodgkin-Huxley model: 2-D FitzHugh-Nagumo model • FitzHugh-Nagumo model retains most important features of the Hodgkin-Huxley model (excitability, quasi-threshold, refractory period, …) • FitzHugh-Nagumo model example for activator-inhibitor system • propagation of action potentials: diffusion term (next week)

  25. Literature • Hodgkin A. L., Huxley A. F. (1952) A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve. Journal of Physiology. 117:500-544 • FitzHugh R. (1955) Mathematical models of threshold phenomena in the nerve membrane. Bull. Math. Biophysics. 17:257-278 • Nagumo J., Arimoto S., and Yoshizawa S. (1962) An active pulse transmission line simulating nerve axon. Proc IRE. 50:2061-2070 • „ FitzHugh-Nagumo model“, http://www.scholarpedia.org/article/FitzHugh-Nagumo_model • Cross, M. & Greenside, H. (2009). Pattern Formation and Dynamics in Nonequilibrium Systems. Cambridge: Cambridge University Press • Strogatz, S. H. (1994). Nonlinear Dynamics and Chaos. New York: Perseus Books Publishing, LLC

More Related