1 / 21

Strange responses of the Hodgkin-Huxley model to highly fluctuating inputs

Strange responses of the Hodgkin-Huxley model to highly fluctuating inputs. Yutaka Sakai ( Saitama Univ., Japan ) Masahiro Yamada ( Univ. Tokyo, Japan ) Shuji Yoshizawa ( Saitama Univ., Japan ). class II. HH (Hopf bifurcation). frequency. frequency.

charo
Download Presentation

Strange responses of the Hodgkin-Huxley model to highly fluctuating inputs

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. Strange responses of the Hodgkin-Huxley model to highly fluctuating inputs Yutaka Sakai (Saitama Univ., Japan) Masahiro Yamada (Univ. Tokyo, Japan) Shuji Yoshizawa (Saitama Univ., Japan)

  2. class II HH (Hopf bifurcation) frequency frequency Discontinuous μ μ LIF, HH+A-current (saddle node bifurcation) class I Continuous Neuron: excitable system ~ bifurcation type ~ Behavior for constant current injection silent → periodic firing

  3. Leaky integrate-and-fire(LIF) Model Hodgkin-Huxley(HH) Model Neuron Model (Hodgkin & Huxley 1952: squid axon)

  4. : transient, inactivating HH + A-current (CWM Model) Connor-Walter-McKown(CWM) Model (Connor, Walter & McKown 1977: crab axon )

  5. Saddle-node bifurcation Hopf bifurcation Effect of A-current (Inactivating, ) 2D phase space W V

  6. ??? | | || | | | | | Fluctuating input Spike Sequences of Cortical regular spiking neurons Highly Variable Intervals

  7. Higher balance of fluctuation Stochastic factor increase Higher Variability in ISI sequence | | || | | | | | • Stochastic factor increase Naïve expectation input ??? output

  8. Spike sequence | | || | | | | | T Response to fluctuate input Neuron Model Inter-Spike Interval (ISI) Statistics Mean Interval Coefficient of Variation T : Inter-Spike Interval (ISI)

  9. Effective Strength of input : const. adjust const. Relationship Relationship:“Input fluctuation”– “Output variability” fluctuation LIF or HH variability CV

  10. Difference HH v.s. LIF in CV-σ

  11. Difference: HH v.s. LIF Output Variability for Input Fluctuation HH: monotone decreasing LIF: monotone increasing LIF can never reproduce “monotone decreasing” at any parameter range! at any refractory!

  12. HH + A-current (CWM model)monotone increasing

  13. Summary of Results Output Variability for Input Fluctuation • LIF: monotone increasing • HH: monotone decreasing (Hopf bifurcation) + A-current (Saddle-node bifurcation) • CWM: monotone increasing

  14. Suggestion of Result The strange response of HH : “monotone decreasing variability” seems to originate in Property of Hopf bifurcation . . . Why?

  15. Type of Stable Fixed point ~ Typical behavior before bifurcation class I near saddle-node bifurcation class II near Hopf bifurcation

  16. Essences of the mechanism 1. Discontinuous jump of firing frequency 2. Second firing for a single perturbation 3. Refractory

  17. Near before bifurcation Poisson Bursting Pattern || || ||| || Far before bifurcation Poisson + Ref. Pattern | | | | | | | | Mechanism of decreasing Variability

  18. Higher balance of fluctuation Higher Variability in ISI sequence | | || | | | | | Suggestion input Does Not Always mean output

  19. Difference between Hopf & Saddle-node Throughout concerned parameter range, mean input μ lies inbefore the bifurcation point Before Hopf bifurcation firing spiralstable fix point Before Saddle-node bifurcation non-firing spiral, ornon-spiralstable fix point

  20. Firing Spiral Stable Fix point ~ Typical before Hopf bifurcation

  21. CV-σ ( μ: const ) Jump

More Related