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Excitability

Introduction to Neurobiology - 2004. Excitability. Information processing in the retina. Artificial neural networks. Firing mode of thalamic neurons. Regular firing. A burster. Delayed Burst: Rebound from hyperpolarization. Isopotential model for passive neuron. R. C.

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Excitability

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  1. Introduction to Neurobiology - 2004 Excitability • Information processing in the retina • Artificial neural networks

  2. Firing mode of thalamic neurons Regular firing A burster

  3. Delayed Burst: Rebound from hyperpolarization

  4. Isopotential model for passive neuron R C

  5. Isopotential model for excitable neuron

  6. Integrate - and - fire (I&F) model (Lapicque - 1907) tisi Vth I

  7. Integrate - and - fire (I&F) model with fluctuating input

  8. Spike-rate adaptation Each spike: gsra = gsra +D gsra Integrate - and - fire (I&F) model with adaptation Cortical neuron I&F model neuron I&F f(Hz) I&F + adaptation I(nA)

  9. f(Hz) H&H model + “A” current f(Hz) The squid - H&H model I(nA)

  10. The Hodgkin & Huxley Model J. Physiol. London (1952, a,b,c,d)

  11. Space-clamped (“membrane”) action potential (H&H 1952)

  12. Gating of membrane channels Persistent conductance Transient conductance sensor

  13. Persistent conductance K-conductance (delayed rectifier) n - activation (or gating) variable depolarization sensor n - probability of subunit gate to be open 1- n probability of subunit gate to be close Open Close

  14. Dividing by

  15. Calculating an and bn n approaches exponentially with time-constant For a fixed voltage V

  16. Time-course of potassium conductance (H&H 1952)

  17. Transient conductance Na-conductance m - activation (or gating) variable depolarization h - inactivation (or gating) variable time

  18. Time-course of sodium conductance (H&H 1952)

  19. Time-course of n,m,h following voltage step

  20. 4 4 I g ( V E ) g n ( V E ) g m h ( V E = - + - + - m L L K K K Na The Hodgkin & Huxley Equations )

  21. Time-course of n,m,h during “membrane” action potential

  22. Time-course of underlying conductances during “membrane” action potential (H&H 1952) Note the small % of ion conductance (channels) used during the action potential

  23. Simulated (top) versus experimental “membrane” action potential (H&H 1952)

  24. Temperature effect on action potential Simulated (b) versus experiments (top) (H&H 1952) * Amplitude decreases * Speed increases * no propagation for T > 330 C Good fit with: a, b multiply by f f = 3*e(T-6.3)/10 ; q10 = 3

  25. Stochastic opening of voltage-gated ion-channels (underlying excitability) Holding potential Sakmann and Neher, 1991

  26. The “soup” of diverse excitable ion channels (beyond H&H and the squid giant axon)

  27. Kinetics of the “A” (K+) current 50 mV -100 mV Activation msec inactivation 20-30 msec 1nA 40 msec Transient K+ current; blocked by 4-AP (not by TEA)

  28. 2 1 3 Function of the “A” (K+) current 1. Delays onset of AP 2. Enables very-low firing rate for weak depolarizing input (due to fast activation and slow inactivation) 3. Enables high-frequency for large inputs (strong inactivation)

  29. “A” (K+) current enables low-firing rates Fast activation - delays 1st spike Prevents Vm from reaching threshold Inactivaes and enables Vm to reach threshold

  30. “IT” (Ca+2) current produces burst of Na + spikes Na spikes riding on “Ca spike” Release from prolong hyperpolarization: IT de-inactivates (h=1)

  31. Kinetics of the variety of excitable ion channels

  32. Function of variety of excitable ion channels

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