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

2. Regular firing A burster Firing mode of thalamic neurons

3. Delayed Burst: Rebound from hyperpolarization

7. RC Isopotential model for passive neuron

8. Isopotential model for excitable neuron

9. Integrate - and - fire (I&F) model (Lapicque - 1907) V th I t isi

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

11. I(nA) f(Hz) Cortical neuronI&F model neuron Spike-rate adaptation Each spike: g sra = g sra +  g sra Integrate - and - fire (I&F) model with adaptation I&F I&F + adaptation

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

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

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

15. Gating of membrane channels senso r Persistent conductanceTransient conductance

16. senso r Persistent conductance K-conductance (delayed rectifier) n - activation (or gating) variable n - probability of subunit gate to be open 1- n probability of subunit gate to be close OpenClose depolarization

17. Dividing by

18. For a fixed voltage V n approaches exponentially with time-constant Calculating  n and  n

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

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

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

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

25. I m  g L (V  E L )  g K n 4 (V  E K )  g K m 4 h(V  E Na ) The Hodgkin & Huxley Equations

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

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

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

29. Temperature effect on action potential Simulated (b) versus experiments (top) (H&H 1952) * Amplitude decreases * Speed increases * no propagation for T > 33 0 C Good fit with:  multiply by   e    

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

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

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

36. 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) 1 2 3

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

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

39. Kinetics of the variety of excitable ion channels

40. Function of variety of excitable ion channels