Part I: Single Neuron Models

1. Swiss Federal Institute of Technology Lausanne, EPFL Laboratoryof Computational Neuroscience, LCN, CH 1015 Lausanne Part I: Single Neuron Models BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapters 2-5

2. Chapter 2: Detailed neuron models Hodgkin-Huxley model BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 2

3. Molecular basis action potential -70mV Na+ K+ Ca2+ Ions/proteins

4. 100 I mV C gK gl gNa 0 stimulus Hodgkin-Huxley Model inside Ka Na outside Ion channels Ion pump

5. inside Ka Na outside Ion channels Ion pump stimulus m0(u) h0(u) u u Hodgkin-Huxley Model pulse input I(t)

6. Hodgkin-Huxley Model 100 refractoriness Action potential mV 0 0 ms 20 strong stimuli Strong stimulus

7. Hodgkin-Huxley Model Hodgkin-Huxley Model Hodgkin-Huxley Model 100 Stimulation with time-dependent input current mV 0 I(t)

8. 100 mV 0 mV 5 Subthreshold response 0 Spike -5 Hodgkin-Huxley Model Hodgkin-Huxley Model Hodgkin-Huxley Model 100 mV 0 I(t)

9. Ion channel based model justify From molecules to neuron models neurons signals computational model molecules ion channels Swiss Federal Institute of Technology Lausanne, EPFL Laboratoryof Computational Neuroscience, LCN, CH 1015 Lausanne

10. a Ion Channels investigated in the study of a CGRP NPY CRH SOM pENK Dyn CR SP VIP CCK CB PV b b Kv Kv1 Kv2 Kv3 Kv4 Kv5 Kv6 Kv8 Kv9 Kv KChIP Kv2.1 Kv2.2 Kv1.1 Kv1.2 Kv1.3 Kv1.4 Kv1.5 Kv1.6 Kv4.1 Kv4.2 Kv4.3 Kv3.4 Kv3.1 Kv3.2 Kv3.3 Kv1 Kv2 Kv3 KChIP1 KChIP2 KChIP3 I C gl gNa gKv1 gKv3 schematic mRNA Expression profile Voltage Activated K+ Channels + +

11. stimulus I C gl gNa gKv1 gKv3 Model of fast spiking interneuron inside Ka Na outside Ion channels Ion pump Erisir et al, 1999 Hodgkin and Huxley, 1952

12. Spike I Subthreshold C gl gNa gKv1 gKv3 Model of fast spiking interneuron I(t) Detailed model, based on ion channels

13. I C gl gNa gKv1 gKv3 Model of fast spiking interneuron Current pulse constant current Detailed model, based on ion channels

14. Chapter 3: Two-dimensional neuron models BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 3

15. stimulus m0(u) h0(u) u u Reduction of Hodgkin-Huxley Model 1) dynamics of m is fast 2) dynamics of h and n is similar

16. stimulus Reduction of Hodgkin-Huxley Model: 2 dimensional Neuron Models w I(t)=I0 u

17. stimulus FitzHugh-Nagumo Model 2-dimensional Neuron Models w I(t)=0 u

18. stimulus FitzHugh Nagumo Model w I(t)=I0 u -unstable fixed point -closed boundary with arrows pointing inside limit cycle limit cycle

19. stimulus Discontinuous gain function type II Model w I(t)=I0 u I0

20. stimulus Low-frequency firing type I Model w I(t)=I0 u I0

21. Chapter 4: Formal Spiking Neuron models Integrate-and-fire and SRM BOOK: Spiking Neuron Models, W. Gerstner and W. Kistler Cambridge University Press, 2002 Chapter 4

22. j Spike reception: EPSP Integrate-and-fire Model Spike emission i reset I linear Fire+reset threshold

23. j Nonlinear Integrate-and-fire Model Spike emission i F reset I NONlinear Fire+reset threshold

24. I>I u Nonlinear Integrate-and-fire Model I<I u Quadratic I&F: NONlinear Fire+reset threshold arbitrary F(u)

25. j I&F with time-dependent time constant Spike emission i Soft reset I linear, time-dependent Fire+reset threshold

26. j Spike reception: EPSP Spike reception: EPSP Firing: Spike Response Model Spike emission i Spike emission: AP All spikes, all neurons Last spike of i linear threshold

27. Firing: Last spike of i Full Spike Response Model Spike emission threshold potential Last spike of i Volterra expansion

28. Last spike of i Last spike of i Integrate-and-fire Models LIF NLIF LIF:time dep. SRM0 SRM

29. Last spike of i Last spike of i Integrate-and-fire Models LIF LIF is special case of SRM0 SRM0

30. Last spike of i Last spike of i Integrate-and-fire Models LIF Time-dep.LIF is special case of SRM SRM

31. Comparison: Hodgkin-Huxley and SRM

32. 100 inside Example: refractoriness Ka mV Na 0 outside Ion channels Ion pump stimulus Hodgkin-Huxley Model

33. threshold Firing: Last spike of i Hodgkin-Huxley Model vs. SRM 100 mV Spike emission 0 0 ms 20 Full Spike Response Model potential

34. Firing: Last spike of i Hodgkin-Huxley Model Hodgkin-Huxley Model vs. SRM 1 100 mV mV 0 0 0 ms 20 Full Spike Response Model threshold potential

35. 100 mV 0 mV 5 0 90% of firing times correctly predicted -5 Kistler et al., 1997 Hodgkin-Huxley Model Hodgkin-Huxley Model Hodgkin-Huxley Model 100 mV 0 I(t) Full Spike Response Model

36. Comparison: Detailed model of Fast-spiking interneuron vs. nonlinear I&F or SRM

37. Spike I C gl gNa gKv1 gKv3 threshold model Validation of neuron models I(t)

38. stimulus I C gl gNa gKv1 gKv3 Model of fast spiking interneuron inside Ka Na outside Ion channels Ion pump Erisir et al, 1999 Hodgkin and Huxley, 1952

39. Spike I Subthreshold C gl gNa gKv1 gKv3 Model of fast spiking interneuron I(t) Detailed model, based on ion channels

40. Spike I C gl gNa gKv1 gKv3 threshold model Validation of neuron models I(t)

41. stimulus Reduction of interneuron model To Nonlinear I&F Step 1 keep all ion currents – add threshold Fire+reset Reset – but to which value?

42. Reduction constant current Step 1 keep all ion currents – add threshold Pulse input I(t)

43. Reduction of interneuron model Step 2 separate in fast and slow ion currents Fire+reset Fast: Slow Slow

44. Reduction of interneuron model Step 2 separate in fast and slow ion currents Fire+reset

45. Reduction Constant current Step 2 separate in fast and slow ion currents Pulse input I(t)

46. I C gl gNa gKv1 gKv3 u Validation of neuron models I(t)

47. Comparison interneuron model vs NONlinear Integrate-and-fire (numerical) Fire+reset I(t)

48. Spike I C gl gNa gKv1 gKv3 Reduction of detailed model to SRM x subthreshold I(t) u threshold

49. Reduction of interneuron model To Spike Response Model Spike emission threshold NONlinear Fire+reset threshold

50. Reduction of interneuron model To Spike Response Model Step 1 analyze behavior after a spike