Horacio G. Rotstein Department of Mathematical Sciences New Jersey Institute of Technology

1. The abrupt transition from theta to hyper-excitable spiking activity in stellate cells from layer II of the medial entorhinal cortex Horacio G. Rotstein Department of Mathematical Sciences New Jersey Institute of Technology Network Synchronization: From dynamical systems to neuroscience Leiden (NL) - May 27, 2008

2. Collaborators • Tilman Kispersky Program in Neuroscience - Boston University • Nancy Kopell Math & Center for BioDynamics – Boston University • Martin Wechselberger Math – University of Sidney • John White Biomedical Engineering – University of Utah

3. Entorhinal Cortex & Hippocampus Photomicrograph of a section through the rat hippocampal region (Gluck & Myers). Adapted from Amaral & Witter (1989). Photomicrograph of a section through the rat hippocampal region (Gluck & Myers). Adapted from Amaral & Witter (1989)

4. Stellate cells (SCs) • Entorhinal cortex (EC) is the interface between the neocortex and the hippocampus. • Information flows from the neocortex to the hippocampus through the superficial layers (II and III) of the EC. • SCs are the most abundant cell type in layer II of the EC. • SCs are putative grid cells.

5. Subthreshold oscillations (STOs) • SCs develop rhythmic STOs at theta frequencies (8 – 12 Hz). • Spikes occur at the peaks of STOs but not at every cycle. • Interaction between two currents: h- and persistent sodium. • Single cell phenomenon Depolarization increases from 1 to 3 (Adapted from Dickson et al., J. Neurophysiol., 2000)

6. SCs: Theta regime (background) • SCs have intrinsic biophysical properties that endow them with the ability to display rhythmic activity in the theta frequency regime (8 – 12 Hz) • Subthreshold oscillations (STOs): interaction between a persistent sodium and a hyperpolarization-activated (h-) current. • Spikes • Mixed-mode oscillations (MMOs): STOs interspersed with spikes R., Oppermann, White, Kopell (JCNS – 2005) R., Wechselberger, Kopell (Submitted) Focus issue on MMOs (Chaos 2008)

7. SCs – Hyperexcitable regime (this project) • SCs have intrinsic biophysical properties that endow them with the ability to display spiking activity in the “gamma” frequency regime (~60 Hz). • This time scale can be uncovered by phasic excitation. • The frequency regime depends on a combination of intrinsic and network properties. Kispersky, White & R. , Work in Progress.

8. SC dynamic structure Nonlinearities and multiple time-scales in the subthreshold regime: • How are they created? • How do they depend on the intrinsic SC biophysical properties? • How do they interact with synaptic (excitatory and inhibitory) inputs?

9. SC biophysical model

10. SC biophysical model

11. SC biophysical model

12. Subthreshold oscillations (STOs) and spikes in the SC model

13. STOs generated by persistent sodium channel noise in the SC model

14. Subthreshold Regime: Reduction of Dimensions Multiscale analysis: • Identification of the active and inactive currents • Identification of the appropriate time scales

15. Subthreshold Regime: Reduction of Dimensions Multiscale analysis: • Identification of the active and inactive currents • Identification of the appropriate time scales

16. Subthreshold regime: reduced SC model SC biophysical model Subthreshold regime

17. Subthreshold regime: reduced SC model

18. Subthreshold regime: reduced SC model

19. Subthreshold regime: reduced SC model SC biophysical model Subthreshold regime

20. Subthreshold regime: reduced SC model

21. Nonlinear Artificially Spiking (NAS) SC model

22. Nonlinear Artificially Spiking (NAS) SC model

23. Nonlinear Artificially Spiking (NAS) SC model

24. Inhibitory inputs can advance the next spike by “killing” an STO.

25. Transition from theta to hyper-excitable (gamma) rhythmic activity Experimental (in vitro) results: • There exist recurrent connections among SCs. • These connections are “similar” in normal (control) and epileptic cells. • Recurrent inhibitory circuits are reduced in epileptic cells as compared to normal (control) ones. Recurrent circuits in layer II of MEC in a model of temporal lobe epilepsy. Kumar, Buckmaster, Huguenard, J. Neurosci. (2007)

26. Minimal S-I network model

27. Minimal S-I network model • A minimal S-S network reproduces the experimentally found transition form normal activity to hyper-excitability in SCs due to lack of inhibition

28. Minimal S-I network model • A minimal SIS network reproduces the experimentally found transition form normal activity to hyper-excitability in SCs due to lack of inhibition

29. Minimal SC network model (no inhibition) • A small increase in the SC recurrent synaptic conductance causes an explosion of the SC firing frequency

30. Minimal SC network model (no inhibition) • A small increase in the SC recurrent synaptic conductance causes an explosion of the SC firing frequency

31. Minimal S-I network model • A small increase in the inhibitory input to the SCs brings their frequency back to the theta regime

32. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation Single SC model representing a population of synchronized (in phase) SCs.

33. Single SC + autapse (no inhibition) • Effects of changes in the maximal conductances

34. Single SC + autapse (no inhibition) • Effects of changes in the maximal conductances

35. Single SC (no autapse - no inhibition)

36. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

37. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

38. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

39. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

40. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

41. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

42. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

43. Single SC (no autapse - no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

44. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

45. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

46. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

47. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

48. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

49. Single SC + autapse (no inhibition) • The abrupt changes in the SC firing frequency are the result of phasic (synaptic) and not tonic excitation

50. Dynamic clamp experiments Single SC + autapse (no inhibition) Tilman Kispersky & John White