1. “Modeling Neurological Disease” Fields Introductory Tutorial
Katie A. Ferguson
University of Toronto
Toronto Western Research Institute, UHN
May 17, 2012
Fields Introductory Tutorial
Part of Thematic Program:
“Towards Mathematical Modeling of Neurological Disease from Cellular Perspectives”

3. Schizophrenia and fast-spiking interneurons
Schizophrenia is a mental disorder that affects approximately 1% of the population worldwide
Cognitive deficits, including auditory and visual deficits
Parvalbumin-positive
fast-spiking (FS) interneuron
Hz rhythm associated with feature binding and temporal encoding

4. Schizophrenia and NMDAR
NMDA receptor (NMDAR) antagonists mimic symptoms of schizophrenia
Proposition: NMDA hypofunction is key, PV alteration is secondary
Identifying potential sites of NMDAR hypofunction has been elusive

5. In PFC, the contribution of NMDARs to the activation of specific populations of neurons is poorly understood
How is NMDA hypofunction linked to gamma oscillations abnormalities?
(1) Examine NMDAR contribution to synaptic activation of FS interneurons and pyramidal cells
(2) Look at the influence of AMPARs and NMDARs in the production of gamma

6. Identification of cell types
Figure 1
99 pyramidal cells, 68 FS cells, 45 non-FS interneurons

7. Contribution of NMDA-mediated currents to excitatory postsynaptic currents (EPSCs)
Voltage clamp at -70mV
Figure 2 A

8. Weaker synaptic NMDARs contribution in FS cells
NMDAR antagonist
Figure 2 B,C,D

9. How do AMPARs and NMDARs influence the production of gamma?
Perhaps the fast EPSC kinetics in FS neurons is important for interneuron activity during pyramidal cell-FS neuron feedback loops involved in gamma oscillations
How do AMPARs and NMDARs influence the production of gamma?

10. The Model What cell types to include? Size of network?
Architecture/connectivity of network?
How to model cells?
How to model synapses?

11. The Model What cell types to include? Size of network?
Pyramidal cells (E) and FS interneurons (I)
Size of network?
200 E cells, 40 I cells
Architecture/connectivity of network?
E receives input from 10% of other E cells, 75% of I cells
I receives input from 75% of E cells and I cells
How to model cells?
How to model synapses?

12. How to model cells? Izhikevich (2004) model If V≥Vspike,
White noise
(E cells only)
E cells only
Adaptation
If V≥Vspike,
z→z+d, V→Vrest

13. Cell models FS interneuron model Pyramidal cell model (I cell)
(E cell)
FS interneuron model
(I cell)
Figure 8 A

14. How to model synapses?
AMPA
NMDA
GABA

15. Model synapses
Figure 8 B

16. Fast FS neuron activation crucial for gamma
gni
(FS NMDA)
Figure 8 E

17. Fast FS neuron activation crucial for gamma
gni=0.002 mS/cm2
gni=0.008 mS/cm2
Total current entering I cell
E cell output
Synaptic output of I cell
Figure 8 F,G

18. Discussion
Model used to compare effects of fast AMPAR-mediated vs. slow NMDAR-mediated excitation of FS neurons on the mechanisms of gamma oscillations
Model suggests rapid FS neuron activation is crucial for production of gamma oscillations
Predict NMDAR hypofunction may affect PFC by acting at glutamatergic synapses different from those mediating the activation of FS parvalbumin-positive cells

20. Some Brief Background……
michaelscally.blogspot.com

21. Structural Rearrangement of Dentate Gyrus (DG) after brain insults
Mossy Cells
(excitatory)
Figures 1A,B
Hilar Interneurons (inhibitory)
Granule Cells (excitatory)
Basket Cells (inhibitory)

22. Supp Figure 1

23. The Models Cell types Granule Cells (GC) Mossy Cells (MC)
Hilar Interneurons (HI)
Basket Cells (BC)
Size of network
50,000 GC, 1,500 MC,
500 BC, 600 HI
Structure of cell and synaptic models
Multi-compartment models (9-17 compartments)
AMPA, GABA synapses
Network Architecture
Figure 1 A

24. Network Architecture and Analysis
(1) Control
(2) Hebbian-like connectivity
(3) Overrepresentation of small-motifs
(4) Scale-free topology
(5) Highly interconnected GC hubs without a scale-free topology
Analysis
(1) Latency to full network activation
(2) Duration of network activity
(3) Mean number of spikes fired

25. Control Network
Figures 1 B,C

26. Hebbian-like network – no effect on hyperexcitability
Figures 2 A,B,C

27. Three-Neuron Motifs – no effect on hyperexcitability
Figures 2 D,E,F

28. Scale-free network enhances hyperexcitability
Figures 3 A,B,C

29. Hub Networks – enhanced hyperexcitability
Example with 210 connections for 5% of GCs
(In total, created 7 networks with connections)
Figures 3 D,E,F

30. Directionality of Hubs matters
Figures 4 D

31. Discussion
Specific microcircuit connectivity can have important effects on epileptiform network activity
In the injured dentate gyrus, the presence of a small population of highly interconnected GC hubs strongly contributes to hyperexcitability
hilar basal dendrites

32. Overall Context matters!
What is the question you are trying to answer?
At any level you will be introducing some assumptions (error). What makes most sense for your application?