Katie A. Ferguson University of Toronto Toronto Western Research Institute, UHN

Katie A. FergusonUniversity of Toronto

Toronto Western Research Institute, UHN

May 17, 2012Fields Introductory Tutorial

Part of Thematic Program:“Towards Mathematical Modeling of Neurological Disease from

Cellular Perspectives”

“Modeling Neurological Disease”

• Schizophrenia is a mental disorder that affects approximately 1% of the population worldwide– Cognitive deficits, including auditory and visual

deficits

Schizophrenia and fast-spiking interneurons

25-100 Hz rhythm associated with feature binding and temporal encoding

http://home.physics.ucla.edu/newsletters

Parvalbumin-positive fast-spiking (FS) interneuron

• 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

Schizophrenia and NMDAR

http://pubs.acs.org/cen/coverstory/85/8536cover.html

• 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

Identification of cell types

Figure 1

99 pyramidal cells, 68 FS cells, 45 non-FS interneurons

Contribution of NMDA-mediated currents to excitatory postsynaptic

currents (EPSCs)

Figure 2 A

Voltage clamp at -70mV

Weaker synaptic NMDARs contribution in FS cells

Figure 2 B,C,D

NMDAR antagonist

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

• What cell types to include?• Size of network? • Architecture/connectivity of network?• How to model cells?• How to model synapses?

The Model

• What cell types to include?– 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?

The Model

– Izhikevich (2004) model

How to model cells?

If V≥Vspike, z→z+d, V→Vrest

White noise (E cells only)

E cells onlyAdaptation

Cell models

Pyramidal cell model(E cell)

FS interneuron model(I cell) Figure 8 A

How to model synapses?

AMPA

NMDA

GABA

Model synapses

Figure 8 B

Fast FS neuron activation crucial for gamma

Figure 8 E

gni

(FS NMDA)

Fast FS neuron activation crucial for gamma

Figure 8 F,G

gni=0.002 mS/cm2 gni=0.008 mS/cm2

Total current entering I cell E cell outputSynaptic

output of I cell

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

Some Brief Background……

www.bristol.ac/uk/synaptic/pathways/

michaelscally.blogspot.com

Structural Rearrangement of Dentate Gyrus (DG) after brain insults

Figures 1A,B

Granule Cells (excitatory)

Basket Cells (inhibitory)

Hilar Interneurons (inhibitory)

Mossy Cells(excitatory)

Supp Figure 1

The Models(1) Cell types• Granule Cells (GC)• Mossy Cells (MC)• Hilar Interneurons (HI)• Basket Cells (BC)

(2) Size of network• 50,000 GC, 1,500 MC,

500 BC, 600 HI(3) Structure of cell and synaptic

models• Multi-compartment models

(9-17 compartments)• AMPA, GABA synapses

(4) Network Architecture

• Multi-compartment models (9-17 compartments)

•

Figure 1 A

• Network Architecture(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

Network Architecture and Analysis

Control Network

Figures 1 B,C

Hebbian-like network – no effect on hyperexcitability

Figures 2 A,B,C

Three-Neuron Motifs – no effect on hyperexcitability

Figures 2 D,E,F

Scale-free network enhances hyperexcitability

Figures 3 A,B,C

Hub Networks – enhanced hyperexcitability

Figures 3 D,E,F

Example with 210 connections for 5% of GCs(In total, created 7 networks with 30-210 connections)

Directionality of Hubs matters

Figures 4 D

• 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

Discussion

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?

Overall