“Modeling Neurological Disease”
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”
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
Parvalbuminpositive
fast-spiking
(FS)
interneuron
25-100 Hz rhythm associated with feature
binding and temporal encoding
http://home.physics.ucla.edu/newsletters
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
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)
Voltage clamp
at -70mV
Figure 2 A
Weaker synaptic NMDARs contribution in FS cells
NMDAR
antagonist
Figure 2 B,C,D
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?
The Model
•
•
•
•
•
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?
How to model cells?
– Izhikevich (2004) model
E cells only
If V≥Vspike,
z→z+d, V→Vrest
White noise
(E cells only)
Adaptation
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
gni
(FS NMDA)
Figure 8 E
Fast FS neuron activation crucial for gamma
gni=0.002 mS/cm2
Total current
entering I cell
gni=0.008 mS/cm2
Synaptic
output of I cell
E cell output
Figure 8 F,G
Discussion
• Model used to compare effects of fast AMPARmediated 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……
michaelscally.blogspot.com
www.bristol.ac/uk/synaptic/pathways/
Structural Rearrangement of
Dentate Gyrus (DG) after brain insults
Mossy Cells
(excitatory)
Hilar Interneurons
(inhibitory)
Granule Cells
(excitatory)
Basket Cells (inhibitory)
Figures 1A,B
Supp Figure 1
The Models
Figure 1 A
(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
Network Architecture and Analysis
• 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
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
Example with 210
connections for 5% of GCs
(In total, created 7 networks
with 30-210 connections)
Figures 3 D,E,F
Directionality of Hubs matters
Figures 4 D
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
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?