A brief introduction to Computational Neurosciencerinzel/CMNSF07/Rangan_LMI_Talk_Gateway.pdf · A...
Transcript of A brief introduction to Computational Neurosciencerinzel/CMNSF07/Rangan_LMI_Talk_Gateway.pdf · A...
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A brief introduction toA brief introduction to Computational NeuroscienceComputational Neuroscience
Aaditya RanganCourant, NYU
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Visual PathwayVisual Pathway
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Eye: Retinal CellsEye: Retinal Cells
Black and White Color Sensitive(found in most animals!)
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Brain = 1.5mTONS of neurons! (okay, 1.5 pounds)Brain = 1.5mTONS of neurons! (okay, 1.5 pounds)
nucleus
soma
dendrite
axon
sheath
Schwann cell
node
axon terminal
Cerebral Cortex
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Retinal Receptive Field
Cortical Receptive Field
Thalamic Receptive Field
Cones Rods
Off-center
On-center
45 degree slant135 degree slant
Rods
=
=
Off-center=
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At low contrast, and over intermediate time-scales,
Both the retina and the thalamus function (approximately) as linear transducers
However, there is substantial connectivity and nonlinear processing within the cortex
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LineLine--Motion IllusionMotion Illusion
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Experiment — Line Motion Illusion
Grinvald et al.
Stimulus
ExperimentVoltage
ExperimentVoltage
Stimulus
Time
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Brain = 1.5mTONS of neurons! (okay, 1.5 pounds)Brain = 1.5mTONS of neurons! (okay, 1.5 pounds)
nucleus
soma
dendrite
axon
sheath
Schwann cell
node
axon terminal
soma
axon
inputs
outputs
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input
/
( ) ( ) ( ) ! Pulse Coupled spik
Nonlineare at
1( ) ( ) ( )
( ) EX
t LEAK LEAK EX
k
EX
EX EX
THRESHOLD
kt
k
t
EX
EX
V t G V V G V V
V V T
G t G t t T
t e τ
δτ
α μ −
∂ = − − − −
> →
∂ = − + −
⎡ ⎤= ⎣ ⎦
∑
Simple Neuronal Model Simple Neuronal Model –– Integrate and FireIntegrate and Fire
spike
THRESHOLDV
time
EXV
LEAKV
INV
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V1
G1
V2
G2
Simple Neuronal Model Simple Neuronal Model –– Integrate and FireIntegrate and Fire
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Model Cortex
2mm
Pref
erre
d O
rient
atio
n
Actual Cortex ~25mm2
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,Inhib
( , ) ( ) ( ) ( ) ( ) ! Pulse Coupled spike at
Nonlinear
( , ) ( )i j
t i i LEAK i LEAK i i IN i i EX i i EX
ki TH
GABA
GABA
NM
GABA GABA
RESHOLD i
LOCAL
AMPA DA
kt i i x x j
j k
V x t G V V G V V G V V G V V
V V T
G x t S K t Tα∈
∂ = − − − − − − − −
> →
∂ = −∑{ }
{ }
{ }
Excit
itory
atory
Excita
,
tory,
( , ) (Stimulus) ( )
( , ) ( )
LGN
i i j
i j
NMDA NMDA
LOCAL kt i i x x x j
j k
LONG RANGE kt i
AMP
i
A AMPA
x x jj
AMPA
A
k
NMD
G x t F S K t T
G x t S K t T
α
α∈
−
∈
∂ = + −
∂ = −
∑
∑ ∑
∑ ∑
spike
THRESHOLDV
GABAα
AMPAα
NMDAα
timeLONG RANGEK −LOCALK
time
corti
cal s
pace
Reasonable Neuronal Model Reasonable Neuronal Model –– Integrate and Fire (Integrate and Fire (33 conductance typesconductance types))
7ms
3ms
80ms
EXV
LEAKV
INV
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Stimulus
Experiment
Model
Time
Voltage
Voltage
ModelNMDA
Line Motion Illusion Stimulus
model experiment
Stimulus
Experiment
Model
Voltage
Voltage
ModelNMDA
Drifting SquareStimulus
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Input? What does the Thalamus do?
77 968768584839 116106 1250ms 135291910
30 110spikes/sec
Firing
Rate:
LGN Time Kernel
Firin
g R
ate
16 36 100Time (ms)
1ox1o
LGN Spatial Kernel
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Mechanisms — Intermittently De-Suppressed system
. . .
Time
VisualInput
Input LG
N fromC
orticalR
esponse(S
pikes)
Cortical
NM
DAN
Cortical
VoltageP
rofile
96877768584839 116106 1250
g
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Predictions:
• Not a ‘wave’ of synaptic delays
• LGN time course + Cortical recruitment + Priming effect
• NMDA time-scale crucial
• Not sensitive to Sharp Edges
• Not sensitive to Linearity of Bar
• Proximity matters
• Lower contrast delays recruitment
What is going on?
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Predicted line-motion-like variants
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Hallucinations induced by Lysergic acid diethylamide ?
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Orientation Selectivity
Grinvald et al.
Sur et al.
Orientation Domains approximately 0.5mm across
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Retinotopy: a map from retina to V1
Large region dedicated to the fovea (F)
Visual field
Visual field
Visual cortex
Visual cortex
( )logire r iθ θ→ +
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Could cortical interconnectivity be responsible for spiral hallucinations?(see Bressloff, Cowan et al.)
Coarse-grainedpatches
Embedded I&F neurons
1Retinotopy−
modelmodel
Artists depictionLong rangeconnections
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Linking a Neuronal response to visual input does NOT imply function!
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