A brief introduction to Computational Neurosciencerinzel/CMNSF07/Rangan_LMI_Talk_Gateway.pdf · A...

A brief introduction toA brief introduction to Computational NeuroscienceComputational Neuroscience

Aaditya RanganCourant, NYU

Visual PathwayVisual Pathway

Eye: Retinal CellsEye: Retinal Cells

Black and White Color Sensitive(found in most animals!)

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

Retinal Receptive Field

Cortical Receptive Field

Thalamic Receptive Field

Cones Rods

Off-center

On-center

45 degree slant135 degree slant

Rods

=

=

Off-center=

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

LineLine--Motion IllusionMotion Illusion

Experiment — Line Motion Illusion

Grinvald et al.

Stimulus

ExperimentVoltage

ExperimentVoltage

Stimulus

Time

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

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

V1

G1

V2

G2

Simple Neuronal Model Simple Neuronal Model –– Integrate and FireIntegrate and Fire

Model Cortex

2mm

Pref

erre

d O

rient

atio

n

Actual Cortex ~25mm2

,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

Stimulus

Experiment

Model

Time

Voltage

Voltage

ModelNMDA

Line Motion Illusion Stimulus

model experiment

Stimulus

Experiment

Model

Voltage

Voltage

ModelNMDA

Drifting SquareStimulus

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

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

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?

Predicted line-motion-like variants

Hallucinations induced by Lysergic acid diethylamide ?

Orientation Selectivity

Grinvald et al.

Sur et al.

Orientation Domains approximately 0.5mm across

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→ +

Could cortical interconnectivity be responsible for spiral hallucinations?(see Bressloff, Cowan et al.)

Coarse-grainedpatches

Embedded I&F neurons

1Retinotopy−

modelmodel

Artists depictionLong rangeconnections

Linking a Neuronal response to visual input does NOT imply function!