Model of visual cortex

Preferred direction Null direction

V

GE

GI

Experiments:Université Rene Descartes, Paris (rats and cats, visual cortex neurons, in-vivo, dynamic clamp):

Anton V. Chizhov

Ioffe Physico-Technical Institute of RAS,St.-Petersburg

Introduction

Experiment. Thalamic neuron responses on 3 trials of visual stimulation by movie.

F. Chavane, D. Sharon, D. Jancke, O.Marre, Y. Frégnac and A.

Grinvald // Frontiers in Systems Neuroscience, v.5, article 4, 1-26,

2011.

Local interactions in visual cortex

1 mm

Hypercolumn

Retinotopic projection

Orientation-tuned patchy connections

Ocular dominance

Зрительная кора

Experiment. Responses of a neuron selective to direction of stimulus movement.

Experiment. Orientation map.

Model. Response of 1mm2-area of the cortex on a change of orientation of visual stimulus-bar.

Model. Responses of 2 neurons preferring orthogonal orientations.

Simulation

2-d CBRD model of visual cortex

• Continuum in 2-d cortical space

• 2 layers: 2/3 и 4

• 2 populations: exc. (E) and inh. (I) neurons in each layer

• 3 types of synapses: AMPA, GABA-A and NMDA

• pinwheel-structure of input

• input is the luminance gradient of the visual stimulus

[И.А

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Computational costs for simulation of 1 mm2 of cortex

Monte-Carlo simulation(101-102 ODEs for 1 neuron

+ 2-104 ODEs for synapses)X 2-10 synaptic typesX 102 neurons 1 one column X 101-102 columns in 1 hypercolumnX 101 hypercolumns in 1 mm2

X 102-103 stimulation trialsTotal: 107-1012 ODEs.

CBRD continual model(101 PDEs for 1 neuron

X 2-10 types of neuronsX 101-102 discretization points in t*- space + 101 ODEs for synapses) X (101-102)2 discretization points in (x,y)-space

Total: 105-108 PDEs.

Boundary conditions:

Firing rate:

)(1)exp(2

)(~,),(~2-)(

)),(),(),(),(),(/(

),()(1)(

2

m

*****

TerfT

TFUU

TTFdtdT

UB

ttggttgttgttgttgC

dtdUUBUAUH

T

AHPLHMADRm

m

-- Hazard function

). 0.0117 0.072 0.257 1.1210(6.1exp=)( 4323 TTTTUA

[Chizhov, Graham // PRE 2007,2008]

CBRD model of inhibitory population

[Chizhov et al. // Neurocomputing 2006]

Boundary conditions:

Firing rate:

CBRD model of excitatory adaptive neuron population

2-comp. model [Чижов // Биофизика 2004]

preferred orientation:

pinwheel centers:

gS

t

d

fw

NMDAGABAAMPAs ,,

Synaptic inputs

Synaptic kinetics

Synaptic morphologyIntracortical connections:

Thalamic input:

Connections

740

66

3540

2400

1440

X/Y

L2/3

L4+5+6

E→E

38 1300

2801720720

X/Y

L2/3

L4+5+6

E→I

420

4680

800

L2/3

L4+5+6

I→E

28

220

33490

L2/3

L4+5+6

I→I

Potential connectivity matrix[Binzegger 2004]

Electrophysiological estimations[Thomson 2002, 2007]

postS

postprepostprepre

hitpostprepost

L

postpre

restVV

PSPdaP

g

g

),(

X/Y

L2/3

L4

2.7

1.2

2.0

2.8

I→II→E

E→E E→I

X/Y

L2/3

L4

1.7 2.7

0.6

7.1

9.8

L2/3

L4

2.7 9

2.3

L2/3

L4

10

12

[Bannister, Thomson 2007]

[Tamas 1997]

[Lubke,Feldmeyer 2007]

[Yoshimura, Callaway 2005]

Analysis of the model

CBRD ring model for

HH-neurons with synaptic kinetics

RDA-based ring model for

LIF-neurons with synaptic kinetics

Kolmogorov-Fokker-Planck (KFP)-based ring model for

LIF-neurons with synaptic kinetics

2-d CBRD model for Hodgkin-Huxley (HH)-neurons with

synaptic kinetics

KFP-based ring model for

LIF-neurons with instantaneous synaptic currents

Firing-Rate (FR) ring model with

instantaneous synaptic currents

=

20151050

Hz

Hierarchy of models

Canonical firing-rate ring model [Ben Yishai 1995] [Hansel, Sompolinsky, 1996]

)),((),(=),( . tIt

dttd FRst

FRFR

)(cos ),( ))(cos(21

=),( 02020

IIdtJJtI FR

Virtual rotation effect

Contrast invariance effect

Map 2-d geometry to a ring

Threshold-linear approximation of steady-state firing rate of LIF noisy neuron

pA

Hz

0 100 200 300 4000

20

40

60

80

100

Map CBRD-ring to FR-ring

Assumptions:

Canonical firing-rate ring model with shunt

)),(~,),(~(),(=),( . tstIt

dttd st

FRFR

)(cos~~ )( ))(cos~~(21

=),(~02020

IIdJJtI

)(cos~~ )( ))(cos~~(21

=),(~02020

KKdLLts

Fokker-Planck-based ring model

)(cos~~ )( ))(cos~~(21

=),(~02020

IIdJJtI

)(cos~~ )( ))(cos~~(21

=),(~02020

KKdLLts

)(2)(

)(2

22

resetmV

Lrestm VV

VtsgtI

VVVt

TVVm

V

Vt

2

)(

2-d CBRD

FR-shunt ring FP-shunt ring

CBRD ring, cos-profileCBRD ring, exp-profile

canonical FR ring model

CBRD ring, nonadapt.

CBRD ring, 2-comp. LIF

CBRD ring, 1-comp. LIF

Stationary solutions and the effect of Contrast Invariance

No adaptation + adaptation + adaptation + NMDA

Comparison with experiments

C

Vd

Vd

Vd

Vd

Vs

VsIs

Is

g=Id/(Vd-Vrev)

B

Рис. Согласование модели двух-компонентного нейрона (кружки) с экспериментальными данными (сплошные линии) по одновременным регистрациям на соме и дендрите [Pouille, Scanziani 2004]. A, ответы на стимуляцию в alveus в режиме фиксации тока показаны слева, ответ с фиксацией потенциала на соме -- справа. B, в другой клетке получены ответы на подачу тормозящей проводимости (gin амплитудой 5nS и временной зависимостью, показанной зеленой линией) в режиме dynamic-clamp.

A

[F.Pouille, M.Scanziani //Nature, 2004]

Passive properties of 2-compartment neuron

Рис. Модель и эксперимент [Karnup, Stelzer 1999]

Spiking of single neuron

E X P E R I M E N T

M O D E L

Lower Point Upper Point

M O D E L

E X P E R I M E N T

[Myme et al. 2003]

AMPA- and NMDA-EPSCs

[Dong et al. 2004]

Synaptic currents

EPSCs and IPSCs

E X P E R I M E N T

M O D E L

Spatiotemporal patterns generated by an electrical stimulus reveal clusters of activity. Scale bars in the experiments are 220μm.

E X P E R I M E N T

Activity patterns in visual cortex slices

M O D E L

3.5 ms 6.5 ms [Tucker & Katz, 2003]

3.5 ms 6.5 ms-68.8

-69.4

-70

mV

*

-68.8

-69.4

-70

mV

*

[Tucker & Katz, 2003]PSPs

Responses on electrical stimulation

E X P E R I M E N T

M O D E L

PSPs

ms

mV

0 20 40 60-70

-68

-66

-64

-62 weakmoderatestrong

ms

mV

0 20 40 60

-6

-4

-2

0

2

weakmoderatestrong

ms

mV

0 20 40 60

-68

-66

-64

-62

-60

controlBic

ms

mV

0 20 40 60

-68

-66

-64

-62

-60 controlBic

-69.5

-70

mV

*

*

Stimulation of the diffuse zone and optical claster

2 stimulating electrodes

E X P E R I M E N T

M O D E L

S1

S2

[Tucker & Katz, 2003]

S1

S2

ms

mV

0 20 40 60

-65

-60

expected S1+S2

S1+S2

*

*S1

S2

-69

-70

mV

*

*

E X P E R I M E N T

M O D E L

S1

S2

[Tucker & Katz, 2003]

ms

mV

0 20 40 60

-70

-65

-60

expected S1+S2

S1+S2

S1

S2

*

*S1

S2

Stimulation of two diffuse zones

2 stimulating electrodes

Vo

ltag

e(m

V)

Hz

-70

-60

-50

-40

0

25

50

75neuron preferred 0o-oriented bar

Time (ms)

Vo

ltag

e(m

V)

Hz

0 50 100 150 200 250 300-70

-60

-50

-40

20

40

60

80neuron preferred 45o-oriented bar

Excitatory neurons

Interneurons

ExperimentModelV

olta

ge

(mV

)

Hz

-70

-60

-50

-40

0

25

50

75neuron preferred 0o-oriented bar

Time (ms)

Vo

ltag

e(m

V)

Hz

0 50 100 150 200 250 300-70

-60

-50

-40

20

40

60

80neuron preferred 45o-oriented bar

StimulusVisual cortex

1 mm

E X P E R I M E N T

M O D E L

E X P E R I M E N T

Visual stimulation

Explanation:

Model

Visual illusion (tilt after-effect)

60

40

20

0

Hz

x

xx

x

x x x

xx

x xxx

x x x 50

25

0

Hz

x

xx

x

x x x

xx

x xxx

x x x

Hypothetic effect of depression of the “background” image by binocular vision

Thanks to colleagues:

Lyle Graham

Adrien Schramm

Erez Persi

Elena Smirnova

Anatoly Buchin

Andrey Turbin