Hierarchy of visual cortex models

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

Experiment. Orientation map.

1 mm

Experiment. Responses of a thalamic neuron on 3 repetitions of a movie-stimulus.

Visual cortex

Cortical neurons with similar receptive fields are united in columns.in somatosensory cortex (Mountcastle, 1957);in auditory cortex (Brugge&Merzenich, 1973);in visual cortex (Hubel&Wiesel, 1965).

Hypercolumn is a minimal functional unit, uniting columns with all different orientations.

The pictures of orientation columns in cat and monkey visual cortex, obtained by electrophysiology with deoxyglucose.

Hubel&Wiesel

The PINWHEEL

The pictures of hypercolumns, obtained by voltage sensitivedyes.

Bonhoeffer&Grinvald

2-d CBRD model of visual cortex

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 columnX 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.

CBRD model of inhibitory population

Boundary conditions:

Firing rate:

CBRD model of excitatory population

Boundary conditions:

Firing rate:

preferred orientation:

Synaptic inputs

Synaptic morphologyIntracortical connections:

Thalamic input:

pinwheel centers:

Synaptic kinetics gS

t

d

fw

CBRD model: Hazard function

Results

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.

Single neuron activityE X P E R I M E N T

M O D E L

M O D E L to M O D E LSingle population activity

[Myme et al. 2003]

AMPA- and NMDA-EPSCs

[Dong et al. 2004]

Synaptic currentsEPSCs 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 TActivity 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-60

-65

-70

mV

* -60

-65

-70

mV

*

ms

mV

0 20 40 60 80 100

-6

-4

-2

0

2

weakmoderatestrong

ms

mV

0 20 40 60 80 100

-70

-68

-66

-64

-62

weakmoderatestrong

[Tucker & Katz, 2003]PSPs

Responses on electrical stimulationE X P E R I M E N T

M O D E L

PSPs

ms

mV

0 20 40 60 80 100

-68

-66

-64

-62

-60

controlBic

ms

mV

0 20 40 60 80 100-70

-68

-66

-64

-62 controlBic

-60

-63

mV

*

*

2 stimulating electrodesE 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 60-70

-65

-60

S1+S2

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

Contrast invariance effect

Visual illusion (tilt after-effect)

Explanation: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

=

Hierarchy of visual cortex models20151050

Hz

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

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:

2-d RD model

FR-shunt ring KFP-shunt ring

RD ring, cos-profileRD ring, exp-profile

canonical FR ring model

RD ring, nonadaptive

RD ring, 2-comp. LIF

RD ring, 1-comp. LIF

Thanks to colleagues:

Lyle Graham Erez PersiElena SmirnovaAnatoly BuchinAndrey Turbin