Modeling Primary Visual Cortex (of Macaque)

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Modeling Primary Visual Cortex (of Macaque)

• David W. McLaughlin
• Courant Institute Center for Neural Science
• New York University
• dmac_at_courant.nyu.edu
• Santa Barbara Aug 01

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Input Layer of V1 for Macaque

• Modeled at
• Courant Institute of Math. Sciences
• Center for Neural Science, NYU
• In collaboration with
• ? Robert Shapley
• Michael Shelley
• Louis Tao
• Jacob Wielaard

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Visual Pathway Retina --gt LGN --gt V1 --gt Beyond
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• Why the Primary Visual Cortex?

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1
• Input from LGN well understood (Shapley, Reid,
  )

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1
• Input from LGN well understood (Shapley, Reid,
  )
• Anatomy of V1 well understood (Lund, Callaway,
  ...)

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1
• Input from LGN well understood (Shapley, Reid,
  )
• Anatomy of V1 well understood (Lund, Callaway,
  ...)
• The cortical region with finest spatial
  resolution --

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1
• Input from LGN well understood (Shapley, Reid,
  )
• Anatomy of V1 well understood (Lund, Callaway,
  ...)
• The cortical region with finest spatial
  resolution --
• Detailed visual features of input signal

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• Why the Primary Visual Cortex?
• Elementary processing, early in visual pathway
• Neurons in V1 detect elementary features of the
  visual scene, such as spatial frequency,
  direction, orientation
• Vast amount of experimental information about V1
• Input from LGN well understood (Shapley, Reid,
  )
• Anatomy of V1 well understood (Lund, Callaway,
  ...)
• The cortical region with finest spatial
  resolution --
• Detailed visual features of input signal
• Fine scale resolution available for possible
  representation

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Our Model

• A detailed, fine scale model of a layer of
• Primary Visual Cortex
• Realistically constrained by experimental data

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Our Model

• A detailed, fine scale model of a layer of
• Primary Visual Cortex
• Realistically constrained by experimental data
• A max-min model --
• in that in its construction, we attempt to make
  maximal use of experimental data,
• minimal use of posited architectural assumptions
• which are not supported by direct experimental
  evidence (such as Hebbian wiring schemes).

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Overview One Max-Min Model of V1
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Overview One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  construction and performance by experimental
  data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels

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Overview One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  construction and performance by experimental
  data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels
• Linearity of Simple Cells -- produced by (i)
  averages over spatial phase, together with
  cortico-cortical overbalance for inhibition

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Overview One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  construction and performance by experimental
  data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels
• Linearity of Simple Cells -- produced by (i)
  averages over spatial phase, together with
  cortico-cortical overbalance for inhibition
• Complex Cells -- produced by weaker (and varied)
  LGN input, together with stronger cortical
  excitation

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Overview One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  construction and performance by experimental
  data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels
• Linearity of Simple Cells -- produced by (i)
  averages over spatial phase, together with
  cortico-cortical overbalance for inhibition
• Complex Cells -- produced by weaker (and varied)
  LGN input, together with stronger cortical
  excitation
• Operates in a high conductance state -- which
  results from cortical activity, is consistent
  with experiment, and makes integration times
  shorter than synaptic times, an emergent
  separation of temporal scales with functional
  implications

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Overview One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  construction and performance by experimental
  data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels
• Linearity of Simple Cells -- produced by (i)
  averages over spatial phase, together with
  cortico-cortical overbalance for inhibition
• Complex Cells -- produced by weaker (and varied)
  LGN input, together with stronger cortical
  excitation
• Operates in a high conductance state -- which
  results from cortical activity, is consistent
  with experiment, and makes integration times
  shorter than synaptic times, an emergent
  separation of temporal scales with functional
  implications
• Together with a coarse-grained asymptotic
  reduction -- which unveils cortical mechanisms,
  and will be used to parameterize or scale- up
  to larger more global cortical models.

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Features of the Single Layer, Local Patch Model

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic
• Excitation longer range than inhibition

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Features of the Single Layer, Local Patch Model

• Integrate fire, point neuron model
• 16,000 neurons/sq mm
• 12,000 excitatory, 4000 inhibitory
• A patch (1 sq mm) of 4 orientation hypercolumns
• Orientation pref from convergent LGN input
• Coupling architecture, set by anatomy
• Local connections isotropic
• Excitation longer range than inhibition
• Cortical inhibition dominant

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Conductance Based Model
? E,I
vj? -- membrane potential -- ? Exc,
Inhib -- j 2 dim label of location
on cortical layer VE VI -- Exc Inh
Reversal Potentials


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Conductance Based Model
? E,I
Schematic of Conductances


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Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t)
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Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)

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Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise)
(synaptic time scale)
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Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise) (cortico-cortical)
(synaptic time scale)
(LExc gt LInh) (Isotropic)
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Conductance Based Model
? E,I
Schematic of Conductances

g?E(t) gLGN(t) gnoise(t)
gcortical(t) (driving term)
(synaptic noise) (cortico-cortical)
(synaptic time scale)
(LExc gt LInh)
(Isotropic) Inhibitory Conductances g?I(t)
gnoise(t) gcortical(t)
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Elementary Feature Detectors

• Individual neurons in V1 respond preferentially
  to elementary features of the visual scene
  (color, direction of motion, speed of motion,
  spatial wave-length).

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Elementary Feature Detectors

• Individual neurons in V1 respond preferentially
  to elementary features of the visual scene
  (color, direction of motion, speed of motion,
  spatial wave-length).
• Three important features

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Elementary Feature Detectors

• Individual neurons in V1 respond preferentially
  to elementary features of the visual scene
  (color, direction of motion, speed of motion,
  spatial wave-length).
• Three important features
• Spatial location (receptive field of the neuron)

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Elementary Feature Detectors

• Individual neurons in V1 respond preferentially
  to elementary features of the visual scene
  (color, direction of motion, speed of motion,
  spatial wave-length).
• Three important features
• Spatial location (receptive field of the neuron)
• Spatial phase ? (relative to receptive field
  center)

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Elementary Feature Detectors

• Individual neurons in V1 respond preferentially
  to elementary features of the visual scene
  (color, direction of motion, speed of motion,
  spatial wave-length).
• Three important features
• Spatial location (receptive field of the neuron)
• Spatial phase ? (relative to receptive field
  center)
• Orientation ? of edges.

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Grating Stimuli Standing Drifting
Two Angles Angle of orientation -- ? Angle
of spatial phase -- ? (relevant for standing
gratings)
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Orientation Tuning Curves(Firing Rates Vs Angle
of Orientation)
Spikes/sec ?

• Terminology
• Orientation Preference
• Orientation Selectivity
• Measured by Half-Widths or Peak-to-Trough

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Orientation Preference

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Orientation Preference

• Model neurons receive their
• orientation preference
• from convergent LGN input

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Orientation Preference

• Model neurons receive their
• orientation preference
• from convergent LGN input
• How does the orientation preference ?k of the kth
• cortical neuron depend upon the neurons
• location k (k1, k2) in the cortical layer?

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Cortical Map of Orientation Preference

• Optical Imaging
• Blasdel, 1992
• Outer layers (2/3) of V1
• Color coded for angle of
• orientation preference

---- ? 500 ? ? ----
? right eye ? left eye
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Pinwheel Centers
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4 Pinwheel Centers
1 mm x 1 mm
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Orientation Selectivity

• While the model neurons receive their
• orientation preference hardwired
• from convergent LGN input
• they receive their orientation selectivity
  diversity from cortico-cortical
  activity

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Orientation Tuning Curves

• 
  __ __ __
  Cortex off

Spikes/sec ?
Ringach, Hawken Shapley
McLaughlin,Shapley,Shelley Wielaard

PNAS 00
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Orientation Selectivity(Measured by the
circular variance of the tuning curves)
CV 1, poorly tuned 0, very
selective A measure of height-to-trough Useful
for population studies

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Orientation Selectivity -- Population
Behavior(CV Circular Variance of Tuning Curves)
CV 1, poorly tuned 0, very selective
____ Excitatory Inhibitory
Ringach, Hawken Shapley
McLaughlin,Shapley,Shelley Wielaard PNAS 00
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Spatial Distributions of Firing Rates and
Orientation Selectivity (Relative to Locations of
Pinwheel Centers)
? Poorly tuned ? Selective
Spikes/sec ?
Firing Rates
Circular Variance (of Orientation Selectivity)
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• Experimental Evidence on
• Spatial Distribution of
• Orientation Selectivity
• (relative to pinwheel centers)
• Maldonado, Gray, Goedecke
• Bonhoffer, Science 97
• In cat
• Data converted to CVs
• by M. Shelley
• Selectivity is diverse
• More selective (?) near pinwheels

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Cortical Mechanism For Spatial Distribution Of
Orientation Selectivity

• Discs of incoming
• inhibition
• Radius set by axonal
• arbors of inh. neurons
• While inhibition is
• local in cortex,
• Near pinwheels, it is
• global in orientation

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Simple and Complex Cells

• Simple cells respond linearly
• to properties of the stimulus a network
  property.
• In a nonlinear network, simple is not
  sosimple.
• Simple Cells
• Wielaard, Shelley, McLaughlin
  Shapley,
• to appear, J. Neural Science (2001)
• Simple Complex Cells
• Tao, Shelley, McLaughlin Shapley, in
  prep (2001)

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Simple vs Complex Cells

• Simple cells respond linearly to properties
  of visual stimuli --

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Simple vs Complex Cells

• Simple cells respond linearly to properties
  of visual stimuli --
• (i) Follow spatial phase of standing grating

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Simple vs Complex Cells

• Simple cells respond linearly to properties
  of visual stimuli --
• (i) Follow spatial phase of standing grating
• (ii) Respond temporally at the fundamental
• (1st harmonic)

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Simple vs Complex Cells

• Simple cells respond linearly to properties
  of visual stimuli --
• (i) Follow spatial phase of standing grating
• (ii) Respond temporally at the fundamental
• (1st harmonic)
• Complex cells -- phase insensitive
• large second harmonics

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Experimental Measurements Simple and Complex
Cells
Simple Cell
? Phase
Time ?
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Model Results Contrast Reversal (For Optimal
and Orthogonal Phase)
Cortex On
Cortex Off
Membrane Potential
Optimal Phase
Firing Rates
Orthogonal Phase
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Mechanisms by which the Model Produces Simple
Cells

• Inputs to Cortical Cell
• From LGN
• (Frequency doubled at
• orthogonal to optimal phase)
• From Other Cortical
• Neurons

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Mechanisms by which the Model Produces Simple
Cells

• Inputs to Cortical Cell
• From LGN
• (Frequency doubled at
• orthogonal to optimal phase)
• From Other Cortical
• Neurons (Also freq doubled,
• because of averaging over
• random phases -- whose
• distribution is broad
• (De Angelis, et al 99)

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Mechanisms by which the Model Produces Simple
Cells

• Inputs to Cortical Cell
• From LGN
• (Frequency doubled at
• orthogonal to optimal phase)
• From Other Cortical
• Neurons (Also freq doubled,
• because of averaging over
• random phases -- whose
• distribution is broad
• (De Angelis, et al 99)

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Mechanisms by which the Model Produces Simple
Cells

• Inputs to Cortical Cell
• From LGN
• (Frequency doubled at
• orthogonal to optimal phase)
• From Other Cortical
• Neurons (Also freq doubled,
• because of averaging over
• random phases -- whose
• distribution is broad
• (De Angelis, et al 99)
• Cortical Overbalance for
• Inhibition (Borg-Graham,
• et al 98 Hirsch, et al 98
• Anderson, et al 00)
• Cancellation

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Simple Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms

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Simple Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.

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Simple Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.
• (iii) Balance produces linearity of simple
  cells

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Simple Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.
• (iii) Balance produces linearity of simple
  cells
• Indeed, this balance can be broken by
  pharmacologically weakening inhibition --
  converting simple cells to complex
• Expt refs -- Sillito (74) Fregnac and Schulz
  (99) Humphrey (99)

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Simple vs Complex Cells
Continued

• The model also contains complex cells (but, as
  yet, not enough, and the complex cells are not
  selective enough for orientation)

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Simple vs Complex Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.

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Simple vs Complex Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
  of) complex cells

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Simple vs Complex Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
  of) complex cells
• (i) Weaker (and varied) LGN input

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Simple vs Complex Cells

• Recall mechanisms which produce (linear responses
  of) simple cells
• (i) Averaging over spatial phases in
  cortico-cortical terms
• (ii) Overbalance for inhibition in
  cortico-cortical terms.
• Mechanisms which produce (nonlinear responses
  of) complex cells
• (i) Weaker (and varied) LGN input
• (ii) Stronger cortico-cortical excitation
• (Abbott, et al, Nature Neural Science 98)

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Simple vs Complex Cells
Continued

• Drifting grating stimulation
• Distributions of simple and complex cells
• Expt -- Ringach, Shapley Hawken
• Model -- Tao, Shelley, McLaughlin Shapley

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Expts ( Ringach, Shapley Hawken)
Model (Tao, Shelley, McL Shapley) (Preliminary)
(Similar to earlier results of De Valois, et al)
In V1, 40 Simple
In 4C?, 55 Simple
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1 mm x 1mm Local Patch of 4C? 1 mm x 1mm
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Active Model Cortex - High Conductances
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Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice

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Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice

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Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice
• gt gInh gtgt gExc

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Active Model Cortex - High Conductances

• Background Firing Statistics
• gt gBack 2-3 gslice
• Active operating point
• gt gAct 2-3 gBack 4-9 gslice
• gt gInh gtgt gExc
• Consistent with experiment
• Hirsch, et al, J. Neural Sci 98
• Borg-Graham, et al, Nature 98
• Anderson, et al, J. Physiology 00
• Lampl, et al, Neuron 99

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• Conductances Vs Time
• Drifting Gratings -- 8 Hz
• Turned on at t 1.0 sec
• Cortico-cortical
• excitation weak relative to LGN
• inhibition gtgt excitation

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Distribution of Conductance Within the
Layer ltgTgt Time Average ? SD(gT)
Standard Deviation Of Temporal Fluctuations ?
Sec-1
Sec-1
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Active Cortex - Consequences of High Conductances

• Separation of time scales

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Active Cortex - Consequences of High Conductances

• Separation of time scales
• Activity induced ?g gT-1 ltlt ?syn (actually, 2
  ms ltlt 4 ms)

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Active Cortex - Consequences of High Conductances

• Separation of time scales
• Activity induced ?g gT-1 ltlt ?syn (actually, 2
  ms ltlt 4 ms)
• Membrane potential instantaneously tracks
  conductances on the synaptic time scale.
• Definition of Effective Reversal Potential
• V(t) VEff(t) VE gEE(t) - VI gEI(t)
  gT(t)-1
• Where gT(t) denotes the total conductance

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Conductance Based Model
? E,I
dv/dt gT(t) v - VEff(t) , where gT(t)
denotes the total conductance, and VEff(t)
VE gEE(t) - VI gEI(t) gT(t)-1 If
gT(t) -1 ltlt ?syn ? v ? VEff(t)


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High Conductances in Active Cortex ? Membrane
Potential Tracks Instantaneously Effective
Reversal Potential
Active
Background
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Effects of Scale Separation
?g 2 ?syn ?g ?syn ?g ½ ?syn
____(Red) VEff(t) ____(Green) V(t)
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Active Cortex - Consequences of High Conductances

• Thus, with this instantaneous tracking (on the
  synaptic time scale),
• cortical activity can convert neurons from
  integrators to burst generators coincidence
  detectors.

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Coarse-Grained Asymptotics
102
Coarse-Grained Asymptotics

• Using the spatial regularity of cortical maps
  (such as orientation preference), we coarse
  grain the cortical layer into local cells or
  placquets.

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Cortical Map of Orientation Preference

• Optical Imaging
• Blasdel, 1992
• Outer layers (2/3) of V1
• Color coded for angle of
• orientation preference

---- ? 500 ? ? ----
? right eye ? left eye
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Coarse-Grained Asymptotics

• Using the spatial regularity of cortical maps
  (such as orientation preference), we coarse
  grain the cortical layer into local cells or
  placquets.
• Using the separation of time scales which emerge
  from cortical activity,

106
Coarse-Grained Asymptotics

• Using the spatial regularity of cortical maps
  (such as orientation preference), we coarse
  grain the cortical layer into local cells or
  placquets.
• Using the separation of time scales which emerge
  from cortical activity,
• Together with an averaging over the irregular
  cortical maps (such as spatial phase)

107
Coarse-Grained Asymptotics

• Using the spatial regularity of cortical maps
  (such as orientation preference), we coarse
  grain the cortical layer into local cells or
  placquets.
• Using the separation of time scales which emerge
  from cortical activity,
• Together with an averaging over the irregular
  cortical maps (such as spatial phase)
• we derive a coarse-grained description in terms
  of the average firing rates of neurons within
  each placquet

108
?
109
Uses of Coarse-Grained Eqs

• Coarse-grained equations can be used to unveil
  the models mechanism for
• Better selectivity near pinwheel centers

110
Spatial Distributions of Firing Rates and
Orientation Selectivity (Relative to Locations of
Pinwheel Centers)
? Poorly tuned ? Selective
Spikes/sec ?
Firing Rates
Circular Variance (of Orientation Selectivity)
111
m F cEE KEE ?m? cEI KEI ?n? n
F cIE KIE ?m? cII KII ?n?
---------------------------------------- For
ease, specialize cEE cIE cII
0 m F cEI KEI ?n? n F
That is, -----------------------------------------
----- m F cEI KEI ? F ?
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m(?) F (?) cEI ?? KEI (? -?) ? F (?)
? ------------------------------------------
----- m(?) F (?) cEI ? F (?) ?
FARR m(?) F (?) cEI ? ?? F (?)
? NEAR
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Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers

115
Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers
• (ii) Balances for simple and complex cells

116
Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers
• (ii) Balances for simple and complex cells
• Input-output relations at high conductance

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One application of Coarse-Grained Equations
118
Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers
• (ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
  of distinct models of the cortex

119
Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers
• (ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
  of distinct models of the cortex
• Most importantly, much faster to integrate

120
Uses of Coarse-Grained Eqs

• Unveil mechanims for
• (i) Better selectivity near pinwheel centers
• (ii) Balances for simple and complex cells
• Input-output relations at high conductance
• Comparison of the mechanisms and performance
  of distinct models of the cortex
• Most importantly, much faster to integrate
• Therefore, potential parameterizations for more
  global descriptions of the cortex.

121
Conductance Based Model
? E,I
-- 16,000 neurons per mm2 --
Locally, connections are isotropic but
-- Long range coupling is
spatially heterogenous and
orientation specific


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Lateral Connections and Orientation -- Tree
Shrew Bosking, Zhang, Schofield Fitzpatrick J.
Neuroscience, 1997
123
Scale-up Dynamical Issuesfor Cortical Modeling

• Temporal emergence of visual perception
• Role of temporal feedback -- within and between
  cortical layers and regions
• Synchrony asynchrony
• Presence (or absence) and role of oscillations
• Spike-timing vs firing rate codes
• Very noisy, fluctuation driven system
• Emergence of an activity dependent, separation of
  time scales
• But often no (or little) temporal scale
  separation

124
Summary One Max-Min Model of V1

• A detailed fine scale model -- constrained in
  its construction and performance by
  experimental data
• Orientation selectivity its diversity from
  cortico-cortical activity, with neurons more
  selective near pinwheels
• Linearity of Simple Cells -- produced by (i)
  averages over spatial phase, together with
  cortico-cortical overbalance for inhibition
• Complex Cells -- produced by weaker (and varied)
  LGN input, together with stronger cortical
  excitation
• Operates in a high conductance state -- which
  results from cortical activity, is consistent
  with experiment, and makes integration times
  shorter than synaptic times, a separation of
  temporal scales with functional implications
• Together with a coarse-grained asymptotic
  reduction -- which unveils cortical mechanisms,
  and will be used to parameterize or scale- up
  to larger more global cortical models.