The Simple and the Complex in Visual Cortex Dynamics

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Lecture 2
Michael Shelley Courant Institute Center for
Neural Science, NYU Louis Tao Mathematical
Sciences, New Jersey Institute of Technology
Barcelona, March 2005
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V1 the Visual Pathway
Cortical Map of Orientation Preference
---- Ý 0.5mm ß ----
Blasdel I992
Blasdel (1992)
right eye
Lateral Geniculate Nuclei (LGN)
left eye
Primary Visual Cortex (V1)
V1 laminae
Many neurons in V1 are sensitive
to stimulus orientation
?
4C primary input layer
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Simple Complex Classification

• Hubel Wiesel (1962)
• Simple "linear" spatio-temporal filters
• Contrast Reversal
• (1) temporal response at driving frequency
• (2) sensitive dependence on spatial phase
  (grating location)
• V1 40 Simple
• Complex everything else
• Contrast Reversal
• (1) frequency doubled
• (2) phase insensitive

Contrast Reversal Simple vs. Complex
j
frequency-doubled response
orthogonal phase
j
q
Contrast Reversal at 8 Different Spatial Phases
De Valois et al. (Vis. Res. 1982)
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intracellular voltage of a simple cell
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Different tasks in visual perception? Simple
cells Sensitive to signed edge contrast
Necessary for spatial
organization of scenes. Complex cells Cannot
represent signed edge contrast,
but are sensitive to texture.
Recent Experiment
The Classical View
The Hierarchical Model (HW 1962)
LGN drives Simple cells, whose pooled outputs
drive Complex cells. Very specific coupling.
Ringach, Shapley, Hawken JNS 2002
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A Neuronal Network Model (4C?)
Network of Integrate Fire (IF),
conductance-based, point neurons
LGN input to cortex is only excitatory
Conductances
Nonlinearity from spike-threshold Whenever vi
Vthres ( 1), neuron "fires", spike-time
recorded, and vi Vreset ( 0). vi is held at
Vreset for an absolute refractory period tref.
vi membrane potential of ith neuron gL
leakage conductance gEXC and gINH Excitatory
Inhibitory condces VE and VI Excitatory
Inhibitory reversal pots
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Elements of (local) NYU-I Simple cell model
Cortex Cortico-cortical coupling is isotropic
w. LEgtLI Weighted primarily as a balance
between lgn excitation and cortical
inhibition LGN input Orientation preference
set in pinwheel map. Preferred spatial
phase is randomized.
(SEE, SEI, SIE, SII) (0.8, 7.6, 1.5, 7.6)
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Drifting grating stimulus (MSSW 2000, PNAS)
Broad (in ?) inhibition near pinwheel center
yields sharper tuning there. Experiment suggests
no large differences (more on this later).
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Cycle averaged dynamics at preferred stimulus
orientation
Cortico-cortical conductances are flat in
time due to averaging over random
input phases. Very different from
Push/Pull models inhibition is
anti-phase (very controversial, but seems to be
settling in favor of broad phase input)
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Contrast reversal stimulus at preferred stimulus
orientation
preferred phase
orthogonal phase
Nonlinear LGN Input gLGN at Various Spatial
Phases
Wielaard, Shelley, McLaughlin, Shapley JNS 2001
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?
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"Simple" cell response at preferred and
orthogonal phases
cortico-cortical conductances are
frequency doubled and phase invariant due to
averaging over many input phases.
"Simple" Response Basically, an interaction
between LGN excitation, phase averaged cortical
inhibition, and thresholding
Frequency-doubled phase-insensitive cortical
inhibition removes frequency-doubled LGN
excitation at orthogonal phase
Wielaard, Shelley, McLaughlin, Shapley JNS 2001
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Frequency-doubled Excitatory and Inhibitory Input
to Simple Cells (L. Borg-Graham)
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"Simple" Response
Nonlinear LGN Input gLGN at Various
Spatial Phases
"Simple" Response Basically, an interaction
between LGN excitation, cortical inhibition, and
thresholding
Preferred
Frequency-doubled phase-insensitive cortical
inhibition removes frequency-doubled LGN
excitation at orthogonal phase
Orthogonal
Wielaard, Shelley, McLaughlin, Shapley JNS 2001
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Starting to sound like complex cells NYU-II
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The LGN input confers preferred angle,
preferred spatial phase, strength of input.
Reid Alonso 1995
De Angelis et al (1999)
LGN strength distribution
Blasdel (1992)
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• Important Features of Coupling
• Nonspecific and Isotropic (egalitarian) cortical
  coupling,
• w. monosynaptic inhibition of shorter
  length-scales
• Fitzpatrick et al 85, Lund 87,
  Callaway Wiser 96
• Total (LGN cortical) excitation on a cell is
  constant
• Miller 96, Royer Pare 02
• Combined AMPA and NMDA excitation

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Visual Stimulus Drifting Grating at 8 Hz
Voltage Time Traces
Time
1 mm
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The (egalitarian) model cortex (Tao, Sh,
McLaughlin, Shapley, PNAS 2004)
Simple
Complex
Contrast Reversal at 8 different spatial
phases
preferred
DeValois et al. 1982
orthogonal
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"Simple" Response
Nonlinear LGN Input gLGN at Various
Spatial Phases
"Simple" Response Basically, an interaction
between LGN excitation, cortical inhibition, and
thresholding
Preferred
Frequency-doubled phase-insensitive cortical
inhibition removes frequency-doubled LGN
excitation at orthogonal phase
Orthogonal
Wielaard, Shelley, McLaughlin, Shapley JNS 2001
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Complex response
Little or no LGN input
Time
Complex response A balance between cortical
inhibition and cortical self-excitation
(possible instability) Cortico-cortical
conductances are frequency-doubled, and
insensitive to spatial phase
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Drifting Grating Modulation Ratio
Drifting Grating Stimulus and S/C characterization
m
Simple
F1/F0 1.7
m
Complex
F1/F0 0.05

• Isotropic coupling random phase (DG) cortical
  conductances unmodulated
• Standard Characterization of Responses
  Modulation Ratio F1/F0

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Experiment (Ringach, Shapley Hawken JNS 2002)
Our Model Modulation Ratio of Firing Rate
Simple
Complex
In V1, 40 Simple 50 Simple in 4Ca
60 Simple
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Average Conductances
gtot
Total conductance is high, i.e., ?g ltlt ?syn
Cortical Inhibition dominant Borg-Graham et al
98, Hirsch 98, Anderson et al 00 Noisy,
high-conductance networks can give nicely graded
responses.
gI
gE
Shelley, McLaughlin, Shapley, Wielaard JCNS 2002
glgn
Total Excitation roughly constant
F1/F0
Complex
Simple
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Extracellular vs. Intracellular F1/F0 Distribution
Firing Rate m
Reversal Potential VS
Unimodal distribution reflects egalitarian
nature of network Wide distribution of
LGN/cortex couplings
Simple
Complex
Thresholding can lead to bimodal extracellular
distribution even with unimodal intracellular
distribution (Mechler Ringach 2002)
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Unimodal F1/F0 distribution measured in
experiments (cat)
Comparison to experiment (data from Ferster and
colleagues - replotted by F. Mechler)