V1 Dynamics and Sparsity and Multiple Feature Maps Michael Shelley – Courant Institute/CNS, NYU...
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V1 Dynamics and Sparsity and Multiple Feature Maps
Michael Shelley – Courant Institute/CNS, NYU
Collaborators: Bob Shapley – CNS/CIMS David Cai -- CIMS Dave McLaughlin – CIMS/CNS Louis Tao -- NJIT Wei Zhu -- CNS/CIMS
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IE
IE
LGN
SimpleComplex
Inhibitory Excitatory
V1
Important Features:• Nonspecific and Isotropic (egalitarian) cortical coupling (I&II) (monosynaptic inhibition of shorter length-scale) Fitzpatrick et al 85, Lund 87, Callaway & Wiser 96• LGN imparts random preferred spatial phase (I&II) De Angelis et al (1999)• Combined AMPA and NMDA excitation (II)• Total (LGN + cortical) excitation on a cell is (approx) constant (II) Miller 96, Royer & Pare 02
NYU V1modelsI & II
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Drifting Grating & Modulation RatioSi
mpl
eC
ompl
ex
Isotropic coupling & random phase: (DG) cortical conductances unmodulated Standard Characterization of Responses: Modulation Ratio F1/F0
F1/F0 = 1.7
F1/F0 = 0.05
(2 / )1 0 0 0/ ( ) ( )i tF F dt m t e dt m t
Drifting Grating Stimulus and S/C characterization
m
m
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Sim
ple
Com
plex
Ringach, Shapley & Hawken JNS 2002
extracellular modulation ratio
intracellular modulation ratio
Priebe et al, Nat. Neuro. 2004
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But …• complex cells poorly tuned• increasing self-excitation led to bistability & high firing rates• marked near/far from pinwheel tuning differences (Sur’s lab: intracellular differences, but little extracellular)
Our previous work suggested that recurrent excitation could be stabilized and graded by intrinsic fluctuations in the local circuit. Cai et al, PNAS 2004
Approach here: Probabilistically sparsify the network and simultaneously boost efficacy of active connections (psp’s are fewer and bigger).
Numerology: Mason, Nicoll, Stratford 1991 Thomson et al 2002 suggests O(102) presynaptic cortical cells give drive
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For each of potentially presynaptic neurons, connect w. probability : w.
Example: excitatory conductance to postsynaptic cell
0 1
1
:
with probabili p ty ;
eff
ext kE E E k E l
k l
k
k
Np N pN p
g F s a G tpp
t
p
othe 0 rwise
0.1~100eff
pN
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2i Circular variance:
measures selectivity: Near 1 is well-tuned, near 0 is poorly
CV[m]=1
t
/
un
-
ed
e m m
tuned complex cellssmall near/far diffs
statistically contrastinvariant
experimentShapley et al
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complex complex complexsimplesimplesimple
near pinwheel center iso-orientation domain
intracellular conductances somewhat morebroadly tuned or diverse at p.w. centers
Well-tuned complex cells both near and far from p.w. centers.
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What underlies the tuning and the stability? Fluctuations.
In V1 model, histogram of diff.in spike count on increment and decrementof slowly modulated contrast.
Hysteresis in excitatory complex cell network
~100effN 800effN inputG
Firi
ng R
ate
Simple, homogeneously coupled modelnetwork fashioned after V1 model.50% receive external excitatory drive (simple)50% receive strong cortical excitation (complex)
Existence of critical gain point we call fluctuation controlled criticality
hyste
ric lo
op
grad
ed re
spon
se
criti
cal g
ain
Ex.C.Ex.C.
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or or
How about “functional” sparsity? Many visual neurons are silent except when driven by near-optimal stimuli, e.g. optimal orientation & spatial frequency (w. Shapley & W. Zhu)
tuning curves for orientationand spatial frequency.Xing, Ringach, Shapley, Hawken ‘04
s.f.
0 2π 1010.1
firingrate
• No observed relation between preferred orientation and spatial frequency.• In our previous models, LGN drive has single preferred s.f.
cycles/deg
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89 cellslayer 4Ca
But, strong relation between degree of selectivity for orientation and s.f.
peak s.f.
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Spatial frequency mapping remains contentious … Hubener, Shoham, Grinvald, Bonhoeffer ’97 Everson et al 1998 Issa, Trepel, Stryker 2000 orientation map of
high spatial freq.response
orientation map oflow spatial freq.
response
high low
Sirovich & Uglesich2004
Suggests the spatial frequency is not a well-structured map,consistent with electrophysiology.
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Modification of NYU-II:
• Add diversity in preferred spatial frequency of LGN drive to V1.• Keep # of LGN cells independent of pref. s.f.• 50% “even”, 50% “odd” structure.
or orodd
even
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Some results
F1/F0 preferred s.f.%
of c
ells
# of
cel
ls
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CV
[fir
ing
rate
]LSFV
s.f. orientation
As with expt., find correlation betweentuning of orientation and tuning of s.f.
Two sample cells
still working on complex cell tuning …
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Thanks
&
Thanks to Jerry