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

I

E

I

E

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

Drifting Grating & Modulation RatioS

imp

leC

omp

lex

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

Sim

ple

Com

plex

Ringach, Shapley & Hawken JNS 2002

extracellular modulation ratio

intracellular modulation ratio

Priebe et al, Nat. Neuro. 2004

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

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

N

p N pN p

g F s a G tp

pt

p

othe 0 rwise

0.1

~100eff

p

N

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

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.

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

Fir

ing

Rat

e

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 r

espo

nse

criti

cal g

ain

Ex.C.Ex.C.

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

89 cellslayer 4Ca

But, strong relation between degree of selectivity for orientation and s.f.

peak s.f.

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.

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

Some results

F1/F0 preferred s.f.%

of

cell

s

# of

cel

ls

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 …

Thanks

&

Thanks to Jerry