A theory of ongoing activity in V1 (Goldberg et al 2004)

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Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple “attractor” states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feedforward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.
1 . Goldberg JA, Rokni U, Sompolinsky H (2004) Patterns of ongoing activity and the functional architecture of the primary visual cortex. Neuron 42:489-500 [PubMed]
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Model Information (Click on a link to find other models with that property)
Model Type: Connectionist Network;
Brain Region(s)/Organism:
Cell Type(s):
Gap Junctions:
Simulation Environment: XPPAUT;
Model Concept(s): Spatio-temporal Activity Patterns; Rate-coding model neurons; Olfaction;
Implementer(s): Goldberg, Joshua [JoshG at ekmd.huji.ac.il];
# This is an XPP realization of the noisy ring model that appears in 
# Goldberg JA, Rokni U and Sompolinsky H. Patterns of Ongoing Activity and the
# Functional Architecture of the Primary Visual Cortex. Neuron, 42:489-500 (2004).

# must have the file CosIntCol20.tab in the same directory as NoisyRing.ode

# In order to see the population activity do
# Viewaxes, Array and then fill out 
# *Column 1:m11
# NCols:20
# Row 1:0
# NRows:4000
# RowSkip:5
# Zmin:0
# and adjust Zmax according to your simulation

# The phase diagram of this model is shown in fig. 3A of the above paper. In order to 
# get a noisy "hill" of activity lambda must be larger than 1 and mu must be positive.

# parameters (gain and mean of Gaussian noise)
p lambda=1.8, mu=1
# mu here is equivalent to T/Sigma_n in the figure in the paper.
# note lambda=1.1, mu=5 are other possible defaults

# threshold linear gain function

# stochastic integration, w is local uncorrelated Gaussian white noise
weiner w[11..30]

#the model

#Coupling Matrix
table coscol CosIntCol20.tab
# this table is cosine coupling divided by 20
# recurrent feedback is given by h
special h=mmult(20,20,coscol,m11);

# order parameters of model
rnull=sum(0,19) of (shift(m11,i'))/20
rfundc=sum(0,19) of (shift(m11,i')*cos(2*pi*i'/20))/20
rfunds=sum(0,19) of (shift(m11,i')*sin(2*pi*i'/20))/20
aux r0=rnull
aux r1=sqrt(rfundc^2+rfunds^2)
aux phiang=atan(rfunds/rfundc)

# r1 is order 1 for a "hill of activity" and is order 1/sqrt(20) otherwise

@ total=1000,xlo=0,xhi=1000,ylo=0,yhi=10,dt=0.05,bounds=10000,meth=euler