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Alex Roxin,

It seems likely that many aspects of higher brain function involve the concerted activity of large numbers of interacting neurons. Inspired by this insight, much theoretical effort has been put into understanding the collective behavior of coupled neurons in computational models. However, such models have proven difficult to constrain given the paucity of large-scale, simultaneous recordings of neuronal activity, largely due to technical impediments. With the advent of voltage-sensitive dye and Ca2+ imaging techniques, it is now possible to record the activity of large numbers of neurons simultaneously, opening the doors to quantitative studies of network-wide neuronal interactions in brain tissue.

Here we discuss the analysis of calcium-imaging data from slices of primary visual cortex and medial prefrontal cortex in mice from the laboratory of Rafael Yuste. Intracellular recordings confirmed that calcium-signal transients in individual cells in these slices corresponded to transitions between cortical up- and down-states. Earlier work on these data revealed the presence of reliably repeating spatio-temporal sequences of calcium-transients [1,2], which appeared more often than chance compared to selected surrogate time series. We have revisited these data and compared the frequency of occurrence of such patterns to several possible models. We analyzed 15 data sets totaling over an hour of recordings in over 2000 cells.

Of the 15 data sets we find that the occurrence of repeating
spatio-temporal patterns in 10 of them is consistent with each neuron
behaving as an independent Poisson process with a refractory period.
In four of the data sets, the patterns are best described by a
probabilistic network model for which we
extract a transition probability matrix describing
interactions between neurons.
We study the structure of the resulting connectivity
matrices and find, consistent with data from paired intracellular
recordings [3], highly nonrandom features including an
over-representation of doublet and triplet interactions.
Interestingly, however, we find that the statistical property of the
connectivity which most directly influences the firing patterns of
the cells is the degree distribution, i.e. the number of links into
and out of each cell. We find a large number of `hubs', cells with
an especially large number of links.

[1] R. Cossart, D. Aranov and R. Yuste*Nature*
**423**:283-288 (2003).

[2] Y. Ikegaya et al., *Science*
**304**:559-564 (2004).

[3] S. Song et al., *PloS Biology*
**3**:507-515 (2005).