Weak pairwise correlations imply strongly correlated network states in a neural population

Schneidman, Elad
Berry, Michael J. II
Segev, Ronen
Bialek, William

¹Joseph Henry Laboratories of Physics, ²Department of Molecular Biology, and ³Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544, USA.

doi:10.1038/nature04701

Received 22 September 2005; accepted 6 March 2006.

Published online 9 April 2006.

Supplementary Information is linked to the online version of the paper at www.nature.com/nature.

Author Information Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to E.S. ([email protected]).

Nature 440(7087):p 1007-1012, April 20, 2006.

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.