On The Structure Of Cortical Micro-Circuits Inferred From Small Sample Sizes

Abstract

The structure in cortical micro-circuits deviates from what would be expected in a purely random network, which has been seen as evidence of clustering. To address this issue we sought to reproduce the non-random features of cortical circuits by considering several distinct classes of network topology, including clustered networks, networks with distance-dependent connectivity and those with broad degree distributions. To our surprise we found that all these qualitatively distinct topologies could account equally well for all reported non-random features, despite being easily distinguishable from one another at the network level. This apparent paradox was a consequence of estimating network properties given only small sample sizes. In other words, networks which differ markedly in their global structure can look quite similar locally. This makes inferring network structure from small sample sizes, a necessity given the technical difficulty inherent in simultaneous intracellular recordings, problematic. We found that a network statistic called the sample degree correlation (SDC) overcomes this difficulty. The SDC depends only on parameters which can be reliably estimated given small sample sizes, and is an accurate fingerprint of every topological family. We applied the SDC criterion to data from rat visual and somatosensory cortex and discovered that the connectivity was not consistent with any of these main topological classes. However, we were able to fit the experimental data with a more general network class, of which all previous topologies were special cases. The resulting network topology could be interpreted as a combination of physical spatial dependence and non-spatial, hierarchical clustering.\n\nSignificance StatementThe connectivity of cortical micro-circuits exhibits features which are inconsistent with a simple random network. Here we show that several classes of network models can account for this non-random structure despite qualitative differences in their global properties. This apparent paradox is a consequence of the small numbers of simultaneously recorded neurons in experiment: when inferred via small sample sizes many networks may be indistinguishable, despite being globally distinct. We develop a connectivity measure which successfully classifies networks even when estimated locally, with a few neurons at a time. We show that data from rat cortex is consistent with a network in which the likelihood of a connection between neurons depends on spatial distance and on non-spatial, asymmetric clustering.