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Abstract

Studies of anatomical and functional connectivity lay down a basis for our understanding of the brain networks [1]. On a macroscale the measures are based on the coarse observations that allow capturing major connection tracts in the brain. However, on mesoscale and microscale, derivation of the networks’ connectivity have to rely on observation form a tiny fraction of the system. The inference of the whole network properties thus has to be done by extrapolation from the observed set to an unobserved one [2]. Our primary goal here is to understand how to make this inference rigorously.

Network science’ tools describe relevant network properties, but so far it is not known how the subsampling alters them. One of centrally used observables to characterize brain network is a small-worldness index: an average clustering coefficient divided by a diameter of the network. In a set of different network classes (random, small-word, scale-free) we demonstrate analytically and numerically that the average local clustering coefficient is preserved by subsampling (Figure A). Therefore changes in the small-worldness under subsampling is driven by changes in the inferred diameter. We observe that the diameter is strongly influenced by the subsampling thus our inference of small-worldness without correction for the sample size is biased. As next step, we are aiming at finding regularities in diameter changes under subsampling.

The brain networks have a highly complex structure, that is not captured by the simple random networks we consider in theoretical studies. To account for it, we investigate functional networks extracted from the developed cultures using High-Density Multi-Electrode Array (HD-MEA). We pre-process the recordings using SpiCoDyn package [3] and employ transfer entropy (TE) as a measure capturing information flow [4]. We define functional connectivity by conventional thresholding the TE matrix at the level of one standard deviation above the mean. We consider different window-subsampling of the full HD-MEA (Figure B). The threshold for significant functional connections depends on the sampled set (Figure C). Thus the network inferred from the subsampling of the whole system differs from the subnetwork with the same nodes inferred from the complete recordings. Next, we are going to study how the difference in thresholding alters our inference of the underlying network properties and how we can define a more sampling-independent thresholding strategy.