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Reconstructing networks from spike train data

For networks with sparse connectivity, the underlying structure can be inferred from measured correlations

The relation between causation and correlation is often difficult to assess: Just because things happen close by in time or space does not mean that there must exist a causal relationship between them. Neuroscientists have to deal with this problem when they try to infer physical synaptic connections between neurons from measured correlations in their activity. Specifically, they look at the sequences of brief electrical impulses, so-called spike trains, through which most of the communication between neurons in the nervous system happens. A major obstacle is that shared presynaptic neurons, as well as other indirect links between neurons, can cause correlations, even if no direct connection is present.
Volker Pernice and Stefan Rotter from the Bernstein Center Freiburg describe the resulting ambiguity, along with a new method to resolve it, in the current issue of the Journal of Statistical Mechanics. To this end, they employ a mathematical model that they had suggested recently, and which describes how the underlying connectivity determines correlations in spike train data.

In their new paper, they could now show that, under certain conditions, it is possible to solve the inverse problem: to reconstruct a network from the somewhat limited information contained in activity correlations of individual cells. To do this successfully, they had to work with the assumption that only few of the potential connections in neural networks actually exist. Experimental work has shown that this is indeed the case in the brain. To their own surprise, the scientists found that they could even recover the directions of the connections between cells. In contrast to the case of a technical conductor like a metal wire, neuronal signals are always transmitted in one specific direction, from one nerve cell to another one. That the analysis method could indeed determine this direction was by no means obvious, as the activity correlations, on which the analysis was based, per se do not suggest a direction.

The basic idea of the study by Pernice and Rotter is to find the minimal wiring diagram that is consistent with the given data. This notion has already been successfully applied in other fields, like signal processing and machine learning.  Although the present study is concerned with correlations in spike trains of single neurons, it could also be applied to other types of data, e.g. data measured in the human brain using functional magnetic resonance imaging.
 

Original article:

Volker Pernice and Stefan Rotter (2013) Reconstruction of sparse connectivity in neural networks from spike train covariances. J. Stat. Mech., P03008. doi:10.1088/1742-5468/2013/03/P03008
 

Image:

Even if no direct connection exists between neurons, indirect paths (top) cause correlations. Because the contributions of indirect paths depend on the direction of the links, the underlying directed connections (bottom left) can be inferred under certain conditions (bottom right).

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