Uncovering functional signature in neural systems via random matrix theory

Assaf Almog,Ori Roethler,Jos H T Rohling,Stephan Michel,Diego Garlaschelli,M Renate Buijink,Johanna H Meijer

doi:10.1371/journal.pcbi.1006934

Abstract

Neural systems are organized in a modular way, serving multiple functionalities. This multiplicity requires that both positive (e.g. excitatory, phase-coherent) and negative (e.g. inhibitory, phase-opposing) interactions take place across brain modules. Unfortunately, most methods to detect modules from time series either neglect or convert to positive, any measured negative correlation. This may leave a significant part of the sign-dependent functional structure undetected. Here we present a novel method, based on random matrix theory, for the identification of sign-dependent modules in the brain. Our method filters out both local (unit-specific) noise and global (system-wide) dependencies that typically obfuscate the presence of such structure. The method is guaranteed to identify an optimally contrasted functional ‘signature’, i.e. a partition into modules that are positively correlated internally and negatively correlated across. The method is purely data-driven, does not use any arbitrary threshold or network projection, and outputs only statistically significant structure. In measurements of neuronal gene expression in the biological clock of mice, the method systematically uncovers two otherwise undetectable, negatively correlated modules whose relative size and mutual interaction strength are found to depend on photoperiod.

Highlights

Understanding how billions of neurons collectively self-organise into a functionally ordered brain able to coordinate a variety of neural, cognitive and bodily processes is probably the most fundamental quest in neuroscience
In recent years an increasing number of studies demonstrate that functional organization of the brain has a vital importance in the manifestation of diseases and aging processes. This functional structure is composed of modules sharing similar dynamics, in order to serve multiple functionalities
The results represent a great potential for detecting hidden functional synchronization and de-synchronization in brain networks, which play a major role in the occurrence of epilepsy, Parkinson’s disease, and schizophrenia

Summary

Introduction

Understanding how billions of neurons collectively self-organise into a functionally ordered brain able to coordinate a variety of neural, cognitive and bodily processes is probably the most fundamental quest in neuroscience. Evidence has accumulated that the functional organisation of the brain is modular and hierarchical [1] This means that the brain appears to be partitioned into mesoscopic ‘functional modules’ where each module is composed of neurons with a relatively similar dynamical activity, while different modules are comparatively less related to each other. An anatomically well-defined brain region can be functionally heterogeneous [6, 7] and sometimes even display anti-correlation between the activity of some of its parts [8, 9] These examples indicate the lack of a one-to-one correspondence between structural and functional modules, showing that it is in general impossible to infer the latter purely from spatial information. Both structural and functional brain networks are characterized by plasticity, i.e. possibility of temporal rearrangements, but at typically different spatial and temporal scales

Objectives

Results

Discussion

Conclusion