Uncovering functional signature in neural systems via random matrix theory

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. Author Summary 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. Here we present a novel method, based on random matrix theory, for the identification of functional modules in the brain. Our approach overcomes known inherit methodological limitations of current methods, breaking the resolution limits and resolves a cell to cell functional networks. Moreover, 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.