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.Theoretical Physic

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Single-cell period variability (SD) shows regional differences, especially after exposure to long photoperiod.

<p>Regional averages of single-cell period variability binned from all recordings for six areas of the anterior (top panels) and posterior SCN (bottom panels), in long (LP, left panels) and short photoperiod (SP, right panels). As indicated by the color bar on the right, dark (blue-black) colors indicate small, and light (green-yellow) colors indicate larger period variability. Scale bar: 200 μm.</p

Peak time of PER2::LUC expression is similar in anterior and posterior SCN in both long and short photoperiod.

<p>(A) Overlays of brightfield images of anterior SCN cultures from short (SP) and long photoperiod (LP), with the corresponding bioluminescence image. Scale bar: 200 μm. (B) Intensity traces of PER2::LUC expression from single cells. Raw traces of bioluminescence intensity from the anterior SCN from SP (<i>n</i> = 183 cells; top panel), with corresponding smoothed traces (middle panel), and smoothed traces from the anterior SCN from LP (<i>n</i> = 177 cells; bottom panel). (C) Average peak time of PER2::LUC rhythms per slice, of the anterior and posterior SCN in LP (green squares, <i>n</i> = 5) and SP (red circles, <i>n</i> = 4) are plotted as external time (ExT). Grey background indicates projected dark period of light regime preceding the experiment. Black bars indicate mean ± SEM; * <i>p</i> < 0.05.</p

Exposure to long photoperiod increases peak time distribution.

<p>(A) Representative histograms of peak times of two individual slices from the anterior SCN in long (LP, <i>n</i> = 177 cells) and short photoperiod (SP, <i>n</i> = 183 cells) plotted in external time (ExT). (B) Phase distribution is defined as the standard deviation (SD) of peak time, of the first cycle <i>in vitro</i> (top panel). Phase distribution was calculated per slice, and is shown for the anterior and posterior SCN (bottom panel), in LP (green squares) and SP (red circles). Black bars indicate mean ± SEM; *** <i>p</i> < 0.001.</p

Single-cell period variability (SD) increases after exposure to long photoperiod.

<p>(A) Representative examples of the variability in single-cell cycle-to-cycle interval from anterior SCN slices in long (LP, <i>n</i> = 177; top panel) and in short photoperiod (SP, <i>n</i> = 183; bottom panel). Black traces show the cycle-to-cycle interval of individual cells for the first three cycles <i>in vitro</i>; colored traces show the average period per cycle for the presented slice. (B) Cycle interval is defined as the cycle-to-cycle time difference between the half-maximum of the rising edge of the PER2::LUC expression rhythm. The variability in period is defined as the standard deviation (SD) of the cycle interval of individual cells, calculated for the first three cycles <i>in vitro</i> (top panel). Single-cell period variability was averaged per slice and is shown for the anterior SCN, in LP (green squares) and SP (red circles; bottom panel). Black bars indicate mean ± SEM. (C) Linear regression of the relationship between single-cell period variability and peak time SD for all recordings (<i>n</i> = 18, <i>p</i> < 0.001).</p

Functional clusters show distinct spatial distribution and region specific rhythm characteristics.

<p>(A) Representative examples of the communities detected by an advanced, unsupervised method for correlation matrix analysis [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0168954#pone.0168954.ref015" target="_blank">15</a>]. The community detection method automatically divided the SCN in two distinct regions, a ventromedial (VM) and dorsolateral (DL) region in the anterior SCN (middle panel), and a medial (M) and lateral (L) region in the posterior SCN, in both long (LP; left panel), and short photoperiod (SP, right panel). (B) Peak times in external time (ExT) were averaged per region, per slice. Darkness and light of the previous light regime are represented by grey and white background respectively. (C) Phase distribution, defined as peak time standard deviation (SD), was calculated per region, per slice. (D) Single-cell period variability was averaged per region, per slice. All data are shown for the VM and DL region in the anterior, and M and L region in the posterior SCN, in LP (green squares) and SP (red circles). Black bars indicate mean ± SEM; * <i>p</i> < 0.01.</p