Uncovering functional brain signature via random matrix theory

The brain is 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 the joint effects of local (unit-specific) noise and global (system-wide) dependencies that empirically obfuscate 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. The neurons alternating between the two modules define a candidate region of functional plasticity for circadian modulation

Phase Shifting Capacity of the Circadian Pacemaker Determined by the SCN Neuronal Network Organization

In mammals, a major circadian pacemaker that drives daily rhythms is located in the suprachiasmatic nuclei (SCN), at the base of the hypothalamus. The SCN receive direct light input via the retino-hypothalamic tract. Light during the early night induces phase delays of circadian rhythms while during the late night it leads to phase advances. The effects of light on the circadian system are strongly dependent on the photoperiod to which animals are exposed. An explanation for this phenomenon is currently lacking.We recorded running wheel activity in C57 mice and observed large amplitude phase shifts in short photoperiods and small shifts in long photoperiods. We investigated whether these different light responses under short and long days are expressed within the SCN by electrophysiological recordings of electrical impulse frequency in SCN slices. Application of N-methyl-D-aspartate (NMDA) induced sustained increments in electrical activity that were not significantly different in the slices from long and short photoperiods. These responses led to large phase shifts in slices from short days and small phase shifts in slices from long days. An analysis of neuronal subpopulation activity revealed that in short days the amplitude of the rhythm was larger than in long days.The data indicate that the photoperiodic dependent phase responses are intrinsic to the SCN. In contrast to earlier predictions from limit cycle theory, we observed large phase shifting responses in high amplitude rhythms in slices from short days, and small shifts in low amplitude rhythms in slices from long days. We conclude that the photoperiodic dependent phase responses are determined by the SCN and propose that synchronization among SCN neurons enhances the phase shifting capacity of the circadian system

Phase resetting of the mammalian circadian clock relies on a rapid shift of a small population of pacemaker neurons.

The circadian pacemaker of the suprachiasmatic nuclei (SCN) contains a major pacemaker for 24 h rhythms that is synchronized to the external light-dark cycle. In response to a shift in the external cycle, neurons of the SCN resynchronize with different pace. We performed electrical activity recordings of the SCN of rats in vitro following a 6 hour delay of the light-dark cycle and observed a bimodal electrical activity pattern with a shifted and an unshifted component. The shifted component was relatively narrow as compared to the unshifted component (2.2 h and 5.7 h, respectively). Curve fitting and simulations predicted that less than 30% of the neurons contribute to the shifted component and that their phase distribution is small. This prediction was confirmed by electrophysiological recordings of neuronal subpopulations. Only 25% of the neurons exhibited an immediate shift in the phase of the electrical activity rhythms, and the phases of the shifted subpopulations appeared significantly more synchronized as compared to the phases of the unshifted subpopulations (p<0.05). We also performed electrical activity recordings of the SCN following a 9 hour advance of the light-dark cycle. The phase advances induced a large desynchrony among the neurons, but consistent with the delays, only 19% of the neurons peaked at the mid of the new light phase. The data suggest that resetting of the central circadian pacemaker to both delays and advances is brought about by an initial shift of a relatively small group of neurons that becomes highly synchronized following a shift in the external cycle. The high degree of synchronization of the shifted neurons may add to the ability of this group to reset the pacemaker. The large desynchronization observed following advances may contribute to the relative difficulty of the circadian system to respond to advanced light cycles

Width and time of peak activity for both components.

<p>(A) Raw multiunit activity data following a shift of the light-dark cycle. After smoothing of the data, the trough between both components was determined as well as the peak times. The width of the unshifted and the shifted component was determined by drawing a horizontal line from the trough to the opposing slope of the component's peak. The ZT refers to the shifted Zeitgeber time. (B) The peak time for the unshifted and shifted component was at ZT 2.7±0.4 h, and at ZT 6.6±0.4 h respectively. The difference in peak time was significant (p<0.01). (C) The width of the peak of the unshifted and shifted component was 5.7±0.4 h and 2.2±0.3 h, respectively, which was significantly different (p<0.01).</p

Simulations of electrical activity patterns with two components.

<p>The black line shows the resulting multiunit pattern of two components with peak activity at ZT 9 (red dotted line) and ZT 13 (blue dotted line). The neurons of each component show a Gaussian distribution with certain distribution-width (σ). (A) Both populations have the same number of neurons and the same distribution. This leads to a single peak in the multiunit activity pattern. (B) The number of neurons in the shifted component is decreased, resulting in a unimodal multiunit pattern. (C) The number of neurons in the shifted component is decreased and the distribution of the shifted component is narrower, which leads to a bimodal multiunit pattern. (D) If the number of neurons is slightly increased with respect to (C), and the distribution of the shifted component is still narrow, the second peak becomes rapidly higher, see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0025437#pone-0025437-g001" target="_blank">figure 1</a> C. (E) Search-space that shows the effect of the number of neurons in each component and of their relative distribution to the multiunit pattern. The multiunit pattern becomes bimodal when the number of neurons of the shifted component is relatively small as compared to the total number of neurons (x-axis) and when the degree of synchronization of the shifted component is high (y-axis). The examples shown in (A)-(D) are depicted by the dots in the search-space.</p

Relative number of action potentials contributing to each component.

<p>(A) The total area under each of the components was used to determine the relative number of action potentials contributing to each component. (B) Gaussian functions fitted to the smoothed multiunit activity pattern. The black line is the smoothed multiunit activity pattern. The blue line is the total fitted pattern, and the Gaussian functions are shown below the fitted signal. (C) The area of the unshifted component as determined in (A) was 74% of the total area, while the area of the shifted component was 26%. (D) The relative area of the unshifted component, as determined in (B), was 79%, and of the shifted component was 21%.</p

Subpopulation analysis of the electrical activity profile after an advancing shift.

<p>The peak times of the subpopulations, indicated by the dots, were determined relative to the light-dark cycle after an advancing shift of 9 h. The top lines of the figure show the LD cycles before the shift and after the shift of the light-dark cycle. In the lower figure the numbers of subpopulations per hour were fitted by two Gaussian functions. The proportion of subpopulations that shifted to the middle of the new light period was 19% of the total amount of subpopulations.</p

Subpopulation analysis of the electrical activity profile after the shift in LD.

<p>(A and B) Two examples of the subpopulations (left ordinate axis) and multiunit activity pattern (right ordinate axis) for the same recording. The peak times of the subpopulations, indicated by the dots, were determined relative to the trough of the multiunit pattern (indicated by the red vertical line). (C) The number of subpopulations found in the unshifted component was higher than that in the shifted component, and showed a broader distribution.</p

Four examples of bimodal multiunit electrical activity recordings, showing two characteristic components.

<p>The left peak in each recording is unshifted component, while the right peak is the shifted component. The shifted light-dark schedule is depicted in the background, with gray indicating night and white indicating day. Time axis depicts the new phase, following the shift.</p