Animals
Adult male C57BL/6 mice (7–8 weeks old) were used for the generation of chronic restraint stress (CRS)-induced mouse model of depression. All mice were housed under a 12-h light/dark cycle and had ad libitum access to food and water. Animal care and handling were carried out according to the guidelines approved by the Institutional Animal Care and Use Committee at the Korea Advanced Institute of Science and Technology.
Generation of CRS-induced depression mouse model and behavioral task
CRS procedure was designed and conducted in line with a previous study [16]. Timeline of CRS is illustrated in Fig. 1a. For the restraint of mice, each mouse was placed in a 50 mL polystyrene tube that has evenly spaced 9 vent-holes (0.5 cm diameter each; 1.0 cm apart from each other) for 6 h, and then the restrained mice were placed in their home cage. Mice experienced restraint once a day from Day 1 to 28 (4 weeks). After 1 (CRS1W) or 3 weeks (CRS3W) (a post-CRS period) following the cessation of the 4-week-CRS, mice were subjected to behavioral tasks. Forced swimming test (FST) was used to measure behavioral despair, an indicator of depression-like behavior in mice [25, 26]. Briefly, mice were placed individually in 2000 ml glass beakers filled with nearly 1400 ml of water (10 cm from the ground, with water temperature of 25 ± 1 °C) and were allowed to swim freely for 6 min. The duration of immobility was measured during the last 4 min of the task. All behavioral tests were video-recorded. For the measurement of locomotor activity (total distance moved) and anxiety level (time in center), open-field test was performed as described previously [9, 27]. Briefly, mice were put in an open-field box made of white plastic walls (40 × 40 × 40 cm) and each mouse was placed in the periphery of the field. Then during the 10-min of video-recorded session, the total distance traveled and the time spent in the center of the box were analyzed with EthoVision (Noldus Information Technology, Wageningen, Netherlands).
Electrode implantation and in vivo electrophysiology for EEG
EEG surgery and recording in vivo was performed as described previously [9, 27]. Animals (CRS1 W, n = 6; CRS3 W, n = 8) underwent EEG surgery on the 29th day after CRS. Animals were anesthetized by intraperitoneal injection of ketamine (90 mg/kg) and xylazine hydrochloride (40 mg/kg). Electrode implantation was performed with a stereotaxic apparatus (Kopf Instruments, Tujunga, CA, USA). EEG recordings were obtained with tungsten electrodes (0.005 in, 2 MΩ), positioned in eight cortical regions, based on a mouse brain atlas: frontal cortices (AP +1.5 mm, L ± 0.2 mm, and DV −1.0 to −1.1 mm), somatosensory cortices (AP 0.0 mm, L ± 1.5 mm, and DV −1.0 to −1.1 mm), parietal cortices (AP −2.0 mm, L ± 2.5 mm, and DV −1.0 to −1.1 mm), and visual cortices (AP −3.5 mm, L ± 1.5 mm, and DV −1.0 to −1.1 mm) in each hemisphere (Fig. 2a). A reference electrode was inserted on the skull above the cerebellum. The electrodes were fixed to the skull with cyanoacrylate adhesive and dental acrylic cement. EEG recordings of CRS1W group were performed on the 35th day, and EEG recordings of CRS3 W group were performed on the 49th day. EEG recordings were combined with video monitoring, and EEG-video recording data were obtained continuously, 2 h/day, for 2 days. EEG activity was recorded after the signal was amplified 1200-fold, band pass-filtered at 0.1-500 Hz, and digitized at a sampling rate of 1600 Hz using a digital EEG system (Comet XL, Astro-Med, West Warwick, RI, USA). The EEG-video data obtained were analyzed offline using PSG Twin (Astro-Med), Clampfit (Axon Instruments, Foster City, CA, USA), and Matlab (MathWorks, Natick, MA, USA).
EEG analysis
Continuous EEG signals from the animals for two epochs, each consisting of 1 min of data from different days, in which they were in a resting state (i.e., awake and no movement), were analyzed to check the stability of the findings (Additional file 2: Figure S1). Then, continuous 1-min-long EEG signals from the last day of recording were used for analyses. The five EEG frequency-bands—delta (1.5–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), and gamma (30–80 Hz)—were analyzed for functional connectivity.
Cross-correlation: For cross-correlation analysis, the measurement set is denoted as M = {m1, m2,…, m8} consisting of eight nodes (i.e., eight brain regions) where we have measurement mi at the ith node. We calculated cross-correlation matrix through the following equation:
$$ corr(m_{i} ,m_{j} ) = \left\langle {\frac{{m_{i} }}{{\left\| {m_{i} } \right\|}},\frac{{m_{j} }}{{\left\| {m_{j} } \right\|}}} \right\rangle $$
Pearson’s correlation coefficient was used to obtain pairwise-correlation values at zero lag.
Persistent brain network homology: We used multiscale network modelling technique known as persistent brain network homology to compare the networks of CRS models and controls effectively. Detailed procedures to quantify topological features based on persistent homology were described in a previous study [9, 27, 28]. In brief, we used networks generated at every possible threshold and to seek evolutionary changes in the subnetwork clusters by increasing the threshold in correlation matrix, which was visualized by dendrogram. The distance matrix cM between two EEG measurements mi and mj through the following equation:
$$ c_{M} (m_{i} ,m_{j} ) = \sqrt {1 - corr(m_{i} ,m_{j} )} . $$
The brain network can be viewed as the weighted graph (M,cM) where M is a set of measurements at each brain region (= node) and cM is the metric defined on that set. We connect the nodes i and j with an edge if the distance cM (mi, mj) ≤ ε for some threshold value ε. Then the binary network B(M,ε) at threshold ε is a graph consisting of 0-simplices (nodes) and 1-simplices (edges). Start with ε = 0 and increase the ε at each iteration. The value of ε is taken discretely from the smallest cM(mi,mj) to largest cM(mi,mj). By increasing ε, more connected edges may be involved. If two nodes are already connected directly or indirectly via other intermediate nodes in smaller ε then at larger ε we don’t connect them. As a topological view of brain network, Rips complex was used to represent simplical complexes. Rips complex is defined as a simplical complex consisting of nodes and edges, whose k-simplices correspond to edges as a (k + 1)-simplices which are links of two nodes within the distance ε. Rips filtration reflects the multiscale networks, the sequence of nested Rips complexes over different scales. One of the topological features, Betti number β0, is a measure of the number of the connected components in the network. We could visualize those topological changes using barcode and dendrogram according to β0. We consider the network consisting of 0- and 1-complexes (nodes and edges). Our main concern is the changes of the zeroth Betti number β0, which measures the number of connected networks (CNs). The changes of β0 are visualized using the barcode. The vertical and horizontal axes in the barcode represent the indices of CN and filtration values respectively. The barcode of β0 is basically a decreasing function showing when CNs are merging to form a bigger network component. The number of CNs at the certain filtration value is same to the number of bars. If we rearrange the bars according to the node index instead of CN index in the vertical axis, we obtain single linkage dendrogram (SLD). While the barcode of β0 shows the global changes of the connected structure of network when the bars are ended, the SLD shows the local changes when the bars are merged. SLD between the nodes was calculated, which is usually used in hierarchical clustering. Given the network with distance cM, we calculated SLD (dM), which was defines as:
$$ d_{M} (m_{i} ,m_{j} ) = \hbox{min} \{ \mathop {\hbox{max} }\limits_{l = 0, \ldots ,k - 1} C_{M} (w_{l} ,w_{l = 1} )/m_{i} = w_{0} , \ldots , w_{k} = m_{j} \} $$
where mi = w0,…,wk = mj be a path between mi and mj. SLD is the minimum distance between two nodes when they belong to the same connected component during Rips filtration. It represents the hierarchical clustered structure of brain network in an algebraic form which can be used for a quantitative measure to discriminate brain networks. Using SLD calculated from persistent network homology, we could obtain the distance between two nodes after network construction without specific threshold. Each entry in the single-linkage matrix is a model-based predicted functional distance between the two nodes, mi and mj. The model-predicted distances from single-linkage matrices were tested with the Kruskal–Wallis test at the 0.05 level of significance with a Bonferroni correction.
Statistical analyses
Data collected were expressed as mean ± standard error of the mean (S.E.M.). For intergroup comparisons of behaviors, a one-way ANOVA or Mann–Whitney U test was used for comparisons among groups or between dependent variables. A P value <0.05 was considered significant. Kruskal–Wallis test was performed for the statistical comparison of slopes and final filtration values of the barcodes between the groups. Kruskal–Wallis test was used to compare pairwise single linkage matrices with a Bonferroni correction. SPSS 21.0 (SPSS Inc, Chicago, Ill, USA) and Matlab were used for the statistical analyses.
