Neural systems can be modeled as complex networks in which neural elements are represented as nodes linked to one another through structural or functional connections. The resulting network can be analyzed using mathematical tools from network science and graph theory to quantify the system's topological organization and to better understand its function. Here, we used two-photon calcium imaging to record spontaneous activity from the same set of cells in mouse auditory cortex over the course of several weeks. We reconstruct functional networks in which cells are linked to one another by edges weighted according to the correlation of their fluorescence traces. We show that the networks exhibit modular structure across multiple topological scales and that these multi-scale modules unfold as part of a hierarchy. We also show that, on average, network architecture becomes increasingly dissimilar over time, with similarity decaying monotonically with the distance (in time) between sessions. Finally, we show that a small fraction of cells maintain strongly-correlated activity over multiple days, forming a stable temporal core surrounded by a fluctuating and variable periphery. Our work indicates a framework for studying spontaneous activity measured by two-photon calcium imaging using computational methods and graphical models from network science. The methods are flexible and easily extended to additional datasets, opening the possibility of studying cellular level network organization of neural systems and how that organization is modulated by stimuli or altered in models of disease.

Two-photon microscopy

Four mice were implanted with cranial windows over auditory cortex. Briefly, the mice were anaesthetized with 1.5-3\% isoflurane and a 3mm circular craniotomy was performed over auditory cortex (stereotaxic coordinates) using a 3mm biopsy punch. An adeno-associated virus (AAV) vector encoding the calcium indicator GCaMP6s (AAV1-SYN-GCAMP6s, UPENN vector core) was injected for expression in layer 2/3 neurons in left A1 within the window (750 nl, 1.89 * 10-12 genome copies per ml) . After injection a glass circular 3mm coverslip (size 0, Warner Instruments) was placed in the craniotomy and fixed in place using a mix of Krazy glue and dental cement. A custom-made stainless steel head-plate (eMachine Shop) was fixed to the skull using C\&B Metabond dental cement (Parkell). All imaging sessions were carried out inside a single-walled acoustic isolation booth (Industrial Acoustics) as previously described. Mice were placed in the imaging setup, and the headpost was secured to a custom base (eMachine Shop) serving to immobilize the head. Mice were gradually habituated to the apparatus over 3 days, 3-4 weeks after surgery. 

Using two-photon microscopy (Ultima in vivo multiphoton microscope, Bruker) changes in fluorescence of GCaMP6s in transfected neurons caused by fluctuations in calcium activity were recorded in awake, head-fixed mice. We recorded from the same cells over many days in layer 2/3 of auditory cortex, using blood vessel architecture, depth from the surface, and the shape of cells to return to the same imaging site. Laser power at the brain surface was kept below 30 mW. Chronic imaging of the same field of view across days was carried out for the duration of the experiment. 

Recordings were made at 512*512 pixels and 13-bit resolution at approximately 30 frames per second. Spontaneous activity was recorded for 10 minutes in each session. Publicly available toolboxes were used to register the resulting images, select regions of interest, estimate neuropil contamination, and extract the changes in fluorescence from each cell. Upon conclusion of the imaging sessions, brains were extracted following perfusion in 0.01M phosphate buffer pH 7.4 (PBS) and 4\% paraformaldehyde (PFA), post-fixed in PFA overnight and cryopreserved in 30\% sucrose solution for 2 days prior to slicing. The location and spread of GCaMP6s was confirmed through fluorescent imaging. These methods are consistent with the recommendations of the American Veterinary Medical Association (AVMA) Guidelines on Euthanasia.

Cell tracking over days

To identify ROIs from different imaging sessions that correspond to the same cell we performed a multi-step routine: (1) The mean fluorescence images from each day were registered by transforming the coordinates of landmarks present in both images in MATLAB (2017a) using the fitgeotrans function. The resulting transformation was used to transform the ROIs from the second imaging session to match the first; all sessions were aligned to the first imaging session. (2) We calculated the distance between all pairs of centroids across the two sessions. For each ROI from session 2, we computed the percentage overlap of the 10 cells with the smallest centroid distances from session 1. Cells that had more than 1 ROI with higher than 20\% overlap were manually inspected; the ROI that matched the current cell was selected from the overlapping ROIs or none were selected if it was unclear whether they were the same cell. A good match was determined by considering the percent overlap and the shape of the ROIs. All other cells were assigned the closest ROI as matching. (3) We manually inspected any cells that had duplicate matching ROIs; again considering the shape and the percent overlap of matching ROIs, we selected the ROI that matched that cell, or we decided that none was a good match. (4) To check for false positive matches, we manually inspected any matches where the centroid distances were greater than the mean + 1 std of all the matches, and any matches that had less than 30\% ROI overlap; the match was deemed good or not depending on the match criteria. Neurons that were not matched to any ROI were counted as different or new and assigned a new cell number. This process was repeated for subsequent sessions, registering the imaging field to the first session and comparing the ROIs to the cumulative ROIs from previous sessions. A final manual inspection of all the unique ROIs was performed after all the imaging sessions were registered; ROIs that overlapped were excluded from the dataset since it was unclear whether they were the same or different cells.