All animals were paired-housed under standard conditions (12 h light/dark, constant temperature environment, free access to food and water) according to the Chinese Ministry of Science and Technology Laboratory Animals Guidelines and experiments were approved by the local ethical committee of Guangzhou University. This is a non-survival procedure. 

NOTE: For data shown in the representative results, APP/PS1 (B6C3-Tg (APPswe, PSEN1dE9) 85Dbo/J) double-transgenic mice and littermate wild-type (WT) controls at 3-5 months of age, were used for recordings (n = 10, per group).

1. Animal anesthesia and surgery

1. Weigh and anesthetize the mouse by your approved anesthesia regimen from your local animal care committee. 
2. Perform a tail or toe pinch with forceps to confirm deep anesthesia prior to surgery.
3. Position the mouse in a stereotaxic apparatus and fix its head.
4. Apply eye ointment on both eyes to keep moist. Follow your local animal care guidelines regarding pre- and postoperative analgesia. 
5. Shave the hair using surgical clippers. Make a small incision (12-15 mm) in the middle of the exposed surgical area with scissors. Using forceps, gently pull the scalp away from the midline.
6. Separate the skin gently and remove residual tissue. Clean the skull using hydrogen peroxide-coated cotton buds.
7. Drill two small holes of radii 1.0-1.5 mm on both left and right sides of the skull to allow insertion of the recording microelectrodes into the M2 regions under a stereomicroscope (Figure 1A).
   NOTE: Stereotaxic locations of bilateral M2: 1.94 mm anterior to the bregma, 1.0 mm lateral to the midline, and 0.8-1.1 mm ventral to the dura.
8. Remove the dura mater carefully with a tungsten needle.
9. Pull glass borosilicate micropipettes (outer diameter: 1.0 mm) as recording microelectrodes with resistance of 1-2 MΩ.
10. Insert two separate recording microelectrodes filled with 0.5 M NaCl into the holes using mechanical micromanipulators (at 60°, Figure 1B).

2. LFP recordings in bilateral M2 of mice

1. Lower the left and right glass electrodes slowly into appropriate coordinates of bilateral M2 (Figure 1C).
2. For quality control, test the resistance of each electrode using the differential amplifier before capturing LFPs.
3. Set the recording process at 0.1 Hz high-pass and 1,000 Hz low-pass with 1,000x amplification.
4. Collect digitized raw LFP data of at least 60 s spontaneous activities in stable state, with mice breathing evenly at a respiratory rate of 2 breaths per second under anesthesia.
5. After recording, slowly raise the electrodes out of the brain, then euthanize the mice by fast cervical dislocation.
6. Save the data and analyze offline.

3. Cross-correlation analysis

1. Click Analysis – Waveform correlation in the analysis software and import the data.
2. Parameter settings
   1. Define one waveform channel signal as the first channel and the other as the reference. Set width as 2 and offset as 1 (Figure 2A).
   2. Set the duration of both LFPs for 100 s by selecting the start time and end time. Press the Process button to perform cross-correlation analysis (Figure 2B).
      NOTE: Simultaneous bilateral signals with such durations would be long enough to show neuronal spontaneous activities, thereby revealing the basic properties of synchronization.
3. Click File – Export As, then save the cross-correlation results corresponding to the resulting pop-up chart in .txt format.
4. Open the .txt file (Figure 2C), remove the correlation values at time lags ranged 0 ± 0.01 s (since two continuous gamma waves have at least 0.01 s interval), then average the rest of the cross-correlation data in the negative time lag part or average the rest of the cross-correlation data in the positive time lag part.

4. Coherence analysis

1. Import and run the data in the analysis software.
2. Assign the two LFP signals to be the first and second waveform channels separately. Then set the block size value (Figure 3A).
   NOTE: Block size means the number of data points used in the FFT. The larger the block size, the better the frequency resolution. Here we recommend setting it as 4096.
3. Move the dotted lines manually to ensure the time accuracy for signals in both channels are being set as the same period (Figure 3B). Press the Add Area button to load the area and perform coherence analysis.
4. Click File – Save As to save the coherence results corresponding to the resulting pop-up chart in .txt format (Figure 3B).