Pair-wise phase consistency for LFP-LFP phase synchrony

We calculated the phase synchrony between LFPs recorded in CA1 and EC or CA1 and CA3 on each theta cycle using wavelets in similar way to the spike-field PPC calculation (Vinck et al., 2012), as shown previously (Rohenkohl et al., 2018). The wavelet cross spectrum Bk between two signals xt and yt (e.g. signals from CA1 and EC or CA1 and CA3) was calculated for the kth theta cycle as Bk={bt,f=WCt,f,t=Tk,Tk+1,⋯,Tk+1}, in which WCt,f denotes the wavelet cross spectrum around each local time-frequency point t,f. Similar to the FPP matrix Ak(f,θ) defined above, Bk was normalized into a 81(Frequency)×20thetaphase cross-spectrogram (FPC) matrix, denoted as Bk(f,θ). Thus Wkf,θ≜angle(Bk(f,θ)) is the phase lag between the two signals for a given frequency f and theta phase θ. The pair-wise phase consistency for LFP-LFP analysis is then defined as follows:

where N is total number of hippocampal theta cycles. This PPC ranges from -1 to 1 and measures the consistency of the phase lag between the two signals in different frequency bands and theta phases, where -1 denotes no phase locking while 1 denotes a fixed phase lag between two LFPs across all theta cycles.

LFP gamma power is not uniformly distributed across all theta phases and therefore we selected specific phases of theta in which to compute PPC. EC and CA3 are considered source regions of CA1 gamma and, in line with these areas as gamma sources, we observed that the EC-CA1 and CA3-CA1 PPC increased slightly earlier than CA1 gamma power. Thus to measure the possible driving force for CA1 gamma power, we averaged the PPC within a phase interval around the gamma field center but shifted to include earlier phases. Specifically, PPC was averaged from the gravity phase center minus seven phase standard deviations to the gravity phase center plus one phase standard deviation. These phase standard deviations were calculated within the CA1 gamma field.