Phase spectrum between the two cells Phase is plotted against frequency.

Error bars are 95% confidence limits ont he phase estimate.

1600- CM 7-1 n=50399 CM 2-2 n=45157 100 0 D Power spectra 372 trials ms 500 CM7-1 CM2-2 ■2 1 0 1 C CM 2-2>CM 7-1 300 -50 0.006-1 Hz E Coherence 0.06

I

coherence in both frequency bands; 23% were coherent in the 18-25 Hz band and 26% in the 30-37 Hz band. In many cases only one or two frequency bins showed significant coherence in either o f these bands. The number o f pairs coherent in each band was not significantly different (Chi-squared test). The median coherence value was rather similar for each band (0.0030 0.0032); these values indicate very weak coherence. The distribution histogram o f phases in each band is shown in Fig. 5.5.2; the phases seem centred around zero in each case. The mean phase lag between pairs o f cells coherent in the 18-25 Hz band was 1.6°, compared with -4.2° for coherence in the higher frequency band.

In summary, 1 have demonstrated significant coherence between pairs o f cells in the cortex in the ranges 18-25 Hz and 30-37 Hz. The level o f coherence was substantially lower than that seen for cell-LFP coherence, and the coherence spectra rarely showed distinct peaks, as in the cell-LFP data. The phase relationships o f cells to one another were always o f the constant phase type, and the phases were clustered around zero.

A 18-25 Hz n = 1 8 3 90< 180° -90° 0° 180 24 B 30-37 Hz n = 1 9 9

Fig.5.5.2 Phase relationship for coherent cell pairs in M L

Circular distribution histograms of phase relationship between pairs o f cells

which were coherent in the ranges 18-25 Hz (A, n=165)) and 30-37 Hz (B, n=192). Scaling is indicated by the numbers on the circumference o f the plot.

5.6 Contribution of population synchrony to coherence between pairs of cells.

It is of interest to examine the contribution of cell-LFP phase locking to the coherence between pairs of cells. This is an analogous problem to that attempted in the time domain, (section 5.1). In the frequency domain, however, a quantitative solution can be reached, which was impossible in the time domain.

For this analysis, the same 1,061 cell pairs as in section 5.5 were used. For each pair of cells in a session, the coherence and phase spectra were obtained for each cell with an LFP from the one of the electrodes during the session. The LFP chosen was the one which seemed to be coherent with the most cells. Then, the cell-LFP coherence and cross-spectra were used to derive predictions mathematically of the celll-cell2 coherence and phase.

If the coherence between cell n and the LFP is represented as CnLpp(f) then the prediction for cell 1-cell 2 coherence, 60) is:

p ( C 12(f)) = C„LFp(f) X CnLFp(f), (13)

and the prediction for the phase relationship between cell 1 and cell 2, <)>j2(f) is:

0i2(/) = arg

4-^LFP i f )

(14)

where XnLFp(f) represents the cross-spectrum of cell n and the chosen LFP, and AlfpO)

represents the autospectrum of the LFP signal. Again, this phase prediction needs to be adjusted by 180°, according to the quadrant given by the signs of its numerator and denominator.

For all 1061 pairs of cells recorded, the actual cell-cell coherence and the predicted cell-cell coherence were compared over the ranges 18-25 Hz and 30-37 Hz, and also over the larger range 15-40 Hz, so that more frequency bins could be tested (27 bins as compared to 7 in each of the two smaller ranges). There is no appropriate

0.03- 0.00- 0 10 20 30 40 50 180- 0- -180 10 20 30 Hz 0.010- 4 ^ 20 30 40 0 10 50 Hz 40 50 Hz

Fig. 5.6.1. Prediction of coherence and phase between a cell pair, using cell-LFP coherence.

A. Coherence spectra of PTN4-1 (red) and CM 5-1 (black) vs LFP from electrode 7.Dotted line indicates p=0.05 level.

B. Coherence spectra o f actual PTN4-1 vs CM5-1 coherence (black) and coherence predicted (red) using the cell-LFP coherence (see text for methods).

C. Phase spectrum for actual (black) and predicted (red) cell-cell coherence. Predicted phase values are plotted for each significant actual phase value. See text for calculation o f predicted phase

significance test for values of predicted coherence, so the values of coherence at each frequency were only compared if actual coherence in that bin was significant (p<0.05, see equation 5, above). To compare the values of actual and predicted coherence, paired t-tests were used to test actual versus predicted coherence for each frequency range.

To compare the actual versus predicted phases, the predicted phase at each frequency in the range 15-40 Hz was tested to see if it fell within the 95% confidence limits on the actual phase for that frequency.

Figure 5.6.1 shows typical data for one pair of cells which showed significant actual cell-cell coherence. The cells shown were a PTN and a CM cell recorded in the left hemisphere of monkey 33 on electrodes 4 and 5 respectively. Fig. 5.6.1 A shows the cell-LFP coherence spectra for the two cells. It is clear that both cells are significantly phase-locked to the LFP from electrode 7.

Fig. 5.6.IB shows the predicted and actual coherence spectra for this pair of cells. The actual coherence spectrum has 4 significant bins below 18 Hz, 2 in the range 18-25 Hz, but none in the range 30-37 Hz. The predicted coherence by contrast has no significant bins in any frequency range. In fact, it is still 10 times smaller than the p=0.05 significance level even at its peak value. Interestingly, the peak predicted coherence occurs at 37 Hz, whereas the peak in actual coherence occurs at a much lower frequency, of 15 Hz. We can deduce from this that not only does the cell-LFP synchrony account for less than 10% of the cell-cell synchrony in this example, but that the contribution it makes is at a higher frequency. That is, if the cell-LFP synchrony was the only factor producing the cell-cell coherence, the actual coherence would be much lower, and its peak would be at 37Hz, at which frequency the cells are most strongly coherent with the LFP.

Fig. 5.6.1C shows the actual and predicted phase spectra for this pair of cells. It can be seen that there are only 2 frequency bins (out of 8 bins with significant coherence)