illustrates membrane potential traces of three simultaneously recorded neurons and their correlations. The three neurons were recorded at locations A, B, and D as indicated in the inset by red letter labeling of the respective electrodes and next to the membrane potential traces. An electrode C, recording from which is not shown in the figure is labeled with a light gray letter in the inset. Same code will be used also in following figures of this type. In all three pairs of neurons, membrane potential changes were strongly correlated with the peak at r=0.84, 0.63, and 0.73 between cells separated by 4, 8, and 12 mm, respectively (). Strong membrane potential correlations were typical for our sample (). Correlation between membrane potential changes was strongest in pairs composed of neighboring neurons with horizontal separation <0.3 mm (averaged r=0.56±0.16, n=112 pairs). With larger distances between cells, correlation was slightly smaller but still very strong. At distances between two neurons in a pair of 4, 8, 12 mm, mean values of the correlation peaks were 0.47±0.17 (4 mm, n=76), 0.48±0.21 (8 mm, n=45), and 0.44±0.2 (12 mm, n=41), respectively. Thus, even in neurons located up to 12–13 mm one from the other, which was the largest separation studied, membrane potential changes were typically strongly correlated. Interestingly, the pattern of distance-dependence of the correlation strength was similar to the distance-dependence of state overlap: strongest in neighboring neurons and slightly decreasing to a plateau in neurons separated by a few millimeters (compare and ).
Fig. 5 Long-range correlation of membrane potential changes in neocortical cells during slow oscillation. (a, b) Membrane potential traces of three simultaneously recorded neurons (a) and their pairwise correlation (b). The recorded neocortical neurons were (more ...)
The shift of the crosscorrelogram peak had a tendency to increase with the increasing distance (). It was 4±7 ms for crosscorrelations between neighboring neurons with <0.3 mm separation (n
=111 pairs), 10±22 ms in pairs of neurons separated by 4 mm (n
=75), 15±23 ms for 8 mm (n
=44), and 39±64 ms for 12 mm separation (n
=35). The shift of the peak could occasionally reach up to 150–260 ms, compatible with earlier study of the correlation between extracellularly recorded signals during slow oscillation (Amzica and Steriade, 1995a
). With increasing distance between neurons in a pair, the variability of the peak shift also increased dramatically, indicating a heterogeneity of temporal relations between slow oscillation of membrane potential in different cell pairs. Furthermore, large peak shifts were found in cell pairs with weaker correlation (). Notably, even in pairs with maximal separation between the recorded neurons (~12–13 mm), the shift of crosscorrelation peak could be close to zero, indicating that even in distant neurons membrane potential changes could take place essentially synchronously. This observation is consistent with the present finding of fast, all-or-none-like spread of large amplitude LFP patterns in the monkey cortex (Thiagarajan et al., 2010
The above analysis shows that during slow oscillation, an overall correlation between membrane potential changes is strong, even in neurons separated by ~12–13 mm (maximal distance in the present data sample). How is this pattern of highly correlated changes of the membrane potential in neocortical neurons during slow oscillation related to the correlation pattern during periods without slow oscillation? To address this question, we used occasional periods of recordings without slow oscillation. shows membrane potential traces of two neurons separated by ~5 mm one from the other. In this recording, periods without slow oscillation and with slow oscillation can be clearly distinguished. During a period without slow oscillation, membrane potential changes in two neurons were uncorrelated (, left panel). Just few seconds later, when the slow oscillation developed, changes of the membrane potential in these same neurons became highly correlated (, right panel, r
=0.54). The dramatic decrease of the membrane potential correlation in distant neurons during periods without slow oscillation as compared to the periods with the slow oscillation was typical in our sample (). During periods without the oscillation, the correlation was very weak in pairs of neurons separated by ~5 mm (mean r
=6), and absent in pairs of neurons separated by ~13 mm (r
=14). Both values were significantly smaller than measured in the same pairs of neurons but during periods of slow oscillation (r
=0.56±0.05 and 0.37+0.17, respectively). Scatter in shows the relation between the correlation strengths during periods with and without slow oscillation for cell pairs in which correlation was calculated for both conditions. All data points in the scatter are located above the main diagonal, showing that without the slow oscillation correlation was always weaker. One consequence of this relation would be the dependence of the correlation strength on the expression of the slow correlation during the period used for calculating the correlation. For the periods with clear, well-developed slow oscillation, the correlation should be stronger than for the periods including intervals of less regular oscillation, which occurred close to transitions from or to periods without the slow oscillations. Indeed, when we reinspected results presented in and , we found that in pairs with low correlation values or low state overlap the analyzed periods included intervals with less expressed or absent slow oscillation in one of the recorded neurons. Although this dependence holds for all neurons, the correlation of membrane potential changes in five pairs of neighboring neurons for which periods with and without slow oscillation were available remained strongly correlated even without the slow oscillation (r
=5 triangle symbols in ). Strong correlation of the membrane potential changes in neighboring neurons even without slow oscillation is consistent with a previous report on highly correlated membrane potential fluctuations in closely located neurons in the visual cortex (Lampl et al., 1999
Fig. 6 High correlation of membrane potential changes in distant neocortical cells is restricted to periods of slow oscillation. (a) Simultaneous intracellular recording from two neocortical neurons during periods without slow oscillation and during slow oscillation, (more ...)
Thus, in neurons separated by <0.3 mm horizontally, membrane potential changes are correlated both during periods with and without slow oscillation. In pairs of cells separated by several millimeters, strong membrane potential correlations were observed only during periods of slow oscillation, while without slow oscillation correlation was weak or absent. These results suggest that correlation of membrane potential changes in distant neurons is imposed by the slow oscillation. Therefore, next we studied the contribution of different phases of the slow oscillation and different frequency components of membrane potential fluctuations to the observed strong overall correlation.