Hippocampal network dynamics constrain the time lag between pyramidal cells across modified environments

Abstract

The hippocampus provides a spatial map of the environment. Changes in the environment alter the firing patterns of hippocampal neurons, but are presumably constrained by elements of the network dynamics. We compared the neural activity in CA1 and CA3 regions of the hippocampus in rats running for water reward on a linear track, before and after the track length was shortened. A fraction of cells lost their place fields and new sets of cells with fields emerged, indicating distinct representation of the two tracks. Cells active in both environments shifted their place fields in a location-dependent manner, most notably at the beginning and the end of the track. Furthermore, peak firing rates and place-field sizes decreased, whereas place-field overlap and coactivity increased. Power in the theta-frequency band of the local field potentials also decreased in both CA1 and CA3, along with the coherence between the two structures. In contrast, the theta-scale (0-150 ms) time lags between cell pairs, representing distances on the tracks, were conserved, and the activity of the inhibitory neuron population was maintained across environments. We interpret these observations as reflecting the freedoms and constraints of the hippocampal network dynamics. The freedoms permit the necessary flexibility for the network to distinctly represent unique patterns, whereas the dynamics constrain the speed at which activity propagates between the cell assemblies representing the patterns.

Figure 1.

Place fields on a linear track with modified lengths. CA1 (a) and CA3 (b) place fields are ordered for a rat running left to right on a linear track before and after the length is shortened. Many fields vanished and others shifted to new locations on the short track. Others fired only on the short track. c, Histograms indicate preferred firing locations for the long (top) and short (bottom) tracks. The white portions of the histograms represent cells that fired only in that environment. The dark (black for long, red for short) portions of the histograms represent cells that had place fields in both environments. d, The peak firing rates (left) were lower and field-sizes (right) were smaller on the short track than on the long track. Colors correspond to cells shown in e: the positions of place fields on the long and short tracks are suggestive of four general categories (shown in black, green, blue, and cyan; see Results). The diagonal, corresponding to a rescaling, is plotted in magenta, and the identity is plotted in orange. f, The amount of place-field shifting was related to the place-field location on the long track. Fields at the beginning (green) shifted out toward the center, whereas fields at the end (blue) shifted in toward the center. The orange line indicates no shift (identity). g, The population firing rates increased from the long to the short track for pyramidal cells (top) but were conserved for interneurons (middle). The cofiring among the pyramidal population (bottom) also increased from the long to the short track.

Figure 2.

The average profiles (across all sessions and animals) of different variables are calculated for the long (black) and short (red) tracks. a, Significant differences were observed for the population firing rates of pyramidal cells, which cannot be accounted for by the different running speed profiles (d, e). b, The interneuron firing rates were not systematically different. c, The spiking profiles were similar between the long and short track, with higher occupancy at the beginning of the track. d, The running speed profiles reflect a higher peak running speed in the middle of the short track. e, Firing rate is plotted against running speed for each position pixel on the track (see also supplemental Fig. S5, available at www.jneurosci.org as supplemental material). The best-fit lines are also shown. The higher firing rates on the short track cannot be explained by running speed. f, The theta-frequency increases by a small (0.6%) but significant (rank-sum, p < 10⁻²⁰) amount from the long to the short track. The local field potential theta power decreased in both CA1 (g) and CA3 (h) on the short track. i, Coherence in the theta-frequency band also decreased between the two structures (see also supplemental Fig. S7, available at www.jneurosci.org as supplemental material).

Figure 3.

Sequence compression. a, The theta-scale time lag was correlated with the distance between the preferred place-field firing locations for both the long (black) and short (red) track lengths. All cell pairs on each track were included. The error bars denote the large SDs within each distance bin. These relationships are well described by sigmoids. b, Several examples from panel a are shown, with the reference (blue) and overlapping (green) place fields shown in the left columns, and theta-scale time lags shown in the right.

Figure 4.

Theta-scale timing was preserved between long and short tracks. a, The timing on the short track was identically (gray line) related to the timing on the long track. b, Cell-pair distances were also correlated between the long and short tracks, with deviation from the identity most noticeable at large pair-distances on the long track. c, When the pairs were shuffled between equidistant pairs, the correlation in theta-scale timing was considerably weakened.

Figure 5.

Theta time scale relationship of neuron pairs remained stable after track length change. Each panel (a–d) depicts a reference place field (blue) and overlapping place field (green) on the long (top, black) and short (bottom, red) track. Left to right, The first column depicts the firing rates versus position. The second column illustrates the phase and position of each spike in the place fields. The third column plots the unfiltered cross-correlogram between the reference and related cell, with the time lag of the peak from the bandpass-filtered CCG indicated by the arrow. Note that the time lag of the peak changed very slightly for the cell pairs, even though the firing rate maps changed substantially. The fourth column depicts the smoothed cross-correlograms on a 1 s long behavioral time scale.

Figure 6.

The time lag between pairs after large distance changes. a, The top panel shows color-coded lines connecting the same pairs on the long and short track. The color code is based on the time slopes (histogram shown on the bottom panel). Most cell pairs showed very little change in the theta-scale time lag (as reflected by the horizontal lines), resulting in different sequence compression on the long versus short tracks for this subset (inset). Similar analysis performed on surrogate equidistant datasets (black) indicates an expected peak at a slope of 1.0 ms/cm (bottom). The two slope distributions were significantly different (Kolmogorov–Smirnov test, p < 10⁻¹⁴). b, In a shuffled equidistant dataset, the timing preservation vanished. The histogram (bottom) follows the expected distribution.

Figure 7.

Model for temporal lag stability. Pyramidal cell (1) excites a second pyramidal cell (2) and an interneuron (inh 2; other sources of depolarization are not shown). In this model, cells fire when excitation exceeds inhibition. The middle panel depicts the excitatory drives for the two interdependent place cells 1 (green) and 2 (blue) on the long track, with inhibition for each superimposed with a dashed lined. The inhibition of cell 2 is delayed relative to cell 1, resulting in net time lag dt. When the track length is shortened (bottom), the rise in excitatory drives occur over a shorter duration (i.e., fewer theta cycles), and the place fields are shifted relative to each other. Inhibition in the place cells preserves timing with an appropriate shift, relative to that of the long track (superimposed in cyan), thus maintaining the time lag.