Spatial information outflow from the hippocampal circuit: distributed spatial coding and phase precession in the subiculum

Abstract

Hippocampal place cells convey spatial information through a combination of spatially selective firing and theta phase precession. The way in which this information influences regions like the subiculum that receive input from the hippocampus remains unclear. The subiculum receives direct inputs from area CA1 of the hippocampus and sends divergent output projections to many other parts of the brain, so we examined the firing patterns of rat subicular neurons. We found a substantial transformation in the subicular code for space from sparse to dense firing rate representations along a proximal-distal anatomical gradient: neurons in the proximal subiculum are more similar to canonical, sparsely firing hippocampal place cells, whereas neurons in the distal subiculum have higher firing rates and more distributed spatial firing patterns. Using information theory, we found that the more distributed spatial representation in the subiculum carries, on average, more information about spatial location and context than the sparse spatial representation in CA1. Remarkably, despite the disparate firing rate properties of subicular neurons, we found that neurons at all proximal-distal locations exhibit robust theta phase precession, with similar spiking oscillation frequencies as neurons in area CA1. Our findings suggest that the subiculum is specialized to compress sparse hippocampal spatial codes into highly informative distributed codes suitable for efficient communication to other brain regions. Moreover, despite this substantial compression, the subiculum maintains finer scale temporal properties that may allow it to participate in oscillatory phase coding and spike timing-dependent plasticity in coordination with other regions of the hippocampal circuit.

Figure 1.

Single-unit recording in the subiculum. A, A Nissl-stained coronal section, ∼6.8 mm posterior from bregma, showing representative recording sites in the intermediate subiculum. The arrows indicate two tetrode penetration tracks. Scale bar, 500 μm. B, Spike autocorrelograms and mean extracellular spike waveforms of three representative subicular neurons. Spike autocorrelograms were computed with 1 ms bins. Mean spike waveforms were computed with spikes aligned on the initial negativity (trough). The bursting neuron at top is distinguished by the short-lag peak in its autocorrelogram, as quantified by the burst index. The fast-spiking neuron at bottom is distinguished by the narrow and nearly symmetric negative and positive phases of the spike waveform. C, Summary of mean firing rate and burst index for all neurons recorded in the subiculum. Each symbol corresponds to a single neuron. Fast-spiking neurons (putative inhibitory interneurons) are plotted as circles, and non-fast spiking neurons (putative pyramidal neurons) are plotted as triangles. Symbols are color-coded by anatomical location along the transverse axis of the subiculum. Mean rates increased from proximal to distal subiculum. D, Spike waveform width and trough/peak asymmetry for the same neurons shown in C. E, Summary of mean firing rate and burst index for all neurons recorded in distal area CA1 and in the CA1/subiculum transition zone. Fast-spiking neurons (putative inhibitory interneurons) are plotted as circles, and non-fast spiking neurons (putative pyramidal neurons) are plotted as triangles. F, Spike waveform width and trough/peak asymmetry for the same neurons shown in E.

Figure 2.

Spatial representation in the subiculum. A–C, Each panel shows position-phase firing-rate maps and spike-amplitude cluster plots for one neuron. The top and bottom rows correspond to sessions 1 and 3 which were in the same environment. Each position-phase firing-rate map shows the estimated firing rate of the neuron as a function of the rat's linearized position and the phase of theta oscillations in the LFP. Separate firing-rate maps are shown for the right-bound and left-bound directions of travel in the environment. Linearized position was measured with respect to the midpoint of the track, and theta phase was defined so that the positive peak of the theta oscillation was at 0°. The firing-rate maps are duplicated over two cycles of theta to clearly show their phase-periodicity. To the right, cluster plots show spike amplitudes recorded on pairs of tetrode channels. Black points correspond to spikes from the neuron, and gray points correspond to spikes from other neurons. A, A representative neuron in the proximal subiculum. B, A representative neuron in the middle subiculum. C, A representative neuron in the distal subiculum.

Figure 3.

A, Summary of mean firing rate and spatial activity fraction for all putative principal neurons recorded in the subiculum. Only valid running passes during task sessions were included in the calculation of mean firing rate. Each symbol corresponds to a single neuron. Symbols are color-coded by anatomical location along the transverse axis of the subiculum. Spatial representation within the subiculum exhibits a proximal-distal gradient. B, Summary of mean firing rate and spatial activity fraction for all putative principal neurons recorded in distal area CA1 and in the CA1/subiculum transition zone. Comparison of A and B reveals that neurons in area CA1 have lower mean firing rates and finer spatial selectivity than neurons in the subiculum. C, Firing rate versus spatial activity pattern for each unit in each recording session, across rats and brain regions.

Figure 4.

Information-theoretic comparison of spatial representations in the subiculum and in area CA1. A, Relationship between mean firing rate and mutual information conveyed by single neurons in the subiculum. model neurons whose position-phase firing-rate maps were matched to experimental data from putative principal neurons in the subiculum. Symbols are color-coded according to the location of the neuron along the transverse dimension of the subiculum. Neurons with mean firing rates <1 spikes/s have low mutual information, whereas higher firing rates are compatible with high mutual information. B, Relationship between mean firing rate and the spatial information conveyed by model neurons whose position-phase firing-rate maps were matched to experimental data from putative principal neurons in the CA1/subiculum transition zone and in distal area CA1. Mean firing rates is strongly correlated with mutual information, and the distribution is skewed so that most neurons are clustered close to zero mean firing rate and convey almost no information. C, Histograms of spatial information conveyed by neuronal ensembles of different sizes in different subregions. Each subpanel is a histogram of mutual information for ensembles of model neurons of a given size. From left to right, columns correspond to single neurons, pairs of neurons, triplets of neurons, etc. Each row represents data from an anatomical subregion. As expected, the distributions shift to the right as the ensemble size increases; however, this shift is larger in the distal and middle subiculum than in the proximal subiculum and in distal area CA1 and the CA1/subiculum transition zone. For single neurons and pairs, the distribution of mutual information is skewed toward zero in the more proximal subregions. As one can also see in B, the mode of the distribution of mutual information among single neurons in area CA1 is near zero. D, E, Medians and interquartile ranges of the histograms shown in C. Mutual information increases nearly linearly with the number of neurons in the ensemble. For a given ensemble size, neurons in the proximal subiculum convey as much spatial information as do neurons in distal area CA1 and the CA1/subiculum transition zone, and neurons in the middle and distal subiculum convey more spatial information.

Figure 5.

Examples of remapping in the subiculum. A–F, Each panel shows position-phase firing-rate maps of a single neuron in the same direction of travel in both environment 1 and environment 2, along with a comparative overlay of the spatial firing-rate profiles in the two environments. Arrows indicate the direction of travel. To show firing-rate differences, the firing-rate maps in each pair are plotted with the same color scale. Dark blue is zero, and dark red is the maximum firing rate encountered in either environment. A, B, Representative neurons in the proximal subiculum. C, D, Representative neurons in the middle subiculum. E, F, Representative neurons in the distal subiculum.

Figure 6.

Remapping of spatial representations across environments. A, Scatter plot of mean firing rates in environment 1 versus environment 2 for putative principal neurons in the subiculum. Mean firing rates were computed during times when the rat was running toward a food well with a speed of least 10 cm/s and the LFP theta power ratio was above threshold. Symbols are color-coded according to the location of the neuron along the transverse dimension of the subiculum. The dashed diagonal line has unity slope. B, A similar scatter plot of mean firing rates in environment 1 versus environment 2 for putative principal neurons in the CA1/subiculum transition zone and in distal area CA1. C, Cosine similarity of position-phase firing-rate maps between two sessions in the same environment (horizontal axis) and between two different environments (vertical axis), for neurons in the subiculum. Departures below the dashed diagonal unity line indicate dissimilar spatial representations in environment 1 versus environment 2. Each symbol corresponds to a neuron and a direction of travel (right-bound or left-bound). Symbols are color-coded according to the location of the neuron along the transverse dimension of the subiculum. D, The same cosine similarity measures for neurons in the CA1/subiculum transition zone and in distal area CA1. E, Normalized overlap of position-phase firing-rate maps between two sessions in the same environment (horizontal axis) and between two different environments (vertical axis), for neurons in the subiculum. Again, departures below the dashed diagonal unity line indicate dissimilar spatial representations in environment 1 and environment 2. Symbols are the same as in C. F, The same normalized overlap measures for neurons in the CA1/subiculum transition zone and in distal area CA1. G, Mutual information between spike responses and environment, conditioned on linearized position in the environment, for ensembles of neurons in the subiculum. Each plotted point is the median of the conditional mutual information for ensembles of a given size. Error bars indicate the interquartile range of values. Symbols and lines are color-coded according to the location of neurons along the transverse dimension of the subiculum. H, Medians and interquartile ranges of conditional mutual information for ensembles of neurons in distal area CA1 and in the CA1/subiculum transition zone.

Figure 7.

Theta phase modulation of single-unit spiking in the subiculum. A, Theta phase tuning curves of putative principal neurons in the subiculum. Each row of the color map shows the instantaneous firing rate of a single neuron as a function of the phase of theta oscillations in the LFP. Instantaneous firing rates were estimated with an Epanechnikov kernel smoother (15° half-width) and normalized by the maximum for each neuron. Neurons are sorted by their preferred theta phase, indicated by white dots for neurons that are significantly modulated at the 0.05 statistical significance level. To show periodicity, tuning curves are displayed over two full cycles of theta. B, Corresponding population firing rates, averaged over principal neurons in the distal, middle, and proximal thirds of the subiculum. C, Histograms of spike phase concentration parameters for neurons in the distal, middle, and proximal thirds of the subiculum. Larger values indicate stronger phase locking to LFP theta oscillations.

Figure 8.

Theta phase precession in unitary place fields. A, Illustration of the place field segmentation method. A position-phase firing-rate map is shown for a representative neuron in the subiculum. Segmented place fields are outlined in a dashed white contour, and white arrows indicate the principal axis of phase precession within each field. B, Summary of field length and phase precession slope for all unitary place fields of subicular neurons with significant position-phase correlations. Each symbol corresponds to a unitary place field. Symbols are color-coded according to the anatomical location of the neuron along the transverse axis of the subiculum. Phase precessions slope is positively correlated with field length, so that larger place fields have shallower slopes. C, Summary of preferred theta phase and peak firing rate for the same unitary place fields as in B. The vertical line indicates the mean phase for all segmented place fields, which is near to the trough of the LFP theta oscillation. D, Summary of field length and phase precession slope for all unitary place fields of CA1 neurons with significant position-phase correlations. E, Summary of preferred theta phase and peak firing rate for the same unitary place fields as in D.

Figure 9.

Spectral analysis of theta phase precession. A, The spike phase spectrum of a representative neuron in the subiculum. This example corresponds to the same neuron, environment, and direction of travel that is shown in Figure 7A. The top shows the estimated power spectral density, while the bottom shows the estimated first derivative of the spectrum with respect to frequency. Note that this first derivative was estimated using the covariance of the multitaper eigenspectra, not by numerical differentiation of the estimated power spectral density. The solid vertical line indicates the peak frequency, which is greater from unity, indicating phase precession. Gray lines in the top are spike phase spectra computed for 500 surrogate spike trains in which spikes were independently jittered within a single theta cycle. This shuffle test shows that the peak in the observed spike phase spectrum is statistically significant. B, Summary of peak frequencies for all spike phase spectra of subicular neurons that have significant peaks. Each symbol corresponds to spike phase spectrum of a single neuron in a particular environment and direction of travel. Spatial activity fractions were computed from the corresponding firing-rate maps. The spike phase spectra of fast-spiking neurons (putative inhibitory interneurons) are plotted as circles, and the spike phase spectra of non-fast spiking neurons (putative pyramidal neurons) are plotted as triangles. Symbols are color-coded according to the anatomical location of the neuron along the transverse axis of the subiculum. The peaks of the spike phase spectra for putative principal neurons occur at frequencies that are shifted above unity, and the distribution of peak frequencies is similar across proximal-distal locations within the subiculum. C, Summary of peak frequencies for all spike phase spectra of CA1 neurons that have significant peaks.