Temporal pattern separation in hippocampal neurons through multiplexed neural codes

Abstract

Pattern separation is a central concept in current theories of episodic memory: this computation is thought to support our ability to avoid confusion between similar memories by transforming similar cortical input patterns of neural activity into dissimilar output patterns before their long-term storage in the hippocampus. Because there are many ways one can define patterns of neuronal activity and the similarity between them, pattern separation could in theory be achieved through multiple coding strategies. Using our recently developed assay that evaluates pattern separation in isolated tissue by controlling and recording the input and output spike trains of single hippocampal neurons, we explored neural codes through which pattern separation is performed by systematic testing of different similarity metrics and various time resolutions. We discovered that granule cells, the projection neurons of the dentate gyrus, can exhibit both pattern separation and its opposite computation, pattern convergence, depending on the neural code considered and the statistical structure of the input patterns. Pattern separation is favored when inputs are highly similar, and is achieved through spike time reorganization at short time scales (< 100 ms) as well as through variations in firing rate and burstiness at longer time scales. These multiplexed forms of pattern separation are network phenomena, notably controlled by GABAergic inhibition, that involve many celltypes with input-output transformations that participate in pattern separation to different extents and with complementary neural codes: a rate code for dentate fast-spiking interneurons, a burstiness code for hilar mossy cells and a synchrony code at long time scales for CA3 pyramidal cells. Therefore, the isolated hippocampal circuit itself is capable of performing temporal pattern separation using multiplexed coding strategies that might be essential to optimally disambiguate multimodal mnemonic representations.

Fig 1. Temporal pattern decorrelation at the level of single dentate granule cells.

(A) Histology of the DG in a horizontal slice (Cresyl violet/Nissl staining; scale bar: 250 μm), overlaid with a schematic of the experimental setup: a theta pipette in the ML is used to focally stimulate the perforant path (input) while a responding GC is recorded via whole-cell patch-clamp (output). GCL: granule cell layer, H: hilus, ML: molecular layer. Celltype color code: green for granule cell (GC); red for fast spiking interneuron (FS); orange for hilar mossy cell (HMC); black for CA3 pyramidal cell. Solid lines represent dendrites and dashed lines axons (B) Examples of input sets. Top: each input set is constituted of five different trains of electrical pulses following a Poisson distribution and an average rate of 10 Hz. Bottom: correlation coefficient matrix for each input set, each square is the Pearson’s correlation coefficient (R) between two input trains considered as vectors of spike counts with a binning window (τ_w) of 10 ms. R_input is the average of coefficients, diagonal excluded. We used 11 such input sets (R_input = 0.11 to 1). (C) Current-clamp recordings of the membrane potential of a single GC in response to a single input set (average R_input = 0.76). Each input set (five input trains) is repeated ten times, yielding a recording set of fifty output voltage traces. (D) Sorted input and output rasters from the recording set in C (each parent input train has ten children output trains forming an output subset, with matching colors). PW means pairwise. (E) Left: Corresponding 55x55 correlation coefficients matrix using a τ_w of 10 ms. Each small grey square represents the correlation coefficient between two spike trains. The average of coefficients from children output trains corresponding to one of the ten pairs of input trains (identified by color-coded squares), was computed to yield ten pairwise R_output coefficients. This excludes comparisons between outputs generated from the same parent input. Right: mean across multiple cells, following the same color-code as displayed in the matrix on the left. (F) Pattern separation graph showing the mean ± SEM pairwise R_output across 102 recordings (from 28 GCs), for 11 different input sets (i.e. 110 pairwise R_input). Values under the identity line (dashed) demonstrate that output spike trains were less similar to each other than inputs, and thus that pattern separation was performed. Blue indicates significant difference from the identity line (one-sample t-test on the difference pairwise Rinput—pairwise R_output, p < 0.05). The solid grey line is a parabolic fit to the 102 recording sets. [Fig adapted from Madar et al. (2019) [40] (Fig 1, 2 and 5)]We first reanalyzed a dataset, presented in Madar et al. (2019) [40], of GC recordings performed in response to input sets constituted of 10 Hz Poisson trains (Fig 1B). A pairwise similarity analysis (Fig 1E), with the Pearson's correlation coefficient R as a measure of similarity, confirmed our finding that the output spike trains of GCs are significantly less correlated than their inputs at both low and high input correlations (Fig 1F). As detailed in Madar et al. (2019) [40], even the repetition of the same input train leads to decorrelated output trains, due to the probabilistic nature of synaptic transmission.

Fig 2. Orthogonalization of input spike trains is a strong component of temporal pattern separation by single granule cells.

(A-C) Six hypothetical cases of pairs of spike trains and their associated Pearson's correlation coefficients (R), normalized dot products (NDP, cosine of the angle between two vectors) and scaling factors (SF, ratio of the norms), showing that the three metrics assume different neural codes and are not equivalent. (A) Synthetic spike trains (X and Y pairs) divided into six bins, with the corresponding number of spikes per bin. (B) R between each pair of X and Y describes the linear regression between the number of spikes in the bins of X versus the corresponding bins in Y (jitter was added to make all points visible). (C) Geometric view of vectors X and Y, where each bin is a dimension of a 6-dimensional space, and the number of spikes in a bin is the coordinate along this dimension. NDP measures how far from orthogonal two spike trains are and SF measures how different their binwise firing rates are. (A-C) NDP and R are sensitive to whether spike trains have spikes in the same bins or not (row 1), whereas SF is sensitive to differences in spike counts per bin (row 2), although neither NDP nor R is purely about "bin synchrony" (row 3). Note that these examples provide the intuition that orthogonal vectors (NDP = 0) necessarily correspond to a negative correlation between the spike trains (row 1 and 5) but that anticorrelated spike trains (R < 0) are not necessarily orthogonal (row 6), and that orthogonal spike trains are not necessarily perfectly anticorrelated as in row 1 because R, unlike NDP, considers common silent bins as correlated (row 5). See also S1 Fig. (D) Vector representation of experimental data from one recording set, showing the average similarity between a set of input spike trains (dashed line and green angle, R_input = 0.76) and the average similarity between the fifty corresponding output spike trains excluding comparisons between outputs from same parent input (solid line, purple angle). The angles are derived from the NDP whereas the lengths of each vector express differences in binwise firing rates (SF). Here, outputs are more orthogonal (closer to 90°) than their inputs with little difference in scaling. (E-F) Pattern separation graphs showing the pairwise output similarity as a function of the pairwise input similarity, as measured by the NDP or SF (mean+/-SEM) across 102 recording sets (28 GCs) for 11 different input sets. As in Fig 1F, blue indicates a significant difference from the identity line (one-sample t-test, p < 0.05). The solid grey line is a parabolic (E) or linear (F) fit to the 102 recording sets. (E) Outputs are closer to orthogonality (NDP = 0) than their respective inputs, demonstrating strong levels of pattern separation through orthogonalization at the 10 ms time scale. (F) At the 10 ms time scale, pattern separation by scaling is present for inputs very similar in terms of SF (SF_input close to 1), but weak, at least over the span of tested SF_input values.

Fig 3. Single granule cells exhibit pattern separation on millisecond to second time scales using different codes.

(A-C) Pattern separation/convergence assessed at different time scales and using different measures of similarity (S). Top: pairwise S_output (average across recording sets) as a function of pairwise S_input, measured with different binning windows τ_w. Solid curves are linear fits. Each color corresponds to a different τ_w ranging from 10 ms to 500 ms. Bottom: Effect of τ_w on the effective decorrelation (S_input−S_output), interpolated from the linear regressions. Note that as τ_w increases, pattern separation through decorrelation (R) or orthogonalization (NDP) becomes weaker while it becomes stronger through scaling (SF). (D) Similarity between spike trains is here assessed with the binless SPIKE metric, directly using spike times. Left: example of two input spike trains associated with two output spike trains from a GC recording set, and the corresponding distances D(t) between spike trains. D(t) can then be integrated over time to give a single value D. Middle: example of 55x55 matrix of SPIKE similarity (1-D) between all spike trains of an example recording set. 0 means that spikes of two trains never happened close in time, and 1 that they were perfectly synchronous. The output SPIKE similarity (SPIKE_output) is defined as the average similarity excluding comparisons between spike train from the same parent input train (i.e. average of the 10 pairwise SPIKE_output). Right: SPIKE_output of the same 102 GC recordings as in Figs 1–3, as a function of SPIKE_input, fitted with a parabola (red line). Most data points are below the dashed identity line indicating that output spike trains are less similar than inputs. The average SPIKE_input-SPIKE_output is significantly above 0 for all input sets except the two most dissimilar (SPIKE_input = 0.74, 0.78) (one-sample T-tests, p < 0.05).

Fig 4. Pattern convergence via scaling in single granule cells.

(A-B) Two new input sets were designed to explore single GCs computations on inputs with a wide range of pairwise similarity as measured by SF. Both input sets have ten input trains of 2 s, and were repeated five times during the whole-cell patch-clamp recording of a single GC, yielding 50 output spike trains. (A) Left: Input set A was constituted of spike trains following a Poisson distribution, each with a different firing rate (FR), increased from 7 to 31.5 Hz, but with an average R_input constrained around 0.75 (τ_w = 10 ms). The ten input trains were thus well correlated but varied in their firing rate. Middle: matrix of SF coefficients for each pair of trains in input set A, showing a wide range of values unlike the 11 input sets with 10 Hz trains used in previous experiments. Right: SF values are indeed sensitive and anti-correlated to differences in overall firing rate between two spike trains (data points correspond to pairs of trains). (B) Because SF is dependent on how differently clustered spikes are in two different trains, SF can vary even when the overall firing rate is the same. Left: Input set B was constituted of spike trains with 21 spikes (FR = 10.5 Hz) that were clustered in more or fewer bins, leading to trains with varying burstiness and thus a wide range of SF values (Middle). R was not constrained but ended up close to 0 for all pairs. Right: SF values are indeed sensitive and anticorrelated to differences in Occupancy (average number of spikes per occupied bins), a direct measure of burstiness when FR is constant across trains (data points correspond to pairs of trains). (C) Pattern separation graphs showing the pairwise output similarity as a function of the pairwise input similarity, as measured by SF, across 5 GCs responses to input set A and 3 GCs responses to input set B (Both input sets tested GC responses over 45 pairwise R_input). Left and Middle: Mean+/-SEM. Blue indicates a significant difference from the identity line (one-sample t-test, p < 0.05). The solid grey line is a linear fit to the 5x45 (Left) or 3x45 (Middle) data points. Both experiments confirm that, at the 10 ms time scale, GCs exhibit pattern separation through scaling for highly similar input trains (SF close to 1) as in Fig 2F, but show that GCs can exhibit pattern convergence for more dissimilar inputs (SF < 0.7). Right: Mean across GC recordings for both experiments combined, measured at different time scales. It confirms that SF_output decreases when using larger binning windows, leading to more pattern separation for high input similarity and lower pattern convergence for lower input similarities.

Fig 5. Granule cells input-output transformations in terms of firing rate and burstiness.

(A) Graphs shown correspond to the same GC in response to either input set A or B. Data points correspond to individual spike trains, (black empty circles for inputs: 10 trains per set; green filled circles for GC outputs: 50 trains per set). For each spike train, we measured its overall FR, binwise Compactness and binwise Occupancy, all spike train features providing information on sparseness and burstiness (see Methods). Error bars correspond to two different measures of dispersion. Black: mean +/- SD; red: min-max center of gravity ± the mean absolute difference (self-comparisons and comparisons between output trains with the same parent input train were excluded). Comparing mean values of a given spike train feature between inputs and outputs shows the direction of the transformation from inputs to outputs. Comparing the dispersion between inputs and outputs shows whether pattern separation (larger output dispersion) or convergence (smaller output dispersion) was achieved through a neural code focused on the measured spike train feature. (B) For each output spike train, the output spike train measures of Compactness, Occupancy or overall FR is plotted against the measure of its parent input train (input set A or B). For all time scales, GCs have generally higher Compactness than their inputs, but maintain a low and narrow range of Occupancy regardless of their input statistics, showing that GCs are sparser (see S1 Table). Consistently, GCs maintain a lower FR than their inputs.

Fig 6. Depending on input statistical structure, granule cells exhibit pattern separation or convergence via burstiness and firing rate codes.

(A) Pattern separation graphs showing the average pairwise output absolute difference across GC recordings as a function of the pairwise input absolute difference, for the binwise Compactness (Left), binwise Occupancy (Middle) and overall FR (Right). Insets zoom in on the smallest values of the input-axis. Experiments using input set A and B were combined. Note that because we plot the absolute difference between two spike trains (i.e. the distance between two data points in Fig 5A) and not a measure of similarity, pattern separation corresponds to points above the identity line (dashed) and pattern convergence to points below. Error bars are SEM (not displayed in middle graph for readability). Right: input set A recordings (PΔFR) in black, input set B (B 10.5 Hz) in green. (B) The difference in dispersion (Dispersion_output−Dispersion_input; dispersion is the mean absolute difference, i.e. red bars in Fig 5A) of binwise Compactness, binwise Occupancy or overall FR for each GC recording set from three experiments using different types of input sets: Poisson trains with 10 Hz FR and varying R (P10Hz: 102 recordings, 28 GCs), Poisson trains with R ≈ 0.75 and varying FR (PΔFR, i.e. input set A: 5 GCs), trains with 10 Hz FR and varying burstiness (B 10.5 Hz, i.e. input set B: 3 GCs). Positive values correspond to pattern separation through variations of the given spike train property (Compactness, Occupancy or FR) and negative values to pattern convergence. Asterisks denote significant difference from 0, i.e. either pattern separation or convergence (one-sample t-test, p < 0.05. See Table 2).

Fig 7. Inhibition controls levels of pattern separation in granule cells through different neural codes.

(A) Single GCs were recorded twice in response to the same input set (P10Hz, R = 0.76 at τ_w = 10 ms, shown in Fig 1B): First in normal aCSF, then under conditions of partial inhibitory block (aCSF + 100 nM gabazine, gzn), without changing any other parameter (i.e. same stimulation location and intensity). (B) Partial disinhibition of GCs led to higher FR and a higher propensity to fire small bursts of spikes riding on the same EPSP, as illustrated in A and evidenced by an increased p(Burst) (probability of firing more than one spike between two input pulses). FR and p(Burst) were computed for each recording set (n = 7 GCs). Paired t-test (FR and p(Burst) respectively): p = 0.02, p = 0.04. (C) Pattern separation graphs showing the pairwise output similarity as a function of the pairwise input similarity, as measured by R, NDP or SF at the 10 ms time scale (mean+/-SEM) across recordings in 7 GCs. Data points below the identity line (dashed) correspond to pattern separation. Partial block of inhibition in GCs led to a significant decrease in pattern separation through all similarity metrics (ANCOVA with separate-lines model fitting 70 data points per treatment group: p < 0.0001). Solid lines are the linear fits used for the ANCOVA. (D) Cumulative frequency distributions of the distance of (pairwise S_input, pairwise S_output) data points to the identity line in pattern separation graphs as in C (insets show medians). Positive values of the x-axis correspond to pattern separation, and negative values to pattern convergence. Red curves (after gzn) are all shifted to the left of their black counterparts (before gzn), showing a decrease in pattern separation at all time scales. The shift is more pronounced at larger time scales for R and NDP, at smaller time scales for SF. ANCOVA on (pw S_input, pw S_output) data points with separate-lines model: p < 0.0001 for τ_w up to 1000 ms for R and NDP, p < 0.02 for SF. (E) Average levels of pattern separation via Compactness, Occupancy or FR codes were measured for each recording set (as in Fig 6B). Surprisingly, partial block of inhibition did not significantly change the variations in FR or binwise Compactness of output spike trains, but it led to less pattern convergence or even pattern separation through variations of Occupancy (paired t-test: p = 0.008, 0.024, 0.031 for τ_w = 10, 20 and 50 ms respectively, p > 0.05 for larger τ_w).

Fig 8. Levels of pattern separation through orthogonalization and scaling differ between hippocampal celltypes.

(A) Temporal pattern separation assays were performed by single whole-cell current-clamp recordings from GCs (green, same experiments as Figs 1–3), FSs (red), HMCs (orange) and CA3 PCs (black). For GCs, FSs and HMCs, input sets with Poisson trains of 10 Hz FR (e.g. Fig 1B) were delivered by stimulating in the outer molecular layer (OML), and recordings done in regular aCSF. For CA3 PCs those stimulus parameters rarely if ever elicited spiking, therefore input sets were constituted of Poisson trains with a 30 Hz FR delivered in the GCL, and recordings were performed under partial block of inhibition (100 nM Gabazine). Control experiments (teal) were performed in GCs under the same pharmacological conditions using 30 Hz input sets, but the stimulations were delivered in the OML. The membrane potential was maintained around -70 mV (between -70 and -60 mV for CA3 PCs). Note: although all celltypes and treatments are displayed on the same graphs for concision (B-D and Fig 9), CA3 PCs should only be directly compared to their corresponding GC controls. (B) Top: Pattern separation graphs showing the pairwise output similarity as a function of the pairwise input similarity, as measured by NDP or SF at the 50 ms time scale (mean+/-SEM: 28 GCs, 3–13 recordings per input set; 4 FSs, 4 recordings per input set; 11 HMCs, 5–7 recordings per input set; 14 CA3 PC + gzn, 6–9 recordings per input set; 13 control GCs + gzn, with 11 recordings per input set). Same color code as in A. Data points below the identity line (dashed) correspond to pattern separation. All celltypes performed pattern separation through both orthogonalization and scaling but with different levels. Bottom: We performed ANCOVAs with separate-lines model for all five celltypes (e.g. solid lines shown in the top graphs) for 11 different time scales (5–1000 ms). Dashed horizontal line represents significance level at 0.05: orthogonalization and scaling levels differ between celltypes at most time scales. (C-D) Slope and intercept of the linear models (e.g. solid lines in B, top) used to fit [S_input, S_output] data points for a given celltype and time scale. Shaded patches correspond to the 95% confidence interval of the parameter estimate. Significant differences between celltypes in pattern separation functions (with Tukey-Kramer correction for multiple comparisons) are detailed in Table 3.

Fig 9. Levels of pattern separation and convergence through burstiness and firing rate codes differ between hippocampal celltypes.

(A) Assessment of burstiness in different celltypes (binless analysis). Left: Cumulative frequency distributions of interspike intervals (ISI) observed in the output spike trains of different hippocampal celltypes and their associated input trains. ISI of all recordings of a given celltype or input set type were pooled. The ISIs were normalized to their median for a given celltype or input type, such that their cumulative distribution would cross at frequency = 0.5, and that all exponential cumulative distributions characteristic of a Poisson process (as both type of input sets are) would be super-imposed or very close to each other. Thus, GCs are visually close to an exponential distribution, suggesting their output is close to a Poisson process, i.e. not bursty. Distributions falling away from their corresponding input distribution suggest that spikes are organized in a non-Poisson manner, suggestive of a bursty behavior. In this sense, HMCs, CA3 PCs and their GC controls seem to exhibit a similar bursty behavior, and FSs an even more bursty one. Right: Quantification of the burstiness of each recording set (102 for GCs, 20 for FSs, 18 for HMCs, 15 for CA3 PCs+gzn and 22 for GCs+gzn). Burstiness was assessed as the Kullback-Leibler divergence from P to M, with M the frequency distribution of normalized ISI in an output set (50 output trains), and P the frequency distribution of normalized ISI in the associated input set type (either Poisson 10Hz or Poisson 30 Hz input sets were combined, as in A). The higher the divergence, the burstier a cell is. This analysis confirms that GCs outputs are close to a Poisson process, and that all other celltypes and conditions are significantly burstier (Kruskal-Wallis one-way ANOVA: p < 0.0001; post-hoc t-tests with Tukey-Kramer correction for multiple comparisons: p < 0.01 for all GC (10Hz) to other celltypes comparisons. CA3 PCs and GC controls (30Hz) are not significantly different (p = 0.99) nor FSs and HMCs (p = 0.64)). Box plots: central mark and edges are the median, the 25th and the 75th percentiles, respectively. Whiskers are most extreme data points not considered outliers (red +). (B) Average levels of pattern separation via binwise Compactness, binwise Occupancy or FR codes were measured for each recording set of every celltype, as in Fig 6B (negative values indicate pattern convergence). Levels were different between celltypes (Kruskal-Wallis one-way ANOVA: p < 0.0001 at all time scales; post-hoc t-tests with Tukey-Kramer correction for multiple comparisons in Table 4).