## Abstract

Place cells in the CA1 region of the hippocampus express location-specific firing despite receiving a steady barrage of heterogeneously tuned excitatory inputs that should compromise output dynamic range and timing. We examined the role of synaptic inhibition in countering the deleterious effects of off-target excitation. Intracellular recordings in behaving mice demonstrate that bimodal excitation drives place cells, while unimodal excitation drives weaker or no spatial tuning in interneurons. Optogenetic hyperpolarization of interneurons had spatially uniform effects on place cell membrane potential dynamics, substantially reducing spatial selectivity. These data and a computational model suggest that spatially uniform inhibitory conductance enhances rate coding in place cells by suppressing out-of-field excitation and by limiting dendritic amplification. Similarly, we observed that inhibitory suppression of phasic noise generated by out-of-field excitation enhances temporal coding by expanding the range of theta phase precession. Thus, spatially uniform inhibition allows proficient and flexible coding in hippocampal CA1 by suppressing heterogeneously tuned excitation.

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## Acknowledgements

We thank J. Osborne and S. Sawtelle for assistance in designing the experimental set up, W.-L. Sun and J. Macklin for developing the LFP fiber probe, M. Copeland for histology, D. Linaro and D. Jin for contributing software tools, J. Lou for help with the treadmill diagram, and members of the Spruston laboratory for discussions. This work was supported by the Howard Hughes Medical Institute.

## Author information

### Authors and Affiliations

### Contributions

C.G. and J.C.M. designed the research. C.G. and K.C.B. performed *in vivo* recordings. C.G. and J.C.M. analyzed the experimental data. A.D.M. designed and implemented the computational model with critical input from J.C.M. and S.R. A.D.M. developed software and analyzed the results of the numerical simulations. All authors wrote the manuscript.

### Corresponding author

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Integrated supplementary information

### Supplementary Figure 1 Characterization of VGAT-ires-CrexAi35D and GAD2-ires-CrexAi35D mice.

(a) Fluorescence in situ hybridization in the dorsal hippocampus of the VGAT-ires-Cre driver line. Shown are probes labeling vgat (green), gad2 (red) and cre (blue). 20 μm-thick cryostat sections from perfusion-fixed brains were used for RNAscope fluorescent triple-label in situ hybridization. (b) Magnified view of the region depicted in a. (c-d) Same as a-b for the GAD2-ires-Cre driver line. This experiment was repeated twice for each genotype. (e) Comparison of place field sizes, derived from the firing rate (left) and the slow V_{m} (right). Place field size was calculated as the fraction of the linear track between two threshold (20% of the peak value of the activity map) crossings (n=32 place cells from 17 VGAT-ires-Cre x Ai35D animals and n=13 place cells from 10 GAD2-ires-Cre x Ai35D animals; firing rate: 44±3 vs. 52±5%, *P* = 0.157; slow V_{m}: 64±3 vs. 64±5%, *P* = 0.897). (f) Comparison of place field characteristics; left: in-field firing rate (8.1±0.8 vs. 9.4±1.8 Hz, *P* = 0.528); middle: in-field Δslow V_{m} (6.7±0.7 vs. 6.6±1.3 mV, *P* = 0.578); right: in-field intracellular theta V_{m} envelope (2.05±0.10 vs. 2.13±0.19 mV, *P* = 0.872). Grey circles represent individual neurons. Black lines represent mean ± s.e.m. Significance assessed with Wilcoxon rank sum tests. ns: not significant.

### Supplementary Figure 2 Representative examples of firing rate maps.

(a) Pre-existing place cells. (b) Experimentally induced place cells. (c) Spatially selective interneurons. Shown are only laps without current injection or light application (lap numbers indicated on the left). Color maps show firing rates in Hz. #Experiment indicated in the upper left corner of the firing rate map.

### Supplementary Figure 3 Characterization of interneuron subtypes: putative axo-axonic cell.

(a) Left: raw V_{m} trace (black) and extracellular theta oscillation (green) for 5 consecutive laps. Middle: Enlarged view of an AP with spike amplitude and spike width (mean ± s.e.m.). Right: V_{m} after AP removal. (b) Spatial modulation. Left: firing rate. Grey lines illustrate individual laps and the mean across laps is shown in black. Red line indicates Gaussian fit. Middle: mean slow V_{m}. Right: mean intracellular theta envelope. (c) AP firing properties. Left: ISI distribution. Middle: Theta phase preference. Red line indicates cosine fit. Right: AP frequency distribution. Bin size is 140 ms. (d) Subthreshold V_{m} characteristics. Left: V_{m} distribution. Bin size is 0.2 mV. V_{m} distributions were calculated from the raw V_{m} trace after AP removal. Middle: Power spectral density analysis with theta-to-gamma ratio. Inset shows enlarged view of the AP-deleted V_{m} trace indicating the presence of fluctuations in the theta and gamma-oscillation range. Right: V_{m} autocorrelation. (e) SPW/R-associated activity. Left: raw V_{m} trace and band-pass filtered (100-250 Hz) LFP (asterisk indicates ripple). Middle: Enlarged view. Right: mean number of APs and ΔV_{m} associated with sharp wave/ripples. Shown are data from the neuron in a.

### Supplementary Figure 4 Characterization of interneuron subtypes: putative basket cell.

(a) Left: raw V_{m} trace (black) and extracellular theta oscillation (green) for 5 consecutive laps. Middle: Enlarged view of an AP with spike amplitude and spike width (mean ± s.e.m.). Right: V_{m} after AP removal. (b) Spatial modulation. Left: firing rate. Grey lines illustrate individual laps and the mean across laps is shown in black. Red line indicates Gaussian fit. Middle: mean slow V_{m}. Right: mean intracellular theta envelope. (c) AP firing properties. Left: ISI distribution. Middle: Theta phase preference. Red line indicates cosine fit. Right: AP frequency distribution. Bin size is 140 ms. (d) Subthreshold V_{m} characteristics. Left: V_{m} distribution. Bin size is 0.2 mV. V_{m} distributions were calculated from the raw V_{m} trace after AP removal. Middle: Power spectral density analysis with theta-to-gamma ratio. Inset shows enlarged view of the AP-deleted V_{m} trace indicating the presence of fluctuations in the theta and gamma-oscillation range. Right: V_{m} autocorrelation. (e) SPW/R-associated activity. Left: raw V_{m} trace and band-pass filtered (100-250 Hz) LFP (asterisk indicates ripple). Middle: Enlarged view. Right: mean number of APs and ΔV_{m} associated with sharp wave/ripples. Shown are data from the neuron in a.

### Supplementary Figure 5 Characterization of interneuron subtypes: putative bistratified cell.

(a) Left: raw V_{m} trace (black) and extracellular theta oscillation (green) for 5 consecutive laps. Middle: Enlarged view of an AP with spike amplitude and spike width (mean ± s.e.m.). Right: V_{m} after AP removal. (b) Spatial modulation. Left: firing rate. Grey lines illustrate individual laps and the mean across laps is shown in black. Red line indicates Gaussian fit. Middle: mean slow V_{m}. Right: mean intracellular theta envelope. (c) AP firing properties. Left: ISI distribution. Middle: Theta phase preference. Red line indicates cosine fit. Right: AP frequency distribution. Bin size is 140 ms. (d) Subthreshold V_{m} characteristics. Left: V_{m} distribution. Bin size is 0.2 mV. V_{m} distributions were calculated from the raw V_{m} trace after AP removal. Middle: Power spectral density analysis with theta-to-gamma ratio. Inset shows enlarged view of the AP-deleted V_{m} trace indicating the presence of fluctuations in the theta and gamma-oscillation range. Right: V_{m} autocorrelation. (e) SPW/R-associated activity. Left: raw V_{m} trace and band-pass filtered (100-250 Hz) LFP (asterisk indicates ripple). Middle: Enlarged view. Right: mean number of APs and ΔV_{m} associated with sharp wave/ripples. Shown are data from the neuron in a.

### Supplementary Figure 6 Characterization of interneuron subtypes: putative O-LM cell.

(a) Left: raw V_{m} trace (black) and extracellular theta oscillation (green) for 5 consecutive laps. Middle: Enlarged view of an AP with spike amplitude and spike width (mean ± s.e.m.). Right: V_{m} after AP removal. (b) Spatial modulation. Left: firing rate. Grey lines illustrate individual laps and the mean across laps is shown in black. Red line indicates cosine fit. Middle: mean slow V_{m}. Right: mean intracellular theta envelope. (c) AP firing properties. Left: ISI distribution. Middle: Theta phase preference. Red line indicates cosine fit. Right: AP frequency distribution. Bin size is 140 ms. (d) Subthreshold V_{m} characteristics. Left: V_{m} distribution. Bin size is 0.2 mV. V_{m} distributions were calculated from the raw V_{m} trace after AP removal. Middle: Power spectral density analysis with theta-to-gamma ratio. Inset shows enlarged view of the AP-deleted V_{m} trace indicating the presence of fluctuations in the theta and gamma-oscillation range. Right: V_{m} autocorrelation. (e) SPW/R-associated activity. Left: raw V_{m} and band-pass filtered (100-250 Hz) LFP (asterisk indicates ripple). Middle: Enlarged view. Right: mean number of APs and ΔV_{m} associated with sharp wave/ripples. Shown are data from the neuron in a.

### Supplementary Figure 7 Comparison of interneuron subtypes.

Quantified are AP theta phase preference, V_{m} frequency modulation, V_{m} autocorrelation, and SPW/R-associated activity for each of the following putative interneuron subtypes: axo-axonic cells (n=3), basket cells (n=6), bistratified cells (n=11), and O-LM cells (n=7).

### Supplementary Figure 8 Spatial modulation of CA1 interneurons.

(a) Representative examples for spatially unmodulated interneurons. (b) 7 spatially modulated interneurons were identified in our dataset of 27 interneurons. (a-b) Grey lines illustrate individual laps and the mean across laps is shown in black. Red lines indicate the 95% confidence intervals of the shuffled (1000 times) data. Asterisks mark locations (>3.6 cm, at least 3 spatial bins) that exceed the 95% confidence intervals of the shuffled data. (c) Spatial information per neuron (bits) for place cells and interneurons. (d) Information rate per neuron (left: bits per second, right: bits per spike) for place cells and interneurons.

### Supplementary Figure 9 Effect of interneuron silencing on pyramidal cell activity.

(a) Activity maps (100 spatial bins of 1.8 cm each) for slow V_{m} depolarization (Δslow V_{m}, relative to baseline V_{m}), intracellular theta oscillation (theta V_{m}) envelope and firing rate. Top: control, bottom: Arch activation in interneurons. (b) Comparisons of Δslow V_{m} (left), theta V_{m} envelope (middle) and firing rate (right) with and without light. Shown are averages of ten spatial bins totaling 18 cm centered either at the peak of the place field (n=32 neurons; Δslow V_{m}: 6.2±0.7 vs. 9.2±0.7 mV, *P* = 2.6E-8; theta V_{m}: 1.91±0.08 vs. 2.25±0.08 mV, *P* = 0.0003; firing rate: 7.5±0.8 vs. 15.2±1.1 Hz, *P* = 4.7E-9) or at the minimum value (n=29 neurons; Δslow V_{m}: 0.3±0.1 vs. 3.1±0.4 mV, *P* = 9.3E-8; theta V_{m}: 1.07±0.04 vs. 1.38±0.08 mV, *P* = 1.4E-5; firing rate: 0.5±0.1 vs. 3.3±0.8 Hz, *P* = 2.3E-5). Grey circles represent individual neurons. Black and orange circles represent the population mean for control and light condition, respectively. (c) Comparison of changes in Δslow V_{m} and theta V_{m} induced by light stimulation between periods before and after experimental induction of place fields in silent cells (n=7; Δslow V_{m} in field: 3.0±0.3 vs. 3.1±0.6 mV, *P* = 0.998; Δslow V_{m} out of field: 3.3±0.3 vs. 3.1±0.5 mV, *P* = 0.688; theta V_{m} in field: 0.27±0.025 vs. 0.31±0.037 mV, *P* = 0.688; theta V_{m} out of field: 0.26±0.058 vs. 0.25±0.038 mV, *P* = 0.938). Values represent mean ± s.e.m. Significance assessed with Wilcoxon signed rank tests. Asterisks denote significant difference (p<0.05). ns: not significant.

### Supplementary Figure 10 Comparison of inhibitory modulation of spatial selectivity in pre-existing and experimentally induced CA1 place cells.

(a) Pre-existing place cells. Mean activity maps (Δslow V_{m}, theta V_{m}, and firing rate) aligned to the firing field center (n=10-12 neurons; Δslow V_{m} *P* <0.05 for all spatial bins; theta V_{m} *P* <0.05 for bins 1 and 3-10, bin 2 *P* = 0.519; firing rate *P* <0.05 for bins 1 and 3-10, bin 2 *P* = 0.058) and comparison of V_{m} variance between position-matched periods with and without light (in field: n=11 neurons, 6.39±0.71 vs. 8.97±1.05, *P* = 0.001; out of field: n=11 neurons, 3.46±0.40 vs. 5.93±1.03, *P* = 0.007). (b) Induced place cells. Mean activity maps (Δslow V_{m}, theta V_{m}, and firing rate) aligned to the firing field center (n=14-20 neurons; Δslow V_{m} P <0.001 for all spatial bins; theta V_{m} *P* <0.05 for bins 1-9, bin 10 *P* = 0.268; firing rate *P* <0.05 for all spatial bins) and comparison of V_{m} variance between position-matched periods with and without light (in field: n=20 neurons, 6.99±0.49 vs. 9.64±0.61, *P* = 0.0003; out of field: n=13 neurons, 2.86±0.27 vs. 4.41±0.65, *P* = 0.005). (a-b) Grey circles represent individual neurons, black and orange circles represent population averages for control and light conditions, respectively. Significance assessed with Wilcoxon signed rank tests. Exact n and *P* values in Supplementary Table 3. (c) Difference in Δslow V_{m}, theta V_{m}, firing rate and V_{m} variance between control and light condition in pre-existing vs. induced place cells. Compared are averages of ten spatial bins totaling 18 cm centered either at the peak of the place field (Δslow V_{m}: 2.8±0.5 (n=12) vs. 3.2±0.6 mV (n=20), *P* = 0.774; theta V_{m}: 0.48±0.12 (n=12) vs. 0.26±0.11 mV (n=20), *P* = 0.158; firing rate: 8.0±1.9 (n=12) vs. 7.4±1.1 Hz (n=20), *P* = 0.985; Vm variance: 2.6±0.6 (n=11) vs. 2.6±0.6 (n=20), *P* = 0.792) or at the minimum value (Δslow V_{m}: 2.6±0.6 (n=13) vs. 2.8±0.5 mV (n=16); *P* = 0.714; theta V_{m}: 0.35±0.11 (n=13) vs. 0.27±0.09 mV (n=16), *P* = 0.619; firing rate: 3.2±1.5 (n=13) vs. 2.5±0.9 Hz (n=16), *P* = 0.846; V_{m} variance: 2.5±1.0 (n=11) vs. 1.6±0.5 (n=13), *P* = 0.424). Grey circles represent individual neurons. Significance assessed with Wilcoxon rank sum tests. Data shown as mean ± s.e.m.; asterisks denote significant difference (p<0.05); ns: not significant.

### Supplementary Figure 11 Effect of interneuron silencing on input resistance and *V*_{m} autocorrelation.

(a-b) Current waveforms and resulting raw V_{m} traces (black) and V_{m} traces after AP removal (red) for one control (a) and one light-on (b) lap. Top: extracellular theta oscillation (green, theta LFP). Shaded orange region depicts light period. (c) Input resistance (R_{n}) as a function of theta phase. Data was binned in 10 bins of 36˚ each. Shown are mean R_{n} values (± s.e.m.) obtained for control and light periods (n=12 neurons; bin 1-7&9 *P* <0.05, bin 8 *P* = 0.244, bin 10 *P* = 0.122; exact *P* values in Supplementary Table 3). Two theta cycles are shown for better visibility. (d) Input resistance (R_{n}) as a function of position relative to the firing field center. Data was binned in 10 bins of 18 cm each. Shown are mean R_{n} values (± s.e.m.) obtained for control and light periods and pooled across all theta phases. Number of neurons included in each data point is indicated below the traces (for bin 1-10 *P* <0.05; exact *P* values in Supplementary Table 3). (e) In field and out of field V_{m} autocorrelation; black: control, orange: light. (f) Mean in field and out-of-field V_{m} autocorrelations and exponential fits for control (black) and light (orange) periods. Time constants τ are derived from exponential fits. (g) Population data for all neurons (in field: n=31, 40±2 vs. 46±2 ms, *P* = 0.004; out of field: n=24, 34±2 vs. 40±2 ms, *P* = 0.008). Grey circles represent individual neurons. Black and orange circles represent mean values (± s.e.m.) for control and light conditions, respectively. Significance assessed with Wilcoxon signed rank tests. Asterisks denote significant difference (p<0.05). ns: not significant.

### Supplementary Figure 12 Excitatory and inhibitory synaptic inputs in the computational model of CA1 place cells.

(a) Circuit diagram depicts CA1 pyramidal neurons embedded in a local network containing six classes of inhibitory interneurons, and receiving two major excitatory input pathways. Each of the excitatory and inhibitory inputs to pyramidal neurons was modeled as targeting different somatodendritic domains. (b) The number of synapses made by each input source onto each type of subcellular compartment for a representative example simulated CA1 place cell.

### Supplementary Figure 13 Modeling inhibitory modulation of CA1 place cell dynamics.

(a) Simulations run in the absence of amplification of synaptic signals by NMDA-Rs or Na^{+} channels (Fig. 5g) required that the number of AMPA-R-only excitatory synapses be approximately doubled in order to generate a comparable ΔV_{m} (out: -0.014±0.0245 vs. 1.519±0.045, t(4)=38.674, *P* <0.0001; in: 5.457±0.0440 vs. 7.049±0.058, t(4)=55.004, *P* <0.0001). This manipulation resulted in decreases in theta V_{m} (out: 0.644±0.011 vs. 0.878±0.0298, t(4)=7.0963, *P* = 0.002083; in: 1.204±0.0325 vs. 1.402±0.041, t(4)=4.5917, *P* = 0.01009). (b-c) Probing somatic membrane input resistance in the model with step current injections revealed a weak dependence of input resistance on theta phase (b) consistent with inhibitory conductance peaking at the trough of extracellular theta (180°), and a weak dependence on spatial location (c), resulting from changes in the activation of voltage-dependent membrane conductances during increased spiking in field. Reducing inhibitory conductance in the model resulted in increases in apparent input resistance (mean ± s.e.m. across all theta phases and spatial bins: 44.715±0.280 (black) vs. 51.906±0.344 (orange), t(4)=15.584, *P* <0.0001). (a-c) Shown are averages across 5 simulated CA1 place cells (10 trials per condition per cell), with shading indicating ± s.e.m. Significance was assessed using two-tailed paired t-tests. (d) Shown are representative example traces from the model for recordings of the following parameters: soma V_{m} in and out of field (black), spine V_{m} (green) for individual spines either receiving a CA3 input with a place field located either outside (left) or inside (right) that of the CA1 place cell, branch V_{m} (red) for the parent branches of the corresponding spines, and currents through AMPA-Rs (cyan) and NMDA-Rs (black) in the corresponding spines. (e) In the model, complete removal of synaptic inhibition results in persistent AP firing throughout the simulated track, with bouts of somatic Na^{+}-channel inactivation.

### Supplementary Figure 14 Adding noise to CA1 place cell simulations.

(a-b) Traces depict simulated raw membrane potential (V_{m}) (black) and filtered V_{m} after AP removal (red: slow V_{m}, < 2Hz; blue: theta V_{m}, 5-10 Hz) recorded from the model place cell during simulated traversal of a linear track. Shown are recordings from individual trials either in the control condition (a), or with inhibitory firing rates reduced (b), with additional ~0.8 Hz theta-modulated background excitation from each active CA3 and ECIII input, resulting in increased spiking out of field compared to the results in Fig 5. Orange bar indicates period of reduced inhibition. (c) Mean activity maps for slow V_{m} depolarization, (left, Δslow V_{m}, relative to baseline V_{m}, out: 0.068±0.093 vs. 3.265±0.107, t(4)=60.72, *P* <0.0001; in: 6.550±0.076 vs. 10.239±0.080, t(4)=46.249, *P* <0.0001) and intracellular theta oscillation envelope (middle, theta V_{m}, out: 1.346±0.048 vs. 2.120±0.096, t(4)=7.001, *P* = 0.002191; in: 2.519±0.068 vs. 3.272±0.098, t(4)=6.658, *P* = 0.002643) obtained from the model (black: control; orange: reduced inhibition). (d-e) Mean activity map for AP firing rate (right, out: 0.983±0.226 vs. 9.658±0.400, t(4)=23.779, *P* <0.0001; in: 28.678±0.333 vs. 55.025±0.375, t(4)=47.621, *P* <0.0001). Same data is depicted at a different scale in (e). (f) Mean activity map for variance of simulated V_{m} fluctuations recorded from model place cells (mean ± s.e.m., out: 2.123±0.060 vs. 4.386±0.134, t(4)=17.068, *P* <0.0001; in: 5.508±0.090 vs. 7.647±0.174, t(4)=10.034, *P* = 0.0005546). (c-f) Solid lines and shading represent mean ± s.e.m. across five simulated cells (10 trials per condition per cell). Significance was assessed from data in 600 ms bins in or out of field using two-tailed paired t-tests.

## Supplementary information

### Supplementary Text and Figures

Supplementary Figures 1–14, Supplementary Tables 1–3, and Supplementary Modeling (PDF 7809 kb)

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Grienberger, C., Milstein, A., Bittner, K. *et al.* Inhibitory suppression of heterogeneously tuned excitation enhances spatial coding in CA1 place cells.
*Nat Neurosci* **20**, 417–426 (2017). https://doi.org/10.1038/nn.4486

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DOI: https://doi.org/10.1038/nn.4486