Post-Inhibitory Rebound Spikes in Rat Medial Entorhinal Layer II/III Principal Cells: In Vivo, In Vitro, and Computational Modeling Characterization

Abstract

Medial entorhinal cortex Layer-II stellate cells (mEC-LII-SCs) primarily interact via inhibitory interneurons. This suggests the presence of alternative mechanisms other than excitatory synaptic inputs for triggering action potentials (APs) in stellate cells during spatial navigation. Our intracellular recordings show that the hyperpolarization-activated cation current (I_h) allows post-inhibitory-rebound spikes (PIRS) in mEC-LII-SCs. In vivo, strong inhibitory-post-synaptic potentials immediately preceded most APs shortening their delay and enhancing excitability. In vitro experiments showed that inhibition initiated spikes more effectively than excitation and that more dorsal mEC-LII-SCs produced faster and more synchronous spikes. In contrast, PIRS in Layer-II/III pyramidal cells were harder to evoke, voltage-independent, and slower in dorsal mEC. In computational simulations, mEC-LII-SCs morphology and I_h homeostatically regulated the dorso-ventral differences in PIRS timing and most dendrites generated PIRS with a narrow range of stimulus amplitudes. These results suggest inhibitory inputs could mediate the emergence of grid cell firing in a neuronal network.

Introduction

As a rat navigates its environment, grid cells in the medial entorhinal cortex (mEC) spike in a regular array of locations corresponding to the vertices of triangles tessellating the explored space (Fyhn et al. 2004; Hafting et al. 2005; Moser and Moser 2008). The size of triangles correlates with the location of the grid cell along the dorsal to ventral axis of the mEC (Hafting et al. 2005; Brun et al. 2008) and it is believed to be a mechanism used by the animal to scale space. The mEC thus transforms sensory inputs from the environment into durable allocentric representations that could be used for path integration (Fyhn et al. 2004). Intracellular recordings from mEC Layer-II stellate cells (mEC-LII-SCs) and Layer-II/III pyramidal cells (mEC-LII/III-PCs) during spatial navigation showed that these cells exhibit grid cell firing properties (Domnisoru et al. 2013; Schmidt-Hieber and Häusser 2013). Spatio-temporal computations performed in mEC most likely involve synaptic interactions between mEC-LII-SCs and local inhibitory interneurons (Pastoll et al. 2013; Couey et al. 2013). Recent data suggest that mEC-LII-SCs are indirectly connected mostly through inhibitory interneurons and that synaptic inhibition in mEC-LII-SCs is substantially stronger than excitation (Pastoll et al. 2013; Beed et al. 2013; Couey et al. 2013). Furthermore, the remarkable diversity in the morphological and intrinsic properties of entorhinal cortex interneurons (Tahvildari et al. 2012; Ferrante et al. 2015) may underlie their complex role in orchestrating spatial memory functions by this brain region.

GABAergic interneurons are classically thought to prevent post-synaptic cell firing (Jahnsen and Llinas 1984; Miles et al. 1996; McCormick and Bal 1997; McCormick 1998; Person and Perkel 2005), synchronize oscillations (Steriade et al. 1993; Buzsaki 2002; Buzsaki and Draguhn 2004), or buffer a steep neuronal input–output frequency relationship (Ferrante et al. 2009). Nevertheless, target cell rebound spikes may be elicited in response to inhibitory signals (Jahnsen and Llinas 1984; McCormick and Bal 1997; McCormick 1998) and a mechanistic explanation of grid cell firing could involve post-inhibitory rebound spikes (PIRS) (Hasselmo 2013). Hence, a post-inhibitory rebound is a period of intrinsically generated neuronal excitability following the termination of inhibition. PIRS have been recorded in vitro in mEC-LII-SCs (Alonso and Llinas 1989; Alonso and Klink 1993; Dickson et al. 2000; Giocomo et al. 2007; Heys et al. 2010; Shay et al. 2015) but the intrinsic and extrinsic properties modulating the emergence of PIRS have not been systematically analyzed before the present study, particularly, with respect to the cellular position along the mEC dorsal–ventral axis.

PIRS have also been recorded in vivo, for instance between putatively connected entorhinal interneurons using extracellular recording (Adhikari et al. 2012); or in a subset of offset neurons in the inferior colliculus that fire at the termination of sounds (Kasai et al. 2012); or in deep cerebellar nuclear neurons when the incoming inhibitory inputs from Purkinje cells get synchronously activated by climbing fibers (Bengtsson et al. 2011). Before our study, similar in vivo intracellular analyses of PIRS have not been performed in mEC-LII-SCs. Functionally PIRS in mEC grid cells, like in the olfactory bulb (Yokoi et al. 1995; Isaacson and Strowbridge 1998), may sharpen the spatial pattern of activity. Or, perhaps like in subcortical regions (Bottjer 2005), PIRS may regulate persistent firing and rhythms. One of the reasons why only a few examples of PIRS have been observed in vivo is that the specific neuronal connectivity responsible for them may be activity- and/or cell-dependent (Adhikari et al. 2012).

Membrane potential dynamics and intrinsic properties are responsible for the emergence of PIRS, including the effects of the I_h current that responds to hyperpolarization by generating a depolarizing current that slowly turns on and off. When the hyperpolarization generated by the activation of inhibitory synapses decays, the slow offset of the I_h current results in a depolarizing current that lasts longer than the inhibition, giving rise to the characteristic depolarizing overshoot, and providing a mechanism for generating APs. Intuitively, PIRS in mEC neurons should emerge from the synergistic interaction of strong/frequent inhibitory inputs and large I_h conductances. This is because being hyperpolarization-activated, I_h, creates larger depolarizing rebound potentials when stronger (or temporally clustered) inhibitory synaptic inputs interact with larger I_h conductances. mEC-LII-SCs express large amounts of I_h (Alonso and Llinas 1989; Klink and Alonso 1993; Leung and Yu 1998; Heys and Hasselmo 2012; Shay et al. 2012) that coupled with large-amplitude IPSPs (Cunningham et al. 2003) may generate PIRS. Additionally, these strong IPSPs from local PV+ interneurons arrive at a fast (gamma) pace (Cunningham et al. 2003) potentially enabling more temporal summation that might lead to an enhanced probability to generate PIRS. In particular, cortical gamma oscillations are thought to enable associative binding while processing incoming sensory signals (Gray et al. 1989; Singer and Gray 1995; Verala et al. 2001). The frequency of incoming IPSPs from PV+ cells decreases at more ventral positions in mEC (Beed et al. 2013), suggesting that this could be a mechanism enabling the emergence of the larger grid cell firing fields observed in the ventral mEC. Furthermore, IPSPs from PV+ cells may provide recurrent mEC inhibition driven by grid cells (Buetfering et al. 2014), therefore silencing nongrid cells and enabling PIRS in nearby cells expressing I_h.

Countless neuronal functions depend on fine details of complex molecular, circuit, and synaptic architectures that occur between and within cells. Until recently (Micheva and Smith 2007), with the advent of array tomography, simultaneously investigating these 3 levels, even in a single cell (at the nanometer scale) was not possible and it still represents a technological challenge. Specifically, the spatial distribution of ion channels synapses on dendrites of mEC-LII-SCs remains unknown, but knowledge of this could perhaps help us answer important questions. Such as, how perisomatically initiated PIRS backpropagate into the dendrites and how active and passive properties affect this propagation. Somatic recordings of synaptically stimulated dendrites showed the coactivation of inward (i.e., I_Nap and I_CaT,Magee and Johnston 1995) and outward (i.e., I_KA, Hoffman et al. 1997) active properties which in turn can shape unitary α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) conductances (Perez-Rosello et al. 2011). Unfortunately, a similar investigation for γ-aminobutyric acid (GABA)(/hyperpolarization)-activated conductances has not been carried out in mEC-LII-SCs. The ability to generate a rebound spike may be influenced by the spatial distribution of synapses that is highly cell specific (Gulyas et al. 1999), or by the amplitude of the synaptic potentials that may vary with distance from the soma (Magee and Cook 2000).

The cellular properties of mEC-LII-SCs may be specifically tuned to allow them to easily generate PIRS and this could be an important biophysical mechanism enabling the neural substrate to encode spatial navigation in the mEC. Furthermore, neuropharmacological enhancement of I_h can be achieved by administering the anticonvulsant lamotrigine (Poolos et al. 2002; Ferrante et al. 2008) while its down-regulation can be attained through the use of ZD 7288 (Harris and Constanti 1995). The pharmacological up- and down-regulation of I_h in grid cells can be an important target for future drugs aiming to treat diseases affecting spatial memory (e.g., Alzheimer's disease). Recent experiments and simulations have shown (Ascoli et al. 2010) that upon release from hyperpolarizing current step injections, I_KA blockage resulted in perisomatic initiation of PIRS that could be blocked by ZD 7288. Therefore I_KA and I_h could counteract each other in promoting (or inhibiting) PIRS. Despite this extensive wealth of accumulated knowledge (mostly in other brain regions) we are still missing a quantitative description of how mEC-LII/III principal cells generate PIRS and what role they may play in the emergence and modulation of grid cell firing. This would include a comprehensive characterization of the stimuli and neuronal features enabling mEC-LII/III principal cells to generate spikes in response to inhibition.

Materials and Methods

All experimental protocols were approved by the Boston University Institutional Care and Use Committee and The Animal Welfare Act. All experiments were conducted on male and female Long-Evans rats (Charles River Laboratories, Wilmington, MA, USA). Unless otherwise specified, significance (p-value) and correlation coefficient (R) for the in vivo and in vitro results were calculated using the Pearson correlation coefficient (Wessa 2012) and were noted in the respective figure legends.

In Vivo Electrophysiology

All the in vivo data used for this study were from our previous investigations (Tsuno et al. 2013); more details on the methods used to collect these in vivo data can be found in the original manuscript. Briefly, adult (250–400 g) rats were used for these experiments. After the animals were anesthetized a hole was drilled in the skull and a sharp intracellular recording glass electrode was lowered in the mEC (lateral 4.5 mm, 0.35–1.00 mm anterior from the sinus on the cerebellum, angled 12° to anterior, depth 2.0–4.5 mm from the surface) by a micromanipulator (MO-8-W; Narishige). With this experimental setup current stimulations and voltage intracellular recordings were simultaneously performed. In some experiments, 1 mM picrotoxin (#1128; Tocris, Bristol, England, UK) was diluted in the internal solution of the recording electrode.

In vitro Electrophysiology

Brain slicing and recording techniques used here have been previously described (Shay et al. 2012) where more in-depth methodological details can be found. Current-clamp, whole-cell recordings were performed at physiological temperature (36 ± 2°C) from the soma of LII-SCs and LII/III-PCs at different locations along the DV axis of the mEC.

Of note, 17 to 21-day-old male rats were deeply anesthetized with (1.5 mL) isoflurane (Abbot Laboratories) in diffusion chambers. After establishing the absence of tail and pedal reflex, brains were extracted and swiftly placed in ice-cold aCSF (125 NaCl, 2 CaCl, 2.5 KCl, 1.25 NaH₂PO4, 25 NaHCO₃, 25 D-Glucose, and 1 MgCl₂, in mM) with pH of 7.4. Acute (400 µm-thick) horizontal parahippocampal slices were obtained using a vibrating blade microtome (Leica VT1000). Brain slices were incubated for 30 min in a holding chamber filled with aCSF at 31°C and for an additional 30 min at room temperature while being constantly bubbled with a mixture of 95% O2–5% CO2 during the whole experiment.

Recording pipettes were made from borosilicate glass capillaries using a P-90 horizontal puller (Sutter Instruments) and filled with intracellular recording solution containing the following concentrations (in mM): 110 K-gluconate, 20 KCl, 1 EGTA, 2 MgCl₂, 10 HEPES, 2 Na₂ATP, 0.3 Na₂GTP, 10 phosphocreatine, and 0.1% biocytin (for postfix labeling). Filled pipettes had resistances of 4 ± 1 MΩ. An upright microscope (Zeiss Axioskop 2 or Olympus BX51I) equipped with a ×40immersion lens and a near infrared charge-coupled device camera (JAI CV-M50IR) or digital Rolera Bolt camera (QImaging, Surrey, BC, Canada) were used to visualize the cells.

After a strong (>1 GΩ) seal was achieved a negative pressure was applied to the recording electrode to gain whole-cell access, the cells were then allowed 3–5 min to recover. The delay of the spike and the number of the PIRS were calculated as described in Figs 4B and 5A, respectively. In 17 of the 77 SCs recorded, kynurenic acid (2 mM) and picrotoxin (100 μM) were dissolved into extracellular recording solution to block glutamatergic and GABAergic synaptic transmission, respectively. No significant (qualitative or quantitative) differences were observed in these recordings. I_h was blocked in (n = 2) cells with 10 μM application of ZD7288 (Tocris, Sigma) in the extracellular bath solution.

Figure 4.

In vitro, mEC neuronal populations (LII-SCs vs. LII/III-PCs), differences in PIRS properties. (A), Photomicrographs of mEC horizontal slices with insets (on the bottom) showing magnifications of a LII-SC (left) and a LII/III-PC (right) anatomy. (B), SCs (black, number of cells = 77) and PCs (gray, number of cells = 7) differences in PIRS delay (top) and average number of spikes (bottom) as a function of stimulus amplitude. Top, SCs (n = 2454, R = 0.395, P < 0.01), PCs (n = 558, R = 0.435, P < 0.01); bottom, each data point represents the average number PIRS for 120 square pulse stimulation experiments, SCs (n = 71, R = 0.909, P < 0.01), PCs (n = 21, R = 0.762, P < 0.01). Holding voltage = −60.3 ± 7.3 mV; stimulus duration = 42 ± 31 ms. (C), Same as B, but as a function of membrane holding voltage. Top, SCs (n = 2454, R = 0.225, P < 0.01), PCs (n = 558, R = 0.497, P < 0.01); bottom SCs (n = 71, R = 0.758, P < 0.01), PCs (n = 21, R = −0.073, P = 0.375). Fitting lines (in C–D) are fifth order polynomials, dotted lines describe preferred holding voltage to generate PIRS for the 2 cell populations. Stimulus amplitude = −321 ± 190 pA; stimulus duration = 42 ± 31 ms. (D), Same as B but as a function of stimulus duration. Top, SCs (n = 2454, R = −0.388, P < 0.01), PCs (n = 558, R = −0.519, P < 0.01); bottom SCs (n = 47, R = 0.606, P < 0.01), PCs (n = 21, R = 0.895, P < 0.01). AP delays larger than 200 ms are not shown. Holding voltage = −60.3 ± 7.3 mV; Stimulus amplitude = −321 ± 190. To depict the full extent of the variability of the population response each panel shows the effect of one variable (e.g., stimulus amplitude) when all the other variables (e.g., holding voltage and stimulus duration) are independently manipulated.

Figure 5.

In vitro, influence of mEC Dorso-ventral position and resonance frequency on PIRS properties of mEC-LII-SCs and mEC-LII/III-PCs. (A), Injected chirp (ZAP) stimulus (top left), resonance of a mEC-LII/III-PC (top right), resonance of a mEC-LII-SC (bottom right), impedance analysis for both cells and impedance curve fit to estimate the cell's resonant frequency from the peak of the curve (bottom left). (B), Impact of cellular position along the mEC DV axis on PIRS delay (Top) and average number of PIRS (Bottom) for SCs (black) and PCs (gray). Top panels, SCs (n = 2454, R = 0.085, P < 0.01) PCs (n = 558, R= −0.516, P < 0.01). Bottom panels, each data point represents the average number PIRS for 120 square pulse stimulation experiments for SCs (n = 9162, R = 0.067, P < 0.01) and PCs (n = 2689, R = 0.013, P < 0.24). (C), Influence of intrinsic cellular resonance frequency (at about −60 mV) on PIRS delay (Top) and average number of PIRS (Bottom) for SCs and LII/III-PCs. Top panels, SCs (n = 2454, R = −0.122, P < 0.01) PCs (n = 558, R = −0.693, P < 0.01); bottom panels SCs (n = 9162, R = 0.136, P < 0.01) PCs (n = 2689, R = 0.33, P < 0.01).

Signals were sampled at 20 kHz using Clampex 10.0 (Axon Instruments) and recorded with a Multi Clamp 700B amplifier by Axon Instruments. Higher sampling rates were used for illustration purpose. Stimulating current protocols were designed using subsequent pCLAMP current square pulses of different amplitudes (0–1000 pA, with increments of either 25 or 33 pA) and durations (10–50 ms, with 10-ms increments), the cellular holding voltage (−40 to −80 mV) was modulated within a physiological range. Hyperpolarizing synaptic currents were simulated with a double exponential function:

$$I_{\mathrm{Syn}}={e^{(-t/\tau 1}}^{)}-{e^{(-t/\tau 2}}^{)}$$

where, τ1 and τ2 are the rise and decay time constants were set at 1 ms and 5 ms, respectively. Simulated synaptic inputs of increasing magnitude (from −25 pA to −500 pA, Δ = −25 pA) were separated by a 500 ms baseline current (DC). In another experimental condition, we investigated the effect of GABAergic temporal summation leading to PIRS (Fig. 7C–D) by simulating multiple desynchronized (noise = 1) inhibitory synapses (1–10 synapses, 100 pA each) within the duration of half of a theta cycle (i.e., 60 ms).

Figure 7.

In vitro, synaptic stimulus amplitude and temporal summation affect SC ability to generate PIRS. (A) Stellate cell displays rebound spiking in response to injected synaptic currents of different amplitudes (25–500 pA) near AP threshold. (B), Change in the probability of generating PIRS as function of the amplitude of the synaptic current injected (for 5 cells, 20 trials per cell) normalized against the control condition, that is, no synaptic current injection (gray dotted line). Straight line represents linear fit. (C) Rebound spiking in response to temporal summation (within 60 ms) of multiple synaptic stimuli (1–10 stimuli, 100 pA each). (D) Effect of the number of synaptic inputs integrating over time (60 ms) on the probability of generating PIRS (in 4 cells, 20 trials per cells) normalized against the control condition, that is, no synaptic current injection (gray dotted line). Straight line represents linear fit.

A MATLAB generated chirp stimulation (with frequency changing linearly from 0 to 20 Hz in 20 s, steady amplitude ranging between 10 and 100 pA in different neurons) (Erchova et al. 2004) was used to investigate the intrinsic resonance frequency of the cell. In some articles, this is known as a ZAP stimulus. Sag ratios were calculated by dividing the peak trough membrane voltage by the steady state membrane voltage (Giocomo and Hasselmo 2009).

SCs were identified based on their somatic/dendritic anatomical location (LII), post hoc morphology recovery, and electrophysiological signatures (Alonso and Llinás 1989; Alonso and Klink 1993; Dickson et al. 2000; Heys et al. 2010) such as resting membrane potentials (< −55 mV), input resistances (<120 MΩ), strong sag potentials (average ratio = 1.069 ± 0.037), subthreshold membrane potential oscillations, and cluster spiking. As selecting criteria for establishing recording quality we used series resistances (≤30 MΩ) and peak action potentials (>0 mV). Somas of PCs on the other hand, were typically located in LIII, were usually more hyperpolarized, with smaller sag ratios (average ratio = 1.037 ± 0.023), and did not display subthreshold membrane potential oscillations.

Histology

After the in vivo and in vitro experiments were performed, brain slices were postfixed in paraformaldehyde overnight. Biotin-loaded cells were visualized using avidin–biotin complex (Vectastain Elite ABC kit [Standard], #PK-6100; Vector Laboratories) and DAB reactions (DAB Peroxidase Substrate Kit, #SK-4100; Vector Laboratories). The sections were mounted on gelatin-coated slides. The in vivo slices were also counterstained with Neutral Red or Cresyl Violet.

Data Analysis

All in vivo, in vitro, and in silico analyses have been performed using a combination of scripts implemented in MATLAB (Natick, MA Version 7.9, 2009), R, or Microsoft Excel. A MATLAB script was used to extract the 10 ms of voltage data preceding each spontaneous AP. A sliding window in Excel calculated the average derivative of the voltage over 0.5 ms. The IPSP maximum and minimum were found by extracting the voltage values where the derivative of the voltage crossed 0 downward or upward, respectively (see Fig. 2C). Putative IPSPs were extracted and analyzed in terms of amplitude (i.e., maximum-minimum voltage values) and delay of the spike (from the IPSP onset, i.e., maximum voltage value) using R. An IPSP was defined as the largest hyperpolarizing voltage deflection larger than −0.2 mV within the 10 ms preceding the spike. Regular APs were separated by PIRS based of the presence of at least one putative IPSP in front of the spike. Examples of IPSPs of different amplitudes can be found in Figure 2D together with a density plot distribution of all the IPSPs amplitudes recorded in vivo.

Figure 2.

In vivo pharmacological modulation of inhibitory post-synaptic potentials and PIRS Delay. (A), Perithreshold voltage traces showing spontaneous APs in control condition (left), and during the effect of intracellular GABA_A noncompetitive channel blocker picrotoxin (right). (B), Higher magnification of the spikes from the marked rectangle for each condition. The AP in the intracellular picrotoxin conditions (in gray) is characterized by a monotonic increase (building up phase) of the voltage over time. In control conditions (black), neurons tend to show a post-inhibitory rebound spike, as indicated by spiking associated with a pronounced inflection of the voltage within the 10 ms preceding the spike. (C), A sliding window computed a smoothed (over 0.5 ms) derivative of the voltage before the spike to identify the points of maximum (/onset) and minimum (/termination) of the putative IPSP. (D), Density plot of the IPSP amplitudes for the control case (median = 0.5 mV). Inset shows 3 sample IPSPs of different amplitudes (0.4, 0.87, and 1.3 mV) recorded from the same neuron. (E), Left, probability to find an IPSP in the 10 ms preceding the spike. Fractions on top of the bar graph are PIRS/total number of spikes. Data are represented as mean ± SD, n = 6 neurons for the control condition and n = 6 neurons for the intracellular picrotoxin condition. Total time of the recording 600 s for each condition). Right, IPSP amplitude in control condition (black) and with intracellular picrotoxin (gray). (F), PIRS delay for small (<0.5 mV IPSP amplitude) and large (>0.5 mV) IPSP amplitudes for control (black, n = 236) and intracellular picrotoxin (gray, n = 49) conditions. Black horizontal line depicts statistically significant difference (P < 0.05) error bars represent SEM.

Computational Model

The biophysical model presented here builds on previous models (Fransén et al. 2004; Ferrante 2012; Hasselmo 2013) and expands them by using a full set of 22 fully reconstructed mEC-LII-SC morphologies (Garden et al. 2008) and 13 types of active properties (Fransén et al. 2004). Model, neuronal morphologies, ion channels and simulation files are publically shared in the ModelDB section of the SenseLab database (accession number: 155708).

Model and simulations were implemented and run in NEURON Simulation Environment (Hines and Carnevale 1997) v7.3 with variable time step on a 32-bit Xeon (2.53 GHz) quad-core Dell Precision T3500 under Windows 7. Active properties included in the model: a variant of the Hodgkin–Huxley formalism consisting of a fast sodium channel (I_Naf) and an outward delayed rectifier potassium current (I_Kdr); 4 types of I_h kinetic conductances to represent a continuous variation along mEC DV cells (I_hd and I_hv) and the simultaneous presence of fast and slow (I_hf and I_hs) properties in each cell, as previously described in mEC SCs (in Table1 of Shay et al. 2012); a slowly inactivating persistent sodium channel (I_NaP); 3 calcium-activated currents, an afterhyperpolarization potassium current (I_Kahp), a non-selective cation current (I_CAN), and potassium current (I_KCa); a long-lasting voltage-sensitive calcium current (I_CaL); dynamic extracellular calcium accumulation (cacumm); and a passive leak (I_leck) for sodium, potassium, calcium, chloride, and magnesium currents. After fine tuning the model with the above mentioned currents we turned off all the currents that were unnecessary to replicate the experimental evidences. Therefore, for all simulations shown in this article we used a basic set of 6 ion channels: I_Naf, I_Kdr, I_hd, I_hv, I_hf, and I_hs. Unless otherwise noted, active and passive properties were uniformly distributed along the neuronal surface and their maximum conductances were tuned to fit the experimental results. The artificial uniform distribution of channels was to allow evaluation of potential effects of h current with uniform conditions. Ionic channel kinetic parameters have been previously published (Shay et al. 2012) (and can also be retrieved from senselab.yale.med.edu/ModelDB).

Results

Strong Sag Responses and High Resonant Frequencies Suggest Prominent I_h Conductances in SCs

To probe the ability of mEC-LII-SCs (Fig. 1A) to generate PIRS in vivo in anesthetized rats we recorded for 100 s the intracellular voltage of 15 cells from 15 different animals at peri-AP-threshold so that synaptic potentials could generate spontaneous APs (Fig. 1B). We then stimulated each cell on average four times (number of trials = 59) with a 1000 pA hyperpolarizing current step lasting 2 s (as Fig. 1B inset). The hyperpolarizing stimulation produced pronounced sag responses in all SCs, and PIRS in about half of the trials (29 out of 59 trials, 49.1%). This result suggests that strong hyperpolarizing inhibitory input could generate PIRS in mEC-LII-SCs in vivo.

Figure 1.

In vivo and in vitro, evidence and pharmacological modulation of putative post-inhibitory rebound spikes (PIRS). (A), Left, parasagittal histological slice after in vivo recording, mEC-LII cell bodies are visible, hippocampus (HC), lateral entorhinal cortex (LEC), perirhinal cortex (PRh), and visual areas (VI/II) are also labeled for reference. Right, higher magnification showing a morphological identification of a biocytin-labeled mEC-LII-SCs and mEC Layer I–III (LI/III). (B), Left, Voltage traces showing spontaneous spikes, and a post-inhibitory rebound spike (current step amplitude = −1000 pA). Right, Post-inhibitory rebound spike (PIRS) magnification showing sag and rebound potentials. Spike truncated. (C), Neuronal resonance before (left) and after (right) in vitro bath administration of I_h blocker (ZD7288). Bottom right inset shows change in peak resonant frequency after blocking I_h. (D), Number of PIRS before (black) and after blocking I_h (gray) for 2 distinct neurons (empty vs. filled circles). Lines are second order polynomial fits to Cell#50 (solid line) and Cell#51 (dashed line) with R² values reported on top. (E), Sag ratio before (black) and after blocking I_h (gray) for 2 distinct cells (empty vs. filled circles). Lines are linear fits, with the lower limit of R² reported for the 2 cells in control condition (black lines above) and during ZD7288 administration (gray lines below). Top left inset, example of between-cells time constant variability as a function of stimulus amplitude. Bottom right inset, mEC-LII SC time constant when ZD7288 was applied.

I _h Induces Rebound Spiking Following Inhibitory Inputs (PIRS)

I _h is one of the possible intrinsic mechanisms responsible for sag and rebound potentials. During in vitro experiments, we tested whether blocking I_h (with ZD7288) in high (7.8 Hz) and in low (1.94 Hz) resonant frequency SCs would be sufficient to stop the cells ability to produce PIRS for the all range of inhibitory inputs. Blocking I_h prevented the 2 SCs from showing resonance (Fig. 1C).

Blocking I_h also made SCs unable to generate PIRS in response to hyperpolarizing current steps of different amplitudes (Fig. 1D). As expected, in both cells ZD7288 significantly reduced the amplitude of the sag responses as a function of the inhibitory stimulus amplitude (Fig. 1E) and slowed down their sag time constant (Fig. 1E, insets). For both cells (with or without ZD7288) the amplitude of the stimulus was highly predictive (linear correlations, R² > 0.86) of the amplitude of the sag. These results suggest that in mEC-LII-SCs, I_h is a necessary mechanism for PIRS generation.

Spontaneous In Vivo APs are Often Preceded by IPSPs, Suggesting They may be PIRS

We then analyzed the 10 ms preceding the generation of each spontaneous AP during in vivo recording (378 spikes coming from 5 distinct cells, total recording = 600 s) to look for evidence of IPSPs immediately preceding the APs (Fig. 2A,B). An IPSP was defined as the largest hyperpolarizing voltage deflection (larger than −0.2 mV) within the 10 ms preceding the spike. To automatically identify the IPSPs we used a 0.5 ms sliding window to calculate the average derivative of the voltage in the 10 ms preceding the spike. The amplitude of each IPSP was calculated by subtracting the IPSP minimum (the voltage value where the derivative of the voltage crossed 0 upward) from its maximum (the voltage value where the derivative of the voltage crossed 0 downward) as in Figure 2C. The delay of the spike was calculated from the IPSP onset (i.e., maximum voltage value). We expected a monotonically upward change in the graded potential preceding the AP threshold, but surprisingly, we found that most of the APs (62.4%) were immediately preceded by at least one putative IPSP (Fig. 2B–D). To ensure that the hyperpolarizing inflections in the membrane potential were GABAergic in nature (rather than due to the absence of excitation) intracellular picrotoxin was used to block GABA_A receptors. Intracellular picrotoxin reduced the number of IPSPs preceding the AP to 13.5% (Fig. 2E). Notably, intracellular picrotoxin did not significantly affect the average amplitude of the IPSP, but only the likelihood that a spike was a putative PIRS (Fig. 2E). Perhaps because picrotoxin was administered intracellularly, it is possible that due to limits of diffusion, a small subset of GABA_A receptors (the ones that were more distal from the soma/pipette) were not blocked by Picrotoxin, hence their amplitude remained the same. These results (Fig. 2E) hint that in vivo most of the APs in mEC-LII-SC are immediately preceded by one or more IPSPs. Furthermore, this phenomenon can be down-regulated by intracellular picrotoxin suggesting that the biophysical mechanism responsible for the in vivo emergence of PIRS may be the GABA_A (rather than GABA_B) receptor.

We also tested whether IPSPs were facilitating the AP generation by asking if the amplitude of the IPSP predicted the timing of the spike (Fig. 2F). In the control condition, IPSPs larger than the median (0.5 mV) were followed by significantly shorter PIRS delays (4.0 ± 2.63 ms, n = 118) compared with IPSP smaller than the median that produced on average longer PIRS delays (4.8 ± 2.75 ms, n = 118). This result suggests that larger IPSPs play a functional facilitating role in the generation of the APs. With picrotoxin the significance of this relationship was lost and the few PIRS recorded were significantly slower compared with the control condition, both for small and large IPSPs (Fig. 2F). Because we adjusted the base current to keep the neuron at peri-AP-threshold, the firing output between different experiments (e.g., between control and picrotoxin conditions) is not comparable.

When mEC-LII-SCs approach the threshold to generate an AP, timely arrival of IPSPs could have an excitatory effect due to the depolarizing phase of their rebound potentials. Furthermore, GABA may differentially affect the cellular threshold to generate an AP, as well as the cellular firing output in response to the same excitatory input. In order to test these hypotheses and circumvent the limitations of our previous approach we slowly (linearly) increased and then decreased the excitatory current injected in the cells (in a ramp stimulation) and recorded the threshold necessary to generate an AP in vivo, in control and in intracellular picrotoxin conditions. Surprisingly, blocking GABA_A receptors resulted in higher current thresholds necessary to initiate an AP (Supplementary Fig. 1A,B) while simultaneously making these cells more excitable across all input strengths, both at the single cell (Supplementary Fig. 1C left panel) and at the population (Supplementary Fig. 1C right panel) level. This last line of evidence suggests that GABA inputs can make mEC-LII-SCs more likely to fire an AP while concurrently constraining their maximum firing rate as well as their total number of spikes.

Neuronal Voltage State as Well as Inhibitory Stimulus Duration and Amplitude Affect the Delay and the Number of PIRS

The delay of the spike in response to an inhibitory input can be differentially affected by the present neuronal membrane voltage, as well as by the amplitude and duration of the inhibitory inputs. This kind of analysis requires the exploration of a large dataset of neuronal input/output relationships that are simply unattainable in vivo, hence we recorded intracellularly from in vitro slices of mEC-LII-SCs (Fig. 3A). Specifically, we systematically and independently altered the amplitude and duration of a hyperpolarizing (current step) stimulus, as well as the holding voltage of the cell to study how these changes affected the timing of the PIRS (Fig. 3B). It is important to notice that these current step stimuli are intended to mimic barrages of inhibitory stimuli of different durations and amplitude, not single inhibitory synapses. Independently of the stimulus duration and the holding voltage, larger amplitude hyperpolarizing inputs systematically produced PIRS with shorter and less variable delays (Fig. 3C,D), with a consistent shape of the function following a power law as presented in the figure legend. This was one of the most important properties to test for modeling.

Figure 3.

In vitro, single cell quantification of stimulus-dependent changes in post-inhibitory rebound spike delay. (A), Photomicrograph example of a mEC horizontal brain slice (×2 magnification) with inset (on the bottom) showing a ×20 magnification of a SC anatomy and morphology. (B), Hyperpolarizing current stimulation protocol. Holding current, stimulus duration, and amplitude were systematically changed to investigate their impact on the post-inhibitory rebound spike delay. (C), Top, Modulation of PIRS delay (y-axis) by stimulus amplitude (x-axis) and stimulus duration (different symbols) at −61 mV. Fitting lines are power functions. For 50-ms stimulus duration, PIRS delay = 5.57 × (stimulus amplitude)^−0.834, while for 20-ms stimulus duration, PIRS delay = 28552 × (stimulus amplitude)^−2.036. (D), Top, Modulation of PIRS delay (y-axis) by stimulus amplitude (x-axis) and holding membrane voltage (different symbols). At −59 mV, PIRS delay = 10.333 × (stimulus amplitude)^−0.873, while at −64 mV, PIRS delay = 1929.7 × (stimulus amplitude)^−1.656. (C–D), Bottom panels, depict a different cell, to show examples of between-cell variability.

Across all the stimulus amplitudes, shorter duration inhibitory stimuli resulted in longer PIRS delays (Fig. 3C). For instance, halving the duration (from 40 ms to 20 ms) of a 500-pA stimulus made its PIRS delay ∼270% longer (from ∼37 to ∼100 ms). This effect was more substantial for weaker stimuli and diminished as inputs grew stronger. Similarly, for the same input amplitude (500 pA), a mere 5 mV difference in the baseline membrane voltage (−59 and −64 mV) produced a 20 ms difference (i.e., 44% slower) in the delay of the PIRS (from 45 to 65 ms, respectively) as shown in Figure 3D, top panel. Hence, compared with hyperpolarized states, more depolarized voltages (e.g., −59 mV) produced shorter PIRS delays but this was true only with larger stimulus amplitudes (e.g., 500 pA). Indeed, more depolarized states were usually the only ones enabling PIRS with weaker stimuli (e.g., 200 pA) and those produced much longer PIRS delays (120 ms). This is an important consideration for interpreting the cell population results that will be presented later on in Fig. 4C, where depolarized states on average produced slower and more variable PIRS. Furthermore, intrinsic cellular differences (Fig. 3C,D, top vs. bottom panels) made the delay in PIRS response to a similar input duration (e.g., 20 ms) or holding voltages highly variable across cells for all stimulus amplitudes. The relationship between the amplitude of the stimulus and PIRS delays (at each specific stimulus duration and voltage state), can be described by power laws (0.6 < R² < 0.99). These data suggest that across all stimulus amplitudes, PIRS have shorter delays and are temporally more precise when the cell is depolarized and when the afferent hyperpolarizing inputs are stronger or longer lasting.

Given the same inhibitory input mEC-LII-SCs may vary widely in the number of PIRS generated (Supplementary Fig. 2). These differences may play a role in the cellular firing frequency output, as well as in the functional rage of inhibitory input to which the cell responds. We asked what range of stimulus amplitudes allows the transition from 0 to 1 (or more) PIRS at different stimulus durations. Long-lasting stimuli (e.g., 50 ms) can recruit a cell with weaker stimulus amplitudes (Supplementary Fig. 2B top left panel). Moreover, compared with brief inputs (e.g., 30 ms), long inputs (e.g., 50 ms) allow for more rapid transitions from 0 to multiple PIRS (265 vs. 436 pA for 20 and 50 ms, respectively). Some mEC-LII-SCs are able to functionally span a wide range of input amplitudes (∼600 pA) while others can only operate in a very narrow range (∼230 pA) saturating their output (number of elicited spikes) fairly quickly (compare Supplementary Fig. 2B top left vs. bottom left panel). For specific input amplitudes, long-lasting stimuli tend to produce more PIRS. Conversely, compared with baseline currents that shift the membrane potential to peri-AP-threshold voltages, hyperpolarized membrane potentials recruited cells with weaker inputs and simultaneously extended the functional range of input amplitudes to which the cell responds (Supplementary Fig. 2B right). Furthermore, in agreement with the fact that more hyperpolarized states have more I_h activated, they tend to fire more PIRS given the same inhibitory stimulus.

Efficiency of Inhibitory Stimuli as a Mechanism for Spike Generation in mEC SCs

How efficient is the inhibitory-driven mechanism compared with the traditional depolarization-induced mechanism in generating APs? To answer this question we compared the outputs (F–I curves) of depolarizing (Supplementary Fig. 3A) and hyperpolarizing (Fig. 3 and Supplementary Fig. 2) current steps. Similar to PIRS, depolarization-driven AP delays were also highly affected by intrinsic cellular differences (Supplementary Fig. 3B, left and right panels). For instance, given the same holding voltage (−59 mV) and stimulus amplitude (230 pA), Cell#73 was about five times faster than Cell#17 in generating an AP (5 vs. 26 ms, respectively). At the single cell level, most depolarization-induced APs were fast (<20 ms) if compared with PIRS (see Fig. 3 for comparison). This is due to the fact that even when starting from the same holding voltage, depolarizing stimuli bring the potential much closer to threshold. This single cell result was confirmed at the population level (Supplementary Fig. 3D left). On average, the cells transitioned from 0 to multiple spikes in a narrower range of stimulus amplitudes for the excitatory stimuli (Supplementary Fig. 3C) compared with the inhibitory ones (Supplementary Fig. 2B). Surprisingly, small (<200 pA) inhibitory stimuli were more effective than excitatory stimuli in eliciting a spike (Supplementary Fig. 3D, right), but the opposite was true for larger stimuli (>200 pA). These results suggest that although with a slower time course, inhibition in mEC-LII-SCs can be more effective than excitation in eliciting APs.

Intrinsic Differences Between SCs and PCs Affect PIRS Firing Properties

Intrinsic differences between and within cell classes may affect the PIRS properties. To quantify these differences we recorded how changes in stimulus amplitude, stimulus duration, and overall cellular voltage state affect the population of mEC-LII-SCs (n = 77; Fig. 4A left) and mEC-LII/III-PCs (n = 7; Fig. 4A right). To perform this analysis, an extensive dataset of current step experiments was collected, n = 9276 for mEC-LII-SCs and n = 2727 for mEC-LII/III-PCs. The stimulus amplitude produced only minor differences between SCs and PCs in the PIRS delay (Fig. 4B, top), but greatly affected the differences in the number of PIRS (Fig. 4B, bottom). Indeed, 1 nA change in stimulus amplitude (25–1000 pA) produced small differences in the average number of PIRS (from 0.14 to 0.52) of PCs when compared with SCs (from 0 to ∼2 PIRS). These results suggest that compared with PCs, SCs are much more responsive to strong inhibitory inputs; but when PCs fire in response to inhibition their timing is similar to SCs. Similarly, the PIRS firing output of the SCs is more voltage-dependent and prefers more depolarized voltages (around −54.5 mV) while PCs reach their peak PIRS firing rate at about −57.7 mV (Fig. 4C bottom). For instance, at −70 mV about one-fourth of both PC and SC trials generated PIRS, but while PCs did not dramatically change that number across the range of membrane voltages, SCs quadrupled their rate of PIRS output at −50 mV. These data suggest that at the population level as SCs become more depolarized, they fire a greater number of PIRS compared with PCs. Additionally, the delay of PIRS in SCs (and PCs) increases as the membrane potential depolarizes; for instance, at −65 mV the average PIRS delay of SCs is ∼35 ms, while at −40 mV it slows down to ∼80 ms. Lengthening the duration of the stimulus led to a monotonic decrease in the PIRS delay for SCs and PCs (Fig. 4D top). Despite this similarity, compared with PCs, SCs tended to fire more PIRS when the stimulus duration was between 30 and 60 ms (Fig. 4D, bottom) and significantly less when that duration was both increased and reduced. This time course was consistent with the average SC sag time constant (see Fig. 1E inset) that provided the extra driving force to elicit PIRS.

Dorso-ventral Differences in SCs and PCs Relevant to Grid Cell Firing

SCs have different resonant and intrinsic properties that vary along the mEC DV-axis (Giocomo et al. 2007; Giocomo and Hasselmo 2009). For this reason, we decided to investigate how SCs and PCs resonance frequency at rest (around −60 mV) and their mEC DV position affected the rebound spiking properties. Compared with PCs, SCs tend to resonate at higher frequencies (Fig. 5A). Unlike PCs, the average number of PIRS for SCs was affected by the DV position (Fig. 5B). Dorsal cells (2.6 mm) fired on average 0.38 spikes on each trial (38%) while ventral (6.7 mm) fired on average 0.71 spikes for each trial (71%). PIRS of SCs came at slower and more variable delays in more ventral positions while PCs showed faster delays along the same axis and kept their noise level constant. On average, PIRS of neurons (for both PCs and SCs) resonating at high frequencies were quicker and more temporally constrained (Fig. 5). Consistent with previous results (Schreiber et al. 2004) PCs on average exhibited lower resonance strengths (i.e., q-values (Hutcheon et al. 1996)) compared with SCs, therefore, even PCs with high resonant frequencies (>3 Hz) had an overall weak resonant response. Overall these results suggest that PIRS properties in SCs are modulated along the DV axis and that such gradients are consistent with the gradient in grid cell scaling seen along the same axis (Hafting et al. 2005; Brun et al. 2008).

Given the same inhibitory input, SCs produced a larger and quicker sag response (compared with PCs) (Supplementary Fig. 4A), which differentially affected the cell's probability to generate a PIRS. In particular, for weak inputs the sag amplitude of SCs and PCs was similar but as the input grew larger SCs produced a more pronounced sag response (Supplementary Fig. 4B left). Similarly, PCs sag time constant was a lot slower compared with SCs and the time constant of SCs became faster for stronger inputs suggesting a voltage-dependent effect that was not present in PCs (Supplementary Fig. 4B right). Indeed, even at the population level the amplitude of the SC sags and their time constant were highly correlated with the average number of PIRS (Supplementary Fig. 4C,D). The same was not true for PCs. Consistently, SCs with large and fast sag responses produced faster PIRS; while this relationship was less clear in PCs. The striking difference in PCs and SCs sag and resonant responses suggest that I_h is expressed more in SCs.

PIRS Dendritic Propagation and mEC DV Differences Relevant to Grid Cells

The site of initiation and the direction of propagation of an AP are crucial to understand the integrative actions of mammalian neurons in the CNS. This is because multiple AP initiation sites within a neuron may explain how neuronal firing may be controlled by both excitatory and inhibitory inputs as well as by their active properties. To shed some light on this issue we implemented 22 biophysically realistic computational models (Supplementary Fig. 5A,F) of mEC-LII-SCs. The model was validated against different sets of experimental data, such as, I_h resonance properties at the cellular level (Supplementary Fig. 5B,C), PIRS timing response to different stimulus amplitudes (Supplementary Fig. 5D,E), and mEC DV differences in resonance frequency (Supplementary Fig. 5F,G).

Some feed-forward inhibitory interneurons (e.g., PV+ cells) make synaptic contacts in the perisomatic region of principal cells while others may target the dendritic region (e.g., SOM+ interneurons). This may lead to distinct functional consequences in buffering the neuronal input/output of principal cells (Ferrante and Ascoli 2015). Previous studies (Stuart et al. 1997) have shown that in the central nervous system, inhibition is concentrated precisely at the location where it is best suited to inhibit action potential initiation (i.e., close to the hillock segment). On the other hand, the expression of large I_h conductances in mEC stellate cells could enable the generation of PIRS. This could have important consequences for the synchronization of action potential between excitatory inputs arriving in the dendrites and inhibitory inputs arriving in the somatic region. For this to happen, PIRS need to be able to travel from the soma back to the dendrites. Our simulations (Fig. 6A) suggest that in the artificial case of uniform distribution of channels mEC cells could show backpropagation of PIRS (Fig. 6B,C). Unlike other currents, such as I_KA (Migliore et al. 2005), but consistent with previous experimental data on AP backpropagation in hippocampal CA1 PCs (Magee 1998), increasing I_h distribution with the distance from the soma only moderately affected back propagation of PIRS in this artificial case designed to test effects of h current (Fig. 6C).

Figure 6.

Simulations, effects of I_h dendritic spatial distribution on PIRS backpropagation. (A), Schematic of the back propagation protocol in the computational model. PIRS back propagation was studied by eliciting a somatic PIRS with a brief hyperpolarizing current pulse. Stimulating electrode is placed somatically while voltage attenuation is recorded in each of the 84 dendritic compartments. Inset diagram shows the 2 dendritic distributions of I_h used, uniform and increasing with the distance from the soma (as experimentally observed in CA1 Pyramidal neurons in the hippocampus). (B), Voltage traces of a PIRS recorded locally in the soma (black) and distally in a dendritic branch (gray). Note that the 2 voltage traces are almost overlapping, showing little attenuation in the backpropagation of the PIRS from the soma to the distal dendrite. (C) The plot shows the peak AP amplitude along the dendrites of a mEC stellate cell model. Voltage attenuation with distance from the soma (back propagation) for uniform (left) and increasing distribution of I_h (right), as shown in the inset of panel A. This graph shows how the peak voltage of the spike differs during backpropagation from the soma into the distal branches.

We then asked if the intrinsic differences in SC neuronal morphologies (Garden et al. 2008) or I_h kinetic properties (Shay et al. 2012) recorded experimentally along the DV axis of the mEC were responsible for the DV gradient observed in PIRS delay (Fig. 5B top left panel). Neuronal morphology and I_h properties played a compensatory effect in regulating the PIRS delay, with the I_h effect more closely resembling the experimental trend (Supplementary Fig. 6) while the morphology opposed the trend. Forward propagation of PIRS (Supplementary Fig. 7A,B) on the other hand, allowed the stimulated branch to fire twice, first in response to the inhibitory stimulus (PIRS) and later, when the backpropagating PIRS reinvaded the branch after reaching the soma. This mechanism could be used for selectively strengthening synapses of branches that fire PIRS. When the dendritic distribution of I_h was uniform, a narrow range of stimulus amplitudes (50 pA, from 425 to 475 pA) enabled most branches (from 25% to 93%) to fire PIRS (Supplementary Fig. 7C). On the contrary, increasing the distribution of I_h with distance from the soma made the dendrites less prone to generate PIRS and even strong hyperpolarizing stimulation (1000 pA) elicited PIRS in only 39% of the branches. This prediction seems to suggest that the distance-dependent rule of I_h distribution observed in other hippocampal dendrites (Magee 1998) would impair the ability of distal dendrites to generate PIRS but it is also possible that compensatory (distance-dependent) changes in the distribution/expression of AMPA, NMDA (Menon et al. 2013), or GABA receptors could normalize this difference between proximal and distal branches. Indeed, despite this difference in the current necessary to elicit a PIRS, the voltage thresholds in all dendrites were remarkably similar for the 2 dendritic distributions of I_h (Supplementary Fig. 7D). This result suggests that expression/regulation of I_h could be a potential mechanism to enhance or counteract the dendritic ability to fire PIRS. Our model finally suggests that unlike in the somatic recordings, dendrites would require strong activation of GABA_B receptors which have lower equilibrium potential (−95 mV) to elicit spikes in most (70%) branches, assuming uniform I_h distribution (Supplementary Fig. 7D) while GABA_A receptors would only produce PIRS in a small percentage (10%) of branches.

It is important to emphasize that despite the different spatial distribution of I_h (uniform or linearly increasing with distance from the soma) the 2 models that we present here (in Fig. 6 and Supplementary Fig. 7) have the same total amount of I_h conductances expressed in the cell. Our model suggests that, while a moderate amount of I_h is necessary to generate PIRSs, too much I_h may prevent them from happening. This is consistent with the fact that increasing the I_h conductance lowers the cellular input resistance (van Welie et al. 2004). Indeed, lowering the input resistance means that larger hyperpolarizing inputs are necessary to displace the same amount of voltage and generate a PIRS. This is particularly an issue in distal dendrites particularly if we assume that the spatial I_h distribution linearly increases with distance from the soma.

Can the Amplitudes of the Synaptic Conductances and Their Temporal Interactions Predict the Generation of PIRS?

In experiments, we were interested in testing the effect of more realistic synaptic stimuli (i.e., double exponential kinetic currents for the rise and decay phases) on stellate cells PIRS generation in vitro. To test this in experiments, we somatically delivered synaptic inputs (Fig. 7A) of increasing amplitudes (from −25 pA to −500 pA, Δ = −25 pA) separated by a 500-ms baseline current. For each cell we recorded 20 trials, each 12-s long at peri-AP-threshold. These experiments (see Fig. 7A–B) show that the probability of PIRS following single synaptic potentials goes up when the amplitude of the IPSP increases from −25 to −100 pA, values consistent with previous experiments (Deng and Lei 2007). The recruitment of synchronized GABAergic cells is common in neocortex (Benardo 2007). We also tested the effect of synchronized incoming GABAergic synapses using larger hyperpolarizing synaptic currents (100–500 pA). Going from a −25 to a −500 pA in synaptic amplitude more than tripled the probability to generate a PIRS (from 65% to 330%) with a clean linear correlation (R² = 0.79).

We also wanted to test how temporal summation of inhibitory synaptic inputs affects the generation of PIRS? To answer this question we increased the number of synaptic inputs (1–10 synapses, 100 pA each in amplitude) delivered within an interval of 60 ms and recorded the probability of generating a PIRS (Fig. 7C–D). In this context, 100% spike probability refers to the spontaneous firing rate without hyperpolarizing current stimulation. Going from 1 to 10 synaptic inputs doubled the probability of generating a PIRS (from 250% to 500%) with a clean linear correlation (R² = 0.69). Data reported in Figure 7B,D are recorded at peri-AP-threshold but because their holding voltages were different, it is difficult to compare these 2 datasets. In short, these data suggest that realistic synaptic inputs might have a strong effect in generating PIRS in SC near threshold. Particularly, this last piece of evidence suggests that strong and temporally clustered synaptic inputs may play a synergistic role in enabling SC to fire PIRS.

Discussion

Post-inhibitory rebound is a period of increased neuronal excitability following the cessation of inhibition. When the hyperpolarization generated by the activation of inhibitory synapses is removed the slow offset of the I_h current increases the level of a slow depolarizing current, giving rise to the characteristic sag and overshoot, and providing a mechanism for generating post-inhibitory rebound spikes (PIRS). We performed in vivo and in vitro intracellular recordings (supported by a biophysically realistic computational model) modulating the neuronal holding voltage, the amplitude, and duration of hyperpolarizing stimulation in cells from slices at different positions along the mEC DV axis. Furthermore, this study links inhibitory hyperpolarizing input features (i.e., amplitude and duration) and cellular properties (i.e., neuronal morphology and ion channels) to investigate the emergence of spiking outputs (PIRS) possibly relevant for spiking responses of grid cells.

Recent experimental data suggest that principal (stellate) cells in the mEC-LII grid cell network, mostly receive recurrent inhibitory inputs that, coupled with uniform excitation, would be sufficient to generate stable grid cell firing (Couey et al. 2013). Our findings build on these observations by proposing that mEC-LII-SCs may fire in response to inhibition, using their active property, I_h, to produce depolarizing rebounds and spikes. Septal neurons project into entorhinal cortex (Alonso and Köhler 1984) including projections from medial septal GABAergic cells (Köhler et al. 1984; Mizumori et al. 1992). Additionally, during spatial navigation the firing frequency of cells in the medial septum is modulated by speed (King et al. 1998) and head direction (Welday et al. 2011). These GABAergic inputs from medial septum could regulate the timing of mEC interneurons to cause PIRS at specific time points on the theta cycle (Shay et al. 2015). The ability of the medial septum to relay speed and directional information into the mEC can be a potential mechanism for grid cell formation (Hasselmo 2013). For this reason, we tested the modulation of the inhibitory inputs into the mEC neurons.

In particular, we believe the in vivo data (Fig. 2) to be particularly relevant because it suggests that the generation of APs in vivo, in mEC-LII-SCs might be regulated by the activity of inhibitory interneurons. Although this seems reasonable there are at least 2 alternative explanations to why SC firing tends to be preceded by IPSPs: (1) that fast spiking interneurons and SCs share the same source of excitatory inputs generating spikes in both cell types, FS cells fire before stellate cells and project to them; and (2) that reciprocal connections between SCs and interneurons generate fast oscillations where SCs spiking always follows inhibitory input, but is in fact caused by external excitatory inputs to SCs. Our data does not differentiate between these alternative and nonmutually exclusive hypotheses but we believe that probability of generating PIRS may be enhanced in feed-forward inhibitory networks where I_h is expressed. Also, Figure 2B–D shows an ongoing cellular depolarization prior to spiking regardless of IPSP input, in both control and picrotoxin conditions. Thus, while PIRS may contribute to the generation of APs in mEC SCs, these data do not suggest that they are either necessary or sufficient.

Furthermore, the fact that we observed in Fig. 4D a narrow stimulus duration that enhances cellular response (or PIRS generation) is consistent with in vivo recordings showing that mEC-LII-SCs preferably fire in a narrow phase of theta (Quilichini et al. 2010; Domnisoru et al. 2013; Schmidt-Hieber and Häusser 2013) and in vitro results showing that the preferred phase-locking of spikes to theta inputs is enhanced by excitatory and inhibitory synaptic inputs (Fernandez et al. 2013; Rotstein et al. 2005; Stark et al. 2013). The results are also consistent with recent in vitro and in vivo data from our laboratory showing that SCs have a specific phase range of the theta cycle (i.e., between the peak and subsequent descending zero crossing) where incoming hyperpolarizing synaptic inputs elicit PIRSs (Shay et al. 2015; Tsuno et al. 2015). Interestingly, a recent study (Tang et al. 2014) suggests that weakly theta-locked spiking border cells are mostly mEC-LII-SCs, and strongly theta-locked spiking grid cells are mostly mEC-LII-PCs.

Surprisingly, unlike our previous observations in simulations (Migliore et al. 2004, 2005; Ferrante et al. 2013) showing that excitatory inputs easily generate dendritic spikes on tiny dendrites (due to high input impedance) when coupled with I_h, here we report that PIRS are more easily generated on larger volumes (i.e., perisomatic regions), due to the strong dendritic compartmentalization of I_h.

Together, our data suggest that the synergistic interaction between strong (and/or highly timed) incoming hyperpolarizing inhibitory inputs and intrinsic properties of I_h could allow for the emergence and modulation of grid cell firing. In general, our in vivo and in vitro results do not challenge the mainstream hypothesis that grid cells require the excitatory driving force from the hippocampus (Bonnevie et al. 2013). They, on the other hand suggest that excitatory inputs may work in tandem with inhibitory inputs activating I_h to promote grid cell firing during spatial navigation.

Supplementary Material

Supplementary material can be found at http://www.cercor.oxfordjournals.org/online.

Funding

This work was supported by National Institutes of Health grants MH60013 and MH61492 awarded to M.E.H.