J Comput Neurosci (2010) 29:509–519 DOI 10.1007/s10827-010-0214-y

Computational modeling of GABAA receptor-mediated paired-pulse inhibition in the dentate gyrus Peter Jedlicka & Thomas Deller & Stephan W. Schwarzacher

Received: 1 August 2009 / Revised: 11 December 2009 / Accepted: 7 January 2010 / Published online: 23 February 2010 # Springer Science+Business Media, LLC 2010

Abstract Paired-pulse inhibition (PPI) of the population spike observed in extracellular field recordings is widely used as a read-out of hippocampal network inhibition. PPI reflects GABAA receptor-mediated inhibition of principal neurons through local interneurons. However, because of its polysynaptic nature, it is difficult to assign PPI changes to precise synaptic mechanisms. Here we used a detailed network model of the dentate gyrus to simulate PPI of granule cell action potentials and analyze its network properties. Our computational analysis indicates that PPI results mainly from a combination of perisomatic feed-forward and feedback inhibition of granule cells by basket cells. Feed-forward inhibition mediated by basket cells appeared to be the most significant source of PPI. Our simulations suggest that PPI depends more on somatic than on dendritic inhibition of granule cells. Furthermore, PPI was modulated by changes in GABAA reversal potential (EGABA) and by alterations in intrinsic excitability of granule cells. In summary, computer modeling provides a useful tool for determining the role of synaptic and intrinsic cellular mechanisms in paired-pulse field potential responses. Keywords GABA . Network . Perisomatic inhibition . Basket cell . Feed-forward . Feedback inhibition Action Editor: Frances K. Skinner Thomas Deller and Stephan W. Schwarzacher joint last authors Electronic supplementary material The online version of this article (doi:10.1007/s10827-010-0214-y) contains supplementary material, which is available to authorized users. P. Jedlicka (*) : T. Deller : S. W. Schwarzacher Institute of Clinical Neuroanatomy, Goethe-University, NeuroScience Center, 60590 Frankfurt am Main, Germany e-mail: [email protected]

1 Introduction In the hippocampus, GABAergic synapses act as the major sources of inhibition (Freund and Buzsáki 1996; Coulter and Carlson 2007; Houser 2007). Fast inhibitory transmission is predominantly mediated by ionotropic GABAA receptors (GABAARs). The functional integrity of inhibitory transmission is important for the precise regulation of neuronal excitability (Atallah and Scanziani 2009). Therefore, it is important to study delicate control mechanisms which exist in neurons to regulate the function of inhibitory synapses. Paired-pulse measurements of evoked extracellular field potentials are often employed in anesthetized transgenic animals to study functional changes of GABAergic inhibition and neuronal excitability in vivo (e.g. Stoenica et al. 2006; Jedlicka et al. 2009b; Winkels et al. 2009). In the dentate gyrus, electrical stimuli delivered to perforant path elicit field excitatory postsynaptic potentials (fEPSPs). These field potentials are generated by granule cells (GCs) as the perforant path stimulation activates excitatory synapses located along GC dendrites in the dentate outer molecular layer. The slope of the fEPSP is a measure of synaptic strength at perforant path-granule cell synapses. If the stimulation intensity reaches the threshold for GC action potentials, fEPSPs are accompanied by a population spike. The size of the population spike reflects the number and synchrony of discharging GCs (Andersen et al. 1971). Paired-pulse inhibition (PPI) of the population spike is widely recognized as a read-out of hippocampal network inhibition as it reflects GABAAR mediated inhibition of principal neurons through local interneurons in the neural circuit (Sloviter 1991; Tuff et al. 1983; Oliver and Miller 1985; Lomo 2009). In the dentate gyrus, paired-pulse stimulation of perforant path inputs results in population spike depression at short inter-stimulus intervals (PPI) followed by facilitation at longer intervals (paired-pulse

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disinhibition, PPDI; Fig. 1). PPI of GC spikes occurs due to the summed action of the GABAAR-dependent inhibitory postsynaptic currents (IPSCs) generated by inhibitory circuits in the dentate gyrus. PPDI (facilitation) of granule discharges is thought to be the result of various mechanisms including the reduction of GABAergic inhibition mediated by presynaptic GABABRs and rebound GC firing due to preceding hyperpolarization (Davies et al. 1991; Bliss et al. 2007). PPI has been shown to be a measure of the efficacy of GABAergic inhibition (Sloviter 1991; Moser 1996; Sayin et al. 2003; Zappone and Sloviter 2004; Naylor and Wasterlain 2005; Naylor et al. 2005). However, because of its polysynaptic nature, it is difficult to assign PPI changes to respective synaptic mechanisms. Therefore, here we used a detailed network model of the dentate gyrus (Santhakumar et

Fig. 1 GABAergic paired-pulse inhibition (PPI) in the dentate gyrus in vivo (a) Paired-pulse inhibition and disinhibition of the population spike (PPI/PPDI) in the dentate gyrus of wild-type C57/BL6 (WT) mice (n= 10). PPI reflects GABAergic network inhibition. Top: Sample traces represent paired-pulse responses showing PPI and PPDI at 20 ms and 60 ms inter-stimulus intervals, respectively. Calibration: 2 mV, 10 ms. The timing of stimuli corresponds to the timing of stimulation artefacts in the inset. Adapted from Jedlicka et al. 2009b. (b) Basic dentate gyrus circuitry: PP: perforant path, GC: granule cells, BC: basket cells, HC: hilar cells. For the reason of clarity, MCs are not shown although they were included in the simulations. PP-stimulation initiates feedforward excitation of GCs (PP → GC) along with feed-forward (PP → BC → GC) and feedback inhibition (PP → GC → BC (or HC) → GC) responsible for the PPI of GC spikes

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al. 2005; Morgan et al. 2007) to simulate PPI of GC action potentials and analyze its network properties. The aim of our study was to explore the following questions: Is PPI of spiking activity in the population of GCs predominantly mediated by feed-forward or feedback inhibitory circuits? Does PPI depend mainly on GABAergic inhibition in the dendritic or somatic region of the GCs? Do changes in intrinsic properties of GCs contribute to alterations of PPI? How do depolarizing shifts in GABAA reversal potential modulate paired-pulse GC responses?

2 Methods An established computational model of the dentate gyrus network was used as described before (Santhakumar et al. 2005; Winkels et al. 2009). Briefly, the network model contained 4 major dentate cell types: 500 granule cells (GCs, cells 0–499), 15 mossy cells (MCs, cells 506–520), 6 basket cells (BCs, cells 500–505), and 6 hilar cells (HCs, cells 521–526) representing a 2000:1 scaled-down version of the dentate gyrus (Santhakumar et al. 2005; Morgan et al. 2007). Simulation files were downloaded from the ModelDB website (Davison et al. 2004; Hines et al. 2004): http://senselab.med.yale.edu/modeldb/. All simulations were carried out with the NEURON simulation program (Hines and Carnevale 1997). For details of structural, passive and active properties of model cells, and synaptic and network parameters, see Santhakumar et al. (2005) and Table 1. Parameters used in our simulations were identical to parameters in the published network model, including GABAAR conductances. Similarly to the original model, perforant-path synapses were modeled using strong synaptic conductance (GPPtoGC = 20 nS, GPPtoBC = 10 nS, GPPtoMC = 2.5 nS) to ensure that all GCs will fire after a single stimulus. To explore the effects of the reduction of GABAA or AMPARs on dentate network activity, GABAA/ AMPAR conductances were diminished at GABAergic or glutamatergic synapses, respectively (see Results). To simulate PPI of GC discharges, double-pulse stimulation was delivered to perforant path synaptic inputs using varying inter-pulse intervals. For data analysis, the activity of the dentate gyrus network was visualized using spike time raster plots. The activity of GCs was presented as the percentage of the maximal number of GC action potentials. In vivo electrophysiological recordings in the dentate gyrus were carried out as described before (Winkels et al. 2009; Jedlicka et al. 2009a, b). Briefly, adult mice were anesthetized with an intraperitoneal injection of urethane. A bipolar stimulation electrode was positioned in the angular bundle of the perforant path. A recording electrode was placed in the granule cell layer of the dentate gyrus. To measure paired-pulse inhibition (PPI) and disinhibition (PPDI) of the

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Table 1 Selected parameters of dentate network GABAA synapses

PP (AMPA) synapses GC (AMPA) synapses EGABA

Sodium channels BC resting potential

gBC-GC (nS) BC-GC conv. gBC-MC (nS) gBC-BC (nS) gHC-GC (nS) HC-GC conv.

1.6 1.2±0.3 1.5 7.6 0.5 1.92±0.3

gHC-MC (nS) gHC-BC (nS) gPP-BC (nS) gPP-GC (nS) gGC-BC (nS) gGC-HC (nS) BC-GC (soma) (mV) HC-GC (dendrite) (mV) gNa (S/cm2) (mV)

1 0.5 10 20 4.7 0.5 −70 −70 0.12 (0.2 in MCs) −60

Some of these parameters were varied as explained in the relevant figures. See Santhakumar et al. 2005 for further details on passive, active and synaptic parameters and on network connectivity. conv. = convergence (mean ± SD) synapses/postsynaptic cell. In Fig. 6, maximal strength of PP inputs (gPP-BC = 20 nS; gPP-GC = 40 nS) was used (see Winkels et al. 2009). Note that somatic and dendritic inhibitory inputs had an average conductance of 1.92 nS and 0.96 nS, respectively (unitary synaptic conductance x convergence)

et al. 2003; Zappone and Sloviter 2004; Lomo 2009; Jedlicka et al. 2009a, b; Winkels et al. 2009). PPI of GC population spikes depends on GABAergic synaptic inhibition in the dentate network as it can be blocked or enhanced with GABAAR antagonists or agonists, respectively (Sloviter 1991; Steffensen and Henriksen 1991; Rich-Bennett et al. 1993; Bronzino et al. 1997; Kang et al. 2006). In anesthetized mice, PPI can be evoked using paired stimuli delivered to perforant path fibres at inter-pulse intervals of less than 40–50 ms (Fig. 1(a)). PPI is measured by decrease in the amplitude of the second population spike compared with first. The amplitude of the population spike reflects the number of synchronously firing neurons (Andersen et al. 1971; Varona et al. 2000). Thus, in the dentate network, paired-pulse stimulation recruits GABAergic inhibitory circuits suppressing GC discharges following the second stimulus. Interneurons involved in these inhibitory circuits control dentate gyrus excitability in vivo. 4.2 Computational modeling of paired-pulse inhibition

Differences between groups were statistically analyzed by an unpaired 2-tailed Student’s t-test. Group values are reported as means ± S.E.M unless stated otherwise.

A variety of changes in synaptic transmission or intrinsic cellular properties could contribute to alterations of PPI. We used a realistic computer model of the dentate circuit (Santhakumar et al. 2005; Morgan et al. 2007) to better understand the relationship between paired-pulse field responses and network/synaptic events. This network model comprises perforant path inputs and synaptic connections of granule (GC), mossy (MC), basket (BC) and hilar (HC) cells (see Methods and Santhakumar et al. 2005). Model neurons are based on realistic morphological and electrophysiological data. To simulate PPI of GC firing, network activity was initiated by a paired-pulse synchronous activation of perforantpath synaptic inputs to all postsynaptic cells with varying interpulse intervals. As the network model contains only GABAARs and PPDI is thought to depend partially on GABAB autoreceptors, we simulated only the PPI part of the PPI/PPDI curve. In the paired-pulse simulations, GC firing was suppressed after the second pulse, similarly to the experimentally observed PPI phenomenon (Fig. 2(a)). This double-pulse related inhibition was dependent on GABAergic mechanisms as indicated by turning off all inhibitory synapses in a bicuculline-like manner (Fig. 2(b), (c)).

4 Results

4.3 Feed-forward and feedback somatic inhibitory circuits contribute to PPI

population spike, maximal double-pulse stimulation (800 µA) and minimum stimulation (evoking 1 mV population spikes) was used in all mice (interpulse intervals 15–1,000 ms, data shown only for maximum stimulation intensity). Five to ten paired-pulse responses were collected at each interpulse interval and averaged. PPI/PPDI curves were fitted using a Boltzmann equation to obtain the mean interpulse interval at which equal amplitudes of the first and second population spike could be observed.

3 Statistical analysis

4.1 GABAergic network inhibition in the dentate gyrus in vivo Paired-pulse ratio of the population spike has been measured and used to investigate GABAergic network inhibition in the dentate gyrus in many previous studies (e.g. Tuff et al. 1983; Oliver and Miller 1985; Moser 1996; Jones et al. 2001; Sayin

In addition to GCs, stimulation of perforant path terminals recruits also GABAergic interneurons. In the model, perforant path inputs activate inhibitory BCs (Fig. 1(b)) which feed forward on the somata of GCs (feed-forward inhibitory loop: PP-BC-GC). Postsynaptic connections of GCs activate BCs as well as HCs mediating feedback

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the removal of feed-forward inhibition (gPP-BC = 0 nS) caused the most severe impairment of PPI (Fig. 3(a), (b)). The silencing of feedback inhibition provided by BCs and HCs (gGC-BC = 0 nS; gGC-HC = 0 nS) induced less significant but still considerable reduction of PPI. Almost no alteration of PPI was observed after selective disruption of feedback inhibition from HCs (gGC-HC = 0 nS). These computational results indicate that feed-forward and feedback inhibition of GCs by BCs are crucial in maintaining PPI of GC spikes. Furthermore, feed-forward inhibition by BCs contributes most strongly to PPI. What is the mechanism of BC fast feed-forward inhibitory action? BCs fire fast and repetitively following perforant path stimulation (see Fig. 2). Our simulations showed that a hyperpolarizing shift in the BC resting potential lead to a significant impairment of PPI similar to the effects of the feed-forward inhibition removal (Supplementary Fig. a, b). Thus, a depolarized resting potential (−60 mV) is crucial for the rapid recruitment of BCs in the feed-forward inhibitory loop mediating PPI (c.f. Jonas et al. 2004). 4.4 Reduction of somatic and dendritic inhibition differentially modulates PPI

Fig. 2 GABAergic PPI in the dentate gyrus in silico (a, b): Left: Simulated voltage traces of granule cells (GCs), basket cells (BCs), mossy cells (MCs) and hilar cells (HCs) after paired-pulse stimulation of perforant-path inputs in control (A) and modified (B) network model. Note that in the control situation, some GCs did not fire action potentials after the second stimulus (paired-pulse inhibition, PPI). Arrows: PP stimulation. Middle: Spike raster plot of network activity after paired-pulse stimulation of perforant-path inputs (17 ms interpulse interval) in the dentate gyrus network model. Time (in ms) is on the horizontal axis and index of neurons in the network on the vertical axis. Each point represents an action potential. Note the reduced number and synchronicity of granule cell discharges following the second pulse (PPI) in the control network model. Arrows: PP stimulation. Right: Quantification of GC firing. (c): Simulated PPI at various inter-pulse intervals. Note a significant leftward shift of the PPI curve after silencing GABAergic inhibitory transmission in the dentate gyrus model. Plots represent averages of three runs obtained with randomized connectivity. Adapted from Winkels et al. 2009

inhibition of GC somata (BC-GC synapses) and dendrites (HC-GC synapses). To determine the relative contribution of feed-forward and feedback inhibitory circuits to PPI, we silenced their synapses and assessed GC discharges following paired-pulse stimulation in the dentate gyrus model (Fig. 3). As expected, turning off feed-forward/ feedback inhibitory loops led to a reduction of PPI as shown by a leftward shift of the PPI curve (Fig. 3(a)). Interestingly,

Next, we addressed the question how somatic or dendritic inhibition affects paired-pulse modulation of GC firing. Therefore, we studied the effect of the reduction of somatic or dendritic GABAARs on the network activity after pairedpulse stimulation of perforant path fibres. The reduction of somatic GABAAR densities (gBC-GC) induced a significant decrease of PPI (Fig. 4). By contrast, selective reduction of dendritic GABAAR conductances (gHC-GC) did not result in significant changes of simulated PPI. Thus, the analysis of the dentate network model implies that PPI is mainly mediated by somatic inhibition provided by BCs contacting GC bodies. Our control simulations with an increased strength of dendritic HC-GC synapses (Supplementary Fig. c) suggest that, to be capable of modulating PPI, the overall conductance of dendritic feedback inhibitory synapses needs to be significantly larger than the experimentally determined strength of HC-GC synapses. 4.5 EGABA controls PPI The efficiency of GABAAR-dependent inhibition depends on intracellular chloride concentration which determines GABAA reversal potential (EGABA; Farrant and Kaila 2007; Jedlicka and Backus 2006). Altered expression of proteins involved in the regulation of chloride homeostasis has been reported to modulate PPI in the dentate gyrus (Kwak et al. 2006; Kang et al. 2006). Hence we wanted to test the dependence of simulated PPI on EGABA. A hyperpolarizing shift of EGABA (−90 mV; control EGABA at BC-GC and HC-

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Fig. 3 PPI results from a combination of perisomatic feed-forward and feedback inhibition of granule cells by basket cells (a) Systematic removal of feed-forward/feedback inhibitory loops reduced network

inhibition as shown by a leftward shift of the PPI curve (see text). (b) Dependence of PPI on feed-forward-and feedback-driven inhibitory circuits (17 ms inter-pulse interval)

GC synapses was −70 mV) enhanced PPI, whereas depolarizing shifts of EGABA (−60, −50 mV: shunting inhibition; −30 mV: excitation) reduced PPI (Fig. 5(a), (b)). These data were consistent with the experimental results showing augmented PPI associated with increased immunoreactivity of voltage gated chloride channel 2 which maintains low chloride concentration (and hyperpolarizing EGABA) in

neurons (Kwak et al. 2006). Furthermore, consistent with the crucial role of BC-mediated somatic inhibition in PPI, depolarizing shift of somatic EGABA in GCs significantly impaired PPI, in contrast to depolarizing shift of GC dendritic EGABA (Fig. 5(c)).

Fig. 4 Somatic inhibition contributes more than dendritic inhibition to PPI (a) Reduction in strength of somatic BC-GC synapses reduced network inhibition of GCs as shown by a significant leftward shift of the PPI curve. In contrast, reduction in strength of dendritic HC-GC synapses did not impair PPI. (b) Quantification of the dependence of PPI on somatic and dendritic inhibitory circuits (17 ms inter-pulse interval)

Fig. 5 EGABA determines PPI (a) Hyperpolarizing change of EGABA (shift from −70 mV to −90 mV) prolonged PPI. By contrast, depolarizing shifts of EGABA (toward −60, −50 mV and −30 mV) shortened PPI. (b) Quantification of simulation results from (A) at 17 ms inter-pulse interval. (c) Depolarizing shift of somatic EGABA in GCs strongly reduced their PPI whereas depolarizing shift of dendritic EGABA did not alter PPI significantly

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4.6 Intrinsic GC properties affect PPI To explore the interplay between GC excitability and pairedpulse network inhibition, we studied the effects of voltage gated sodium channel (VGSC) density changes on the model network activity after paired-pulse stimulation of perforant path fibres (Winkels et al. 2009). A reduction of VGSC conductances in somatic compartments of dentate cells shifted the PPI curve to the right (Fig. 6). After switching off GABAergic conductances (bicuculline simulation), the PPI differences between the control and the modified network were abolished (Winkels et al. 2009). Interestingly, our simulation data suggested that the disturbance of VGSC distribution in dentate cells is sufficient to explain the electrophysiological changes in ßIV-spectrin mutant mice (quivering mice) displaying a loss of VGSCs (for details, see Winkels et al. 2009). Computational data show that, in the dentate gyrus containing decreased VGSC densities, network excitability decreases owing to impaired spikegenerator properties of GCs and subsequent relative increase of GABAergic control of GC firing.

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cells (BCs). 2. Feed-forward inhibition mediated by BCs is the most significant source of PPI of granule cell (GC) firing. 3. While dendritic inhibition of GCs is not a key determinant of PPI, perisomatic inhibition is crucial in maintaining PPI. 4. Changes in GABAA reversal potential (EGABA) affect PPI. 5. PPI is modulated by alterations in intrinsic excitability of GCs. 5.1 PPI is mediated by feed-forward and feedback inhibition

The main goal of this work was to study how synaptic and intrinsic neuronal properties shape paired-pulse inhibition (PPI) measurements obtained from field recordings in the dentate gyrus. Using a biologically realistic model of the dentate gyrus, our computational analysis provides five major findings: 1. PPI results from feedforward as well as feedback inhibition of GCs by basket

The dentate gyrus is an anatomically and functionally wellcharacterized brain region (Amaral et al. 2007; Ribak and Shapiro 2007) for which a detailed, data-driven, large-scale model has recently become available (Santhakumar et al. 2005; Morgan et al. 2007; Prinz 2008). Using this model, we sought to determine the relative contribution of feedforward and feedback inhibitory circuits to paired-pulse suppression of GC discharges. The glutamatergic GCs and GABAergic BCs of the dentate gyrus receive direct excitatory perforant path (PP) inputs. BCs are thus activated by the same afferent input as GCs, thereby providing feedforward inhibition (PP-BC-GC) to these neurons (Freund and Buzsáki 1996; Houser 2007). Both BCs and HCs receive inputs from the GCs and thus provide them with feedback inhibition (GC-BC-GC; GC-HC-GC). Interestingly, in the network model of the dentate gyrus, feed-forward as well as feedback inhibition by BCs was critical for PPI, with feed-forward inhibition contributing most strongly to PPI. This is consistent with experimental data showing that BCs are powerful and fast signaling devices operating with high speed and precision (Kraushaar and Jonas 2000; Jonas

Fig. 6 PPI is enhanced in the network model containing reduced sodium channel densities (a): The time course of PPI and subsequent PPDI in the dentate gyrus of beta-IV-spectrin mutant (quivering qv3j; n=7) and wild-type mice (n=11). Data were fitted using a Boltzmann equation. Note a significant rightward shift in the PPI/PPDI curve of qv3j mice (quantified in Inset diagram by comparing mean inter-pulse intervals at which an equal amplitude of the first and second population spike could be observed). *p<0.05. (b) The density of

voltage gated sodium channels (VGSCs) in somatic compartments of dentate cells was systematically reduced from 90 to 0% of the control value and the inter-pulse intervals were varied. PPI is stronger in the network with reduced VGSC density. Plots represent averages of three runs obtained with randomized connectivity. Inset diagram shows the dependence of PPI on Na+ channel density (13 ms inter-pulse interval). *p<0.05. Adapted from Winkels et al. 2009 (see the publication for more details)

5 Discussion

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et al. 2004; Doischer et al. 2008; Hu et al. 2009). The efficacy and speed of BC-mediated inhibition accounts for fast feed-forward and feedback inhibition in cortical networks (Pouille and Scanziani 2001; Pouille and Scanziani 2004; Bucurenciu et al. 2008). In the dentate gyrus model, a low resting membrane potential (−70 mV) keeps GCs far from action potential threshold (−49 mV) and together with their intrinsic properties (repolarizing potassium channels) makes it difficult to get them to fire (Lytton et al. 1998; Aradi and Holmes 1999). Therefore, model GCs fire only once even after the complete block of inhibitory transmission (Lytton et al. 1998; Santhakumar et al. 2005; Winkels et al. 2009) In contrast, BCs are capable of generating fast and repetitive action potentials following their synaptic activation. This is due to several mechanisms including depolarized resting potential (−60 mV), specific voltage-gated ion channels and rapid GABA release (Jonas et al. 2004; Aponte et al. 2008; Bucurenciu et al. 2008; Brill and Huguenard 2009; Hu et al. 2009). Our simulations confirmed that these specialized properties allow BCs to efficiently participate in feed-forward (and also feedback) inhibition mediating PPI (Sayin et al. 2003). Perforant path stimulation excites BCs with short latency enabling them to control the excitation of the GCs in a feed-forward manner (c.f. Pouille and Scanziani 2001; Hu et al. 2009; see also Pouille et al. 2009). In addition, activated GCs recruit additional BC discharges. Thus, following pairedpulse stimulation, feed-forward and feedback inhibitory potentials summate to produce inhibition of the second GC response. In vivo field recordings revealed that the relative contribution of feed-forward and feedback inhibitory mechanisms depends on the frequency and intensity of stimulation (Sloviter 1991; see also Moser 1996; Lomo 2009). Our simulations suggest that feed-forward inhibition is more relevant to PPI than previously thought, being important even during a single paired-pulse stimulus of strong intensity (c.f. Sloviter 1991). On the other hand, the network model confirms that the combination of feedforward and feedback inhibition results in strong GC inhibition (Sloviter 1991).

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GABAAR conductances impaired simulated PPI of GCs, the reduction of dendritic GABAAR conductances did not result in significant PPI changes. Given that feed-forward inhibition mediated by BCs was the most significant source of PPI of GC firing, it is logical that dendritic inhibition was not a key contributor (since BCs inhibit perisomatic regions). Interestingly, although the average inhibitory conductance at BC-GC synapses was twice as high as the dendritic HC-GC conductance (Table 1), our control simulations indicated that this difference could not account for the soma-specific nature of PPI (Supplementary Fig. c). Thus, the rapid recruitment of BCs by the fast feed-forward circuit appears to be the main cause for the dependence of PPI on somatic inhibition. Together, these simulations support the conclusion that functional somatic GABAARs represent a key mechanism of PPI in the dentate circuit. In summary, computational data indicate that PPI is primarily an indicator of somatic GABAergic inhibition. 5.3 GABA reversal potential Changes in transmembrane chloride gradient regulate GABA reversal potential (EGABA) and influence GABAAR-dependent inhibition (Prescott et al. 2006; Jedlicka and Backus 2006; Farrant and Kaila 2007; Blaesse et al. 2009). Due to the low resting potential of GCs, model interneurons generate shunting, instead of hyperpolarizing, inhibitory potentials (EGABA = −70 mV; Santhakumar et al. 2005). As shown in our PPI simulations, these shunting inhibitory conductances are effective in reducing the firing of GCs in response to the second stimulus (see also Lytton et al. 1998). In addition, whereas hyperpolarizing shifts in EGABA enhanced PPI, depolarizing changes in EGABA caused an impairment of PPI. These network modeling findings support experimental observations indicating that PPI is dependent on EGABA and chloride homeostasis regulation (Kang et al. 2006). Moreover, in agreement with the substantial role of BC-mediated somatic inhibition in PPI, only changes in GC somatic EGABA affected PPI. These data indicate that compartmentspecific alterations of EGABA may significantly modulate the duration of PPI of GCs. 5.4 Intrinsic excitability of GCs

5.2 Perisomatic versus dendritic inhibition Fast-spiking BCs contact the perisomatic region of GCs, exerting powerful control over the output and synchronization of GCs (Miles et al. 1996; Houser 2007; Freund and Katona 2007). Non-fast-spiking HCs innervate GC dendrites in the molecular layer of the dentate gyrus (Freund and Buzsáki 1996; Houser 2007) regulating the efficacy of afferent excitatory inputs (Miles et al. 1996; Maglóczky and Freund 2005). While selective silencing of perisomatic

Network excitability may be altered not only through modulation of synaptic transmission but also by modification of intrinsic currents in neurons. A reduction of somatic voltage gated sodium channel (VGSC) conductances strengthened PPI (Winkels et al. 2009). Computational analysis showed that abnormal VGSC distribution lead to impaired ability of GCs to generate action potentials. The decrease of GC excitability caused a relative increase of GABAergic inhibition efficiency with GABAergic inter-

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neurons exhibiting a stronger inhibitory control over GC firing (Winkels et al. 2009). Thus, altered PPI does not always result from synaptic inhibition changes. It may be an indirect network effect due to changes in intrinsic biophysical properties of GCs. Therefore, when probing GABAergic inhibition, paired-pulse measurements serve as a preliminary method that should be complemented by more direct tests of inhibitory synaptic transmission. 5.5 Model limitations and future directions The dentate gyrus model we used is highly detailed and complex (Santhakumar et al. 2005; see also DyhrfjeldJohnsen et al. 2007; Morgan and Soltesz 2008; Prinz 2008). Nevertheless, a number of components of the dentate network has not yet been incorporated into the model due to lack of electrophysiological data (Morgan et al. 2007). Given the morphological and functional diversity of cortical GABAergic cells (Freund and Buzsáki 1996; Houser 2007; Klausberger and Somogyi 2008), it is likely that the inclusion of additional interneuron subtypes with specific (perisomatic, dendritic, axo-axonic) synapses will improve the quantitative precision of PPI simulations. For example, axo-axonic or chandelier cells (Howard et al. 2005) form synapses on axon initial segments of GCs and are therefore thought to control the output GC spikes. Receiving inputs from GCs, axo-axonic cells are involved in feedback inhibitory circuits, very likely contributing to mechanisms of PPI (Sayin et al. 2003) in a similar manner as BCs. Hilar commissural-association pathway-related (HICAP) cells target proximal dendrites of GCs. Because of the location of their somata in the hilus, these cells also receive incoming synapses from GCs and are thus suitable for dendritic feedback inhibition of GCs, potentially modulating PPI of GC spikes. Indeed, although our simulations suggest that HCs do not contribute significantly to PPI mechanisms, other dendritic interneurons (e.g. HICAP cells) might modulate PPI in cooperation with HCs but only if the total strength of dendritic feedback inhibition is much higher than the physiological strength of HC-GC synapses (Supplementary Fig. c). In addition, interneurons with somata in the molecular layer (e.g. molecular layer perforant path-associated (MOPP) cells) are capable of providing GCs with dendritic feedforward inhibition since they are contacted by direct excitatory inputs from the perforant path (Ferrante et al. 2009). Future experimental and modeling studies will clarify the role of axo-axonic, HICAP and MOPP cells for PPI and dentate gyrus excitability. Fast-spiking BCs are parvalbumin (PV)-positive. The complexity of the dentate gyrus model could be increased by adding second major group of perisomatic interneurons: regular-spiking cholecystokinin-positive BCs (Houser 2007). Importantly, in CA1, only PV-containing BCs

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contribute to fast disynaptic IPSCs mediating feedforward-driven inhibition (Glickfeld and Scanziani 2006). On the other hand, CCK-containing BCs integrate feedforward and feedback excitation from pyramidal cells and discharge only when pyramidal neurons are also firing (Glickfeld and Scanziani 2006; Freund and Katona 2007). Thus, it would be interesting to simulate and analyze PPI in a computational model of the dentate circuitry containing CCK cells which can be recruited only by a combination of a feed-forward and feedback drive. In this context it is notable that seizure-induced loss of CCK interneurons providing axo-somatic inhibition has been reported to underlie reduced PPI (Sayin et al. 2003). Knockout mouse models of reduced excitatory drive onto PV-containing BCs have recently become available (Fuchs et al. 2007; Rácz et al. 2009). Our simulations predict that field recordings in the dentate gyrus of these mice will reveal reduced PPI because of impaired recruitment of perisomatic inhibition of GCs. Interestingly, PPI measured in vitro has a shorter time course (10–20 ms, Kleschevnikov et al. 2004) than PPI recorded in vivo. The reason for this temporal difference is not known but it may be due to severed interneuronal connections in hippocampal slices and/or due to impact of activated extradentate circuits in vivo. PPI in the “isolated” DG network model seems to better correspond quantitatively to the in vitro situation. In the present model, only glutamatergic AMPA and GABAA synapses are modelled. In future dentate gyrus models, additional synaptic receptors (e.g. NMDA, GABAB receptors) should be incorporated and studied in the context of network activity. For example, PPDI is believed to be mediated by GABAB autoreceptors (Steffensen and Henriksen 1991; Davies et al. 1991). Hence the inclusion of GABAB receptors in the network model would allow for realistic simulations of the PPDI part of the PPI/PPDI curve. Furthermore, it would be interesting to add diverse synaptic plasticity mechanisms and investigate their relevance for network excitability changes. Including short-term plasticity (Jalil et al. 2004) would be particularly intriguing since previous experiments and simplified simulations showed that enhanced presynaptic short-term plasticity (paired-pulse facilitation of EPSPs) at PP-BC, GC-BC and PP-GC synapses paradoxically increased PPI of population spikes (Thomas et al. 2005). Moreover, paired-pulse depression of IPSCs which has been reported at BC-GC synapses (Kraushaar and Jonas 2000) represents another potential mechanism for altering PPI in the dentate gyrus. Likewise, long-term plasticity of distinct synaptic connections, e.g. on interneurons mediating feed-forward (Lamsa et al. 2005; Lamsa et al. 2007a) or feedback inhibition (Lamsa et al. 2007b; see also Kullmann and Lamsa 2007) may also have important implications for the network behavior and inhibition and thus should be

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incorporated in dentate network models (c.f. Benuskova and Abraham 2007). Of note, to get a more accurate representation of the paired-pulse field responses in the dentate gyrus, in addition to implementing further mechanisms and biological details, the number of model cells should be upscaled (Morgan et al. 2007) and explicit computation of dentate extracellular potentials based on the distance from a current source to the measurement should be performed (c.f. Gold et al. 2006). In conclusion, computer modeling provides a useful tool for determining the importance of various synaptic and intrinsic cellular mechanisms for paired-pulse field potential responses. Changes in network inhibition play an important role in a variety of pathological conditions including epilepsy and mood disorders (Freund and Katona 2007; Fritschy 2008). Therefore, computational analyses of PPI mechanisms may help better understand the origin of the diseases accompanied by dysfunctions of neuronal excitability (Lytton 2008). Acknowledgments This work was supported by the Deutsche Forschungsgemeinschaft (JE 528/1-1 to P.J. and DE 551/8-1 to T.D.). We thank two anonymous reviewers for their helpful comments and suggestions.

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