Computational modeling of GABAA receptor-mediatedpaired-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 populationspike observed in extracellular field recordings is widely usedas a read-out of hippocampal network inhibition. PPI reflectsGABAA receptor-mediated inhibition of principal neuronsthrough local interneurons. However, because of its poly-synaptic nature, it is difficult to assign PPI changes to precisesynaptic mechanisms. Here we used a detailed networkmodel of the dentate gyrus to simulate PPI of granule cellaction potentials and analyze its network properties. Ourcomputational analysis indicates that PPI results mainly froma combination of perisomatic feed-forward and feedbackinhibition of granule cells by basket cells. Feed-forwardinhibition mediated by basket cells appeared to be the mostsignificant source of PPI. Our simulations suggest that PPIdepends more on somatic than on dendritic inhibition ofgranule cells. Furthermore, PPI was modulated by changes inGABAA reversal potential (EGABA) and by alterations inintrinsic excitability of granule cells. In summary, computermodeling provides a useful tool for determining the role ofsynaptic and intrinsic cellular mechanisms in paired-pulsefield potential responses.

Keywords GABA .Network . Perisomatic inhibition .

Basket cell . Feed-forward . Feedback inhibition

1 Introduction

In the hippocampus, GABAergic synapses act as the majorsources of inhibition (Freund and Buzsáki 1996; Coulter andCarlson 2007; Houser 2007). Fast inhibitory transmission ispredominantly mediated by ionotropic GABAA receptors(GABAARs). The functional integrity of inhibitory transmis-sion is important for the precise regulation of neuronalexcitability (Atallah and Scanziani 2009). Therefore, it isimportant to study delicate control mechanisms which existin neurons to regulate the function of inhibitory synapses.

Paired-pulse measurements of evoked extracellular fieldpotentials are often employed in anesthetized transgenicanimals to study functional changes of GABAergic inhibi-tion and neuronal excitability in vivo (e.g. Stoenica et al.2006; Jedlicka et al. 2009b; Winkels et al. 2009). In thedentate gyrus, electrical stimuli delivered to perforant pathelicit field excitatory postsynaptic potentials (fEPSPs).These field potentials are generated by granule cells(GCs) as the perforant path stimulation activates excitatorysynapses located along GC dendrites in the dentate outermolecular layer. The slope of the fEPSP is a measure ofsynaptic strength at perforant path-granule cell synapses. Ifthe stimulation intensity reaches the threshold for GCaction potentials, fEPSPs are accompanied by a populationspike. The size of the population spike reflects the numberand synchrony of discharging GCs (Andersen et al. 1971).

Paired-pulse inhibition (PPI) of the population spike iswidely recognized as a read-out of hippocampal networkinhibition as it reflects GABAAR mediated inhibition ofprincipal neurons through local interneurons in the neuralcircuit (Sloviter 1991; Tuff et al. 1983; Oliver and Miller1985; Lomo 2009). In the dentate gyrus, paired-pulsestimulation of perforant path inputs results in populationspike depression at short inter-stimulus intervals (PPI)followed by facilitation at longer intervals (paired-pulse

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. SchwarzacherInstitute of Clinical Neuroanatomy,Goethe-University,NeuroScience Center,60590 Frankfurt am Main, Germanye-mail: jedlicka@em.uni-frankfurt.de

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

disinhibition, PPDI; Fig. 1). PPI of GC spikes occurs due tothe summed action of the GABAAR-dependent inhibitorypostsynaptic currents (IPSCs) generated by inhibitory circuitsin the dentate gyrus. PPDI (facilitation) of granule dischargesis thought to be the result of various mechanisms includingthe reduction of GABAergic inhibition mediated by presyn-aptic GABABRs and rebound GC firing due to precedinghyperpolarization (Davies et al. 1991; Bliss et al. 2007).

PPI has been shown to be a measure of the efficacy ofGABAergic inhibition (Sloviter 1991; Moser 1996; Sayin etal. 2003; Zappone and Sloviter 2004; Naylor and Wasterlain2005; Naylor et al. 2005). However, because of itspolysynaptic nature, it is difficult to assign PPI changes torespective synaptic mechanisms. Therefore, here we used adetailed network model of the dentate gyrus (Santhakumar et

al. 2005; Morgan et al. 2007) to simulate PPI of GC actionpotentials and analyze its network properties. The aim of ourstudy was to explore the following questions: Is PPI ofspiking activity in the population of GCs predominantlymediated by feed-forward or feedback inhibitory circuits?Does PPI depend mainly on GABAergic inhibition in thedendritic or somatic region of the GCs? Do changes inintrinsic properties of GCs contribute to alterations of PPI?How do depolarizing shifts in GABAA reversal potentialmodulate paired-pulse GC responses?

2 Methods

An established computational model of the dentate gyrusnetwork was used as described before (Santhakumar et al.2005; Winkels et al. 2009). Briefly, the network modelcontained 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 versionof the dentate gyrus (Santhakumar et al. 2005; Morgan etal. 2007). Simulation files were downloaded from theModelDB website (Davison et al. 2004; Hines et al. 2004):http://senselab.med.yale.edu/modeldb/. All simulationswere carried out with the NEURON simulation program(Hines and Carnevale 1997). For details of structural,passive and active properties of model cells, and synapticand network parameters, see Santhakumar et al. (2005) andTable 1. Parameters used in our simulations were identicalto parameters in the published network model, includingGABAAR conductances. Similarly to the original model,perforant-path synapses were modeled using strong synap-tic conductance (GPPtoGC = 20 nS, GPPtoBC = 10 nS,GPPtoMC = 2.5 nS) to ensure that all GCs will fire after asingle stimulus. To explore the effects of the reduction ofGABAA or AMPARs on dentate network activity, GABAA/AMPAR conductances were diminished at GABAergic orglutamatergic synapses, respectively (see Results). Tosimulate PPI of GC discharges, double-pulse stimulationwas delivered to perforant path synaptic inputs usingvarying inter-pulse intervals. For data analysis, the activityof the dentate gyrus network was visualized using spiketime raster plots. The activity of GCs was presented as thepercentage of the maximal number of GC action potentials.

In vivo electrophysiological recordings in the dentategyrus were carried out as described before (Winkels et al.2009; Jedlicka et al. 2009a, b). Briefly, adult mice wereanesthetized with an intraperitoneal injection of urethane. Abipolar stimulation electrode was positioned in the angularbundle of the perforant path. A recording electrode was placedin the granule cell layer of the dentate gyrus. To measurepaired-pulse inhibition (PPI) and disinhibition (PPDI) of the

Fig. 1 GABAergic paired-pulse inhibition (PPI) in the dentate gyrus invivo (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 tracesrepresent paired-pulse responses showing PPI and PPDI at 20 ms and60 ms inter-stimulus intervals, respectively. Calibration: 2 mV, 10 ms.The timing of stimuli corresponds to the timing of stimulation artefactsin the inset. Adapted from Jedlicka et al. 2009b. (b) Basic dentate gyruscircuitry: PP: perforant path, GC: granule cells, BC: basket cells, HC:hilar cells. For the reason of clarity, MCs are not shown although theywere included in the simulations. PP-stimulation initiates feedforwardexcitation 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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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, datashown only for maximum stimulation intensity). Five to tenpaired-pulse responses were collected at each interpulseinterval and averaged. PPI/PPDI curves were fitted using aBoltzmann equation to obtain the mean interpulse interval atwhich equal amplitudes of the first and second populationspike could be observed.

3 Statistical analysis

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

4 Results

4.1 GABAergic network inhibition in the dentate gyrus in vivo

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

et al. 2003; Zappone and Sloviter 2004; Lomo 2009; Jedlickaet al. 2009a, b; Winkels et al. 2009). PPI of GC populationspikes depends on GABAergic synaptic inhibition in thedentate network as it can be blocked or enhanced withGABAAR antagonists or agonists, respectively (Sloviter1991; 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 pairedstimuli delivered to perforant path fibres at inter-pulseintervals of less than 40–50 ms (Fig. 1(a)). PPI is measuredby decrease in the amplitude of the second population spikecompared with first. The amplitude of the population spikereflects the number of synchronously firing neurons (Andersenet al. 1971; Varona et al. 2000). Thus, in the dentate network,paired-pulse stimulation recruits GABAergic inhibitory cir-cuits suppressing GC discharges following the secondstimulus. Interneurons involved in these inhibitory circuitscontrol dentate gyrus excitability in vivo.

4.2 Computational modeling of paired-pulse inhibition

A variety of changes in synaptic transmission or intrinsiccellular properties could contribute to alterations of PPI. Weused a realistic computer model of the dentate circuit(Santhakumar et al. 2005; Morgan et al. 2007) to betterunderstand the relationship between paired-pulse fieldresponses and network/synaptic events. This network modelcomprises perforant path inputs and synaptic connections ofgranule (GC), mossy (MC), basket (BC) and hilar (HC) cells(see Methods and Santhakumar et al. 2005). Model neuronsare based on realistic morphological and electrophysiologicaldata. To simulate PPI of GC firing, network activity wasinitiated by a paired-pulse synchronous activation of perforant-path synaptic inputs to all postsynaptic cells with varying inter-pulse intervals. As the network model contains onlyGABAARs and PPDI is thought to depend partially onGABAB autoreceptors, we simulated only the PPI part of thePPI/PPDI curve. In the paired-pulse simulations, GC firingwas suppressed after the second pulse, similarly to theexperimentally observed PPI phenomenon (Fig. 2(a)). Thisdouble-pulse related inhibition was dependent on GABAergicmechanisms as indicated by turning off all inhibitorysynapses in a bicuculline-like manner (Fig. 2(b), (c)).

4.3 Feed-forward and feedback somatic inhibitory circuitscontribute to PPI

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

Table 1 Selected parameters of dentate network

GABAA synapses gBC-GC (nS) 1.6

BC-GC conv. 1.2±0.3

gBC-MC (nS) 1.5

gBC-BC (nS) 7.6

gHC-GC (nS) 0.5

HC-GC conv. 1.92±0.3

gHC-MC (nS) 1

gHC-BC (nS) 0.5

PP (AMPA) synapses gPP-BC (nS) 10

gPP-GC (nS) 20

GC (AMPA)synapses

gGC-BC (nS) 4.7

gGC-HC (nS) 0.5

EGABA BC-GC (soma) (mV) −70HC-GC (dendrite)(mV)

−70

Sodium channels gNa (S/cm2) 0.12 (0.2 in MCs)

BC resting potential (mV) −60

Some of these parameters were varied as explained in the relevantfigures. 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) wasused (see Winkels et al. 2009). Note that somatic and dendriticinhibitory inputs had an average conductance of 1.92 nS and 0.96 nS,respectively (unitary synaptic conductance x convergence)

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inhibition of GC somata (BC-GC synapses) and dendrites(HC-GC synapses). To determine the relative contributionof feed-forward and feedback inhibitory circuits to PPI, wesilenced their synapses and assessed GC dischargesfollowing paired-pulse stimulation in the dentate gyrusmodel (Fig. 3). As expected, turning off feed-forward/feedback inhibitory loops led to a reduction of PPI as shownby a leftward shift of the PPI curve (Fig. 3(a)). Interestingly,

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 andHCs (gGC-BC = 0 nS; gGC-HC = 0 nS) induced less significantbut still considerable reduction of PPI. Almost no alterationof PPI was observed after selective disruption of feedbackinhibition from HCs (gGC-HC = 0 nS). These computationalresults indicate that feed-forward and feedback inhibition ofGCs by BCs are crucial in maintaining PPI of GC spikes.Furthermore, feed-forward inhibition by BCs contributesmost strongly to PPI.

What is the mechanism of BC fast feed-forward inhibitoryaction? BCs fire fast and repetitively following perforantpath stimulation (see Fig. 2). Our simulations showed that ahyperpolarizing shift in the BC resting potential lead to asignificant impairment of PPI similar to the effects of thefeed-forward inhibition removal (Supplementary Fig. a, b).Thus, a depolarized resting potential (−60 mV) is crucialfor the rapid recruitment of BCs in the feed-forwardinhibitory loop mediating PPI (c.f. Jonas et al. 2004).

4.4 Reduction of somatic and dendritic inhibitiondifferentially modulates PPI

Next, we addressed the question how somatic or dendriticinhibition affects paired-pulse modulation of GC firing.Therefore, we studied the effect of the reduction of somaticor dendritic GABAARs on the network activity after paired-pulse stimulation of perforant path fibres. The reduction ofsomatic GABAAR densities (gBC-GC) induced a significantdecrease of PPI (Fig. 4). By contrast, selective reductionof dendritic GABAAR conductances (gHC-GC) did notresult in significant changes of simulated PPI. Thus, theanalysis of the dentate network model implies that PPI ismainly mediated by somatic inhibition provided by BCscontacting GC bodies. Our control simulations with anincreased strength of dendritic HC-GC synapses (Supplemen-tary Fig. c) suggest that, to be capable of modulating PPI, theoverall conductance of dendritic feedback inhibitory synap-ses needs to be significantly larger than the experimentallydetermined strength of HC-GC synapses.

4.5 EGABA controls PPI

The efficiency of GABAAR-dependent inhibition dependson intracellular chloride concentration which determinesGABAA reversal potential (EGABA; Farrant and Kaila 2007;Jedlicka and Backus 2006). Altered expression of proteinsinvolved in the regulation of chloride homeostasis has beenreported to modulate PPI in the dentate gyrus (Kwak et al.2006; Kang et al. 2006). Hence we wanted to test thedependence of simulated PPI on EGABA. A hyperpolarizingshift of EGABA (−90 mV; control EGABA at BC-GC and HC-

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 stimulationof perforant-path inputs in control (A) and modified (B) networkmodel. Note that in the control situation, some GCs did not fire actionpotentials after the second stimulus (paired-pulse inhibition, PPI).Arrows: PP stimulation. Middle: Spike raster plot of network activityafter paired-pulse stimulation of perforant-path inputs (17 ms inter-pulse interval) in the dentate gyrus network model. Time (in ms) is onthe horizontal axis and index of neurons in the network on the verticalaxis. Each point represents an action potential. Note the reducednumber and synchronicity of granule cell discharges following thesecond pulse (PPI) in the control network model. Arrows: PPstimulation. Right: Quantification of GC firing. (c): Simulated PPI atvarious inter-pulse intervals. Note a significant leftward shift of thePPI curve after silencing GABAergic inhibitory transmission in thedentate gyrus model. Plots represent averages of three runs obtainedwith randomized connectivity. Adapted from Winkels et al. 2009

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GC synapses was −70 mV) enhanced PPI, whereas depola-rizing shifts of EGABA (−60, −50 mV: shunting inhibition;−30 mV: excitation) reduced PPI (Fig. 5(a), (b)). These datawere consistent with the experimental results showingaugmented PPI associated with increased immunoreactivityof voltage gated chloride channel 2 which maintains lowchloride concentration (and hyperpolarizing EGABA) in

neurons (Kwak et al. 2006). Furthermore, consistent withthe crucial role of BC-mediated somatic inhibition in PPI,depolarizing shift of somatic EGABA in GCs significantlyimpaired PPI, in contrast to depolarizing shift of GCdendritic EGABA (Fig. 5(c)).

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

Fig. 3 PPI results from a combination of perisomatic feed-forwardand feedback inhibition of granule cells by basket cells (a) Systematicremoval 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 inhibitorycircuits (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) at17 ms inter-pulse interval. (c) Depolarizing shift of somatic EGABA inGCs strongly reduced their PPI whereas depolarizing shift of dendriticEGABA did not alter PPI significantly

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4.6 Intrinsic GC properties affect PPI

To explore the interplay between GC excitability and paired-pulse network inhibition, we studied the effects of voltagegated sodium channel (VGSC) density changes on the modelnetwork activity after paired-pulse stimulation of perforantpath fibres (Winkels et al. 2009). A reduction of VGSCconductances in somatic compartments of dentate cellsshifted the PPI curve to the right (Fig. 6). After switchingoff GABAergic conductances (bicuculline simulation), thePPI differences between the control and the modifiednetwork were abolished (Winkels et al. 2009). Interestingly,our simulation data suggested that the disturbance of VGSCdistribution in dentate cells is sufficient to explain theelectrophysiological changes in ßIV-spectrin mutant mice(quivering mice) displaying a loss of VGSCs (for details,see Winkels et al. 2009). Computational data show that, inthe dentate gyrus containing decreased VGSC densities,network excitability decreases owing to impaired spike-generator properties of GCs and subsequent relativeincrease of GABAergic control of GC firing.

5 Discussion

The main goal of this work was to study how synapticand intrinsic neuronal properties shape paired-pulseinhibition (PPI) measurements obtained from field record-ings in the dentate gyrus. Using a biologically realisticmodel of the dentate gyrus, our computational analysisprovides five major findings: 1. PPI results from feed-forward as well as feedback inhibition of GCs by basket

cells (BCs). 2. Feed-forward inhibition mediated by BCsis the most significant source of PPI of granule cell (GC)firing. 3. While dendritic inhibition of GCs is not a keydeterminant of PPI, perisomatic inhibition is crucial inmaintaining PPI. 4. Changes in GABAA reversal potential(EGABA) affect PPI. 5. PPI is modulated by alterations inintrinsic excitability of GCs.

5.1 PPI is mediated by feed-forward and feedbackinhibition

The dentate gyrus is an anatomically and functionally well-characterized brain region (Amaral et al. 2007; Ribak andShapiro 2007) for which a detailed, data-driven, large-scalemodel 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 feed-forward and feedback inhibitory circuits to paired-pulsesuppression of GC discharges. The glutamatergic GCs andGABAergic BCs of the dentate gyrus receive directexcitatory perforant path (PP) inputs. BCs are thus activatedby the same afferent input as GCs, thereby providing feed-forward inhibition (PP-BC-GC) to these neurons (Freundand Buzsáki 1996; Houser 2007). Both BCs and HCsreceive inputs from the GCs and thus provide them withfeedback inhibition (GC-BC-GC; GC-HC-GC). Interesting-ly, in the network model of the dentate gyrus, feed-forwardas well as feedback inhibition by BCs was critical for PPI,with feed-forward inhibition contributing most strongly toPPI. This is consistent with experimental data showing thatBCs are powerful and fast signaling devices operating withhigh speed and precision (Kraushaar and Jonas 2000; Jonas

Fig. 6 PPI is enhanced in the network model containing reducedsodium channel densities (a): The time course of PPI and subsequentPPDI in the dentate gyrus of beta-IV-spectrin mutant (quivering qv3j;n=7) and wild-type mice (n=11). Data were fitted using a Boltzmannequation. Note a significant rightward shift in the PPI/PPDI curve ofqv3j mice (quantified in Inset diagram by comparing mean inter-pulseintervals at which an equal amplitude of the first and secondpopulation spike could be observed). *p<0.05. (b) The density of

voltage gated sodium channels (VGSCs) in somatic compartments ofdentate cells was systematically reduced from 90 to 0% of the controlvalue and the inter-pulse intervals were varied. PPI is stronger in thenetwork with reduced VGSC density. Plots represent averages of threeruns obtained with randomized connectivity. Inset diagram shows thedependence of PPI on Na+ channel density (13 ms inter-pulseinterval). *p<0.05. Adapted from Winkels et al. 2009 (see thepublication for more details)

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et al. 2004; Doischer et al. 2008; Hu et al. 2009). Theefficacy and speed of BC-mediated inhibition accounts forfast feed-forward and feedback inhibition in cortical net-works (Pouille and Scanziani 2001; Pouille and Scanziani2004; Bucurenciu et al. 2008).

In the dentate gyrus model, a low resting membranepotential (−70 mV) keeps GCs far from action potentialthreshold (−49 mV) and together with their intrinsicproperties (repolarizing potassium channels) makes itdifficult to get them to fire (Lytton et al. 1998; Aradi andHolmes 1999). Therefore, model GCs fire only once evenafter the complete block of inhibitory transmission (Lyttonet al. 1998; Santhakumar et al. 2005; Winkels et al. 2009)In contrast, BCs are capable of generating fast andrepetitive action potentials following their synaptic activa-tion. This is due to several mechanisms including depolar-ized resting potential (−60 mV), specific voltage-gated ionchannels and rapid GABA release (Jonas et al. 2004;Aponte et al. 2008; Bucurenciu et al. 2008; Brill andHuguenard 2009; Hu et al. 2009). Our simulationsconfirmed that these specialized properties allow BCs toefficiently participate in feed-forward (and also feedback)inhibition mediating PPI (Sayin et al. 2003). Perforantpath stimulation excites BCs with short latency enablingthem to control the excitation of the GCs in a feed-forwardmanner (c.f. Pouille and Scanziani 2001; Hu et al. 2009;see also Pouille et al. 2009). In addition, activated GCsrecruit additional BC discharges. Thus, following paired-pulse stimulation, feed-forward and feedback inhibitorypotentials summate to produce inhibition of the secondGC response.

In vivo field recordings revealed that the relativecontribution of feed-forward and feedback inhibitorymechanisms depends on the frequency and intensity ofstimulation (Sloviter 1991; see also Moser 1996; Lomo2009). Our simulations suggest that feed-forward inhibitionis more relevant to PPI than previously thought, beingimportant even during a single paired-pulse stimulus ofstrong intensity (c.f. Sloviter 1991). On the other hand, thenetwork model confirms that the combination of feed-forward and feedback inhibition results in strong GCinhibition (Sloviter 1991).

5.2 Perisomatic versus dendritic inhibition

Fast-spiking BCs contact the perisomatic region of GCs,exerting powerful control over the output and synchroniza-tion of GCs (Miles et al. 1996; Houser 2007; Freund andKatona 2007). Non-fast-spiking HCs innervate GC den-drites in the molecular layer of the dentate gyrus (Freundand Buzsáki 1996; Houser 2007) regulating the efficacy ofafferent excitatory inputs (Miles et al. 1996; Maglóczky andFreund 2005). While selective silencing of perisomatic

GABAAR conductances impaired simulated PPI of GCs,the reduction of dendritic GABAAR conductances did notresult in significant PPI changes. Given that feed-forwardinhibition mediated by BCs was the most significant sourceof PPI of GC firing, it is logical that dendritic inhibition wasnot a key contributor (since BCs inhibit perisomatic regions).Interestingly, although the average inhibitory conductance atBC-GC synapses was twice as high as the dendritic HC-GCconductance (Table 1), our control simulations indicated thatthis difference could not account for the soma-specific natureof PPI (Supplementary Fig. c). Thus, the rapid recruitment ofBCs by the fast feed-forward circuit appears to be the maincause for the dependence of PPI on somatic inhibition.Together, these simulations support the conclusion thatfunctional somatic GABAARs represent a key mechanismof PPI in the dentate circuit. In summary, computational dataindicate that PPI is primarily an indicator of somaticGABAergic inhibition.

5.3 GABA reversal potential

Changes in transmembrane chloride gradient regulate GABAreversal potential (EGABA) and influence GABAAR-dependentinhibition (Prescott et al. 2006; Jedlicka and Backus 2006;Farrant and Kaila 2007; Blaesse et al. 2009). Due to the lowresting potential of GCs, model interneurons generateshunting, instead of hyperpolarizing, inhibitory potentials(EGABA = −70 mV; Santhakumar et al. 2005). As shown inour PPI simulations, these shunting inhibitory conductancesare effective in reducing the firing of GCs in response to thesecond stimulus (see also Lytton et al. 1998). In addition,whereas hyperpolarizing shifts in EGABA enhanced PPI,depolarizing changes in EGABA caused an impairment ofPPI. These network modeling findings support experimentalobservations indicating that PPI is dependent on EGABA andchloride homeostasis regulation (Kang et al. 2006). More-over, in agreement with the substantial role of BC-mediatedsomatic inhibition in PPI, only changes in GC somaticEGABA affected PPI. These data indicate that compartment-specific alterations of EGABA may significantly modulate theduration of PPI of GCs.

5.4 Intrinsic excitability of GCs

Network excitability may be altered not only throughmodulation of synaptic transmission but also by modifica-tion of intrinsic currents in neurons. A reduction of somaticvoltage gated sodium channel (VGSC) conductancesstrengthened PPI (Winkels et al. 2009). Computationalanalysis showed that abnormal VGSC distribution lead toimpaired ability of GCs to generate action potentials. Thedecrease of GC excitability caused a relative increase ofGABAergic inhibition efficiency with GABAergic inter-

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neurons exhibiting a stronger inhibitory control over GCfiring (Winkels et al. 2009). Thus, altered PPI does notalways result from synaptic inhibition changes. It may bean indirect network effect due to changes in intrinsicbiophysical properties of GCs. Therefore, when probingGABAergic inhibition, paired-pulse measurements serve asa preliminary method that should be complemented bymore direct tests of inhibitory synaptic transmission.

5.5 Model limitations and future directions

The dentate gyrus model we used is highly detailed andcomplex (Santhakumar et al. 2005; see also Dyhrfjeld-Johnsen et al. 2007; Morgan and Soltesz 2008; Prinz 2008).Nevertheless, a number of components of the dentatenetwork has not yet been incorporated into the model dueto lack of electrophysiological data (Morgan et al. 2007).Given the morphological and functional diversity of corticalGABAergic cells (Freund and Buzsáki 1996; Houser 2007;Klausberger and Somogyi 2008), it is likely that theinclusion of additional interneuron subtypes with specific(perisomatic, dendritic, axo-axonic) synapses will improvethe quantitative precision of PPI simulations. For example,axo-axonic or chandelier cells (Howard et al. 2005) formsynapses on axon initial segments of GCs and are thereforethought to control the output GC spikes. Receiving inputsfrom GCs, axo-axonic cells are involved in feedbackinhibitory circuits, very likely contributing to mechanismsof PPI (Sayin et al. 2003) in a similar manner as BCs. Hilarcommissural-association pathway-related (HICAP) cells tar-get proximal dendrites of GCs. Because of the location of theirsomata in the hilus, these cells also receive incoming synapsesfrom GCs and are thus suitable for dendritic feedbackinhibition of GCs, potentially modulating PPI of GC spikes.Indeed, although our simulations suggest that HCs do notcontribute significantly to PPI mechanisms, other dendriticinterneurons (e.g. HICAP cells) might modulate PPI incooperation with HCs but only if the total strength of dendriticfeedback inhibition is much higher than the physiologicalstrength of HC-GC synapses (Supplementary Fig. c). Inaddition, interneurons with somata in the molecular layer(e.g. molecular layer perforant path-associated (MOPP)cells) are capable of providing GCs with dendritic feed-forward inhibition since they are contacted by directexcitatory inputs from the perforant path (Ferrante et al.2009). Future experimental and modeling studies willclarify the role of axo-axonic, HICAP and MOPP cells forPPI and dentate gyrus excitability.

Fast-spiking BCs are parvalbumin (PV)-positive. Thecomplexity of the dentate gyrus model could be increasedby adding second major group of perisomatic interneurons:regular-spiking cholecystokinin-positive BCs (Houser2007). Importantly, in CA1, only PV-containing BCs

contribute to fast disynaptic IPSCs mediating feed-forward-driven inhibition (Glickfeld and Scanziani 2006).On the other hand, CCK-containing BCs integrate feed-forward and feedback excitation from pyramidal cells anddischarge 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 acomputational model of the dentate circuitry containingCCK cells which can be recruited only by a combination of afeed-forward and feedback drive. In this context it is notablethat seizure-induced loss of CCK interneurons providingaxo-somatic inhibition has been reported to underlie reducedPPI (Sayin et al. 2003). Knockout mouse models of reducedexcitatory drive onto PV-containing BCs have recentlybecome available (Fuchs et al. 2007; Rácz et al. 2009). Oursimulations predict that field recordings in the dentate gyrusof these mice will reveal reduced PPI because of impairedrecruitment of perisomatic inhibition of GCs.

Interestingly, PPI measured in vitro has a shorter timecourse (10–20 ms, Kleschevnikov et al. 2004) than PPIrecorded in vivo. The reason for this temporal difference isnot known but it may be due to severed interneuronalconnections in hippocampal slices and/or due to impact ofactivated extradentate circuits in vivo. PPI in the “isolated”DG network model seems to better correspond quantita-tively to the in vitro situation.

In the present model, only glutamatergic AMPA andGABAA synapses are modelled. In future dentate gyrusmodels, additional synaptic receptors (e.g. NMDA,GABAB receptors) should be incorporated and studied inthe context of network activity. For example, PPDI is believedto be mediated by GABAB autoreceptors (Steffensen andHenriksen 1991; Davies et al. 1991). Hence the inclusionof GABAB receptors in the network model would allowfor realistic simulations of the PPDI part of the PPI/PPDIcurve. Furthermore, it would be interesting to add diversesynaptic plasticity mechanisms and investigate theirrelevance for network excitability changes. Includingshort-term plasticity (Jalil et al. 2004) would be particu-larly intriguing since previous experiments and simplifiedsimulations showed that enhanced presynaptic short-termplasticity (paired-pulse facilitation of EPSPs) at PP-BC,GC-BC and PP-GC synapses paradoxically increased PPIof population spikes (Thomas et al. 2005). Moreover,paired-pulse depression of IPSCs which has been reportedat BC-GC synapses (Kraushaar and Jonas 2000) representsanother potential mechanism for altering PPI in the dentategyrus. Likewise, long-term plasticity of distinct synapticconnections, e.g. on interneurons mediating feed-forward(Lamsa et al. 2005; Lamsa et al. 2007a) or feedbackinhibition (Lamsa et al. 2007b; see also Kullmann andLamsa 2007) may also have important implications for thenetwork behavior and inhibition and thus should be

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incorporated in dentate network models (c.f. Benuskovaand Abraham 2007).

Of note, to get a more accurate representation of thepaired-pulse field responses in the dentate gyrus, in additionto implementing further mechanisms and biological details,the number of model cells should be upscaled (Morgan etal. 2007) and explicit computation of dentate extracellularpotentials based on the distance from a current source to themeasurement should be performed (c.f. Gold et al. 2006).

In conclusion, computer modeling provides a useful tool fordetermining the importance of various synaptic and intrinsiccellular mechanisms for paired-pulse field potential responses.Changes in network inhibition play an important role in avariety of pathological conditions including epilepsy andmood disorders (Freund and Katona 2007; Fritschy 2008).Therefore, computational analyses of PPI mechanisms mayhelp better understand the origin of the diseases accompaniedby dysfunctions of neuronal excitability (Lytton 2008).

Acknowledgments This work was supported by the DeutscheForschungsgemeinschaft (JE 528/1-1 to P.J. and DE 551/8-1 to T.D.).We thank two anonymous reviewers for their helpful comments andsuggestions.

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