Epileptogenesis due to glia-mediated synaptic scaling

*Author for c

Received 6 SeAccepted 13 O

Epileptogenesis due to glia-mediatedsynaptic scaling

Cristina Savin*, Jochen Triesch and Michael Meyer-Hermann

Frankfurt Institute for Advanced Studies, Ruth Moufang Strasse 1,60438 Frankfurt am Main, Germany

Homeostatic regulation of neuronal activity is fundamental for the stable functioning of thecerebral cortex. One form of homeostatic synaptic scaling has been recently shown to bemediated by glial cells that interact with neurons through the diffusible messenger tumournecrosis factor-a (TNF-a). Interestingly, TNF-a is also used by the immune system as a pro-inflammatory messenger, suggesting potential interactions between immune systemsignalling and the homeostatic regulation of neuronal activity. We present the firstcomputational model of neuron–glia interaction in TNF-a-mediated synaptic scaling. Themodel shows how under normal conditions the homeostatic mechanism is effective inbalancing network activity. After chronic immune activation or TNF-a overexpression byglia, however, the network develops seizure-like activity patterns. This may explain whyunder certain conditions brain inflammation increases the risk of seizures. Additionally,the model shows that TNF-a diffusion may be responsible for epileptogenesis after localizedbrain lesions.

Keywords: homeostasis; synaptic scaling; neuron–glia interaction;neuro-immune interaction; epilepsy

1. INTRODUCTION

For the brain, as for any biological system, the onlyconstant is change. In order to maintain corticalnetworks in a dynamic regime that allows for efficientinformation processing a variety of homeostaticmechanisms are used (Turrigiano & Nelson 2004).Such activity regulation occurs on a wide range of timescales—from milliseconds to days—and affects bothintrinsic neuron properties and synaptic strength.

A powerful mechanism for regulating overall net-work activity is synaptic scaling, which scales allexcitatory synapses of a neuron to compensate forchanges in synaptic drive. This type of homeostaticregulation has been demonstrated in various experi-mental settings (Turrigiano et al. 1998; Turrigiano2007) and its theoretical properties have been studiedin computational models (Abbott & Nelson 2000). Theprecise biological signalling mechanisms underlyingsynaptic scaling remain poorly understood, however.

Recent evidence suggests that glia—support cells inthe brain—and the soluble form of tumour necrosisfactor-a (TNF-a) may be involved in a specific form ofsynaptic scaling (Beattie et al. 2002; Stellwagen &Malenka 2006). It was shown that acute application ofTNF-a or its long-term production after chronicactivity blockade increases AMPA receptor surfaceexpression in hippocampal neurons, thus strengtheningexcitatory synapses. Furthermore, the surplus TNF-a

orrespondence ([email protected]).

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that accompanies chronic activity blockade is producedby local glial cells (Stellwagen & Malenka 2006).Specifically, it is thought that glial cells estimate thesynaptic drive to neurons via neurotransmitter spil-lover at the synapses (Volterra & Meldolesi 2005).Activated glial cells, in turn, stimulate the post-synaptic neurons via TNF-a, inducing an increase inexcitatory synaptic strength. The process is accom-panied by the endocytosis of GABAA receptors(Stellwagen & Malenka 2006), which results in adecrease in inhibitory synaptic strength. In summary,the neuromodulator TNF-a (Pan et al. 1997; Vitkovicet al. 2000) seems to be of vital importance forbalancing neuronal activity in the cortex.

Interestingly, TNF-a also plays an important role inthe immune system. It is a pro-inflammatory cytokinewhose levels can rise dramatically during local acuteimmune responses. A 10-fold increase in serum isfrequently found, and even 100-fold increases are seenduring sepsis (Damas et al. 1992; Haagmans et al. 1994;Galic et al. 2008). Produced by immune cells such asmonocytes, T-lymphocytes and phagocytes, TNF-a canactivate neutrophils and macrophages, control therecruitment of immune agents from the blood andregulate the permeability of the blood–brain barrier(BBB) to soluble molecules (Deli et al. 1995; Rosenberget al. 1995; Bechmann et al. 2007).

The dual role of TNF-a as both pro-inflammatorycytokine and neuromodulator leads to the interestinghypothesis that TNF-a produced during an immune

in the brain may interfere with theresponse

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668, 655� J. R. Soc. Interface (2009)

doi:10.1098/rsif.2008.0387

Published online 4 November 2008

This journal is q 2008 The Royal Society

TNF-a production

TNF-a diffusion

synapticscaling

synaptic footprint

neuron network

glia

glutamatespillover

Figure 1. Overview of the model of homeostatic synapticscaling by neuron–glia interaction: glial cells estimate thesynaptic drive received by neurons via glutamate spillover.Glial cells adjust their TNF-a production as a function of theestimated glutamate level. Diffusing TNF-a reaches theneurons and triggers the scaling of excitatory synapses.

C. Savin et al.Epileptogenesis and synaptic scaling656

homeostatic regulation of synapses, potentially increas-ing synaptic strength sufficient to trigger paroxysmalactivity. This interference between different signallingpathways could explain some of the recent evidencesuggesting an immune system influence in seizureinitiation in certain pathological conditions (Vezzani2005; Lucas et al. 2006).

In order to investigate the relationship betweenTNF-a and epileptiform activity, we have developed acomputational model of the interaction of neurons andglial cells during homeostatic synaptic scaling. To thebest of our knowledge, it is the first model to simulate anetwork of spiking neurons interacting with a popu-lation of glial cells. As a first attempt of this type, ourmodel cannot aspire to capture the full complexity ofneuron–glia interactions. Instead, it focuses on TNF-a-mediated homeostatic regulation and does notconsider other ways through which glial cells caninfluence neuronal excitability, such as the regulationof extracellular potassium (Kofuji & Newman 2004) orthe release of glutamate or ATP (Newman 2003).

Supporting our hypothesis, the model shows that anoverall increase in TNF-a levels following chronicinflammation or TNF-a overexpression by glia canpush the network activity into a paroxysmal regime. Inaddition, it shows that neuronal hyperexcitability alsoarises after localized disruptions in network structure,resulting from simulated local lesions. In particular,following partial deafferentation, TNF-a produced byglial cells within the lesion area diffuses to theneighbouring tissue and triggers network bursts.

2. MATERIALS AND METHODS

We model the interaction between a population ofneurons and glial cells (figure 1). The neural networkmodel is a two-dimensional sheet of recurrentlyconnected spiking neurons. The synaptic scalingmechanism is modelled after the data from Beattieet al. (2002) and Stellwagen & Malenka (2006).Specifically, glial cells estimate total synaptic drivevia glutamate spillover and produce TNF-a in response.The TNF-a diffuses to neurons and its concentrationcontrols the strength of synaptic connections by scaling

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all excitatory weights of a neuron in a multiplicativefashion. The translation of local glutamate levels intoTNF-a and the adjustment of synaptic weights aremodelled by two sigmoid functions, with parametersestablished by a calibration step.

2.1. Neural network

We use a two-dimensional spiking neuron model(Izhikevich 2003) that can produce a rich set ofdynamical behaviours, while remaining computation-ally feasible,

dvðtÞdt

Z 0:04vðtÞ2 C5vðtÞC140KuðtÞCI ðtÞ

and

duðtÞdt

Z aðbvðtÞKuðtÞÞ;

where v(t) is the membrane potential; u(t) is therecovery variable; I(t) is the total post-synaptic currentfor the neuron; and a and b are model parameters.When the membrane potential reaches the thresholdvalue of 30, a spike occurs, the membrane potential isreset to its rest value and the recovery variable isupdated: vðtÞ)c and uðtÞ)uðtÞCd, where c is themembrane rest potential and d is a parameter of therecovery variable. Different dynamic behaviours can beobtained by varying the parameters a, b, c and d. Weconsider only pyramidal neurons (regularly spiking RS,with aZ0.02, bZ0.1, cZK65 and dZ8) and inhibitoryinterneurons (fast spiking FS, aZ0.1, bZ0.2, cZK65and dZ2).

AMPA and GABAA synapses are modelled asexponentially decaying conductances g, which are instan-taneously increased upon the arrival of an afferent spike:ðdgðtÞ=dtÞZKðgðtÞ=tsynÞC �g

PiDðtiÞdðtK tiÞ; where �g

represents the maximum synaptic increase per spikeevent (here, �gZ1); ti is the time of the ith spike; andD(ti)is a synaptic depression variable described below. Thetime constant tsyn is the synaptic conductance decay,with default values 10 and 20 ms for AMPA andGABAA

synapses, respectively (Moreno-Bote & Parga 2005; fordetails, see appendix A.1).

Excitatory synapses in our model exhibit short-termsynaptic depression, arising due to the temporarydepletion of presynaptic vesicles, with an exponentialrecovery to baseline level (Abbott et al. 1997; Tsodyks &Markram, 1997)

dDðtÞdt

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where U is the fraction of synaptic resources, which isconsumed by a single event (UZ0.05) and tD is the timeconstant of recovery for the synaptic resources (in therange 450–700 ms) (Abbott et al. 1997). In someexperiments we also considered synaptic delays, in therange [0,dmax], drawn from a uniform distribution(dmaxZ32 ms).

The total input current I received by a neuronobtained by summing up the post-synaptic currents forall incoming synapses is

I ðtÞZXi

AiwigiðtÞðEiKvðtÞÞ;

Epileptogenesis and synaptic scaling C. Savin et al. 657

where Ai is a scaling factor, with different values for asynapse connecting an excitatory/inhibitory neuron toan excitatory/inhibitory neuron (default values areAEEZ0.02 for excitatory–excitatory connections andAEIZAIEZAIIZ0.03 for the rest); wi is the strength ofthe ith synapse (wi2[0,1]; gi(t) measures the instan-taneous synaptic conductance for synapse i; Ei is thereversal potential of the synapse (0 for excitatorysynapses and K70 for inhibitory synapses); and v(t) isthe membrane potential of the post-synaptic neuron.

The network consists of N!N neurons (NZ25), 80per cent RS excitatory and 20 per cent FS inhibitoryneurons, organized in a two-dimensional lattice.Neurons connect locally, within a square synapticfootprint of size r!r (rZ7), with probability pconnZ0.2 and periodic boundary conditions. A weakexcitatory input (AinZ0.03) is provided from NinZ25input neurons, which connect to each neuron in thenetwork with probability pinZ0.2 and spike as inde-pendent Poisson processes with a frequency finZ10 Hz.

2.2. Glial model

The glial tissue is organized in a lattice similar to theneuron network, with one glial cell per neuron.Consistent with the assumptions in Stellwagen &Malenka (2006), the glial cells monitor excitatorydrive to neighbouring neurons via glutamate spillover,considered to be proportional to the total drive receivedby the neuron at each position (x,y), averaged overa time window tglut: �I x; yðtÞZð1=tglutÞ

Ð ttKtglut

Ix; yðtÞdt:The neuronal activity is regulated by changes inthe excitatory synaptic strength, corresponding to theAMPAr increases described experimentally. As thereported reduction in GABAA receptors is smaller inrelative magnitude (Stellwagen & Malenka 2006) andgiven that the analysis of the network properties revealsa weak dependence of the activity on AIE (see appendixA.1), our model does not consider GABAA receptorregulation. However, such regulation is expected toexacerbate the results described below (simulationsshowed no quantitative difference in the case when thesame gain factors are considered for both the excitatoryand the inhibitory regulation). Although experimentalreports on synaptic scaling involve pyramidal neurons(Turrigiano et al. 1998; Ogoshi et al. 2005), themodelled scaling affects excitatory synapses on bothpyramidal and inhibitory neurons, for simplicity.

To account for the astrocytic arborization, the localglutamate estimates are convolved with a normalizedGaussian kernel: CglutðtÞZ �I ðtÞ*Gs1

; where GsZð1=2ps2ÞexpðKðx2Cy2=2s2ÞÞ, and �I ðtÞZð�I x; yðtÞÞx; y isthe matrix of glutamate estimates for all neurons at timet (s1Z1.22, corresponding to a cell radius 3).

The TNF-a concentration is determined by the glialproduction, computed as a function of the localglutamate concentration, with an exponential decay,

dctnfðtÞdt

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ttnfand

ctnfNðtÞZ 1K1

1Cexp KcglutðtÞKcglut0

Kglut

� � ;

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where ctnf(t) is the local TNF-a concentration at timestep t; ctnfa(t) represents target TNF-a concentrationfor the current activity level; and ttnf is a time constantfor TNF-a concentration decay. The asymptotic valueof the TNF-a concentration is a function of theglutamate concentration at a glial cell cglutthe parameter cglut0 specifies the target glutamateconcentration value, and Kglut is a scaling parameter(unless specified otherwise, cglut0Z0.52, KglutZ2.5).

TNF-a diffuses to the neighbouring neurons, aprocess modelled by the convolution with anotherGaussian kernel Gs2

, with the default value s2Z1.58(cell radius 4):C 0ZC �Gs2

;where C and C 0 denote thematrices corresponding to the concentration at eachglial cell c and neuron c 0. The TNF-a triggers a changein the average synaptic conductance of the neuron w(t),wðtÞZ 1

N

PiwiðtÞ; described by the equation,

dwðtÞdt

ZKwðtÞKwNðtÞ

tw

and

wNðtÞZ1

1CeK

c0 ðtÞKc tnf0Kc

;

where c0(t) is the local TNF-a concentration at theneuron; tw gives the time scale of the synaptic strengthchange; and c0 and Kc are model parameters withdefault values c0Z0.5 and KcZ0.03.

The total change in conductance is distributed to thesynapses wi in a way that preserves their relativestrength, ðdwiðtÞ=dtÞZðdwðtÞ=dtÞðwiðtÞ=

PiwiðtÞÞ.

While the estimation of synaptic drive and theproductionofTNF-abyglial cells are very slowprocesses,such that observable changes occur on a time scale ofminutes to days (Stellwagen&Malenka 2006), themodeluses much faster time constants in order to reducesimulation time. Specifically, for all results presented, thehomeostatic regulation of synaptic strength occurs of theorderof seconds rather thanhoursordays (timeconstantsfor glutamate estimation tglut, the glial TNF-a pro-duction ttnf and the synaptic modification tw werereduced to 1, 10 and 1 s, respectively). However, sincethe time constants of the homeostatic plasticity are stillmuch slower than the activity dynamics of the spikingnetwork, the qualitative behaviour of the overall model isnot altered.

Little is known quantitatively about the processesunderlying TNF-a production and the correspondingsynaptic scaling. Further experiments are needed toconstrain the model parameters relating neuronalactivity to TNF-a production and increase in synapticstrength. In order to set these ‘free’ parameters of themodel, we use a calibration procedure that assumesthat the synaptic scaling robustly maintains homeo-stasis of the neuronal activity after changes in input(see appendix A.2 for details).

(t), while

3. RESULTS

3.1. Increases in TNF-a can induce seizures

It is established that during chronic inflammation theTNF-a concentration inside the brain can increase(Gutierrez et al. 1993; Hanisch & Kettenmann 2007).

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Figure 2. Effects on network activity due to a TNF-a increase. (a) Changes in average neuronal activity after chronicinflammation (external TNF-a values displayed in different colours; blue, 10K3; yellow, 10K5; red, 10K7). The severity of immuneresponse (b) affects burst frequency and (c) induces an increase in the average firing rate. (d ) Changes in average neuronalactivity in the case of TNF-a overexpression by glia (for different c0 values; blue, 2.0; yellow, 1.0; red, 0.5). The degree ofoverexpression affects (e) burst frequency and ( f ) the average firing rate. Results are averaged over 10 trials, with error barsindicating standard error.

C. Savin et al.Epileptogenesis and synaptic scaling658

Additional TNF-a can either be produced locally or canoriginate in serum and penetrate the BBB. Localproduction is owed mostly to activated microglia, butadditional TNF-a sources are monocytes or lympho-cytes, which can enter the brain due to changes in BBBpermeability (Prat et al. 2005). Also, systemic infec-tions can trigger the activation of immune systemagents inside the brain, in response to endotoxaemia(Rivest et al. 2000; Galic et al. 2008), for example. Thisis of particular interest since bacterial infection (such asbacterial meningitis) is sometimes accompanied byseizures (Vezzani & Granata 2005), suggesting that

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TNF-a or other pro-inflammatory cytokines might bepart of the mechanisms inducing an increased suscep-tibility to seizures during brain infections.

In order to investigate this hypothesis, we consider thecase of a chronic inflammation. As a first approximation,we model the increases in TNF-a levels caused by animmune system activation by a spatially homogeneousTNF-a source. As the synaptic weights are initialized atrandom, the disruption is induced after the network hasreached the homeostatic regime (tZ150 s) and involvesadding a small constant amount of TNF-a at each timestep to the local glial production (figure 2a–c).

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Figure 3. (a) Typical example of network bursts occurringafter a 10% increase in excitatory synaptic strength. (b)Voltage traces of a neuron in the control case (upper) andduring a network burst (lower).

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Epileptogenesis and synaptic scaling C. Savin et al. 659

If the external TNF-a contribution is big enough(greater than 10K6; figure 2b), the local TNF-aconcentration remains elevated, causing an increase inthe average synaptic conductance, accompanied by arise in the average firing rate of the neurons (figure 2c).Additionally, as the excitatory synapses are strength-ened, the activity becomes increasingly synchronized(a detailed analysis of how neuronal synchronizationdepends on the scaling of excitatory synapses can befound in appendix A.1). Transient increases in theinput, due to normal activity fluctuations, are amplifiedby the recurrent excitatory connections and theneuronal network experiences seizure-like bursts(similar to those in figure 3a). Consistent with theexperimental findings (Nita et al. 2006), regular spikingneurons exhibit spike bursts (figure 3b, lower curve),synchronized over the population. For high values ofexternal TNF-a, the effect saturates (figure 2b). Therelationship between average excitatory synapticstrength and the development of network bursts isinvestigated in detail in appendix A.1. Importantly, theanalysis of a reduced population-level version of thesystem shows that the robustness of the system toadditional TNF-a sources depends on the parametersKglut and KC, a result confirmed in simulation (seeappendix A.3). Specifically, the stable state of thesystem is determined by the total gain of the feedbackloop (essentially by the product Kglut�KC). Thestability of the system to a certain destabilizingscenario, such as a chronic immune response, dependscritically on the individual parameters, however. For amild inflammatory state, the network can either remainstable or develop strong seizure-like patterns ofactivity, as a function of KC (See appendix A.3).

Transgenic mice mildly overexpressing TNF-a candevelop spontaneous seizures (Akassoglou et al. 1997)(strong overexpression is usually fatal), an effect alsocaptured by our model. In order to model various levelsof TNF-a overexpression, we simulate an increase inthe target glutamate level of the system (measured byparameter cglut0). This manipulation forces glia toproduce more TNF-a than in the control case. Similarto the effects observed experimentally, the networkreaches a hyperexcitable state, with the probabilityof developing seizures being related to the degree of

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TNF-a overexpression. As shown in figure 2d,e, if thechange in synaptic strength is big enough, the networkactivity becomes paroxysmal.

3.2. A sustained reduction in input can triggerseizures

Simulations used for the calibration of system par-ameters, which involve changes in input firing rate (seeappendix A.2), suggest that the dynamics of thenetwork can change qualitatively due to chronicchanges in the input rates. Therefore, we investigatethe degree of network synchronization, for differentinput frequencies. As before, the system is first allowedto converge to the homeostatic state (150 s). After-wards, the mean input frequency is changed in a stepfunction-like fashion to different levels and thefrequency of the network bursts is evaluated (figure 4).

After a sudden but sustained reduction in input, thenetwork initially falls almost silent, but later recoversits normal activity level due to the strengthening ofexcitatory synapses by synaptic scaling. However, as aresult of the adaptation, the network generates burstsat irregular intervals, provided the remaining input issufficient to drive the network (figure 4b, the 2 Hz case).Correspondingly, after a sudden increase in input, thenetwork responds with an initial burst of activity, afterwhich it slowly recovers to a low-activity regimewithout any seizures. In both the cases, the homeostaticmechanism brings the average firing rate of theneuronal population back to baseline (figure 4c).These results are consistent with those from a recentlypublished work (Frohlich et al. 2008) that consideredonly a simplified one-dimensional network structure,with local connections, facilitating burst propagation.

3.3. Local lesions induce seizures

The experiments involving variations in input ratesdescribed above suggest that the dynamics of thenetwork can change qualitatively for a long-term

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Figure 5. Effects of local lesions. (a) Evolution in time of average synaptic strength for individual neurons after a local lesion ((i)tZ0 s, (ii) tZ150 s, (iii) tZlesion, (iv) tZ300 s, (v) tZ450 s). (b) Corresponding average firing rate for the neuronal population.(c) Increase in burst frequency and (d ) firing rate relative to baseline for different lesion severity levels and (e, f ) lesion sizes. (g)Time evolution of average excitatory synaptic strength for the neurons (i) within and (ii) outside lesions, for a lesion size 15!15and 100% damage of input synapses. Different colours mark different trials. (c– f ) Results estimated over 10 trials, with error barsmeasuring the standard error.

C. Savin et al.Epileptogenesis and synaptic scaling660

reduction in input. Thus, it is plausible to assumethat lesions can also enhance seizure predisposition(Timofeev et al. 2000; Houweling et al. 2005). Incontrast to previous approaches, here we focus on themechanism of homeostatic regulation, specifically onthe spatial effects due to TNF-a diffusion.

We consider localized lesions in the shape of a squareof varying size (figure 5a). The network starts fromrandom initial conditions (tZ0), individual neurons

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having variable average excitatory synaptic strength.In time, the TNF-a-mediated synaptic scaling equalizesthe total excitatory drive to neurons. Deafferentation isinduced when the network has reached a homeostaticstate (tZ150 s) and causes a certain percentage of thesynapses from the input neurons to neurons in thelesion area to be removed. We study the dynamicregime after the lesion, for various lesion sizes anddifferent extents of synaptic damage.

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Figure 6. Effects of local lesions for local synaptic scaling. (a)Evolution in time of average synaptic strength for individualneurons during a 100%, 15!15 local lesion ((i) tZ0 s, (ii)tZ150 s, (iii) tZlesion, (iv) tZ300 s, (v) tZ450 s). (b)Corresponding average activity for the entire neuronal popu-lation, and (c) for separate affected and unaffected neuronpopulations. (d ) Evolution of average weights within (red) andoutside (blue) the lesion. (e) Single trial converge of averageexcitatory weights for a 100% lesion (red, in; blue, out).(f ) Average activity within and outside an 80% 15!15 lesion.

Epileptogenesis and synaptic scaling C. Savin et al. 661

When varying the proportion of deafferentation for afixed lesion size (15!15), the strength of remainingsynapses reaches a value large enough to facilitatenetwork bursts (figure 5b). The burst probabilityincreases with the severity of the lesion (figure 5c),consistent with the results in Houweling et al. (2005).Furthermore, the effect is observable for a wide range ofpartial deafferentation levels, as observed experimen-tally (Timofeev et al. 2000). Similarly, when the lesionaffects a fixed percentage of the input synapses (100%),the network dynamics depend on the size of the affectedarea. For small lesions the effect is negligible, but itincreases with the size of the lesion, as shown infigure 5e. For almost complete deafferentation,however, the seizure-like behaviour disappears (notshown). As neurons in our model have no intrinsicspontaneous activity, the network is driven by theexternal input. Consequently, when the lesion damagesa large number of input connections, the remainingdrive is insufficient to generate any activity (also, theoverall firing rate decreases, as shown in figure 5 f ). Itmay trigger large bursts if the input configuration isright, but most of the times the network is quiescent.

A closer inspection of the evolution of averageexcitatory strength within and outside the lesion area(figure 5g) reveals a potential explanation of the effect.Owing to the decrease in glutamatergic input, glial cellsin the lesion area start producing TNF-a and theaverage excitatory strength increases (to a value higherthan before the lesion, as the rate of the input is higherthan the population firing rate). However, TNF-adiffusion causes the same increase to the weightsoutside the lesion.

As the increased TNF-a production within the lesionalso affects the neighbouring ‘healthy’ neurons, we canassume that TNF-a diffusion may be an important causeof increased synchrony in thenetwork. Inorder to test thishypothesis, we compare the dynamics of the networkafter 100 per cent deafferentation, within a 15!15 area,for various diffusion coefficients. As predicted, when thesynaptic scaling process is local to each neuron, theresponse is restricted to the lesion area (figure 6a) andbursts disappear completely, as shown in figure 6b. Also,note that local synaptic scaling leads to an increasedvariability in average excitatory strength for neurons(figure 6a). For the case of 100 per cent lesion, the damageis too severe for the homeostatic mechanism to be able torecover the original activity level (figure 6c). Also, forlocal regulation convergence becomes significantly slower(figure 6d,e). For an 80 per cent lesion, the activitywithinthe lesion goes back to baseline (figure 6 f ).

Our result suggests that, as predicted, the strength-ening of synapses in neighbouring neurons due to TNF-a diffusion is responsible for the network hyperexcit-ability in the case of localized lesions. When diffusiondoes occur, the actual parameters controlling theastrocytic arborization range and TNF-a diffusion arenot very important, and no systematic differences areobserved in the system dynamics. Importantly, theresult suggests that homeostatic regulationmechanismsthat rely on the diffusion of neuromodulators are proneto become maladaptive in cases of localized disruptionsin the system.

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4. DISCUSSION

We have presented a first model of glial cells interactingwith a population of neurons by homeostatic synapticplasticity. The model suggests that the dual role ofTNF-a as both a pro-inflammatory messenger of theimmune system and as a mediator of synaptic scalingcan lead to interesting interactions. Specifically, itoffers a novel mechanism through which immuneactivity in the brain can influence the dynamics ofcortical circuits and increase seizure susceptibility. Inaddition, our model builds on previous data linkinghomeostatic mechanisms and seizures (Timofeev et al.2000; Houweling et al. 2005; Frohlich et al. 2008) in thecontext of localized lesions. It implements a biologicallyplausible mechanism for the synaptic upregulationfollowing deafferentation. Interestingly, in our model,diffusion of TNF-a through cortical circuits was shown

C. Savin et al.Epileptogenesis and synaptic scaling662

to be critical for the development of paroxysmalactivity. This represents a clear distinction to previousmodels (Houweling et al. 2005; Frohlich et al. 2008),which explicitly implement the homeostatic regulationof synapses as a function of the global populationactivity (corresponding to a large TNF-a diffusion inour model). This is particularly relevant because thedegree of locality of the process was shown to affect thefinal outcome after deafferentation. This effect could beenhanced by other means for spreading of TNF-a fromthe lesion area, such as the range of the astrocyticarborization (a result confirmed in simulations)orbyglialcommunication (e.g. via gap junctions; Giaume &McCarthy 1996). Currently, little is known about howTNF-a and other proteins diffuse through cortical tissueand more data are needed to constrain future models.

At present, the immune system’s influence onseizures is still controversial. Positive evidence for animmune system role in triggering seizures comes fromclinical practice, as anti-inflammatory drugs canprovide effective anti-epileptic treatment in somecases. Another strong indication comes from con-ditions, such as Rasmussen’s encephalitis, that areassociated with an increase in pro-inflammatory mar-kers (Aarli 2000; Vezzani & Granata 2005). Moreevidence comes from animal models. Chronic inflam-mation was shown to trigger spontaneous seizures inmouse models of pneumococcal meningitis, cerebralmalaria or cysticercosis. In the case of meningitis, theincidence of seizures was decreased by treatment usingan inhibitor of a TNF-a-converting enzyme, whichreduces the levels of soluble TNF-a (Meli et al. 2004).Additionally, inflammation induced by lipopolysac-charide (LPS), for example, is known to enhance theeffect of proconvulsive drugs (such as kainic acid), aneffect blocked by anti-inflammatory drugs (Vezzani &Granata 2005). In a different study, systemic infectioncaused by Shigella dysenteriae was reported to enhancethe seizure-inducing effect of pentylenetetrazol, an effectmediated by TNF-a and interleukin-1b, which a sub-sequent study revealed to be non-monotonic as a functionof the TNF-a concentration (Yuhas et al. 2003).

All in all, the outcome of pharmacological manipula-tions of TNF-a levels depends on a variety of factorsincluding concentration, time scale, activated pathwayand receptors involved. As part of a complicatedmolecular network, with multiple regulatorymechanisms running in parallel, TNF-a effects onseizures are manifold. When activating a differentsignalling pathway, the cytokine can have beneficialeffects, improving neuronal survival by the release ofneurotrophic factors (Akassoglou et al. 1997; Balossoet al. 2005). In the case of brain immune systeminterference, a beneficial pharmacological manipulationwould ideally affect the synaptic scaling mechanism,without blocking the protective effects of TNF-a. Apotential target for selectively disabling homeostaticregulation is the TNF-a receptor p55, as protectiveeffects are mediated by a different receptor (p75)(Balosso et al. 2005).

Recent experimental evidence (Galic et al. 2008) hasshown that a LPS-induced infection in rats, occurringduring a critical period in development, induces a long-

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lasting increase in neuronal excitability and seizuresusceptibility. The effect is mediated by TNF-a and canbe mimicked by the intracerebral administration of ratrecombinant TNF-a. The nature of the changesinduced by a transient inflammatory response duringdevelopment is still unclear. However, it is interesting tonote that, although the baselineTNF-a levels seemnot tobe altered in the adult, the cytokine levels following aninduced seizure are increased, potentially also due to anincrease in the number of astrocytes. In the context of ourmodel, it is possible to imagine that the initial inflam-mation may alter the ‘gain function’ for the astrocyticTNF-aproduction,making the systemmoreunstableandthus more prone to seizures. Further experiments areneeded to clarify whether TNF-a-mediated synapticscaling plays a role in this case.

An interesting question in this context is why theimmune system and the synaptic scaling mechanismrely on the same messenger protein, if this can lead tosuch unwanted crosstalk. One possible answer is thatthe immune and nervous systems are usually wellisolated from one another through the BBB. Accordingto an alternative view, TNF-a has an immune-relatedrole in the brain under normal circumstances. Immuneagents are frequently observed in the brain (Bechmannet al. 2007) and glial cells can also acquire immunefunctions (Sebire et al. 1993). From this vantage point,TNF-a is part of a well-balanced network of molecularmechanisms in the homeostatic state. It is only underchronic conditions that the excess of TNF-a turnsharmful and increases seizure susceptibility, while shortand local brain infections do not affect the stability ofthe system.

Taken together, our results illustrate that thereliance of immune signalling and synaptic scaling onthe same messenger molecule, TNF-a, may be respon-sible for infection-related seizures in a number ofconditions. A great challenge for future experimentswould be to carefully analyse the interference betweenthe signalling pathways regulating an inflammatoryresponse and homeostatic synaptic regulation. Speci-fically, we need a better understanding of how the TNF-a signal is translated into AMPAr changes in neurons.

We would like to thank Philipp Wolfrum for helping with thecontrol system analysis and Dr Michael Madeja and DrKarsten Krakow for fruitful discussions. The authors grate-fully acknowledge the support of the Frankfurt Center forScientific Computing. FIAS is supported by the ALTANAAG and the Hertie Foundation. J.T. and C.S. are supportedby EC MEXT-project PLICON. M.M.H. is supported by theEC NEST project MAMOCELL within FP6.

APPENDIX A

A.1. Network parameters

We address the question of how changes in theparameters of the neuron network model alone affectthe dynamics of the neural circuit, especially in relationto the generation of seizure-like events. Such an activityburst is considered to occur when the population firingrate (estimated for 10 ms time bins) is higher than the

(a) (b)

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Hz)

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0.025 0.050 0 0.025 0.050

Figure 7. The dependence of burst frequency and average duration on (a,b) the strength of excitatory-to-excitatory and (c,d )inhibitory-to-excitatory synapses, respectively. Values are estimated over 10 trials, with error bars indicating standard error.

0 0.2 0.4 0.6 0.8 1.00.1

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s)

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(c) (d )

Figure 8. The effects of synaptic depression on network bursts. Burst frequency and duration as a function of parameters (a,c) Uand (b,d ) tD, respectively.

Epileptogenesis and synaptic scaling C. Savin et al. 663

burst threshold (default, 10 Hz). We analyse the effectsof varying the connectivity, synaptic properties andinput frequency in order to determine the conditionsunder which the network becomes hyperexcitable.These results are also used for optimizing the width ofthe time bin and the burst threshold for the synapticscaling simulations (specifically, 30 ms and 10 Hz).

We start by analysing the importance of varying thesynaptic strength of excitatory–excitatory connections.As the strength of excitatory synapses is increased, thenetwork dynamics change from a low firing to largesynchronized population bursts. As shown infigure 7a,b, both the number and duration of burst

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events can be significantly altered by varying thestrength between excitatory synapses. As high TNF-aconcentrations scale up excitatory synapses, this resultsupports the idea that for inflammatory responseswhich raise the TNF-a levels inside the brain suf-ficiently the network activity can become paroxysmal.

In order to determine the effects of inhibition, wehave studied the impact of varying the amount ofinhibition within the neuron population, i.e. the scalingfactor for the inhibitory to excitatory synapses (AIE).The results in figure 7c,d show a decrease in burstduration, but no significant effect on their frequency, inthe parameter range considered.

10 30 50 70 900

1

2

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Hz)

10 30 50 70 9020

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s)

6 10 14 18 220

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Figure 9. Dependence of burst properties on (a,b) network size and (c,d ) connectivity range.

C. Savin et al.Epileptogenesis and synaptic scaling664

It was shown that some amount of inhibition isrequired for preventing the network activity from‘exploding’, but burst termination can also be achievedby other mechanisms as well. As synaptic depressionreduces the efficacy of synapses in response to highactivity, it is probable that the mechanism is alsoimportant for burst termination. To test this hypothesis,we study the parameters influencing synaptic resourcesconsumption (U ) and recovery (tD) and their effects onburst properties. The results illustrated in figure 8demonstrate that short-term synaptic depression playsa role in burst termination, consistent with the findingsreported in Houweling et al. (2005). The fraction ofresources consumed per burst event influences signi-ficantly the burst duration, as slower exhaustion of thesynaptic resources makes bursts last longer. It alsoincreases to some extent the burst frequency. The timeconstant of the recovery tD influences the burstfrequency, since the longer it takes to recover the initialamount of synaptic resources, the longer it takes totrigger another network burst event.

Burst duration values suggested by experimentalfindings are typically larger than those produced in ourmodel, of the order of 200–400 ms (Nita et al. 2006), ascompared with 60–100 ms in simulations. We hypothe-size that the network size is too small for sustaining thesynchronous activity for longer times. In order to test thisassumption, we have systematically varied the networksize, while maintaining the connectivity parametersconstant. This variation is still insufficient to matchexperimental values, but burst duration is increased forlarger networks, as seen in figure 9. Synaptic delays canbe a potential mechanism for prolonging bursts further.By introducing synaptic delays (dmaxZ32 ms), we havebeen able to prolong burst events by asmuch as 25–30 percent. Owing to the computational overhead, mostexperiments do not consider synaptic delays, however.

The range of lateral connectivity also plays a role inthe generation of bursts. When varying the range ofconnectivity and the connection probability such that

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the average incoming drive to neurons is kept constant,bursts occur only if the synaptic footprint is largeenough, suggesting that excitatory loops are essentialfor the emergence of seizure-like behaviour.

Owing to the variability in times between burstevents, it is likely that bursts are triggered byfluctuations in network input. In order to test thishypothesis, we compute a cross-correlogram of theinstantaneous (bin size of 10 ms) rates of input and thepopulation rate of the network, on one hand, and ofthe inputs and burst events, on the other. Both show astrong peak for the network at a time lag ofapproximately 20 ms, as shown in figure 10a. Tofurther confirm that transient increases in input can,on their own, trigger bursts, we perform an additionalexperiment. We change the average frequency of thePoisson process in a short time window (of length10 ms) and monitor whether or not a burst occurs100 ms after this input increase. The cross-correlationof the input–output rates shows similar results to theinitial experiment (figure 10b). Additionally, the burstprobability increases with the increase in frequencyduring the window, further supporting the idea ofbursts as input triggered events (figure 10c).

It is reasonable to assume that network bursts alsolead to an increase in overall neuronal synchronization.More specifically, we analyse how network synchroniza-tion depends on average excitatory synaptic strength,the quantity affected by synaptic scaling (specifically,AEE and AEI). For different scaling factors, the networkactivity is analysed (10 trials, each lasting 10 s). A totalof 1000 pairs of neurons are selected at random andthe cross-correlation coefficient is computed for eachpair. The average cross-correlation coefficients showthat strengthening of lateral excitatory synapsesincreases the synchronization of individual neurons inthe network (figure 11).

The synaptic time constants used in our modelare larger than those used in similar experiments(Houweling et al. 2005). However, these values do not

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Figure 10. (a) Cross-correlation between input and population rate for a 5 s trial, in bursting conditions (AEEZ0.03). (b) Cross-correlation between input rate and burst events, for transient increases the input frequency by an amount Df (AEEZ0.02)(light grey curve, 5; dark grey curve, 15; black curve, 20). (c) Increase in burst probability, following a transient increase ininput frequency.

1.0 1.2 1.4 1.6 1.8 2.00

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Figure 11. Average correlation coefficient of neurons for anincrease of average excitatory strength relative to baseline, fordifferent values of tsyn (see text for details; black curve, 10 ms;grey curve, 5 ms).

Epileptogenesis and synaptic scaling C. Savin et al. 665

play a critical role in the network dynamics. Theoreticalwork predicts that, for an exponentially coupled networkof excitatory and inhibitory neurons, synchronized firingis facilitated by shorter synaptic decay times (Kanamaru&Sekine 2005).We observe the same result in simulationfor tsynZ5 ms, after changing the synapse scalingparameters such that the total current of an ESP ispreserved (namely, AEEZ0.04, AEIZ0.06, AIEZ0.12,AIIZ0.12). Our experiments show an increase in syn-chronization at lower values of the excitatory coupling,for faster synaptic dynamics (figure 11, grey curve).

To summarize the results above, in the neuronalnetwork model considered bursts are triggered bytransient increases in the input, which are amplifiedby the recurrent excitatory architecture to a fullnetwork burst. The activation of the local inhibitorypopulation, together with the depletion of synapticresources terminates a burst event.

A.2. Model calibration

Current experimental data are insufficient for fullydetermining the parameters of the processes involved inTNF-a-mediated synaptic scaling. A reasonable con-straint is that, under normal conditions, the synapticscaling mechanism should be able to maintain homeo-stasis of neuronal activity. In particular, the synaptic

J. R. Soc. (2009)Interface

regulation should be able to preserve the average firing ofthe neurons in response to changes in the input firing rate.

The specific experiment performed involves slowramp changes in input (figure 12a). As previously, thesystem is allowed 150 s to reach a homeostatic statebefore the input rates are modulated. The analysisfocuses on two of the model parameters—the gainvalues for the TNF-a production as a function ofglutamate (Kglut) and the adjustment of excitatorysynaptic strength as a function of TNF-a concentration(Kc). The reciprocal of their product is an importantparameter of the model and can be viewed as a totalgain of the feedback loop (see appendix A.3).

As a calibration step, we select the gain thatmaintains the average population rate constant intime, independent of the change in input. For smallergains, the homeostatic mechanism is not able to fullycompensate for the changes in input, while for largegains the system overcompensates for these variations.As the gain defines a set of possible values for the twomodel parameters mentioned above, we select one suchpair for the subsequent experiments. The particularchoice can, however, be important for some patho-logical disruptions affecting the feedback loop (e.g.during an immune response), and the robustness of thesystem to such events can be enhanced by larger valuesfor Kc (see the analysis of the population behavioursbelow for a more detailed discussion).

For the selected parameters, the firing rates of theneuron population are maintained, as seen in figure 12a(the time average is computed by convolving theoutput firing rate with a Gaussian kernel, with sZ6 s). A more detailed study of the structure of thepopulation firing rate (figure 12b) reveals similar firingpatterns for the increase in input (blue) and constantfiring (grey) regime. In the case of a chronic decrease ininput (red), although the mean output rate is main-tained the activity of individual neurons becomes morecorrelated, as the excitatory weights are increased tocompensate for the input change.

A.3. Stability analysis

Although the homeostatic loop is not linear, looking ata large-scale linear approximation of the system mayenhance our understanding of its behaviour. For ahomogeneous connectivity structure, it is possible toconsider a spatial average of the variables and construct

(b)

time (s)time (s)

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Figure 12. (a) Homeostatic regulation of activity in response to changes in input (i). The low-pass filtered population firing rateafter an input increase (ii) or decrease (iii) is shown. (b) A closer view of the activity corresponding to the grey bars: after chronicinput reduction (iii), the strengthening of excitatory synapses makes neuron firing more synchronized, compared with thehomeostatic regime (i) or the reverse input change (ii). Population rates are estimated in 30 ms time bins.

G3G2G1goalglutamatelevel

TNF-aproduction

synapticscaling

networkactivity

–

Figure 13. Diagram of the large-scale linear approximation ofthe system.

C. Savin et al.Epileptogenesis and synaptic scaling666

a reduced model of the system, whose stability can beanalysed in the framework of linear control systems.

The block diagram of the reduced system is shown infigure 13. Several assumptions are required for thisapproximation to be valid. Firstly, we consider the caseof small variations around the fixed point. Hence, thetwo sigmoid functions that describe the processestranslating glutamate in TNF-a and correspondingsynaptic strength can be linearized around this fixedpoint. Secondly, we assume a linear mapping betweenthe average value of excitatory synaptic strength andthe glutamate level averaged for the neuronalpopulation.

More specifically, when considering the asymptoticvalue of the TNF-a concentration, as a function ofglutamate, linearized around the fixed point ctnf0,together with the exponential decay, we obtain thetransfer function for the TNF-a production as

G1ðsÞZa1

ttnfsC1;

where a1ZKð1=4KglutÞ is the gain of the process.Similarly, the transfer function for the synaptic

strengths regulation is

G2ðsÞZa2

twsC1;

with a2Zð1=4KcÞ.Based on the simulated data, we develop a phenom-

enological model of the network activity as a function ofaverage synaptic strength and input frequency. Forthis, we consider average synaptic weights in the rangeof 0.4–0.6 and input frequencies between 8 and 12 Hz(10 trials are considered for each parameter pair). Foreach trial, the strength of excitatory synapses of eachneuron is multiplicatively scaled such that w is the samefor all neurons. The glutamate levels are estimated for30 ms large bins and a low-pass filtered version of thesignal is computed, similar to the averaging assumedfor the glial cells. The resulting data points are fittedwith a linear function by using the least mean-squares

J. R. Soc. (2009)Interface

method, resulting in a transfer function, G3(s)Za3 witha3Z0.44.

The transfer function of the system can then becomputed as

GðsÞZ G3ðsÞ1CG1ðsÞG2ðsÞ

:

After replacing the expressions for the transferfunctions above, the stability analysis is reduced tostudying the poles of G(s), i.e. the solutions s1 and s2 ofthe equation

ð1CttnfsÞð1CtcsÞCa1a2a3 Z 0:

The roots have negative real parts in all cases, andthe output is oscillatory for complex solutions, corre-sponding to

ðttnf CtcÞ2K4ttnftcð1Ca1a2a3Þ!0;

which reduces to a bound for the product KtnfKc!0.0643. The analytical results are confirmed bysimulations in the neuronal network model. Firstly,experiments confirm that network dynamics do notchange when the total gain of the feedback loop ismaintained constant. Secondly, for the lesion experi-ment (80%, rZ10), lower gains (KtnfKcZ0.125) resultin low burst probability (less than 10%), while for theunderdamped regime (KtnfKcZ0.0075) bursts occur in80 per cent of the cases (results averaged over 10 trials),as predicted by the constraint on the product KtnfKc.

The actual values for the parameters Ktnf and Kc

matter in the cases when disruptions are induced withinthe control loop, e.g. during inflammation. In this case,

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Figure 14. Dependence of excitability increase followinginflammation on Kc, for constant total gain. (a) Populationactivity for Kc Z2.5, single trial. (b) Population activity forKcZ0.025, single trial. (c) Time evolution of averageexcitatory strength for different values of Kc, averaged over10 trials (dashed curve, 2.5; solid curve, 0.25; dotted curve,0.025).

Epileptogenesis and synaptic scaling C. Savin et al. 667

although the total gain is preserved, the networkdynamics change, depending on how sensitive thesynaptic strength is to TNF-a fluctuations. For a mildinflammatory state, induced by an homogeneous TNF-a source with cextZ10K5, the network can eitherremain stable or develop strong seizure-like patternsof activity, as a function of a2 (figure 14). Note that thenetwork dynamics prior to the disruption are virtuallyindistinguishable for all pairs, as predicted by thepopulation-level analysis.

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