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Selvaraj et al. SpringerPlus (2015) 4:155 DOI 10.1186/s40064-015-0836-7

SHORT REPORT Open Access

Optogenetic induced epileptiform activity in amodel human cortexPrashanth Selvaraj1, Jamie W Sleigh2, Heidi E Kirsch3 and Andrew J Szeri1,4*

Abstract

Background: Cortical stimulation plays an important role in the study of epileptic seizures. We present a numericalsimulation of stimulation using optogenetic channels expressed by excitatory cells in a mean field model of thehuman cortex.

Findings: Depolarising excitatory cells in a patch of model cortex using Channelrhodpsin-2 (ChR2) ion channels, weare able to hyper-excite a normally functioning cortex and mimic seizure activity. The temporal characteristics ofoptogenetic channels, and the ability to control the frequency of synchronous activity using these properties are alsodemonstrated.

Conclusions: Optogenetics is a powerful stimulation technique with high spatial, temporal and cell-type specificity,and would be invaluable in studying seizures and other brain disorders and functions.

Keywords: Meso-scale cortical model; Epiletic seizure propagation; Optogenetic stimulation

1 IntroductionIn seizure research, cortical stimulation has been used asa means to study the pre-seizure state, epileptogenesis,the epileptic state and seizure control. In vivo stimulationusing radial electric fields (Richardson et al. 2003), andhigh frequency (Su et al. 2008) and low frequency (Jergerand Schiff 1995) in vitro electrical stimulation are someof the methods that have been used to modulate epilep-tiform activity. However, while electrical stimulation hasexcellent temporal resolution, it does not offer a meansto target specific cell populations in brain regions at mul-tiple different spatial scales. Optogenetics, on the otherhand, offers excellent temporal and spatial resolution. Tar-geted optogenetic stimulation of neurons (Cardin et al.2010) and the effect of optogenetics on neural circuitry(Zhang et al. 2007) point to the novel use of this method asa highly specific cell stimulation technique. Furthermore,optogenetics has been used to inhibit epileptic seizuresin in vivo and in vitro experiments in animals (Krook-Magnuson et al. 2013; Paz et al. 2013; Tønnesen et al.

*Correspondence: aszeri@berkeley.edu1Department of Mechanical Engineering, University of California, Berkeley, CA94720, USA4Center for Neural Engineering and Prosthesis, University of California,Berkeley, CA 94720, USAFull list of author information is available at the end of the article

2009), and the specificity of targeting this technologyoffers would be invaluable in studying the role of individ-ual neurons and neural circuits in epilepsy. Optogenetictechnology involves genetically modifying specific neu-rons to express light sensitive ion channels without chang-ing the cell’s underlying physiology, and requires furtherrigorous testing before it is deemed safe for use in humans.However, the efficacy of this stimulation technique ininhibiting seizures has been examined in a mathematicalmodel of human cortex (Selvaraj et al. 2014). In this arti-cle, we present a study of the potential for optogeneticsas a method to induce seizures in a model human cortexby depolarising the excitatory population in a patch of themodel cortex using ChR2 channels.First, we demonstrate the propagation of seizure waves

through a normally functioning cortex that is stimulatedusing optogenetic channels. Next, we look at the effectof illumination intensity on the onset and frequency ofthe induced seizure waves. Finally, the effect of usingpulsed illumination and its role in varying the frequencyof synchronous activity is discussed.

2 Seizure initiationWe use the meso-scale cortical model developed by Lileyet al. (2001) to simulate the dynamics of a human cortex.

© 2015 Selvaraj et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative CommonsAttribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproductionin any medium, provided the original work is properly credited.

Selvaraj et al. SpringerPlus (2015) 4:155 Page 2 of 6

The non-dimensionalised form of this model can be foundin the appendix.To study the effects of optogenetic stimulation on the

cortex, we use the four statemodel of Channelrhodopsin-2(ChR2) proposed in (Grossman et al. 2011). A meso-scale version of this model described in the appendix, wascombined with the above mentioned cortical model bymodifying the inhibitory cell population to express lightsensitive ChR2 ion channels (Selvaraj et al. 2014). Here,the excitatory population of the cortical model expressesChR2 channels, which changes the equation describingthe dynamics of the mean soma potential of the excitatorypopulation to:

∂ he∂ t

= 1− he +�e(h0e − he

)Iee +�i

(h0i − he

)Iie −u.

(1)

The term u is the stimulation applied to the excitatorypopulation, and is given by,

u = he.GChR2.Rm. (2)

where he is themembrane potential for the excitatory pop-ulation, Rm is the membrane resistance of the cells, andthe conductance of ChR2 channels, GChR2, is defined as

GChR2 = Gmax.gChR2.(1 − exp(−he/U0))

he/U1.NChR2, (3)

where gChR2 is the total conductance of the optogeneticchannels in the O1 and O2 states. U0 and U1 are empiri-cal constants and NChR2 is the number of ChR2 channelsper representative neuron. The expression for gChR2, andvalues and explanations for all parameters can be found in(Selvaraj et al. 2014).

3 Results and discussionWe now present results obtained by optogenetic stimula-tion of a portion of model cortex of dimensions 1400 ×1400 mm2, which is divided into 100 × 100 cells or repre-sentative neuronsa. We stimulate an area of model cortexwith spatial scale of the order of clinical recordings. InFigure 1, a square region in the middle of the cortexof approximate dimensions 280 × 280 mm2 (1/25 thetotal area of the cortex) is modified to express ChR2 ionchannels in the excitatory population, and this region isilluminated with light of a constant 50 mW/mm2 intensitystarting at 0.5 s. An ion channel density of 109ChR2′s/m2

is used to keep illumination intensities within physiolog-ically permissible values and still ensure optimal stimula-tion of the cortex.Figure 1 depicts the birth of a seizure-like wave within

the square patch of stimulated cortex. Neighbouringregions are then excited by the outward propagation oftravelling seizure waves, and the effects of the stimula-tion spread to the entire cortical area. Hyper-excitation

in (Selvaraj et al. 2014) was achieved by increasing sub-cortical inputs to the excitatory population throughoutthe model cortex. This meant the entire cortex was onthe verge of seizing, and a small increase in subcorticalinputs to a column could cause a region of cortex to seize.These seizures originated from a cortical column, andpropagated outwards in spiral waves.Here, spatially uniform travelling waves are formed

by the equal hyper-excitation of cortical macrocolumnswithin a patch of cortex using optogenetic channels, andsubcortical inputs do not play as important a role instarting seizures as illumination intensity increases.It should be noted here that the entire model cortex

is functioning normally, with inhibitory and excitatoryinputs of comparable magnitudes balancing each otherout. However, when adequate optogenetic stimulation isapplied to the excitatory population, it depolarises thesecells, increasing their mean soma potential, which imme-diately increases their firing rate. The local excitatoryand long range contributions to post synaptic activationare increased because of the higher firing rate, produc-ing a further rise in the mean soma potential of bothpopulations, which ultimately leads to even higher fir-ing rates in both excitatory and inhibitory cells. Increasesin inhibitory firing rates trail excitatory ones within amacrocolumn by 1-2 ms for two reasons. One, stimula-tion is applied directly to the excitatory population, andtwo, there are time delays associated with synaptic trans-mission. Spatial connectivity between columns transferssynchronous activity to neighbouring columns of neu-rons outside the stimulated cortical patch, exciting theminto synchronous states facilitating propagation of seizureactivity. As stated earlier, only neurons within the stimu-lated area are hyperexcited while the rest of the cortex isfunctioning normally. This constrains the minimum stim-ulated area necessary to excite the rest of the cortex intoan epileptic state to ∼4% of the total area of the cor-tex. Smaller stimulated regions are not able to supportseizure activity for cortical and optogenetic parametersmentioned above.In Figure 2, we look at the variation of mean soma

potential of the excitatory population at a point within thestimulated patch of cortex, and take a one dimensionalcross section of the two dimensional spatial domain tostudy how different illumination intensities and illumina-tion profiles lead to travelling seizure waves of varyingfrequencies. For all three illumination profiles presentedin Figure 2, stimulation is turned on at t = 0 s. Figures 2aand 2d show the variation of mean soma potential withtime when the cortical patch is constantly illuminatedwith intensities of 30 mW/mm2 and 60 mW/mm2, respec-tively, while Figure 2g uses a 200 ms on 200 ms offpulsed illumination of 60 mW/mm2 intensity as shown inFigure 2i. Figures 2b, 2e and 2h depict travelling waves in a

Selvaraj et al. SpringerPlus (2015) 4:155 Page 3 of 6

Figure 1 Propagation of seizure waves in a 2Dmodel of a normally functioning human cortex when optogenetic stimulation is applied toa 280 × 280mm2 patch in the centre of the cortex. Snapshots are taken from time t = 0.5 s to t = 1 s. Normal cortical function is characterizedhere by the baseline parameters of (Kramer et al. 2006) with Pee = 11.0 and �e = 0.0012. The cortex is stimulated with a constant light intensity of50 mW/mm2 at 0.5 s.

one dimensional slice of the two dimensional domain, andcomprises both stimulated cortex between 560 mm and840 mm, and normally functioning cortex.Higher illumination intensities result in higher conduc-

tances, as shown in Figures 2c and 2f, resulting in cellsbeing depolarised more quickly. For a given illuminationintensity, pulsed light can reduce the frequency of seizurewaves because the stimulatory input rapidly drops to zerowhen light is turned off, sending the cortex back to a nor-mally functioning state. In other words, increasing thetime of no illumination when using a pulsed light sourcedecreases seizure frequency. This difference can be seenbetween Figure 2d, where constant illumination is used,and Figure 2g, where pulsed illumination is used. Counter-intuitively, though, while a higher intensity depolarisescells more quickly, it reduces the frequency of seizurewaves as seen by comparing Figures 2a and 2d. One

possible explanation is that the rate of change of meansoma potential given in equation 1 is lower for higherintensities because the stimulation term, u, is always pos-itive on account of using ChR2, a cation pump. A higherrate of change decreases the time required to change froma lower to a higher firing rate and back. In other words,the rate of change of firing rate increases, which results inhigher frequency oscillations.We turn to bifurcation analysis to give us a picture of

what happens in the cortex when illumination of a cer-tain intensity is used. To perform a bifurcation analysis,we turn off the stochastic and spatial terms in the corticalmodel to obtain an underlying set of deterministic ordi-nary differential equations (ODEs), which helps us gaininsight into the complete system of stochastic partial dif-ferential equations (SPDEs) that describe the mesoscalecortical model intuitively. It has been shown that Hopf

Selvaraj et al. SpringerPlus (2015) 4:155 Page 4 of 6

a b c

d e f

g h i

Figure 2 Optogenetic stimulation of a normally functioning cortex from t = 0 s. (a-c) represent the variation of he with time, travelling wavesin a 1-D slice of the 2-D domain, and the variation of GChR2 with time, respectively, using a constant intensity of 30 mW/mm2. (d-f) show the samefeatures using a constant intensity of 60 mW/mm2. (g-i) show the variation of he at a point, a 1-D slice of the 2-D domain and the pulsedillumination profile with a maximum intensity of 60 mW/mm2.

bifurcations in the dimensionless ODEs can correspondto travelling waves in the SPDE system (Kramer et al.2007). Here, we combine this ODE system with the opto-genetic model to study the dynamics of the combinedsystem.Figure 3a shows the values of �e and Pee that cause

oscillatory behaviour in the ODE model when not stim-ulated (black) and when stimulated (grey) by optogeneticchannels using an illumination intensity of 60 mW/mm2.The red dot in the figure is located at �e = 0.0012 andPee = 11.0, which are used in the full SPDE system sim-ulations shown in Figures 1 and 2. These values lie welloutside the region of epilepsy in the unstimulated cor-tex. The seizure prone area in the parameter space isvastly increased when optogenetic stimulation is applied.It has been observed, but not shown here, that this area isslightly larger with less distinct boundaries for the SPDEsystem owing to stochasticity.A bifurcation analysis of the ODE system yields a

bifurcation diagram depicting the salient features for the

mean soma potential of the excitatory population, he, fordifferent illumination intensities as shown in Figure 3b.We use Pee = 11.0 and �e = 0.0012 for this analysis. Solidlines indicate stable fixed points, while dashed lines rep-resent unstable ones. Dot-dashed lines and dotted linesindicate maximum and minimum values of he achievedduring stable and unstable limit cycles, respectively.The asterisk represents a subcritical Hopf bifurcation at5.1352 mW/mm2, which gives rise to an unstable limitcycle. At 4.7908 mW/mm2 the limit cycle stabilises aftergoing through a saddle node bifurcation, and becomesunstable again after going through another saddle nodebifurcation at 33.8682 mW/mm2. While Figure 3b is trun-cated at 40 mW/mm2, the limit cycle remains unstableand does not terminate well beyond 100 mW/mm2, whichis around the limit of physiologically acceptable illumi-nation intensitiesb. This suggests the combined cortical-optogenetic model is unable to support stable oscillationspast 34 mW/mm2, and at higher intensities, we might beobserving a succession of independent columnar spiking

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a b

c

Figure 3 Seizures with the ODEmodel and frequency response of the SPDE system. (a) effect of optogenetic stimulation on oscillatorybehaviour in the �e - Pee parameter space, using a 60 mW/mm2 illumination intensity (grey) and in an unstimulated cortex (black). The red dotindicates �e = 0.0012 and Pee = 11.0, which are used in the full SPDE system. (b) Bifurcation diagram for the underlying deterministic ODE systemshowing the variation of he for different illumination intensities. Dashed and solid lines indicate unstable and stable fixed points, respectively.Maximum and minimum values of he during stable (dot-dashed) and unstable (dashed) limit cycles arising from a subcritical Hopf bifurcation(asterisk) are also shown. (c) Frequency of seizure waves for a given illumination intensity.

events and not entrained spiking seen during stable oscil-latory behaviour. In the case of an individual spike inmeansoma potential, a cortical column relaxes to its restingpotential before firing again. This takes longer to pro-duce a spike than the case with continuous oscillatorybehaviour, where a column can be excited to spike againbefore reaching resting state. This explains why lowerfrequency seizure waves are observed when higher illu-mination intensities are used, a trend which is shownin Figure 3c after averaging frequency over multiplesimulations of the full SPDE system. For lower intensi-ties, subcortical inputs may aid in exciting or suppress-ing the system, so the probability of producing seizuresdecreases for intensities lower than 25 mW/mm2. Forhigher intensities, the system will almost always produceseizures, but the frequency of seizure waves is dependenton the magnitude of subcortical and long range inputs.Overall, however, we observe a tendency to producelower seizure wave frequencies for higher illuminationintensities.

4 ConclusionWhile this study explores the use of cation pumps in theexcitatory population of the meso-scale cortical model, anequally interesting alternative using anion pumps to sup-press the firing of inhibitory neurons could be investigated.The wide variety of illumination options, light activatedion channels, and their temporal and spatial specificitymake a strong case for consideration of optogenetics as acortical stimulation modality in seizure research.

EndnotesaThe average human cortex has dimensions of

500 × 500 mm2 if it were laid open like a sheet. However,to remain consistent with previous work, and becausedynamics in this model of undifferentiated cortex arescale-free, we have used a larger cortical domain toillustrate seizure waves.

bProlonged exposure (> 0.5 s) at an intensity of 100mW/mm2 caused significant tissue damage in animalmodels (Cardin et al. 2010).

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AppendixThe non-dimensional meso-scale model was first statedin (Kramer et al. 2006), where values and explanations forall variables and constants of the model can be found. Forconvenience, we state the equations here.

∂ he∂ t

= 1 − he + �e(h0e − he

)Iee + �i

(h0i − he

)Iie

(A1)

∂ hi∂ t

= 1 − hi + �e(h0e − hi

)Iei + �i

(h0i − hi

)Iii (A2)

(1Te

∂

∂ t+ 1

)2Iee = Nβ

e Se[he

]+ φe + Pee + �1 (A3)

(1Te

∂

∂ t+ 1

)2Iei = Nβ

e Se[he

]+ φi + Pei + �2 (A4)

(1Ti

∂

∂ t+ 1

)2Iie = Nβ

i Si[hi

]+ Pie + �3 (A5)

(1Ti

∂

∂ t+ 1

)2Iii = Nβ

i Si[hi

]+ Pii + �4 (A6)

(1λe

∂

∂ t+ 1

)2φe = 1

λ2e∇2φe +

(1λe

∂

∂ t+ 1

)Nαe Se

[he

]

(A7)(1λi

∂

∂ t+ 1

)2φi = 1

λ2i∇2φi +

(1λi

∂

∂ t+ 1

)Nαi Se

[he

]

(A8)

All variables have been non dimensionalised and arefunctions of time t, and the two spatial dimensions xand y. The subscripts e and i represent excitatory andinhibitory populations respectively, and variables with twosubscripts represent the transfer of energy from one popu-lation to another. The mean soma potential for a neuronalpopulation is represented by the h state variable, I repre-sents the postsynaptic activation due to local, long-range,and subcortical inputs. φ represents long range (cortico-cortical) inputs.The equations describing the dynamics of the optoge-

netics are,

dNO1dt

= Ka1.NC1 − (Kd1 + e12).NO1 + e21.NO2 (A9)

dNO2dt

= Ka2.NC2 + e12.NO1 + (Kd2 + e21).NO2

(A10)dNC2dt

= Kd2.NO2 − (Ka2 + Kr).NC2, (A11)

where NOi and NCi represent the fraction of channels inthe open and closed states, respectively.Kai are the rates oftransition from the closed states, C1 and C2, to the open

statesO1 andO2 respectively. Conversely,Kdi are the clos-ing rates from the open states to the closed states.Kr is thethermal recovery rate from C2 to C1. e12 and e21 are thetransition rates from O1 to O2 and vice versa. The valuesfor all rate constants can be found in table (Selvaraj et al.2014).

Competing interestsThe authors declare that they have no competing interests.

Authors’ contributionsPS helped develop the concept, performed the simulations presented in thisstudy, and wrote the manuscript. JWS and HEK provided clinical advice andhelped draft the manuscript. AJS helped develop the concept, providedadvice on the analysis of the model, and helped draft the manuscript. Allauthors read and approved the final manuscript.

AcknowledgementThis work was partially supported by the US National Science Foundation(NSF) grant CMMI 1031811.

Author details1Department of Mechanical Engineering, University of California, Berkeley, CA94720, USA. 2Waikato Clinical School, University of Auckland, Hamilton, NewZealand. 3Departments of Neurology and Radiology and Biomedical Imaging,University of California, San Francisco, CA 94143, USA. 4Center for NeuralEngineering and Prosthesis, University of California, Berkeley, CA 94720, USA.

Received: 4 September 2014 Accepted: 18 January 2015

ReferencesCardin J, Carlén M, Meletis K, Knoblich U, Zhang F, Deisseroth K, Tsai LH, Moore

C (2010) Targeted optogenetic stimulation and recordings of neurons invivo using cell type specific expression of channelrhodopsin-2. Nat Protoc5(2):247–254

Grossman N, Nikolic K, Toumazou C, Degenaar P (2011) Modeling study of thelight stimulation of a neuron cell with channelrhodopsin-2 mutants. IEEETrans Biomed Eng 58(6):1742–1751

Jerger K, Schiff SJ (1995) Periodic pacing an in vitro epileptic focus.J Neurophysiol 73:876–9

Kramer M, Szeri A, Sleigh J, Kirsch H (2007) Mechanisms of seizure propagationin a cortical model. J Comput Neurosci 22(1):63–80

Kramer M, Lopour BA, Kirsch HE, Szeri A (2006) Bifurcation control of a seizinghuman cortex. Phys Rev E 73:041928

Liley DTJ, Cadusch PJ, Dafilis MP (2001) A spatially continuous mean fieldtheory of electrocortical activity. Network: Comput Neural Syst 13:67–113

Krook-Magnuson E, Armstrong C, Oijala M, Soltesz I (2013) On-demandoptogenetic control of spontaneous seizures in temporal lobe epilepsy.Nature Communications 4(1376):1–8

Paz TP, Davidson TJ, Frechette ES, Delord B, Parada I, Peng K, Deisseroth K,Huguenard JR (2013) Closed-loop optogenetic control of thalamus as atool for interrupting seizures after cortical injury. Nat Neurosci 16:64–70

Richardson KA, Gluckman BJ, Weinstein SL, Glosch CE, Moon JB, Gwinn RP,Gale K, Schiff SJ (2003) In vivo modulation of hippocampal epileptiformactivity with radial electric fields. Epilepsia 44(6):768–777

Selvaraj P, Sleigh JW, Freeman WJ, Kirsch HA, Szeri AJ (2014) Open loopoptogenetic control of simulated cortical epileptiform activity. J ComputNeurosci 36(3):515–525

Su Y, Radman T, Vaynshteyn J, Parra LC, Bikson M (2008) Effects ofhigh-frequency stimulation on epileptiform activity in vitro: ON/OFFcontrol paradigm. Epilepsia 49(9):1586–93

Tønnesen J, Sørensen A, Deisseroth K, Lundberg C, Kokaia M (2009)Optogenetic control of epileptiform activity. Proc Natl Acad Sci USA106:12,162–12,167

Zhang F, Wang LP, Brauner M, Liewald JF, Kay K, Watzke N, Wood PG, BambergE, Nagel G, Gottschalk A, Deisseroth K (2007) Multimodal fast opticalinterrogation of neural circuitry. Nature 446:633–641