Intrahippocampal gamma and theta rhythm generation in a network model of inhibitory interneurons

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1 0 Neurocomputing } (00) } Intrahippocampal gamma and theta rhythm generation in a network model of inhibitory interneurons TamaH s Kiss, Gergo OrbaH n, MaH teh Lengyel, PeH ter ED rdi* Department of Biophysics, KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, P.O. Box, H- Budapest, Hungary Abstract Hippocampal theta and gamma rhythms often occur together.while gamma activity is supposed to be generated intrahippocampally, the source of theta oscillations is still debated. Here, a network model of hippocampal inhibitory interneurons was capable of generating the gamma rhythm when responding to constant excitation.adding a periodic term to this stimulation resulted in complex pattern generation of the network, also including a theta frequency periodicity in the time dependent network coherence measure.a pyramidal cell model driven by the output of this network proved that membrane potential oscillations in the theta range can be entrained by this intrahippocampal mechanism. 00 Elsevier Science B.V. All rights reserved. Keywords: Synchronised oscillations; Theta and gamma rhythm; Inhibitory neurons. Introduction During di!erent behavioral states di!erent population activities are present in the hippocampal formation.these activities are not independent, gamma frequency activity is usually superimposed on theta oscillations.theta rhythm is a population oscillation with large ( mv) amplitude and with } Hz frequency which was found to occur during several behaviors.experiments after bilateral lesion of the entorhinal cortex suggest that the source of theta rhythm can be extrahippocampal [].However in vitro experiments suggest that it can also be generated internally, by the intrinsic This work was supported by the National Science Research Foundation (OTKA) T 000. * Corresponding author. address: erdi@rmki.kfki.hu (P. ED rdi). 0-/0/$ - see front matter 00 Elsevier Science B.V. All rights reserved. PII: S 0 - ( 0 ) 0 0 -

2 T. Kiss et al. / Neurocomputing } (00) } 0 membrane properties of neurons of the CA region [,].Gamma frequency "eld oscillations re#ect synchronized synaptic potentials in neuronal populations within approximately mm range along the longitudinal axis of the hippocampus []. Frequency of this oscillation is in the 0}0 Hz range.an important and often observed phenomenon is the co-occurrence of theta and gamma activity.physiological experiments revealed that the amplitude of gamma band oscillation is strongly modulated in theta frequency and long term changes of the amplitude and frequency of the two activities are positively correlated [,].However, the possible mechanism of generating gamma-related theta rhythm remained unclear.our aim in this study was to "nd a neurobiologically plausible mechanism explaining the origin of the theta}gamma correlation.. Methods Here the coupled system of a hippocampal inhibitory interneuron network and a CA pyramidal cell was studied. The interneuron network consisted of 0 single compartmental cells with Hodgkin}Huxley type sodium and potassium channels, interconnected through GABA mediated inhibitory synapses (for equations, see []).Network coherence as a function of time was calculated from the cross correlation of discretized spike trains. Instantaneous frequency for a single neuron was de"ned as the reciprocal of its interspike interval. The pyramidal cell was a compartmental Traub' CA pyramidal cell model [].Interneurons innervated the pyramidal cell by GABAergic synapses on the proximal apical dendrites, around the th compartment.synaptic current was in the form of that of Wang and BuzsaH ki [].Although we examined the e!ect of the number of synapses terminating on the pyramidal cell but the simulations presented here were performed with 0 interneuron}pyramidal cell synaptic connections, with one synapse per interneuron.in the discussed model there was no synaptic connections from the pyramidal cell to the interneuron network taken into account.the inhibited pyramidal cell itself was not able to produce action potentials, therefore we applied a tonic depolarization on the somatic or basal dendritic compartments.. Results In a previous work, Wang and BuzsaH ki [] showed that a randomly interconnected inhibitory interneuron network was able to produce emergent synchronized oscillation in the gamma frequency band.first, we con"rmed this result by applying spatially homogeneous, time independent input current to the network, i.e. every cell was stimulated with the same constant inducing current, resulting in tonic depolarization.eigen-frequency of the network was de"ned as the average frequency of cells when responding to a given level of constant current injection (data not shown).

3 T. Kiss et al. / Neurocomputing } (00) } 0 Fig.. (A) Average frequency of an isolated interneuron network ( f ) as a function of frequency of the inducing periodic signal ( f ), for di!erent current levels.note the resonance regime, where f "f occurs. Right box: Eigen-frequency of the network falls in the frequency range of resonance (for the same input current level).(b) Instantaneous frequency ( f ) of three randomly chosen cells at di!erent f values. In the resonance regime f of every cell (dashed and dotted lines) remained identical and constant in time, while non-resonating frequencies induced periodically oscillating time course (solid lines).(c) Time course of f plotted for six arbitrarily chosen interneurons in the case of spatially inhomogeneous time-dependent inducing current.split up into two subpopulations is clearly visible.

4 T. Kiss et al. / Neurocomputing } (00) } 0 Fig..Subthreshold membrane potential oscillation of a single pyramidal cell induced by perisomatic inhibition.(a) Burst tendency was suppressed by interneuronal inhibition.simulation was performed using 0 interconnected inhibiting interneurons each projecting to the somata of the pyramidal cell with one synapse.(b) Low amplitude subthreshold periodic changes of the somatic membrane potential of the pyramidal cell.this "gure is a zoom in of the former time course. As in the previous simulations only an isolated population of hippocampal interneurons were studied, the scope of the model was expanded so that its interactions with other neural populations could also be taken into account [].Motivated by anatomical and physiological experiments, time-periodic excitation was used instead of a constant inducing current to achieve a biologically more plausible scenario.using spatially homogeneous, time dependent periodic inducing current, the network was shown to exhibit robust resonance when the frequency of the inducing signal ( f ) was in an interval around its eigen-frequency (Fig.A).Examining the instantaneous frequencies of single interneurons, it was shown that a super-periodicity was present in the o!-resonance regime (Fig.B). The assumption that every cell receives the same input is only plausible when the propagation of the input signal is su$ciently fast compared to the characteristic cycle length of the oscillation.as this condition is not satis"ed for a large neural population [], the arising phase lag was taken into account by adding a random term from a Gaussian distribution with a standard deviation σ to the phase of the periodic input of each cell.as a result, gamma oscillation spiking of single cells accelerated and decelerated temporarily and regularly every &0 ms (Fig.C), giving rise to a periodically changing phase lag between two subpopulations of interneurons.this change in "ring phase of the subpopulations resulted in a periodically rising and

5 T. Kiss et al. / Neurocomputing } (00) } 0 Fig.. Tonic depolarization on the basal dendritic compartments enhanced "ring capabilities.(a) Time course of membrane potential measured at the somatic compartment of the pyramidal cell (thick line) and synchrony measure of the interneuron network (thin line).note co-occurrence of highly synchronized state of the network and high "ring activity of the pyramidal cell.(b) Low-pass (} Hz) "ltering of the somatic membrane potential. falling in the degree of synchrony of the whole interneuron network (Fig.A).Thus, with this spatially inhomogeneous, time dependent input, the network of hippocampal interneurons was demonstrated to be able to generate gamma-related theta oscillations []. However, there are no simultaneous paired recordings of oscillating interneurons available to date, but there is an abundance of experimental data on pyramidal cells, that are innervated by several interneurons.therefore, to simulate an experimentally measurable system, we investigated the behavior of the pyramidal cell model innervated by this inhibitory network.again, our model scenario was motivated by experimental results [,,].The interneuron network innervated the soma of the pyramidal cell by multiple GABAergic synapses.depending on the number and the position of dendritic synapses, simulations showed the emergence of experimentally observable [] theta range membrane potential oscillations on the dendritic tree and soma of the pyramidal cell (Figs. and A).When applying tonic depolarization through the third basal compartment and the soma "ring probability increased letting theta modulated gamma frequency spiking to evolve (Figs.B, and ).

6 T. Kiss et al. / Neurocomputing } (00) } 0 Fig..Power spectrum of somatic membrane potential of the pyramidal cell.two dominating frequencies are in the theta ( Hz) and the gamma ( Hz) range respectively.. Discussion Fig.. Cross correlogram of "ltered membrane potential oscillation of spiking pyramidal cell and synchrony measure of the interneuron network (see Fig.A).Note the periodicity and the phase delay. Theta frequency periodic membrane potential oscillations of pyramidal cells is supposed to be a result of the interplay of somatic inhibition and dendritic excitation [].Previous works proposed that somatic inhibition arises from the septum and [] is mediated by an inhibitory interneuron network to the somata of pyramidal cells [], while dendritic excitation originates from the entorhinal cortex and propagates through the perforant path [].However, using this model it is hard to see how the somatic and distal dendritic dipoles are coordinated to produce coherent signals. Based on our modelling results, we propose an alternative mechanism for generating gamma related theta oscillations.perforant path terminates on interneurons [,] as well as on the dendritic tree of pyramidal cells, and delivers signals with characteristic frequencies in the gamma and theta bands.electrophysiological experiments showed that principal neurons of CA are resonant to theta frequency [], while in our model network interneurons selected a characteristic frequency in the gamma band.this gamma modulation invading the interneuron network through the perforant path is an appropriate substrate for the spatially inhomogeneous time-periodic input that was necessary to evoke theta oscillations in our network.given these conditions, an intrahippocampal interneuron network appears to be a plausible candidate for the source of theta modulated gamma oscillations in the hippocampus. References [] A.Alonso, E.Garcia-Austt, Neuronal sources of the theta rhythm in the entorhinal cortex of the rat.ii. Phase relations between unit discharges and theta "eld potentials, Exp.Brain Res. () 0}0. [] A.Bragin, G.JandoH, Z. NaH dasdy, J.Hetke, K.Wise, G.BuzsaH ki, Gamma (}0 Hz) oscillation in the hippocampus of the behaving rat, J.Neurosci. () }0.

7 T. Kiss et al. / Neurocomputing } (00) } 0 [] G.BuzsaH ki, F.H.Gage, J.Czopf, A.Bjorklund, Restoration of a rhythmic slow activity (theta) in the subcortically denervated hippocampus by fetal cns transplants, Brain Res.0 () }. [] G.BuzsaH ki, L.S. Leung, C.H. Vanderwolf, Cellular basis of hippocampal eeg in the behaving rat, Brain Res.Rev. () }. [] A.Kamondi, L.AcsaH dy, G.BuzsaH ki, Dendritic spikes are enhanced by cooperative network activity in the intact hippocampus, J.Neurosci. () }. [] B.Kocsis, A.Bragin, G.BuzsaH ki, Interdependence of multiple theta generators in the hippocampus: a partial coherence analysis, J.Neurosci. () 00}. [] L.S. Leung, C.Y. Yim, Intrinsic membrane potential oscillations in hippocampal neurons in vitro, Brain Res. () }. [] L.S. Leung, H.-W. Yu, Theta frequency resonance in hippocampal cal neurons in vitro demonstrated by sinusoidal current injection, J.Neurophysiol. () }. [] G.OrbaH n, T.Kiss, M.Lengyel, P.ED rdi, Hippocampal rhythm generation: gamma related theta frequency resonance in CA interneurons, Biol.Cybernet. (00) }. [] R.D. Traub, R.K.S. Wong, R. Miles, H. Michelson, A model of a CA hippocampal neuron incorporating voltage-clamp data on intrinsic conductances, J.Neurophysiol. () }0. [] X.J. Wang, G. BuzsaH ki, Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model, J.Neurosci. () }. [] A.Ylinen, I.SolteH sz, A.Bragin, M.Penttonen, A.SmH k, G.BuzsaH ki, Intracellular correlates of hippocampal theta rhythm in identi"ed pyramidal cells, granule cells, and basket cells, Hippocampus () }0. Gergo OrbaH n TamaH s Kiss Gergo OrbaH n and TamaH s Kiss were born in Budapest, Hungary, in.they received their M.Sc.degrees in molecular- and biophysics in 000 at the EoK tvok s LoraH nd University of Sciences, Budapest, Hungary and started their Ph.D. courses in the same year at the same university. They joined the CNS group (KFKI R.I.P.N.P., H.A.S.) in. They are interested in understanding physiological phenomena by means of developing suitable and biologically plausible models. MaH teh Lengyel was born in Budapest, Hungary in.he received his M.Sc.in cell, developmental and neurobiology in 000 at the EoK tvok s LoraH nd University of Sciences, and was enrolled to the Behavioral Neuroscience Ph.D. program of the same university in the same year. He has been working with the CNS group (KFKI R.I.P.N.P., H.A.S.) since. His "elds of interest include constructing biologically detailed, realistic or at least plausible models of hippocampus related oscillations, memory processes and navigational skills. PeH ter ED rdi was born in Budapest, Hungary, on December,.He received his M.Sc.in chemistry from EoK tvok s University, Budapest.He is the head of Department of Biophysics of KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, SzeH chenyi Professor at the EoK tvok s University.His main scienti"c interest is the computational approach to the functional organization of the nervous system.