Structural Hierarchies, Theta Rhythm, HippocampalFunction

Peter Erdi

Center for Complex Systems Studies,Kalamazoo College, Kalamazoo, Michigan

Kalamazoo, MI 49006E-mail: perdi@kzoo.edu

Department of BiophysicsKFKI Research Institute for Particle and Nuclear Physics,

Hungarian Academy of Sciences, Budapest, HungaryH-1525 Budapest, P.O. Box 49

Abstract— The connection between different structures beingat different hierarchical level of the cortico-hippocampal forma-tion and their functional role is discussed. At least three differentfunctions, code generation, mood regulation and navigation isbeing integrated into a coherent conceptual framework.

I. I NTRODUCTION

It is generally agreed that the hippocampal formationhas a crucial role in learning and memory processes [1].The hippocampus is reciprocally connected to many neuralcenters and it is thought to prepare information for longterm storage. It has an important role in neurologicaldiseases. Alzheimer’s disease, epilepsy and ischemia areassociated with learning and memory impairment, and areaccompanied by selective neuronal death or characteristicchanges in the hippocampal circuitry. Recent studies havealso indicated that the hippocampal formation is affected inhuman depression as well as in animal models of depression[2], [3] and anxiety [4]. The integration of anatomical,physiological,neurochemical, pharmacological and behavioraldata using computational methods provide a coherent pictureabout the structure–function relationship of the hippocampalcircuitry and to offer a working therapeutic strategy forcontrolling disorders.

Two main, normally occurring, global hippocampal statesare known: the rhythmic slow activity, called the theta rhythmwith the associated gamma oscillation, and the irregular sharpwaves with the associated high frequency (ripple) oscillation.A pathological brain state, associated with epileptic seizuresis also known to occur in the hippocampus [5].

Based on experimental observations in rats, theta oscillationin the hippocampal formation is commonly regarded as thephysiological basis of memory formation [6]. Althoughmost of our information on hippocampal oscillatory activityderived from electrophysiological recordings in anesthetizedand non-anesthetized rodents, recent findings also indicatea similar oscillatory activity in the hippocampal formationof the human brain [7], [8], [9]. In general, theta oscillationin the hippocampal system has been linked to mnemonicprocesses [8], [10], [11], and power of theta oscillation seems

to correlate with the anxiety level [12], [13], [14], [15]

In this paper we integrate several research projects ourresearch group has been involved. It is interesting to see thatstructures at different levels of thehierarchical organizationhave been involved.

First, the role of the interplay between the the interactionof the somatic and dendritic compartments of a pyramidalcell and the external theta excitation in the (double) -codegeneration of spatial information is discussed [16], [17]. Whileour first studies used integrate-and-fire model framework, thesecond adopted compartmental modeling technique.

Second, the interaction among the networks ofhippocampus, medial septum and median raphe nucleus ingenerating and controlling the theta rhythm will be discussed.The effects of allosteric modulators of the benzodiazepinebinding site of the GABAA receptors were studied bymulti-compartmental modeling. and results [18], [19] showedthat impairment/improvement of the inhibitory mechanismsplay a role in mood regulation (see also [20]). We makehints on the functional role of target-specific connections ofthe serotonergic fibers to septal and hippocampal interneurons.

Third, the cortico-hippocampal loop, and its role in the placefield generation will be reviewed. This study has two parts. Inthe first part we show that a feed-forward network connectingentorhinal cortex to hippocampus is sufficient to obtain alocalized place field starting from a much more broadly tunedfield if there is a theta modulation in the system [16]. In thesecond part, an integrated cortico-hippocampal model by usinga lumped model framework elaborated by Freeman (1975) andKozma and Freeman (2003), see also Kozma et al (2003),Kozma et al (in press). The model, which contains samplingof the the environment by theta rhythm, was able to showplace field generation and navigation.

II. SOMATO-DENDRITIC INTERACTION: THE ROLE OF

THETA MODULATION IN CODE GENERATION

Place cell firing conveysdouble coded spatial information:both its firing rate, and the timing of firing relative to thetheta field potential is correlated with the location of theexploring rat [25].

The core of the hypothesis is the specific modulationof the place cell: the cell is supposed to receive inhibitionin phase with theta field potential oscillation on the somaand speed-dependent excitation on the dendrite. There is anoscillation also on dendrite, and it is frequency modulatedby its input. Theinteraction of the somatic and dendriticoscillation determines the probability of the place cell firingFig. 1.

Dendritic membrane potential oscillation (DMPO)frequency modulated bylevel of differential input

Somatic membrane potential

of constant theta

Inhibition causing somatic hyperpolarizingoscillation (SHO)

Excitation withdifferential input (DI)

soma

dend

rite

fluctuations (SMPF) determined by SHO and DMPO

frequency

Fig. 1. Somato-dendritic model of a place cell. SMPF, which determines thefiring probability, is obtained from the interplay of the somatic and dendriticoscillations. Dendritic oscillation is frequency modulated by a velocity-dependent differential input. Based on Fig 1. Lengyel et al. (2003)

The hypothesis has been studied and verified by fourdifferent levels of abstraction: analytical calculation, ratemodel, spiking model [26], compartmental model [17].

We have shown how two compartments of a hippocampalprincipal cell behaving as two dynamically detuned oscillatorscan interact to generate the characteristic firing patterns ofa place cell. Position-dependent firing rate and timing werefound to emerge in our model without positional informationbeing encoded either in a topographical external input or intopographically ordered recurrent connections (Fig. 2).

III. SEPTOHIPPOCAMPAL THETA RHYTHM: THEIR ROLE IN

MOOD REGULATION

Theta frequency oscillation of the septo-hippocampalsystem has been considered as a prominent activity associatedwith cognitive function and affective processes. It is well

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Fig. 2. Generation of the double code: firing rate and phase is position-dependent. A: Trajectory of the animal; B: Speed-proportional differentialinput; C: Phase shift in the dendritic oscillation; D and F: Firing probabilityvs time, and position, respectively; E and G: phase precession vs time andposition, respectively. Based on Fig 3. Lengyel et al. (2003)

documented that anxiolytic drugs reduce septo-hippocampaloscillatory theta activity contributing to their either therapeuticor unwanted side effects.

A skeleton network, i.e. a three-population modelof the hippocampal CA1 region was constructed. Amulticompartmental realization of the pyramidal neuronwas implemented. Two types of interneurons were takeninto account, which had their somata in strata oriens andpyramidale. Stratum oriens interneurons were those havingprojections in the lacunosum moleculare (O-LM interneurons)innervating the most distal dendrites of pyramidal neurons.Basket cells (B) have their soma in the stratum pyramidale.The model of the medial septum consisted of a singleGABAergic neuron population. Periodic theta frequencyoscillations have been shown to exist in septal non-cholinergicneurons and ionic basis for these discharges has also beenestablished. In a combined physiological/computationalstudies to explore the functional role of GABAA receptors intheta oscillation.

Neurotransmission at GABAA receptors were modulated bymeans of pharmacological tools: the actions of the GABAA

receptor positive allosteric modulator diazepam and inverse

agonist/negative allosteric modulator FG-7142 were evaluatedon septo-hippocampal activity. Systemic administrationof diazepam inhibited, whereas FG-7142 enhanced thetaoscillation of MS/DB neurons and hippocampal EEG thetaactivity.

In our model the synaptic current represented the chloridecurrent assigned to the GABA receptor complex. Therefore,we modeled the effect of negative/positive allosteric modu-lators by decreasing/increasing the maximal conductance ofGABAA synapses. The effects of the selective modificationon of GABA synapses was studied by simulations using askeleton network Fig. 3 and Fig. 4.

O−LMI

IB

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excitatory connection

not explicitely modeledpathway

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inhibitory connection

location of pharmaceuticalaction

Fig. 3. Skeleton network of the septohippocampal system

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effect of negative allosteric modulatorwas taken into account by lower synaptic conductance at all pathways

Timing of action potentials tendsto have a well defined value

In all neuron populations clusteringof spikes occurs at lower synapticconductance values

simulated administration ofthe negative allosteric modulator

Theta power in EEG computed fromthe activity of pyramidal neurons shows a significant increase during

negative allosteric modulatorcontrol

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effect of negative allosteric modulatorwas taken into account by lower synaptic conductance at all pathways

Timing of action potentials tendsto have a well defined value

In all neuron populations clusteringof spikes occurs at lower synapticconductance values

simulated administration ofthe negative allosteric modulator

Theta power in EEG computed fromthe activity of pyramidal neurons shows a significant increase during

negative allosteric modulatorcontrol

0

5

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Fig. 4. Controlling the behavior of septal and hippocampal neuron popula-tions. GABAA synapses are modulated by the anxionegic FG-7142 agent. A:Firing histograms of different neuron populations for high and low GABAA

synaptic conductances, respectively. B: Power spectra of the extracellularlymeasured EEG s calculated for simulations. Significant increase in theta powerrelative to the control state was found

Mood regulation models should be extended by taking intoaccount the control mechanisms of the serotoninergic inputoriginated from the midbrain raphe nuclei to the septohip-pocampal theta-generating network.

IV. CORTICO-HIPPOCAMPAL CIRCUIT: PLACE FIELD

GENERATION AND NAVIGATION

A. Theta-modulated feed-forward network

As a continuation of the work on the double-code gen-eration, we studied whether or not a feed-forward networkconnecting entorhinal cortex to hippocampus is sufficient toobtain a more localized place field starting if the startingconfiguration is a much more broadly tuned field.

B. Navigation with the KIV model

K sets represent a family of models of increasingcomplexity that describe various aspects of functioningof vertebrate brains [21]. The extension of the model forcortico-hippocampal system was designed for integratingsensory processing and decision-making. Results obtained bya simplified KIV model for goal-oriented action.

A hippocampus-related navigating algorithm based onthe combination of aperiodic dynamics and reinforcementlearning and sensor sampling with theta rhythm was given(Kozma and Freeman (2003), see also Kozma et al (2003),Kozma et al (in press)).

We apply reinforcement learning combined with non-Hebbian habituation for category formation. This learningis episodic, not continuous, long-term, and irreversible. Itoccurs when the device is moving into its environment andencounters important or unexpected changes in its sensoryinflow. The reinforcement learning takes place in CA3/CA1during the active periods provided by the theta rhythm, ifreinforcement signal is present.

Fig. 5. Navigation accelerated with cortical learning. Navigation to the goalwithout cortical learning (203 steps) and at near-optimal learning rate(56 steps)

The "K" model of the cortico−hippocampal circuitryaccounts for sensory processing and decision making.

Subcortical afferents modify septo−hippocampalrhythm generation

interneuron network generates modulatedΘ

Hippocampal interneuron network

25 ms0.2

mV

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5−HT Slow 5−HT Mod

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Medial Septum

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MSGABA

3. THE ENTORHINO-HIPPOCAMPAL MODEL 82

Figure 9. Theta modulation in the modeled feed-forward network. EC cellswere connected by feed-forward excitatory connections to a single hippocampalpyramidal cell. Perforant path (pp)-specific inhibitory interneuron gated trans-mission of pp synapses. Theta modulation had phasic effects on (1) entorhinalcells, (2) soma of the pyramidal cell, (3) activity of pp-specific inhibition, and itwas also assumed to (4) tonically modulate the dendrite of the hippocampal cell,allowing it to sustain intrinsic membrane potential oscillations.

Septo−hippocampal GABAergic

frequency oscillationγ

Interaction of different cortical and subcortical regions

Cortico−hippocampal circuit generates neuralcoding for spatio−temporal representation

in the generation, modification and utilization of oscillationΘ

Fig. 6. Generation, control and some functions of hippocampal theta rhythm

The hippocampal formation and cortex complete theirfunctions by sampling the environment at theta rate. To achievethis periodicity, KIV relies on the septum to generate the thetaframe rate as a gating function. Temporal framing is done in allsensory systems. Examples of this sampling are the saccadicmovement in visual system, sniffing in olfaction, and perhapssomething similar in the cochlea.

To test our navigation algorithm a a simple 2D multiple T-maze environment has been chosen. In this environment, themovement can take place along a grid. Consequently, at anyinstance, the robot can chose the next move from one of the4 direct neighbors of the given grid point.

If the robot is properly learned the environment, it wouldnavigate efficiently and find a reasonably optimal path to thegoal based on the use of the internally formed cognitive mapusing its classification landscape. Cortical learning improvedthe efficiency of the navigating algorithm very much, as Fig.5 shows it.

V. CONCLUSIONS

Generation, control and the multiple functional role couldbe conceptually integrated by taking into account the structuralhierarchies of the hippocampus, see Fig. 6.

Many functional aspects of theta rhythm have been ne-glected. E.g. recently it was suggested [27] that theta rhythmmay allow rapid transitions between encoding and retrieval.This hypothesis, and many others, should be incorporated intoa more general theory.

ACKNOWLEDGMENT

The author would like to thank Walter Freeman, ZsofiaHuhn, Tamas Kiss, Robert Kozma, Mate Lengyel, GergoOrban, Zoltan Szatmary and Derek Wong for their cooperation.

This work was supported in part by the Hungarian Sci-entific Research Fund (OTKA) under grant no. T-038140;the Henry R. Luce Foundation and a research grant fromPharmacia/Pfizer Incorporation.

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