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Orbán1,21Department of Biophysics, KFKI Research Institute for Particle and Nuclear Physics, Hungarian Academy of Sciences, Budapest; 2Collegium Budapest, Institute for Advanced Study; Budapest, Hungary; and 3Center for Complex Systems Studies, Kalamazoo College, Kalamazoo, Michigan
Submitted 23 November 2006; accepted in final form 20 July 2006
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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; Vértes and Kocsis 1997) and was shown to be synchronized over spatial scales 
2 mm (Bullock et al. 1990). Synchronization of theta activity was suggested to be brought about by extrinsic (Alonso et al. 1987; Mitchell and Ranck 1980; Petsche et al. 1962) and intrinsic mechanisms (Chapman and Lacaille 1999; Kocsis et al. 1999; Strata 1998). Although the septal pacemaker hypothesis is supported by both physiological (Bland et al. 1999) and computational (Wang 2002) studies, producing a coherent hippocampal theta might require additional mechanisms (Buzsáki 2002; King et al. 1998). Importantly, intracellular equivalent of theta oscillation was identified in individual CA1 neurons in the form of subthreshold oscillations, and activity of these neurons was also modulated by theta activity (Soltész and Deschenes 1993). The subthreshold oscillation was proven to be carried by rhythmic GABAA inhibitory postsynaptic potentials (IPSPs) (Ylinen et al. 1995). Further studies showed that pharmacological modulation of GABAA receptors was shown to alter hippocampal theta in vivo (Hajós et al. 2004; Ongini et al. 1983). Recently, it has been shown in vivo that different neuron populations tend to fire at different phases of extracellularly measured theta (Csicsvári et al. 1999; Skaggs et al. 1996), and interneuron subclasses proved to be distinguishable based on their preferred action potential timing relative to theta (Klausberger et al. 2003, 2004). The question whether and how intrinsic mechanisms contribute to the synchronization of hippocampal neuron populations in the theta frequency band remains open.
The view that external input paces the firing of neuron populations is supported by their anatomical organization (Freund and Buzsáki 1996; Pawelzik et al. 2002), enabling them to collect afferents from the entorhinal cortex and, in the case of CA1, the CA3 region of the hippocampus. The idea of internal modulation of firing patterns is supported by physiological properties of hippocampal interneurons that might underlie the relay of fast feedback inhibition subserving pyramidal cells synchronization (Jonas et al. 2004). Also, an internal effect in the hippocampus is the intrinsic resonance of pyramidal cells to theta-frequency periodic inputs (Strata 1998). Furthermore, a recent in vitro study has shown that theta could be elicited in a CA1 slice (Gillies et al. 2002), and timing of different neuronal classes was similar to those measured in vivo. Taken together, these studies indicate that patterning of hippocampal neuron population activities has to rely on the anatomical organization and dynamics of the hippocampus.
Preferential discharge of basket cells, whose primary target is the perisomatic region of pyramidal cells (Freund and Buzsáki 1996), precedes that of pyramidal cells by 60 ms (Klausberger et al. 2003). The timing of pyramidal cell firing by basket cells was previously suggested by Buzsáki et al. (1983) and Fox (1989), but the precise mechanism remained to be elucidated. A possible mechanism of pyramidal cell timing was given by Cobb et al. (1995), who revealed a postinhibitory "rebound depolarization" in the membrane potential traces of CA1 pyramidal cells but intrinsic currents responsible for the phenomenon were not identified.
Pharmacological profile of theta activity poses constraints on plausible mechanisms underlying its generation. During ketamine and urethane anesthesia, theta was proven to be atropine sensitive, whereas theta measured in behaving animals does not show this property (Vanderwolf et al. 1988). Carbachol models of theta activity rely on the activation of muscarinic receptors (Williams and Kauer 1997) therefore are sensitive to atropine. However, the in vitro theta elicited by activation of metabotropic glutamate receptors was shown to be atropine resistant (Gillies et al. 2002). Furthermore, similar to in vivo models (Buzsáki 2002), this model was shown to depend on intact N-methyl-D-asparate (NMDA) transmission and blockade of GABAA also attenuated the extracellularly measured theta oscillation. An additional characteristic feature of this in vitro model was its sensitivity to the blockade of the hyperpolarization-activated current (Ih). Although it is known that Ih is present in multiple cell populations, including pyramidal (Magee 1998) and oriens lacunosum-moleculare interneurons (O-LM cells) (Maccaferri and McBain 1996), the identity of those effectively contributing to the generation of theta was not determined. Also, blockade of Ih was found to disrupt firing of O-LM cells in CA1 (Gillies et al. 2002). O-LM cells are prone targets of the recurrent axons of pyramidal neurons. Their discharge is in an almost perfect overlap with that of pyramidal cells in the hippocampal CA1 region. The question therefore is how O-LM neurons contribute to the dependence of hippocampal theta activity on glutamatergic transmission components.
We used compartmental modeling techniques to study the conditions necessary for the emergence of theta oscillation in the hippocampal CA1 circuitry. The main objective was the study of processes that set the firing phase differences of neuron populations participating in theta oscillation. We used a three-population intrahippocampal network model of area CA1 and aimed at providing a mechanism of the in vitro model of atropine-resistant theta oscillations (Gillies et al. 2002). First, we explored the properties of interactions between neuron populations and revealed that nonlinearity realized by the activation of Ih channels is effective in the precise timing of pyramidal cell firing. Second, we examined the properties of theta oscillations and showed that delay relationships between firing of neuron populations relied on intrahippocampal interactions. Third, we examined the pharmacological profile of the population oscillation, showing the role that Ih and glutamate receptors possibly play.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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, 2004). In addition, lacunosum-moleculare interneurons were shown to exhibit slow intrinsic periodic spiking (2–5 Hz) as well (Chapman and Lacaille 1999). From the great variety of these cell types, we confined our study to those that are likely to participate in feedback inhibition of pyramidal cells. Based on their location and the termination pattern of recurrent collaterals, basket cells and O-LM cells were taken into account. The computational model of hippocampal CA1 consisted of three neuron populations including pyramidal neurons and two types of interneurons: O-LM cells and basket interneurons. Computer simulations used conductance based model neurons described by the Hodgkin-Huxley formalism. Neuron types
The multicompartmental pyramidal cell model was an extended version of the 256 compartmental model of Warman et al. (1994). The original model contained seven types of ionic currents: sodium (INa), delayed rectifier potassium (IK), A-type potassium (IK(A)), muscarinic potassium (IK(M)), C-type potassium (IK(C)), low threshold calcium (ICa), and calcium concentration–dependent potassium (IK(AHP)). In addition to the originally implemented currents, we added hyperpolarization-activated nonspecific cation current (Ih). Ih channels are confined to the dendritic regions of pyramidal cells; therefore studying the effects of Ih on somatic firing necessitated the usage of a multicompartmental model. Distribution and kinetic parameters of Ih channels were set according to the data provided in the paper of Magee (1998). The Ih current was described by equations of the standard Hodgkin-Huxley formalism: Ih = ghh(Vm – Eh), where gh was the maximal synaptic conductance, and Eh was the reversal potential of the current. Maximal conductance of Ih was 10 pS/cm2 at the soma and increased linearly as a function of the distance from the soma reaching a maximum at the most distal apical dendrites of 100 pS/cm2. The reversal potential was set to 0 mV. The gating variable h was described by first-order kinetics, in the form of dh/dt = [h
(V) – h]/
h(V). Values for h(V) and h(V) were fitted on data by Magee (1998).
Pyramidal cells received a constant depolarizing current, which was injected in their somata. Strength of this depolarization varied from cell to cell and was picked from a Gaussian distribution. Width of the Gaussian was typically set to 30 pA. Mean level of the tonic depolarizing current varied between 0 and 700 pA and was 600 pA if not stated otherwise.
Basket neurons formed the fast spiking neuron population of the pyramidal layer. The single-compartmental model contained only two active currents: INa and IK (Orbán et al. 2001; Wang and Buzsáki 1996). Gate speed variable 
was set to 2. A constant depolarizing current was given to each basket neuron, whose level was 1.4 µA/cm2 throughout the simulations. Firing frequency of the uncoupled neurons was 81 Hz. The cell surface was set to be equal to the area of a sphere with a radius of 20 µm.
O-LM interneurons represented one of those interneuron populations whose somata resided in the oriens/alveus border. Besides INa and IK, the single-compartmental model featured high-threshold calcium, hyperpolarization-activated potassium, and hyperpolarization activated mixed cation currents (Wang 2002). The O-LM neuron was able to generate repetitive action potentials autonomously. For the regulation of the firing rates of O-LM neurons, we occasionally added a constant hyperpolarizing or depolarizing current, but its default value was 0 µA/cm2. Firing frequency of neurons without synaptic input was 4.9 Hz. In addition, heterogeneity of O-LM cells was introduced by adding a tonic hyperpolarizing current to each cell heterogeneously and setting its level according to a Gaussian distribution. SD of the distribution was 0.07 µA/cm2 on Figs. 5, 6H, and 7. Spatial dimensions were the same as used for the basket neurons.
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9, whereas the number of O-LM cells was 30 in Fig. 5. Results were also tested with a network consisting of 200 basket cells, 90 O-LM cells, and varied number of pyramidal cells; an example of simulations with 30 pyramidal neurons is shown in Fig. 7A. Increasing the number of O-LM cells while keeping convergence-divergence levels constant did not result in significant changes in the activity of pyramidal cells; thus we did not study this factor. Using a lower number of pyramidal cells in the model is justified by the sparse recurrent collaterals in the CA1 region of the hippocampus.
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Synaptic contacts were either inhibitory or excitatory (Fig. 1). At each neuron population, postsynaptic neurons were selected randomly; therefore the spatial aspects of synaptization were ignored. Synaptic contacts established by pyramidal cells were glutamatergic. In most simulations, only NMDA receptor–mediated transmission was used, but in several simulations, 
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor–mediated excitatory postsynaptic potentials were also taken into account (Fig. 9). Both AMPA and NMDA synapses obeyed first-order kinetics (Destexhe et al. 1998). We modified the original model of NMDA synapse by changing the parameters determining the magnesium dependency of the NMDA channel (Kuner and Schoepfer 1996):b([Mg2+], V) = 1/{1 + exp(vV)[Mg2]/
}, with v = –41 mV–1, = 1.57 mM, and [Mg2+] = 2 mM.
Synapses established by interneurons were inhibitory and were mediated by GABAA receptors. Synaptic current was in the standard form of Isyn = gsyns(V – Esyn), where the activation variable s obeyed first-order kinetics ds/dt = F (Vpre)(1 – s) – 
s (Wang and Buzsáki 1996). In the previous equation, F(Vpre) was described by F(Vpre) = 1/1 + exp[–(Vpre – 
syn)/K). Parameters characterizing synaptic contacts between neurons were as follows: for basket-to-pyramidal cell and O-LM cell-to-pyramidal cell connections: = 10 ms–1, = 0.07 ms–1, K = 2 mV, Esyn = –80 mV; for basket-to-basket cell connections: = 10 ms–1, = 0.07 ms–1, K = 2 mV, Esyn = –75 mV; for O-LM cell-to-basket cell connections, the decay was slower (Hájos and Mody 1997): = 20 ms–1, = 0.05 ms–1, K = 0.5 mV, Esyn = –80 mV. Release threshold syn was set to 0 mV at each GABAA synapse.
For each cell type, the pattern of synaptic contacts was random: convergence and divergence were set, whereas pre- and postsynaptic neurons were selected randomly. Throughout the paper, convergence numbers denote the exact number of efferent synapses on a single neuron, and similarly, divergence numbers denote the exact number of target neurons a neuron is innervating. Magnitudes of synaptic conductances for the established contacts were tested in a wide range; therefore both the ranges and default values (in parentheses) are given. Unless otherwise noted default values were used for figures shown throughout this paper. Synaptic strengths were set homogeneously for a given pair of pre-, and postsynaptic neuron population, no variance in the maximal synaptic conductance of individual contacts was introduced.
Recurrent collaterals of pyramidal cells are confined to the stratum oriens (Knowles et al. 1982) and are sparse in the CA1 region; therefore pyramidal cell-to-pyramidal cell connections were ignored. Pyramidal cells, however, provide the main excitatory input for oriens interneurons, including O-LM cells (Blasco-Ibanez and Freund 1995; Lacaille et al. 1987). Synaptic transmission was either mediated by NMDA receptors (Nyíri et al. 2003) or both NMDA and AMPA receptors (Baude et al. 1995; Nusser et al. 1998). Facilitation at these synapses was ignored (Ali and Thomson 1998). Each O-LM cell was innervated by 1.6–5 pyramidal cells (default 2.4); maximal synaptic conductance was 0.5–1.1 nS (default 0.7 nS) at NMDA receptors and 1 nS at AMPA receptors. Pyramidal cells were shown to innervate basket neurons as well (Ali et al. 1998); therefore these connections were also implemented in our model. In these connections, however, NMDA receptor–mediated synaptic currents were not included as in the CA1 region of the hippocampus. NMDA receptor contacts were shown to be predominant on O-LM cells and less on parvalbumin positive, presumably basket, cells (Nyíri et al. 2003). Convergence of pyramidal cells was between 0 and 10 (default 0); maximal synaptic conductance of AMPA synapses was 1 nS.
O-LM cells projected to pyramidal cells (Gulyás et al. 1993a; McBain et al. 1994), establishing contacts through GABAA receptor–mediated synapses. In addition, O-LM cells were shown to innervate interneurons as well (Katona et al. 1999), and interneurons with similar dendritic but different axonic arborization were shown to terminate on other local interneurons in the CA1 region (Gulyás et al. 2003). Although there is no data available on the physiological identity of these two types of interneurons, for simplicity, we used the same neuron population for the innervation of both pyramidal and basket neurons and used the term O-LM cells for these neurons. Convergence of O-LM neurons on pyramidal cells (Sík et al. 1995) was in the range of 8–20 (default 8) and was distributed on distal apical dendritic compartments on different branches of the dendritic tree. Maximal synaptic conductance was varied between 0.5 and 1.1 nS (default 0.88 nS). Convergence of O-LM neurons on basket cells (Katona et al. 1999) was in the range of 3 to 5 (default 5), whereas maximal synaptic conductance was 0.7–1.1 nS (default 0.88 nS).
Basket cells have axons largely confined to the stratum pyramidale and are known to form baskets on the somata of pyramidal cells. In the presented model, basket cells projected principally to the somata of pyramidal neurons (80%) and also terminated on the proximal apical dendrites (Freund and Buzsáki 1996; Sík et al. 1995). Convergence of basket cells on pyramidal cells was calculated from the divergence (Sík et al. 1995) and the relative number of the two cell types. Accordingly, convergence of basket cells on pyramidal cells varied between 10 and 30 (default was 20) However, the divergence of basket cells did not match the values obtained from experimental studies. As the pyramidal neuron was a multicompartmental implementation, it was not cost effective to have the same ratio of pyramidal cells and basket cells as would be in the case of an experimental situation. The low number of pyramidal cells was justified by the fact that recurrent collaterals are sparse in the CA1 region of the hippocampus (Lopes da Silva et al. 1990). Inhibitory synapses between basket cells and pyramidal cells were mediated by GABAA receptors; maximal synaptic conductance was 0.7–1.4 nS (default 1.1 nS).
Parvalbumin containing putative basket neurons also have been shown to establish connections with other parvalbumin containing neurons (Sík et al. 1995). We set the divergence factor of basket cells according to this labeling study; thus a single basket neuron innervated 60 other basket cells on average. Maximal synaptic conductance was set to 0.25 nS.
When the network size was altered, convergences were kept constant to keep the depolarization level and thus average firing rates of individual cells unchanged. Table 1 shows a summary on connections among cell types.
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Population activity was characterized by an extracellular field potential, which was calculated using data obtained from pyramidal cells. The overwhelmingly larger number of pyramidal cells in the real neural tissue legitimized the method of using only pyramidal cell activity for this calculation. All simulated pyramidal cells were placed on the circumference of a 4 µm-radius circle and total transmembrane current in a compartment divided by the inverse of the distance of the respective compartment was summed for each compartment. Filtering properties of the extracellular medium was taken into account by low-pass filtering the signal (0–150 Hz), thus reducing the contribution of fast events to the EEG. Theta power was determined as the peak of the power spectrum of the EEG trace in the range of 3–8 Hz.
Integration time step was 1e–5 s, and numerical integration was carried out with the Exponential Euler method. Initial conditions were random, and to provide an initial uniform distribution of pyramidal cell spikes, pyramidal cells were hyperpolarized for a time interval of length picked from a uniform distribution.
Simulations were performed with the GENESIS neural simulator program in Linux environment on a 16-node Beowulf cluster, also using the computational resources of the RMKI LCG center and the Hungarian ClusterGrid.
Data analysis
Reliability of disinhibition (R) was measured as the ratio of pyramidal cell spikes in a time window succeeding the beginning of disinhibition and total number of spikes fired during the simulation. Disinhibition was achieved by the suppression of action potential firing of either a fraction or all neurons innervating the pyramidal cell, depending on the protocol. Suppression of presynaptic action potentials was a result of hyperpolarizing the presynaptic neurons in a short time interval. Disinhibition was delivered periodically (period is denoted by DP) for a given time length (DTW). Width of the time window used to determine R was one-tenth of DP. Reliability of disinhibition was calculated according to the formula
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PHASE DISTRIBUTION HISTOGRAMS.
Preferred phase of a given cell's firing relative to a reference signal was analyzed, and histograms representing firing probability of individual cells as a function of phase of the reference signal were prepared. Reference signal was acquired from the hippocampal CA1 field potential by filtering it with a Gaussian filter. Phase (
) of an action potential in degrees relative to the reference signal is calculated by the = 360°(t – T1)/(T2 – T1) equation, where t is the time of action potential occurrence, T1 and T2 are times of local maxima of the reference signal preceding and succeeding t, respectively.
The mean of phase distribution histograms was calculated by calculating circular mean of the histogram, in the form
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(k) is the time of individual spikes and 2
in the index denotes modulo. Angular deviation was calculated as
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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), their interactions shape the population activity. To analyze the role individual cell populations and connections play in shaping the population activity and parameters individually testable, pairwise interactions between neuron populations were studied. According to the scenario presented in our paper, recurrent collaterals of pyramidal cells excite O-LM neurons through NMDA receptor–mediated synapses, which excitation evokes action potentials in target neurons. Next, O-LM neurons inhibit a fraction of the basket cell population through GABAA synapses. Synchronized inhibition partially suppresses firing of basket neurons, which in turn disinhibit target pyramidal cells, where slow Ih deactivation results in rebound action potentials in pyramidal cells.
In the following sections of RESULTS, components of this cycle were studied separately. In the first three sections, synaptic properties of the network were explored in pairwise interactions between basket neurons–pyramidal neurons; O-LM neurons–basket neurons; and pyramidal neurons–O-LM neurons, respectively. First, properties of basket cell–pyramidal cell coupling were explored to determine the conditions necessary for gating of pyramidal cell action potentials Second, the modulation of basket cell firing rate by partially synchronous IPSPs was analyzed. Third, the synchronization properties of O-LM cells in response to phasic NMDA receptor–mediated input were analyzed. In the fourth section, we turn to the intrinsic properties of the pyramidal neuron enabling phasing of pyramidal cell activity by basket neurons. The role of hyperpolarization-activated current was analyzed in interpopulation interactions of basket and pyramidal cells by examining requirements of eliciting temporally precise rebound action potentials in pyramidal cells. Next, characteristics of theta oscillations were studied using the interconnected network of basket cells, O-LM cells, and pyramidal cells. Finally, contribution of glutamatergic transmission components and the hyperpolarization activated current to population oscillations were examined.
Reliability of pyramidal cell burst generation caused by disinhibition by basket neurons
It was previously shown in in vitro conditions that a sequence of fast IPSPs can synchronize pyramidal cell firing through the generation of a depolarizing overshoot in postsynaptic pyramidal neurons (Cobb et al. 1995). Because of the unique perisomatic location of basket cell synapses on pyramidal cells, these connections were regarded as key components in the timing of action potential generation. We studied the mechanism of how disinhibition of a pyramidal cell could result in rebound depolarization and finally in a rebound burst. For this, a randomly interconnected basket cell network was modeled, a fraction of which innervated the perisomatic region of a pyramidal neuron. In the presence of tonic depolarization basket cells provided rhythmic hyperpolarization of the pyramidal cell's soma through GABAA-mediated IPSPs. Disinhibition of the target pyramidal cell was modeled by suppressing basket cell firing by manually giving a hyperpolarizing step current in a given time window (DTW; Fig. 2A). Suppression of basket cell firing was periodic (length of period is denoted by DP) resulting in periodic rebound burst generation by pyramidal cells. For a given experiment, pyramidal cell firing times relative to the disinhibition were averaged using multiple periods.
Suppressing basket cell action potentials often elicited bursts of action potentials at the target pyramidal neuron (Fig. 2A) but effectiveness of rebound burst generation showed considerable variability. Factors determining the reliability of disinhibition (R; Fig. 2, A and B; also see METHODS) included the convergence of basket cells on pyramidal cells, the depth of basket cell modulation (i.e., number of suppressed basket cells), and the width of the disinhibition time window. Reliability of disinhibition increased with increasing number of innervating basket cells but saturated as a result of sublinear summation of IPSPs (data not shown). In the case when inhibition was only partially suppressed, that is, firing was only suppressed at a fraction of innervating basket cells, a clear decrease in R was observed (Fig. 2C). Reliability of disinhibition (R) rapidly increased when the ratio of disinhibited basket cells reached 60%, where R was 56 ± 7% (SE), meaning that the majority of pyramidal cell action potentials occurred immediately after disinhibition. In vivo data are available on such deep modulation of basket cells during theta activity (Klausberger et al. 2003), which promotes the plausibility of this mechanism to enable precise timing of pyramidal neurons.
Width of the DTW had little effect on R over a broad width range (Fig. 2D). Furthermore, disinhibition window width as short as 
10 ms proved to be sufficient to elicit postsynaptic response. This result also shows that high-frequency bombardment of the pyramidal cell was necessary for precise timing of postsynaptic pyramidal cells. At lower disinhibition period (DP; higher frequency), the reliability of disinhibition remained low, independent of the window width (Fig. 2D), indicating that broader disinhibition time window cannot compensate the large difference between disinhibition period and preferred frequency of the target neuron. Furthermore, a pyramidal neuron being subject to constant depolarizing current tends to generate bursts of action potentials with a certain frequency. This frequency also affects the effectiveness of periodical disinhibition. We tested this effect by changing the disinhibition period instead of altering the frequency the pyramidal cell tends to fire with (2 Hz at 0.6-nA depolarizing current and 20 basket cells innervating the pyramidal cell). Reliability of disinhibition dropped seriously at small disinhibition periods and remained higher in an extended range after peaking at 230 ms (Fig. 2E). The result confirms that basket cells are able to set the timing of the model target pyramidal cell in an extended frequency range.
Modulation of basket cell network firing rate by synchronous IPSPs
Model O-LM interneurons established synaptic contacts with basket cells. We assumed a sparse connection between O-LM neurons and basket neurons (see METHODS) and studied whether limited convergence of O-LM neurons on basket neurons can provide the suppression necessary for the effects shown in the previous section. Furthermore, we also checked whether periodically firing O-LM cells whose action potentials occur at dispersed phases can achieve similarly effective suppression of basket cells.
Simulations were performed with a population of O-LM neurons connected to a population of basket cells at various O-LM-to-basket cell divergence numbers and different maximal synaptic conductance at these synapses. Measures to quantify width and depth of inhibition of the basket cell population were set up (Fig. 3A). Two different protocols were used for the characterization of the interaction between the two cell populations. First, all O-LM neurons fired at the same time (Fig. 3, B and C), thus causing simultaneous inhibition of basket cells. Next, to model a more realistic scenario, O-LM spiking times were set randomly: while individual O-LM neurons fired periodically, the firing phase of each neuron was set according to a Gaussian distribution with a given variance (Fig. 3, D and E). Simulations with simultaneous inhibition revealed that low convergence (as few as 4) was enough to modulate basket cell firing sufficiently for providing pyramidal cell disinhibition (Fig. 3C). Also, width of modulation has reached 10 ms for low convergence numbers and physiologically realistic synaptic strength (Fig. 3B). Nonsimultaneous inhibition increased the width of inhibition (Fig. 3D) and decreased the depth of inhibition (Fig. 3E), but conditions necessary to sufficiently suppress basket cell activity remained unchanged. Note, however, that with synchronous O-LM cell spikes (0-ms dispersion), the maximal depression was reached earlier than with dispersed spikes. At a maximal synaptic conductance of 0.5-nS delay of maximal depression, as measured from the mean of the firing times in the cluster of O-LM cell spikes, was 8.4 ± 1.2 ms at 0-ms dispersion, whereas at a dispersion of 63 ms, the delay was 21.2 ± 1.8 ms (histogram bin size was 200 ms). The fast suppression of basket cells shows that in the case of high O-LM cell synchrony the delay of basket cell suppression is mainly determined by the rise time of the IPSP.
Synchronization properties of the pyramidal cell–O-LM cell coupled oscillator system
Characteristics of phasic innervation of O-LM neurons by pyramidal cells were tested to determine the properties of NMDA receptor–mediated coupling. Synchronization between pyramidal cells and O-LM neurons was studied by simulations where one pyramidal cell innervated one O-LM interneuron through NMDA receptor–mediated synapse. Firing frequency of pyramidal cells and current injected into O-LM neurons were varied. In these simulations, O-LM cell to pyramidal cell feedback was not taken into account. As coupling is weak, synchronization is slow. Therefore we excluded initial transients by ignoring the first 1.5 s of the simulations. Time delays between pyramidal cell spikes and subsequent O-LM cell spikes were collected in a 5-s time interval, and their relative SD was calculated together with the ratio of number of O-LM cell spikes to the number of pyramidal cell spikes (Fig. 4). Small relative SD of spike time delays (dark regions on the figure) occurs in cases when the O-LM cell and the pyramidal cell fire synchronously. Simulations revealed that when depolarization did not drive O-LM cells to exhibit periodic firing behavior (below approximately –1.74-pA injected current; Fig. 4, inset), O-LM cell firing is 1:1 phase locked to pyramidal cell firing. When O-LM cells fire autonomously (injected current is more than approximately –1.74 pA), the period of O-LM cell firing doubles and then triples, whereas the first O-LM spike in a period follows the pyramidal cell spike after a constant time delay for a given pyramidal cell firing frequency. This relation is kept at 2-Hz pyramidal cell frequency. In this depolarization region, synchrony is maintained in narrow areas where period of O-LM cell oscillation is close to an integer multiple of the period of the pyramidal cell oscillation. In summary, even weak phasic NMDA coupling between pyramidal cells and O-LM neurons was capable of synchronizing O-LM cell firing to the action potentials of pyramidal cells.
Hyperpolarization activated current elicited after depolarization
Pyramidal cell action potentials elicited by disinhibition proved to be crucial for the timing of pyramidal cell activity (see Fig. 2). We studied what intrinsic mechanisms contribute to the precise timing of pyramidal neurons. As Ih current was suspected to be responsible for the induction of the generation of action potentials through depolarizing overshoot, we focused our attention on the contribution of Ih current in action potential and burst generation (Fig. 5). Furthermore, the question whether the dynamics of the Ih allows a single IPSC to elicit rebound activity or stronger and longer-lasting hyperpolarization is necessary for reliable rebound spikes was also asked.
Hyperpolarizing step currents were injected into the somatic compartment of the pyramidal cell model and conditions of rebound action potential generation were analyzed in the same compartment (Fig. 5A). To retain the same conditions that were used during simulations on basket cell network–inhibited pyramidal cell, the same tonic depolarization was applied to the soma of the pyramidal neuron. Furthermore, to have a clearer view on the direct effects of inhibition on pyramidal cell firing, we eliminated the spontaneously occurring action potentials of pyramidal cells by setting the sodium conductance of pyramidal neurons to 0 nS. The effect of intrinsic properties on action potential generation was evaluated by measuring the conditions necessary for reaching a predetermined action potential threshold (–52.6 mV). Although this threshold can vary dynamically under physiological conditions (Azouz and Gray 2000), this does not affect the results shown here.
First, maximal conductance of the hyperpolarization-activated current was selectively and systematically varied at different depolarizing current levels (Fig. 5B). Simulation results showed that with decreased Ih, current conductance larger hyperpolarizing pulses were required to drive the pyramidal cell to the firing threshold. Below a given maximal conductance, firing threshold could not be reached in physiological circumstances at a given depolarizing current. Similar results could be obtained in simulations with intact sodium currents but without tonic depolarizing current on pyramidal cells. The only difference was a significantly higher depolarization needed for eliciting action potential in the pyramidal neuron (data not shown).
Next, we measured the minimal strength of the hyperpolarizing current step necessary to depolarize the pyramidal cell to the firing threshold at different pulse widths (Fig. 5C). At short hyperpolarization widths (<30 ms), the strength of the hyperpolarization increased steeply and saturated at about 40 ms at a level of 0.1 nA, when the pyramidal depolarization was 0.5 nA. Although basket cell IPSCs can be as high as 0.1 nA (Maccaferri et al. 2000), the duration is shorter than required for rebound burst generation. Therefore loosely synchronized IPSCs are required for eliciting rebound activity.
We tested explicitly whether hyperpolarization-activated current enhances precision of pyramidal cell spike timing. Pyramidal cells innervated by multiple basket cells were simulated with and without Ih. Firing rate of pyramidal neurons was set inhomogeneously by setting their constant depolarization levels according to a Gaussian distribution. Postinhibitory facilitation of pyramidal cell spikes was probed by suppressing action potentials of all presynaptic basket cells and measuring both the delay and dispersion of pyramidal cell spikes (Fig. 5Da). Delay of action potentials was shown to be significantly larger when Ih was present at all dispersion levels (Fig. 5Db). Similarly, SD of action potential times was severalfold higher without Ih. Increase of dispersion, however, did not affect the average delay of action potentials in either case (Fig. 5Db). In contrast, SD increased with increasing dispersion when Ih was blocked but not when Ih was intact, showing that Ih greatly increases reliability of pyramidal cell timing when heterogeneity disrupts synchronous firing.
There is a trade-off between the level of hyperpolarization-activated conductance and the site of inhibition: with increasing distance from the soma the depolarizing sag elicited by disinhibition becomes larger but this pyramidal response is attenuating toward the soma. To quantify this trade-off, we conducted simulations, where the apical dendrite was stimulated at increasing distances from the soma (Fig. 5E). Simulations have shown that at the proximal apical dendrite after an initial decrease in the minimal pulse necessary to elicit action potential, the necessary pulse amplitude increased substantially beyond 250 µm. These results confirm that, despite that hyperpolarization-activated conductance is low in the soma and proximal dendrites of pyramidal cells, it contributes effectively to postinhibitory depolarization of pyramidal neurons.
Characteristics of theta oscillation
After examining pairwise interactions between neuron populations, we studied the performance of the interconnected three-population network. Connectivity and physiological parameters between neuron populations were set according to the results of the pairwise simulation studies (see METHODS for the specific values). The hippocampal circuitry formed by pyramidal cells and two classes of interneurons was able to generate theta-frequency oscillation as reflected by the firing histograms (Fig. 6A) and the extracellular field potential calculated from the activity of pyramidal neurons (Fig. 6B; see METHODS). To faithfully follow the protocol applied in vitro, synaptic transmission through AMPA synapses was suppressed. Firing histograms of all neuron populations showed theta-frequency modulation, but spike trains of individual pyramidal cells exhibited variability: they either fired spikes regularly in each theta cycle, or skipped a whole cycle (Fig. 6). Average period of firing of neuron populations was 51 ± 15, 118 ± 18, and 284 ± 42 ms for basket cells, O-LM cells, and pyramidal cells, respectively. We tested how activity of pyramidal cells affects the frequency of the population oscillation; therefore the depolarizing current injected into the soma of pyramidal cells was systematically varied. Simulations revealed a monotonous increase in field potential theta frequency over a wide range of tonic depolarizing current levels (Fig. 6E). Behavior of separate cells was described in two ways: autocorrelation functions of individual membrane-potential traces were calculated (Fig. 6, C and D), and description of population activity was given by calculating the average frequency from the position of membrane potential power spectra peaks resulting from multiple trials (Fig. 6E, dashed line). The difference between frequencies of population activity and frequencies derived from individual neurons reveals that pyramidal cells do not necessarily fire action potentials in each cycle; rather, they skip cycles.
Because depolarization level of pyramidal cells has an effect on theta frequency, we studied whether the oscillation is robust against variations in this factor. We set the depolarizing current inhomogeneously, that is, while injecting constant current into pyramidal cells the strength of this current was determined randomly. Strength of injected current was picked from a Gaussian distribution with a given mean and SD was 3, 5, or 10%. Simulations confirmed that this kind of irregularity cannot disrupt the synchronization of cell populations (Fig. 6F). Changes in resting membrane potentials of pyramidal cells, i.e., scattering the reversal potential of the leakage current according to a Gaussian distribution, did not disrupt theta frequency oscillation either (data not shown).
Similarly, we tested whether altered firing properties of O-LM neurons can affect the frequency of population oscillation by injecting a small constant depolarizing current to each O-LM cell. Theta frequency, however, was only slightly affected by this altered O-LM cell behavior (Fig. 6G). Mean frequency of action potentials of individual pyramidal cells did not change but mean frequency of EEG showed an increasing tendency with increased depolarization. Synchronization of the network was tested with sparser pyramidal cell to O-LM cell connections. For this, we used larger number of pyramidal cells while keeping the convergence of pyramidal cells on O-LM cells constant (2.4). We used 15, 30, and 45 pyramidal neurons. Simulations showed that the power of theta did not change significantly with this modification (power of theta was 0.41 ± 0.04, 0.35 ± 0.06, and 0.38 ± 0.04 mV2/Hz at 550-pA pyramidal cell depolarizing current, respectively).
Level of pyramidal cell depolarization affects the frequency of synchronization of neuron populations. Study of pyramidal cell-to-O-LM cell connections has revealed that efficacy of coupling of action potentials could only be achieved in narrow intervals and depended on the frequency of the action potentials of pyramidal neurons (Fig. 4). We performed simulations to explore how the depolarization of pyramidal cells affects synchronization properties of the network. Simulations with increasing pyramidal cell depolarization have shown that strong synchronization states are alternating with weak synchronization states (Fig. 6H). The two strong synchronization states correspond to the 1:1 and 1:2 frequency ratios of O-LM cells and pyramidal cells.
Firing histograms indicated that the preferred phases of neuron populations are locked to each other. Firing phase histograms, which relate firings of neurons to the phase of extracellular theta activity (Fig. 7A) revealed a nearly equal mean firing phase of the pyramidal cell population and O-LM cell population with a 2.2 ± 1.9° lag of pyramidal cells. Basket cells preceded pyramidal cells by 127.2 ± 3.5°. Comparing results obtained for different pyramidal cell depolarization levels, i.e., different frequencies, a similar phase relationship could be established (Fig. 7B).
To check whether a possible basket cell-to-O-LM cell projection affects the relative timing of neuron populations, we performed simulations with different convergence of basket cells on O-LM neurons. For simplicity, dynamics of synapses connecting basket cells to O-LM cells were the same as those connecting basket neurons; maximal synaptic conductance was 0.88 nS. Up to a convergence of 30, simulations did not show any significant difference in the delay of neither basket cells nor pyramidal cells relative to O-LM neurons (data not shown).
Role of hyperpolarization-activated current in the population oscillation
Simulations were performed to test whether depolarizing afterpotentials evoked by the activation of hyperpolarization-activated current indeed support the synchronization of the network. Therefore we studied the case when depolarization of pyramidal cells was dispersed to simulate pyramidal cells with different firing rate, whereas conductance of Ih at different network components was changed. In the model framework, Ih was present both in pyramidal cells and O-LM interneurons. First, Ih conductance was set to 0 pS at both populations. Eliminating Ih caused theta-frequency modulation of neuron populations to disappear (Fig. 8A). Parallel to this, the attenuation of the theta peak in the power spectrum of the EEG was remarkable (Fig. 8B). Comparison of control simulations and simulations performed without Ih conductance shows a significant drop in theta power (Fig. 8C). Contribution of Ih was also studied by reducing Ih conductance selectively at pyramidal cells and O-LM interneurons. Simulations have shown that reducing Ih at O-LM interneurons does not result in reduced theta amplitude (0.38 ± 0.09 compared with 0.38 ± 0.05 mV2/Hz in the control situation). However, a reduction of 55% was observable at simulations performed with blocked Ih at pyramidal cells (0.17 ± 0.04 mV2/Hz, while the mean amplitude was 0.23 ± 0.07 mV2/Hz with blocking at both sites).
Effects of glutamatergic transmission components
We studied network performance while different components of glutamatergic transmission were changed separately. Previously, theta has been shown to emerge in a CA1 slice when AMPA transmission was suppressed, whereas NMDA transmission proved to be necessary for this kind of theta (Gillies et al. 2002). Theta could emerge in our network when the only excitatory synaptic transmission was realized by NMDA synapses (Figs. 6 and 7). Including AMPA receptor–mediated synaptic currents did not alter the power of theta oscillation significantly (in this case convergence of pyramidal cells on basket cells was 7). However, a significant increase was observed in the power at the gamma frequency band (20–80 Hz; 0.32 ± 0.13 mV2/Hz without and 0.87 ± 0.16 mV2/Hz with AMPA receptors). Increased excitation of basket cells caused by stronger pyramidal basket cell coupling resulted in more action potentials synchronized in gamma frequency, which in turn generated more synchronous IPSPs at target pyramidal cells. This subthreshold oscillation resulted in a gamma-frequency peak in the power spectrum of the extracellular field potential. This observation was further confirmed by the fact that increasing the convergence of pyramidal cells on basket neurons resulted in higher gamma activity (Fig. 9A). At higher convergence levels, the power of gamma-band activity could grow higher than the power of theta oscillation. The same increase in gamma power was achieved by increasing the conductance at AMPA synapses while keeping the convergence at a constant level. In this case, however, when AMPA was present both on O-LM cells and basket cells, there was an increase in the power (an increase of 30% with doubling the maximal synaptic conductance of AMPA), but not in the frequency of theta oscillation (data not shown).
We checked whether the enhanced gamma-band activity could be explained by enhancing the fast glutamatergic transmission between pyramidal cells and basket cells. Therefore simulations were performed where AMPA was blocked at pyramidal cell-to-O-LM cell synapses but was intact at pyramidal cell-to-basket cell synapses (Fig. 9B). Simulations have shown that enhanced pyramidal cell-to-basket cell synapses can account for increased power of gamma band activity when AMPA receptors are not blocked.
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Synchronization of neural populations
Synchronization can emerge in a network of neurons in different ways, e.g., by pacemaker neurons, which has been suggested in the visual cortex (Gray and McCormick 1996), by recurrent inhibition (van Vreeswijk et al. 1994; Wang and Buzsáki 1996; Wang and Rinzel 1993), in special cases recurrent excitation (Crook et al. 1998), and by activation of gap junctions (Traub 1995). The anatomical structure of the hippocampus and the relatively slow time-course of theta oscillation (120–200 ms), however, impose constraints on the possible mechanisms. White et al. (2000) proposed that fast and slow GABAA receptors expressed on distinct interneuron populations may contribute to theta activity. They have shown that a weak perforant path–mediated periodic input could organize discharges of the studied GABA cells in such a way that nested gamma (40–80 Hz) and theta oscillations emerged. The presented scenario might be beneficial in conditions when the perforant path input is intact, but it can neither account for theta when entorhinal cortex is removed by lesion (Buzsáki et al. 1983; Ylinen et al. 1995) nor for theta elicited in a CA1 slice (Gillies et al. 2002). Recently, Rotstein et al. (2005) described a mechanism of hippocampal CA1 theta generation in two populations of hippocampal interneurons, where fast-firing neurons innervated slow-firing neurons. In this study, theta-frequency synchronization is mainly driven by slow-firing oriens neurons, which give rise to slow IPSPs that silence the target basket cells for a longer period. Theta-frequency synchronization required the presence of Ih on oriens neurons. In the presented model, the authors assumed all-to-all connectivity, and it is not clear how the model would function under more realistic conditions, with sparser projections from one population to the other. Furthermore, the presented model does not give an account of the effects of glutamatergic transmission components. In our study, we showed that basket cell-to-OLM cell projections do not alter the relative timing of neuron populations during theta-frequency oscillation. However, as Rotstein et al. (2005) point out, this projection might have an effect on the stability of the network oscillation.
Another study highlighted the importance of the septohippocampal feedback (Wang 2002), showing an antiphase synchronization of medial septal GABAergic neurons and putative calbindin immunoreactive, Ih-containing interneurons. Here, the low-frequency synchronization was ensured by clusters of spikes fired by the septal neuron, which suppressed the firing of the hippocampo-septally projecting neurons for an interval comparable with the scale of theta oscillation. Septal phasic drive is an important component of the hippocampal theta but phase preferences of septal units are dispersed (King et al. 1998), and phase relationships of functional groups in the septum show an intricate pattern (Dragoi et al. 1999). If timing of hippocampal inhibitory neurons was achieved by periodic inhibition of these cells by medial septal GABAergic neurons, two problems would arise. First, although medial septal unit firing shows a hippocampal theta-locked behavior (King et al. 1998), preferred firing phases of these units are scattered over a broad interval (King et al. 1998). Second, medial septal units were shown to innervate hippocampal interneurons in a nonselective manner (Freund 1992), postsynaptic targets including both horizontal neurons with cell bodies in the oriens and basket cells; thus it would be hard to explain the difference between O-LM and basket cell firing phase preferences solely on the basis of medial septal interactions. These facts challenge the ultimateness of a scenario where synchrony is maintained by two neuron populations firing in an antiphase manner.
Hippocampal interneurons are known to quickly respond to excitation by emitting action potentials with h
= Ai/d
. Here, 
