A MODEL OF A NEURONAL STRUCTURE ABLE TO GENERATE COLLECTIVE OSCILLATIONS SIMILAR TO HUMAN PARIETAL ALPHA RHYTHM

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1 MODEL OF NEURONL STRUCTURE LE TO GENERTE COLLECTIVE OSCILLTIONS SIMILR TO HUMN PRIETL LPH RHYTHM Otilia Păduraru *, Hariton Costin *+ * Institute for Theoretical Computer Science, Romanian cademy, Iaşi ranch d. Carol I no. 8, Iaşi 755, Romania, Phone: otilia@iit.iit.tuiasi.ro web: + Faculty of iomedical Engineering, Iaşi University of Medicine and Pharmacy Str. Universităţii 16, Iaşi, Romania, hcostin@iit.iit.tuiasi.ro Papers of the First International Congress of the Romanian Society for Cell iology, Iaşi, 7 1 June 2. Part V: Current Problems in Cellular and Molecular iology, C. Crăciun and. rdelean (Eds.), 2, RISOPRINT Publishing House, Cluj-Napoca, p

2 1 MODEL OF NEURONL STRUCTURE LE TO GENERTE COLLECTIVE OSCILLTIONS SIMILR TO HUMN PRIETL LPH RHYTHM Otilia Păduraru*, Hariton-Nicolae Costin *+ * Institute for Theoretical Computer Science, Romanian cademy, Iaşi ranch d. Carol I no. 8, Iaşi 755, Romania, otilia@iit.iit.tuiasi.ro + Faculty of iomedical Engineering, Iaşi University of Medicine and Pharmacy Str. Universităţii 16, Iaşi, Romania, hcostin@iit.iit.tuiasi.ro bstract The present study focused on the rhythmic activity provided by two interconnected networks of model neurons endowed with appropriate intrinsic and synaptic characteristics. The first network consisted of 234 excitatory neurons, assumed to be of pyramidal type. The second network included 441 fastspiking gabaergic neurons, considered as basket cells. The key characteristic of the pyramidal cell is the presence of a calcium current whose dynamics is similar to that of the transient low-threshold calcium current detected in thalamocortical neurons, but with the steady-state activation and inactivation functions shifted towards more positive values. Therefore, even a weaker hyperpolarization was sometimes sufficient to give rise to a rebound spike. The synaptic transmission was mediated by fast MP and G type currents. The simulations showed that, after injecting brief but strong current pulses into a set of randomly chosen pyramidal cells, the whole structure engaged in a rhythmic activity, within alpha frequencies, similar to that detected in human parietal areas. We concluded that, at least theoretically, the core mechanism of the parietal alpha rhythm could be provided by the interplay of two neuronal populations able to synchronize their activities on the post-hyperpolarization responses generated by a particular class of pyramidal neurons. Key words: neocortical neurons, rebound spike, parietal alpha rhythm INTRODUCTION lpha rhythm is the most representative rhythm that appears on an EEG recording, in relaxed, normal human subjects. It covers mainly the occipital, parietal and temporal areas and is dominated by frequencies lying in the 8-13 Hz range [1]. There are important differences between the shapes of the parietal and occipital alpha rhythm. While the occipital alpha is organized in clear, well-shaped fusiform spindles, lasting.5-3 seconds and is characterized by a high degree of symmetry with respect to the two hemispheres, the parietal alpha is represented by spindles whose shape is rather rectangular than fusiform. These latter spindles last longer, are separated by shorter inter-spindle intervals and are less symmetrical. This might suggest a higher autonomy of the parietal alpha rhythm (assuming that its origin is cortical), namely, it might undergo weaker subcortical influences than the occipital alpha. So far, most modeling studies addressing the physiological rhythms have focused mainly on slow-wave sleep spindles [6], gamma rhythm [18], theta rhythm [17]. The present computational study was conducted to test whether the core mechanism of the human parietal alpha rhythm could be provided by the interplay of two neocortical populations, one consisting of pyramidal cells and the other of Gergic cells, able to synchronize their activities on the post-hyperpolarization responses provided by the former type of cells. This assumes that the pyramidal neurons are endowed with intrinsic properties that allow the generation of a rebound suprathreshold depolarization ms after the onset of the synaptically induced hyperpolarization. Consequently, the model pyramidal cell was endowed with a low-threshold Ca 2+ current (I T ), as a key element underlying rebound burst generation.

3 2 Within the cerebral cortex, neurons have been classified as regular spiking (RS), intrinsically bursting (I) and fast-spiking (FS). The intrinsically bursting cells have been detected more frequently in deep layers, but have also been found in superficial layers [3] [4] [8] [11] [12] [15] [19]. The present study assumed that the pyramidal neurons involved in alpha activity are able to generate intrinsic rebound bursts, while the Gergic neurons, considered as basket cells, are of fast-spiking type. METHODS The proposed structure consisted of two networks: one included 234 excitatory neurons, assumed to be of pyramidal type (E-cells), while the other included 441 Gergic neurons, assimilated to basket cells (I-cells). The two networks were organized as 48 x 48 and 21 x 21 matrices of neurons, respectively. The E-cells were allowed to establish synaptic contacts to both types of cells, while the I-cells, only to E-cells. The locally random pattern of connectivity used assumed that a given neuron may contact a randomly chosen number of neurons, kept within a preset interval. The coordinates of the target neurons were also randomly selected within a circle of a given radius. For each neuron, those connections that fell inside the circle centered in its coordinates but outside the target rectangular neuronal area were discarded. Each E E or E I connection was mediated by 5 synaptic junctions and each I E connection, by 3 junctions. oth types of neurons were represented by monocompartmental models. Four voltage-dependent currents (I Na, I K, I T and I ) were inserted into the E-cell and only two (I Na and I K ) into the I-cell. leakage current was also present in both cells. For both types, the expressions of the I Na and I K currents were derived from the equations modeling these currents in hippocampal pyramidal cells [17]. For the E-cell, these equations were adjusted to obtain a spike shape similar to that recorded in human neocortical pyramidal neurons. For the I cell, they were initially modified to replicate the behaviour of a cat visual basket cell, tonically stimulated by a (2 ms,.5 n) injected current [16]. slight change was then operated in order to increase the spike frequency to weak depolarizing currents. The I T current was described by a Goldman-Hodgkin-Katz type equation, starting from the expression of this current elicited from thalamocortical cells [5]. The inactivation function of this current was shifted 3 mv towards more positive values, to allow the cell to generate a rebound burst in response to weaker inhibitory stimuli. 5 mv positive shift was also performed over the activation function to prevent the cell entering spontaneously bursting behaviour, after the first rebound burst. The I current was modeled according to [1]. It was assumed that the concentration of the free intracellular Ca 2+ ions increases due to the I T current and decreases exponentially with a short time constant. The excitatory transmission was mediated by MP receptor-mediated currents while the inhibitory transmission, by G currents. The two types of synaptic currents were modeled by first-order kinetic schemes [7]. It was supposed that a (1 ms, 1 mm) transmitter pulse is released every time the membrane potential exceeded the threshold needed for the exocytosis of the vesicles. ll computations were performed for a temperature of 36 o C, with the NEURON simulation tool [9]. The expressions of all equations and parameters can be found in [14].

4 3 RESULTS Firstly, the behaviour of either type of neuron was investigated in isolation. The E-cell responded with single spikes (that showed a slight degree of adaptation) during positive, long current pulses and with a rebound burst to an adequately chosen negative current (e.g. to a 2 ms, -.19 n pulse). The I-cell fired high frequency single spikes to long positive current pulses. The spike frequency obtained in response to a (2 ms,.5 n) current was 55.8Hz for the E-cell (after adaptation) and Hz for the I-cell [13] C Figure 1. Membrane potential of E-cell 231 () and I-cell 7 (, C). C represents a detail of the -plot. fter t=31 ms, a subthreshold depolarization, then six responses consisting of 3, 1, 4, 1,1, 2 spikes were recorded Figure 2. Number of E-cells () and I-cells () firing simultaneously at each moment t. To investigate the collective behaviour of the interconnected networks, (1 ms,.6 n) initiating stimuli were injected into five groups of 18 randomly

5 4 chosen neurons, with 15 ms delays between two successive groups. Prior to this stimulation, all neurons had been at rest. The responses generated by one E-cell (E231) and one I-cell (I7) were plotted in Fig. 1. The E-cell fired single spikes irregularly, but each supra- or subthreshold event was synchronized to the collective response of the structure. The I-cell usually fired synaptically driven sequences of 1-4 spikes and only rarely generated subthreshold depolarizations. These events were also synchronized, so that it can be assessed that the global behaviour relies on an in-phase mechanism. 1 ms 1 mv Figure 3 verage membrane potential computed over all E-cells (Simulation 1)., Raw results., Smoothed trace. Figure 4 verage membrane potential computed over all E-cells (smoothed traces).. Simulation 2., Simulation 3.

6 5 The number of E-cells (I-cells) firing simultaneously at each moment t was plotted in Fig. 2 (Fig. 2). Due to the externally applied initiating stimuli, more than 1 E- or I-cells fired during the initiation phase. Therefore, at the beginning, the two plots were truncated to emphasize the behaviour of the two neuronal populations after this phase. The average membrane potential, computed over all 234 E-cells was plotted in Fig. 3. This recording was further smoothed by applying a simple 25 point median filter (Fig. 3). The most relevant frequency (as appeared in the power spectrum, not shown here) was equal to 11 Hz. It must be stressed that neither of the two types of neurons can oscillate spontaneously, so that each response was only synaptically driven. This simulation showed that, after injecting brief current pulses into a set of randomly chosen pyramidal cells, the whole structure engaged in a rhythmic activity within alpha frequencies. The results obtained in other two simulations were plotted in Fig. 4. The simulation that provided the collective oscillations plotted in Fig. 4 (simulation 2) used the same connectivity as before, the same E-cell, but a different I-cell. In isolation, this latter cell also fired high frequency spikes in response to long depolarizing stimuli, but each spike was followed by a short but prominent hyperpolarization. s part of the network, this cell showed an increased tendency in firing longer spike sequences every cycle (usually 3-4 spikes/sequence). The simulation that provided the collective oscillations plotted in Fig. 4 (simulation 3) used a different pattern of connectivity but an identical I-cell to that used in Fig. 4. The dynamics of the I T current was also slightly modified. oth plots were obtained after smoothing. The most representative frequency was again 11 Hz. single simulation took about 43 hours when running on a 266 MHz Pentium. DISCUSSION Even if relatively simple, the proposed structure was able to generate collective oscillations similar to human parietal alpha rhythm. These simulations and others not included in this paper revealed the powerful role of the Gergic cells in synchronizing the overall activity. This originates in the fact that all inhibitory neurons fired sequences of high frequency spikes almost every cycle. The inhibitory input provided by these neurons was powerful enough to lead to the generation of a rebound burst in a pyramidal neuron. However, by the time this burst would be evoked, the E-cell received new inhibitory stimuli that cut the additional spikes, leaving at most the first one. In [2], a number of only 1-2 synaptic junctions per pyramidal cell basket cell connection was found in layers II-III of cat visual cortex (areas 17 and 18). However, the present model used 5 synaptic junctions per each such connection to induce longer spike sequences in the I-cells. Other simulations, not included here, revealed that it is important that the I-cell fire longer high frequency trains. network of inhibitory neurons that would fire trains of 1-2 spikes interspersed with subthreshold events, would not be always able to synchronize the E-network. ppendix: Connectivity parameters Rad maxdiv mindiv Div Conv avdiv avconv E E E I I E Table 1

7 6 In Table 1, Rad stands for the radius of a circle within which the center-neuron may contact target neurons; maxdiv (mindiv ) represents the maximum (minimum) divergence of a source neuron with respect to the target area, assuming an infinite structure; Div (Conv ) represents the average divergence (convergence) of a source (target) neuron with respect to the target (source) area, assuming an infinite structure; avdiv (avconv) represents the actual average divergence (convergence) of a source (target) neuron with respect to the target (source) area. This was computed as the mean value of all actual divergence (convergence) factors. The X Y type notation has assumed that X is the source neuronal type and Y the target type. ll parameters have been expressed in number of neurons. REFERENCES [1] rseni C., Roman I. (1986). tlas clinic de electroencefalografie. Editura ştiinţifică şi Enciclopedică, ucureşti. [2] uhl. E.H., Tamás G., Szilágyi T., Stricker C., Paulsen O., Somogyi P. (1997). Effect, number and location of synapses made by single pyramidal cells onto aspiny interneurones of cat visual cortex. J. of Physiology 5: [3] Castro-lamancos M.., Connors. W. (1996). Cellular mechanisms of the augmenting response: short- term plasticity in a thalamocortical pathway. J. of Neuroscience 16: [4] Contreras D., Dürmüller N., Steriade M. (1997). bsence of a prevalent laminar distribution of IPSPs in association cortical neurons of cat. J. of Neurophysiology 78: [5] Coulter D.., Huguenard J.R., Prince, D.. (1989). Calcium currents in rat thalamocortical relay neurones: kinetic properties of the transient, low-threshold current. J of Physiology 414: [6] Destexhe., al T., McCormick D.., Sejnowski T. J. (1996). Ionic mechanisms underlying synchronized oscillations and propagating vawes in a model of ferret thalamic slices. J. of Neurophysiology 76: [7] Destexhe., Mainen Z. F., Sejnowski T. J. (1998). Kinetic models of synaptic transmission. In: Methods in Neuronal Modeling: from Ions to Networks, second edition, Koch C., Segev I. (Eds.), Cambridge: MIT Press, pp [8] Gray C. M., McCormick D.. (1996). Chattering cells: Superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274: [9] Hines M. L., Carnevale N. T. (1997). The NEURON simulation environment. Neural Computation 9: [1] Huguenard, J.R., Coulter, D.., Prince, D.. (1991). fast transient potassium current in thalamic relay neurons: kinetics of activation and inactivation. J. of Neurophysiology 66: [11] McCormick D.., Wang Z., Huguenard J. (1993). Neurotransmitter control of neocortical activity an excitability. Cerebral Cortex V3 N5: [12] Nowak L. G., Sanchez-Vives M. V., McCormick D.. (1997). Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cerebral Cortex V7 N6: [13] Păduraru O. (1998a). Minimal Model for a Neuronal Structure Oscillating in lpha Range. In: The Proceedings of the 6 th International Symposium on utomatic Control and Computer Science, Iasi, Romania, Nov [14] Păduraru O. (1998b). iophysical models of bursting neurons. Research Report II (in Romanian). [15] de la Peña E., Geijo-arrientos E. (1996). Laminar localization, morphology, and physiological properties of pyramidal neurons that have the low-threshold calcium current in the guinea pig medial frontal cortex. J. of Neuroscience 16: [16] Tamás G., uhl E. H., Somogyi P. (1997). Fast IPSPs elicited via multiple release sites by different types of Gergic neurone in the cat visual cortex. J. of Physiology 5: [17] Traub R. D., Miles R. (1991). Neuronal networks of the hippocampus. Cambridge University Press. [18] Traub R. D., Jefferys J. G. R., Whittington M.. (1999). Fast oscillations in cortical circuits. MIT Press. [19] Wang Z., McCormick D. (1993). Control of firing mode of corticotectal and corticopontine layer V burst-generating neurons by norepinephrine, acetylcholine and 1S, 3R-CPD. J. of Neuroscience 13: Correspondence should be addressed to Otilia Păduraru, otilia@iit.iit.tuiasi.ro