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The Journal of Neurophysiology Vol. 79 No. 5 May 1998, pp. 2730-2748
Copyright ©1998 by the American Physiological Society
1 Howard Hughes Medical Institute, The Salk Institute, Computational Neurobiology Laboratory, La Jolla, California 92037; 2 Laboratory of Neurophysiology, School of Medicine, Laval University, Quebec G1K 7P4, Canada; and 3 Department of Biology, University of California San Diego, La Jolla, California 92093
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Bazhenov, Maxim, Igor Timofeev, Mircea Steriade, and Terrence J. Sejnowski. Cellular and network models for intrathalamic augmenting responses during 10-Hz stimulation. J. Neurophysiol. 79: 2730-2748, 1998. Repetitive stimulation of the thalamus at7-14 Hz evokes responses of increasing amplitude in the thalamus and the areas of the neocortex to which the stimulated foci project. Possible mechanisms underlying the thalamic augmenting responses during repetitive stimulation were investigated with computer models of interacting thalamocortical (TC) and thalamic reticular (RE) cells. The ionic currents in these cells were modeled with Hodgkin-Huxley type of kinetics, and the results of the model were compared with in vivo thalamic recordings from decorticated cats. The simplest network model demonstrating an augmenting response was a single pair of coupled RE and TC cells, in which RE-induced inhibitory postsynaptic potentials (IPSPs) in the TC cell led to progressive deinactivation of a low-threshold Ca2+ current. The augmenting responses in two reciprocally interacting chains of RE and TC cells depended also on 
-aminobutyric acid-B (GABAB) IPSPs. Lateral GABAA inhibition between identical RE cells, which weakened bursts in these cells, diminished GABAB IPSPs and delayed the augmenting response in TC cells. The results of these simulations show that the interplay between existing mechanisms in the thalamus explains the basic properties of the intrathalamic augmenting responses.
Rhythmic 7- to 14-Hz stimulation of the thalamus evokes cortical and thalamic responses that grow in size during the first few stimuli, a phenomenon called the augmenting response (Morison and Dempsey 1943 Intrinsic currents
Each TC and RE cell was modeled by a single-compartment that included voltage- and Ca2+-dependent currents described by Hodgkin-Huxley kinetics (Hodgkin and Huxley 1952
Synaptic currents
All synaptic currents were calculated according to
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
). Early investigations showed that decortication reduced but did not abolish the augmentation of repetitive responses recorded from the thalamus; however, removal of the thalamus abolished the repetitive and augmented responses in the cortex evoked by capsular stimulation (Morison and Dempsey 1943). Later studies reported that stimulation of white matter could elicit responses growing in size in cerebral cortex but their patterns were different from thalamically evoked augmenting waves (Morin and Steriade 1981).
an enhanced N-methyl-D-aspartate (NMDA) response via depression of -aminobutyric acid (GABA) mediated inhibitory postsynaptic potential (IPSP) (Metherate and Ashe 1994)and a second that depends on the intrinsic properties of bursting layer V cells (Castro-Alamancos and Connors 1996b). Another possible mechanism is short-term synaptic plasticity, as most excitatory synapses between cortical pyramidal cortical cells are depressed when stimulated at 7-14 Hz (Castro-Alamancos and Connors 1997; Thomson 1997; Tsodyks and Markram 1997). We will consider these cortical mechanisms in a forthcoming paper (see also, Houweling et al. 1997).
; Timofeev and Steriade 1998) and are different from those found in the cortex. It is known that stimulation of afferent pathways in vitro (Crunelli et al. 1988; Hirsch and Burnod 1987) and in vivo (Paré et al. 1991) leads to GABAA- and GABAB-mediated IPSPs. The IPSPs in thalamocortical (TC) cells after the first stimulus in a pulse train at 7-14 Hz hyperpolarizes the cells and progressively deinactivates low-threshold Ca2+ currents (Jahnsen and Llinás 1984a,b). TC cells located near the stimulating electrode receive sufficiently large excitatory postsynaptic potentials (EPSPs) so that high-threshold currents are activated (Pedroarena and Llinás 1997). This high-threshold type of augmenting response in the thalamus occurs only when the balance between synaptic excitation and inhibition is shifted toward excitation and occurs only in a limited region surrounding the stimulating electrode (Steriade and Timofeev 1997), whereas the low-threshold type of augmenting response can be found at sites that are distant from the stimulating electrode (Timofeev and Steriade 1998).
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
)
where Cm is the membrane capacitance, gL is the leakage conductance, EL is the reversal potential, Iint is a sum of active intrinsic currents (Iintj), and Isyn is a sum of synaptic currents (Isynj).
(1)
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FIG. 1.
Structure of synaptic interconnections thalamic reticular (RE)- thalamocortical (TC) networks. A: reciprocal pair of RE-TC cells. B: 2 pairs of RE-TC cells. C: 1-dimensional chain of RE-TC cells. Intensity of stimulation was maximal in the center of the chain and decayed exponentially with distance from the center. 
, excitatory [
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)] synapses; 
, inhibitory [-aminobutyric acid-A (GABAA) and B (GABAB)] synapses.
), a low-threshold Ca2+ dependent current IT (Huguenard and McCormick 1992; Huguenard and Prince 1992), and a potassium leak current IKL (McCormick and Huguenard 1992). A hyperpolarization-activated cation current Ih (Destexhe et al. 1996a; McCormick and Pape 1990) and potassium A current IA (Huguenard et al. 1991) also were included in TC cells.
where gj is the maximal conductance, m(t) is the activation variable, h(t) is the inactivation variable, and (V
(2)
Ej) is the difference between membrane potential and reversal potential.
). The voltage-dependence is described by the first order kinetics of transitions between closed C and open O states of the channels without inactivation
where
(3)
(V), 
(V) are the voltage-dependent transition rates.
Both the open and locked states of the channels contribute to the Ih current
(4)
The equations and values of parameters are given in the APPENDIX.
![<IT>I</IT><SUB>h</SUB><IT>= g</IT><SUB>max</SUB>([<IT>O</IT>] + <IT>k</IT>[<IT>O</IT><SUB>L</SUB>])(<IT>V − E</IT><SUB>h</SUB>)](/content/vol79/issue5/fulltext/2730/img005.gif)
(5)
where gsyn is the maximal conductivity, Esyn is the reversal potential, and [O](t) is the fraction of open channels.
](/content/vol79/issue5/fulltext/2730/img006.gif)
(6)
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) synaptic currents were modeled by first-order activation schemes (see review in Destexhe et al. 1994b). The transmitter T binds to the closed form of receptors C and yields the open form O
The concentration of the released transmitter [T] was modeled by a brief pulse that is triggered when the presynaptic voltage crosses 0 mV.
(7)
Network geometry
We simulated four network models, one consisting of a single pair of TC-RE cells reciprocally connected (Fig. 1A), a second model with two pairs of RE-TC cells (Fig. 1B), a third model with two one-dimensional chains of RE and TC cells (Fig. 1C), and a fourth model that used two-dimensional networks of TC and RE cells. Typically each TC cell had an excitatory connection with its 9 (49 for the 2-dimensional case) nearest neighbors in the chain of RE cells and each RE cell made inhibitory synapses on the 9 (49 for the 2-dimensional case) nearest neighbors from layer of TC cells (and also inside the layer of RE cells). In some cases, we used interconnections with a wider divergence. In this case, the sum of the maximal conductances on a cell was kept fixed by rescaling the maximal conductances for individual synapses (Destexhe et al. 1994a Computational methods
All simulations described in the paper were performed using a fourth-order Runge-Kutta [RK(4)] integration method and in some cases an embedded Runge-Kutta [RK6(5)] method (Enright et al. 1995 In vivo recordings
In vivo intracellular recordings were performed in the ventro-lateral (VL) and lateral posterior (LP) nuclei of dorsal thalamus as well as in rostro-lateral sector of RE nucleus in adult decorticated cats anesthetized with ketamine and xylazine (10-15 mg/kg;2-3 mg/kg im). Experimental preparation as well as the parameters of electrical stimulation and recording methods were identical to those previously described in detail (Steriade and Timofeev 1997 Properties of intrathalamic augmenting responses in vivo
The results reported below are based on in vivo intracellular recordings from >400 TC cells and 92 RE cells in unilaterally decorticated cats.
Augmenting responses in a reciprocal pair of RE-TC cells
Models with a varying number of RE and TC cells and synaptic connectivity were constructed to find conditions that could reproduce the basic experimental finding reported in preceding text. The simplest network model demonstrating augmenting responses during repetitive stimulation was a pair of coupled RE and TC cells (see Fig. 1A). To model the effect of prethalamic stimulation of ascending afferent pathways, an external AMPA response was simulated in a TC cell, whereas the RE cell only received disynaptic input through the TC cell. The external stimulus produced a fast EPSP that evoked a sodium spike in the TC cell that in turn triggered a strong EPSP in the RE cell that elicited a burst of spikes. The feedback from the burst of spikes in the RE cell produced GABAA and GABAB IPSPs in the TC cell, which partially deinactivated the low-threshold Ca2+ currents. The subsequent EPSP evoked by the external stimulus then produced a partial low-threshold Ca2+ spike in the TC cell. Continuous stimulation progressively hyperpolarized the TC neuron due to summation of IPSPs, leading to enhancement of the low-threshold responses. The TC cell reached its maximal hyperpolarization at about the fourth to fifth stimulus (Fig. 4A). The activation of Ih slightly repolarized the TC neuron, which could decrease the level of activation of low-threshold responses. This mechanism was sufficient to produce the augmenting responses in simulating of the reciprocal pair of RE-TC cells (see also further about the role of direct RE stimulation and lateral RE-RE inhibition).
Augmenting responses in two pairs of RE-TC cells
Figure 6 shows the responses of two coupled pairs ofRE-TC cells (shown in Fig. 1B) to repetitive stimulation of both TC cells. The TC cells were identical and equally stimulated. Lateral GABAA inhibition between identical RE cells weakened the bursts in these cells, which diminished the GABAB IPSPs and delayed these augmenting responses in the TC cells (cf. Fig. 4A with Fig. 6A).
Augmenting responses in chains of RE-TC cells
TC and RE cells are organized in an approximately topographic geometry. To study the effects of geometry on the augmenting response, we examined linear chains of 27 RE and 27 TC cells interacting with nine neighbors in the chain as shown in Fig. 1C. Repetitive 10-Hz stimulation of both the RE and the TC cells elicited incrementing activity during the first three to four stimuli in a train of 11 shocks as seen in the progressively increasing number of spikes per burst in the TC cells and by the recruitment of more TC cells that fire action potentials (Fig. 7, A and B). TC cells remote from the stimulation site also participated in the augmenting response after a delay through TC-RE-TC interactions.
Effect of RE cells stimulation
In the model for a pair of coupled RE-TC cells, the external stimulation of RE cells increased low-threshold augmenting responses by reinforcing GABAB IPSPs in TC cells. The responses of the RE-TC network were compared when only the TC cells were stimulated (Fig. 9A) and when there was simultaneous RE-TC stimulation (Fig. 9B). The additional stimulation of RE cells produced stronger burst discharges in the RE cells, which occurred almost simultaneously with EPSPs in TC cells. The result of the earlier RE-evoked GABAA IPSPs was an absence of the action after first stimulus in the TC cells located far from the center of the network. But more powerful burst discharges in the RE cells elicited stronger activation of GABAB receptors and more complete deinactivation of the low-threshold Ca2+ current in TC cells. This resulted in faster augmentation of TC responses starting with the second stimulus.
Role of DC and stimulation intensity
Thalamic augmentation based on the deinactivation of the low-threshold Ca2+ spikes is only effective for some range of membrane potentials. When the thalamic relay cells were sufficiently hyperpolarized or depolarized, the TC cells displayed nonaugmented responses during the entire train of stimuli.
Augmenting responses in the isolated RE nucleus
Because augmenting responses mimic spindle oscillations and spindles can be generated in the isolated RE nucleus in vivo (Steriade et al. 1987
Synaptic conductances
In the preceding simulations, deinactivation of the low-threshold Ca2+ current underlies the augmenting response in TC cells during repetitive stimulation. RE-evoked IPSPs that hyperpolarized the TC cells were responsible for this deinactivation. Thus the strength of synaptic coupling between RE and TC cells affected the development of augmenting responses. To determine the influence of different synaptic conductances, we varied their strengths in the chain of coupled RE-TC cells.
Intrinsic conductances
The intrinsic properties of RE and TC cells have a profound influence on the character of thalamic responses during repetitive stimulation. Here we examine the role of some of the intrinsic currents using simulations of the RE-TC chain.
Two-dimensional network
A one-dimensional chain of RE and TC cells is a crude approximation to thalamic anatomy. Here we consider a two-dimensional network of N × N RE and N × N TC cells. We use "dense proximal connections" (Destexhe et al. 1994a The results of simulations presented in this paper show that the known intrinsic and synaptic properties of TC and RE cells, along with the intrathalamic connectivity, are sufficient to generate augmenting responses to direct stimulation of the thalamus; a network consisting of one TC and one RE cell is the smallest circuit capable of generating augmenting responses with the same properties as those observed experimentally in vivo; increasing the number of cells in the network leads to faster buildup and stronger augmenting responses; a small (~10%) variability of the parameters in the model enhances the augmentation and prevents poststimulus oscillations due to faster desynchronization; the two essential mechanisms needed for the generation of augmenting responses are the low-threshold Ca2+ current and GABAB inhibition; and the augmentation that is observed in regions of the thalamus remote from the site of stimulation could be accounted for by recruitment of TC cells through the lateral connectivity between the inhibitory cells in the RE nucleus.
Thalamic relay cells during repetitive stimulation
In vivo recordings from the dorsal thalamus of decorticated cats anesthetized with ketamine and xylazine have revealed a low-threshold augmenting response generated in the thalamus (Steriade and Timofeev 1997 RE cells during repetitive stimulation
RE cells are critical in generating augmenting responses in TC cells. Powerful IPSPs delivered from RE cells deinactivated the low-threshold Ca2+ current and set up conditions for augmentation to occur in the responses of the thalamic relay cells. The pattern of responses in RE cells during repetitive stimulation was more complex than in TC cells. The resting membrane potential of RE cells in the model was around Predictions of the model
Our analysis of thalamocortical augmenting responses in RE-TC networks makes several predictions that can be tested experimentally.
This research was supported by the Human Frontier Science Program, The Sloan Center for Theoretical Neurobiology, the Howard Hughes Medical Institute, the Medical Research Council of Canada, and the Savoy Foundation.
The membrane potentials of RE and TC neurons are governed by the equations
Intrinsic currents
The voltage-dependent ionic currents INa, IK, IT, and IA are described by equation
Synaptic currents
GABAA and AMPA synaptic currents are given by
Address for reprint requests: T. J. Sejnowski, Howard Hughes Medical Institute, The Salk Institute, Computational Neurobiology Laboratory, 10010 North Torrey Pines Rd., La Jolla, CA 92037. Received 8 October 1997; accepted in final form 23 December 1997.
, 1996a; Dutar and Nicoll 1988)
In this scheme, the binding of transmitter T to the receptors R0 leads to its activated form R1. The inactive form of G proteins, G0, which is supposed to be in excess, transformed to the active form catalyzed by R1. Finally when the active form of the G proteins binds to the closed form of the channel at four binding sites, the channel opens, O. The assumption of quasistationarity for the last reaction leads to the expression [O] = [G]4/([G]4 + K).
(8)
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FIG. 2.
Incremental and decremental responses in RE cell depend on intensity of stimulation. Decorticated animal. At maximal intensity (100%), RE cell displayed augmenting responses (top). Responses at lower intensities were decremental (2 bottom traces, 20 and 10%). Note that at high intensities, of stimuli the 1st spike was antidromic, whereas at lower intensities, it was replaced by monosynaptic an excitatory postsynaptic potential (EPSP) leading to a spike. Also, at low intensities of stimulation, EPSP and low-threshold spike (LTS) could occur with some delay (responses to 2nd and 3rd stimuli at 20%). Image plot displays the responses of a RE cell to 5 thalamic stimuli at 10 Hz with decreasing intensities (from top to bottom, 100 to 10%). Dark brown is 70 mV and below, yellow is 30 mV and above. Contour plots are: white, 60 mV; gray, 50 mV; and black, 40 mV. Responses to 1st, 3rd, and 5th stimuli are expanded (bottom).
). All connections were identical and were described by Eqs. 6-8. Reflective boundary conditions were used. Stimulation of thalamic cells was modeled by AMPA synapses that had a maximal conductance gext = 0.5 µS at the center of stimulation and decayed exponentially with distance x from the center exp(kx) with k = 0.1 (see Fig. 1C). Some of the intrinsic parameters of the neurons in the network (gKL, gh for TC cells and gKL for RE cells) were initialized with some random variability (variance 
~ 20% for gKL and ~ 10% for gh) to diminish the effect of lateral inhibition between reticular neurons and to ensure the robustness of the results.
). The time step was 0.04 ms. Source C++ code was compiled on a Alpha Server 2100A (5/300) using GCC compiler (version 2.7.2.2). A simulation of 1 s of real time for 1 RE-TC pair (2 cells) took 4 s, and for a network with 27 pairs (54 cells), it took 4.2 min. A two-dimensional network (1,458 cells) took ~13.5 h of computer time to simulate 1 s of real time.
; see also companion paper Timofeev and Steriade 1998). An array of four stimulating electrodes, separated by 1 mm, was inserted in the thalamus to cover the territories of VL, anterior and posterior parts of the rostral intralaminar centrolateral (CLa and CLp) nucleus, and LP nucleus. To investigate the possibility of eliciting augmenting responses by stimulation of specific ascending pathways (terminating in the dorsal thalamus only), we stimulated the brachium conjunctivum rhythmically at 10 Hz while recordingin VL.
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
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FIG. 3.
Augmenting responses in ventro-lateral (VL) thalamocortical cell arising from LTSs. Decorticated animal. Top: spontaneous spindle sequence (arrow points to expanded rebound burst). Middle: 5-shock train at 10 Hz produced an augmenting response stemming from hyperpolarized levels of membrane potential and followed by a spindle. Part of response indicated by horizontal bar is expanded (bottom). Progressive hyperpolarization of TC cell led to progressive growing of low-threshold responses. Oblique arrows on (bottom) indicate deflection between EPSP and LTS. Note similar shape of the LTS occurring during the spindle and evoked by stimulation.
). What is the difference between the stimulation of thalamus itself and that of specific ascending prethalamic pathways? During stimulation of ascending afferent pathways, TC cells were excited monosynaptically and RE cells were excited disynaptically. Direct electrical stimulation of the thalamus led to monosynaptic activation of both TC and RE cells, and some TC and RE cells also were excited antidromically. During intrathalamic stimulation, there was a strong gradient in the intensity of stimulation from the position of the electrode tip to distal parts of the excitatory field, while brachium conjunctivum stimuli monosynaptically activated more or less equally a small population of TC cells in a localized region of the thalamus (Rispal-Padel et al. 1987a,b). This suggests that strong activation of cells in the RE nucleus may be needed to obtain augmentation in the isolated thalamus.
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FIG. 4.
Computer simulation of low-threshold augmenting responses in a reciprocal pair of RE-TC cells. Structure of interconnections between RE and TC cells is shown in Fig. 1A (gGABAA(TC) = 0.02 µS,gGABAB = 0.05 µS, gAMPA = 0.07 µS). A: prethalamic stimulus produced an EPSP followed by the RE-induced inhibitory postsynaptic potential (IPSP) in the TC cell, which deinactivated the low-threshold Ca2+ current. Next EPSP then evoked an LTS. - - -, EPSP without LTS after 4th shock (A3, IT channels were blocked just before stimulation). B: additional stimulation of the RE cell resulted in strong GABAB IPSPs in the TC cell and faster augmentation of the TC responses. , time of stimulation in A1 and B1; vertical dashed lines, time of stimulation in A2 and B2.
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FIG. 5.
Frequency dependence of augmenting responses in a reciprocal pair of RE-TC cells shown in Fig. 1A. Both RE and TC cells were stimulated simultaneously. A: paired-pulse stimulation for different interspike intervals displayed the lack of augmentation for high (20 Hz) and low (4 Hz) stimulation frequencies. B: dependence of TC responses on the interstimulus interval during train of 5 shocks. Augmenting responses were observed in the window of interstimulus intervals between ~50 and ~250 ms.
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FIG. 6.
Augmenting responses in 2 coupled pairs of RE-TC cells during exclusive TC stimulation. Role of lateral inhibition. Structure of interconnections between RE and TC cells is shown in Fig. 1B (gGABAA(RE) = 0.09 µS, gGABAA(TC) = 0.02 µS, gGABAB = 0.05 µS, gAMPA = 0.07 µS). A: lateral GABAA inhibition between identical RE cells, which weakened bursts in these cells, diminished GABAB IPSPs and delayed the augmenting response in TC cells. B: depolarization of 1 RE cell by only 1 mV destroyed the synchronization of RE cells and decreased the effect of lateral GABAA inhibition that resulted in faster augmenting responses in the TC cells. , time of stimulation.
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FIG. 7.
Augmenting responses of 27 TC and 27 RE cells during 10 Hz stimulation in the chain of interacting RE and TC cells. Structure of interconnections between RE and TC cells is shown in Fig. 1C(gGABAA(RE) = 0.07 µS, gGABAA(TC) = 0.02 µS, gGABAB = 0.07 µS, gAMPA = 0.07 µS). Nine shocks were applied between t = 0 ms and t = 800 ms. Both RE and TC cells were stimulated simultaneously. Intensity of stimulation was maximal in the center of the chain and decayed exponentially with distance from the center. A and B: diameter of connections for all projections was 9 cells. Expanded traces of A between t = 50 ms and t = 500 ms are given in B. First 4 shocks in the train of 9 shocks evoked incremental responses in the TC cells. RE cells demonstrated a diminished response to the 2nd shock because of the partial inactivation of low-threshold current in these cells and increasing of the responses to the following shocks. Train of stimuli was followed by slow 4-5-Hz poststimulus oscillations. C: diameter of connections for RE-TC, TC-RE projections was 17 cells. Smaller diameter of connections (9 cells) was used for RE-RE projections. Increasing the radius of RE-TC connections decreased the contribution of the individual cells to the whole postsynaptic potential. That resulted in the faster desynchronization of the network after train of stimuli and termination of poststimulus oscillations. Value of membrane potential for each neuron is coded in grey scale from 90 mV (white) to 30 mV (black).
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FIG. 8.
Expanded traces of three TC cells from a chain of RE-TC cells presented in Fig. 7. Insets: responses to the first 3 stimuli at a different time scale. A: TC cell placed far from the center of the chain (cell 3) obtained a low-intensity stimulation that resulted in a weak and delayed augmenting response followed by prolonged 3- to 5-Hz oscillations. Related RE cell showed a strong response to the 1st shocks and very weak responses to subsequent shocks. Poststimulus oscillations were terminated as a result of desynchronization in the network caused by variability in the parameters of the cells. B: TC cell placed closely to the center of the stimulation (cell 7) showed stronger augmentation of the responses and faster termination of the poststimulus oscillations. C: TC cells placed near the center of stimulation (cell 14) showed a fast augmenting responses and just a few cycles of slow poststimulus oscillations. RE cell displayed a diminished response to the 2nd shock and augmentation of the responses to the following shocks.
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FIG. 12.
Role of membrane potential and intensity of stimulation in augmenting responses of RE cells. One RE cell is shown at different levels of DC (A and B) and for different stimulus intensities (C and D) (gGABAA(RE) = 0.07 µS,gGABAA(TC) = 0.02 µS, gGABAB = 0.2 µS, gAMPA = 0.07 µS).Responses to the first 4 stimuli at 10 Hz are expanded at right. A: depolarization of the RE cell by positive DC led to the complete inactivation of the low-threshold current at rest. It eliminated diminishing of the RE bursts for the 2nd shock, and the RE cell displayed augmenting responses during whole train of stimuli. B: responses of the RE cell for DC = 0. First burst discharge in RE cell led to additional inactivation of IT current that resulted in the diminishing of TC responses for the 2nd shock. C: RE cell during low intensity stimulation (gext = 0.1 µS). Forementioned inactivation of the low-threshold current during 1st burst discharge in RE cell resulted in the lack of action potentials starting from the 2nd stimulus in the train. D: RE cell during high-intensity stimulation (gext = 5 µS). Slight diminishing of the burst discharge was observed after the 2nd shock. From the 2nd stimulus, the RE cell displayed an unaugmented response.
). The duration of the poststimulus oscillations depended on the position of the cell in the chain. TC cells located far from the center of stimulation and displaying weak burst discharges were involved in the most prolonged poststimulus oscillations. In contrast, TC cells placed at the center of the chain displayed powerful burst discharges. As a consequence, the intracellular Ca2+ concentration increased rapidly during train of stimuli, and poststimulus oscillations in these TC cells were terminated after one to two cycles.
desynchronization of the networkdepends on parameter variability, the spatial extent of the external stimulation and the radii of connections between TC and RE cells. Three parametersgKL, gh for TC, and gKL for RE cellswere varied (see METHODS). The variability in the potassium leak current (variance ~20%) produced variability in the resting membrane potentials of RE and TC cells (variance ~3 mV), which led to slightly different inactivation of the Ca2+ currents in these cells at rest. The variability of the third parametermaximal conductance of Ih current in TC cells (variance ~10%)made the latencies of repolarization in TC cells different after RE-evoked hyperpolarization, which resulted in asynchronous bursts of TC cells and reduced TC-evoked EPSPs in RE cells during poststimulus oscillations. Increasing the spatial spread of connections decreased the contribution of the individual cells to the whole PSP (see METHODS) and a higher degree of network synchronization was required to elicit augmenting responses. Figure 7C shows the responses of the RE-TC cells in the linear chain with the radius of connections between RE-TC cells twice the size of the network presented in Fig. 7, A and B. The extent of the lateral connections between RE cells projections in vivo is less than that of the RE-TC projections (Cox et al. 1996). Therefore the smaller set of connections was used between the RE cells. Increasing the extent of the connections between RE-TC cells did not change the character of augmentation in the TC cells and its main effect was to hasten the termination of poststimulus oscillations.
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FIG. 9.
Role of additional RE stimulation for augmenting responses. Chain of 27 TC and 27 RE cells is shown during 10 Hz stimulation (gGABAA(RE) = 0.07 µS, gGABAA(TC) =0.02 µS, gGABAB = 0.07 µS, gAMPA = 0.07µS). A: only TC cells were stimulated. B: both TC and RE cells were stimulated. In the latter case, RE cells displayed much stronger burst discharges occurring simultaneously with TC cells' depolarization, which evoked earlier and stronger GABAA-GABAB IPSPs in the TC cells. Earlier GABAA component of IPSP decreased the responses of the TC cells after 1st stimulus. However, the powerful GABAB IPSPs increased hyperpolarization of the TC cells and led to greater deinactivation of the low-threshold Ca2+ current. This resulted in larger LTSs and longer burst discharges in the TC cells. Membrane potential for each neuron is coded in grey scale from 90 mV (white) to 30 mV (black).
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FIG. 10.
Comparison of responses evoked by prethalamic and thalamic stimulation. Expanded traces of 1 TC cell from a chain of 27 cells are shown for different intensities of stimulation. Intensity of stimulation decayed exponentially with distance from the center with a small ratio k = 0.02 (gGABAA(RE) = 0.07µS, gGABAA(TC) = 0.02 µS, gGABAB = 0.07 µS,gAMPA = 0.07 µS). Responses to the first 3 stimuli are expanded at right (2nd and 4th columns) with different time scale. A: only TC cells were stimulated. B: both TC and RE cells were stimulated. With low-intensity input (see A1 and B1), dual (RE and TC cells) stimulation was a necessary condition for developing augmenting responses. Stimulation of TC cells alone elicited single spike responses without augmentation. For moderate intensities of stimulation (see A2 and B2), exclusive TC stimulation resulted in a weak augmentation of TC responses only. In contrast, dual RE-TC stimulation led to strong hyperpolarization of TC cells and greater augmenting responses. In the case of high-intensity stimulation (see A3 and B3), TC cells demonstrated strong (nonaugmented) responses from onset of stimulation. Dual stimulation eliminated time delays between EPSPs in RE and TC cells and all cells were almost simultaneously depolarized.
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FIG. 11.
Role of membrane potential in augmenting responses of TC cells. One TC cell from a chain of RE-TC cells is shown at different levels of DC current during train of stimuli at 10 Hz(gGABAA(RE) = 0.07 µS, gGABAA(TC) = 0.02 µS,gGABAB = 0.07 µS, gAMPA = 0.07 µS). Responses tothe first four stimuli are expanded at right. Augmentation observed for DC = 0 was abolished during both depolarization and hyperpolarization of the cell. A: depolarization of TC cell prevented deinactivation of the low-threshold current during RE-evoked IPSP that resulted in the absence of the LT spikes. B: for DC = 0 the TC cell displayed a fast augmentation of the responses that achieved a maximal strength after the 4th shock. C: at negative levels of DC current the TC cell was hyperpolarized and low-threshold Ca2+ current was deinactivated completely before stimulation. Train of shocks evoked a decremental response because of the partial inactivation of the low-threshold Ca2+ current.
the low-threshold Ca2+ current was inactivated partially during the first burst and repetitive EPSPs further prevented its deinactivation. For high-intensity stimulation (Fig. 12D), RE cells responded with a more powerful burst discharge for the first stimulus but subsequent stimuli evoked similar responses without augmentation.
), we asked whether or not augmenting responses can be elicited in isolated RE neurons and, if so, what are the underlying mechanisms of such responses? Intra-RE synaptic connections include bothGABAA and GABAB components. However, the GABAB component for RE-RE coupling is weaker than for RE-TC projection (Sanchez-Vives et al. 1997; Ulrich and Huguenard 1996). Here we analyze the effect of weak intrareticular GABAB synaptic coupling during repetitive stimulation of the isolated RE nucleus.
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FIG. 13.
Response of RE cells from an isolated reticular nucleus during 8 Hz stimulation (gGABAA(RE) = 0.07 µS). A: reciprocal pair of REcells: only GABAA coupling between RE cells (left) and mixed GABAA-GABAB coupling (gGABAB(RE) = 0.02 µS; right). B: 1-dimensionalnetwork of RE cells with mixed GABAA-GABAB coupling. Weak lateral GABAB inhibition between RE cells led to the augmentation of the RE responses that was absent for GABAA coupling alone. Augmentation was based on deinactivation of the low-threshold Ca2+ current in the RE cells during GABAB phase of IPSP. Value of membrane potential for each neuron is coded in grey scale from 90 mV (white) to 30 mV (black).
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FIG. 14.
Effect of changing synaptic conductances on the development of augmenting responses. One TC cell from a chain of 27 RE and 27 TC cells is shown during 10 Hz stimulation. Responses to the first 4 stimuli are expanded at right. A: maximum conductance of the GABAB receptors gGABAB = 0. Resting synaptic conductances weregGABAA = 0.07 µS between RE cells, gGABAA = 0.02 µSfrom RE cells to TC cells, and gAMPA = 0.1 µS from TC cells to RE cells. Blocking GABAB receptors eliminated the augmentation of the TC cell responses during a train of stimuli. B: gGABAB = 0.05 µS. C: gGABAB = 0.15 µS.Increasing GABAB conductance resulted in the reinforcement of the augmenting responses and decreasing the frequency of post-stimulus oscillations. D: gGABAA = 0.02 µSbetween RE cells. Other parameters were the same as in C. Increasing lateral GABAA inhibition diminished burst discharges in RE cells, resulting in weaker GABAB IPSPs in TC cells and slow developing augmenting responses. E: gGABAA = 0.07 µS from RE cells to TC cells. Other parameters were the same as in C. Stronger RE-evoked GABAA IPSPs in TC cells led to greater hyperpolarization after 1st shock, resulting in a powerful response to the 2nd shock. Large GABAA conductance decreased input resistance of the TC cell for Vm ~ 80 mV. This decreased hyperpolarization of TC cells and delayed augmenting responses during next shocks. F: gGABAA = 0 between RE cells and from RE to TC cells. Other parameters were the same as in C. Suppression of GABAA inhibition had a negligible effect on the augmenting response in TC cells. In the absence of lateral GABAA inhibition, RE cells displayed stronger bursts discharges increasing the augmentation of the TC cell responses and decreasing the frequency of the post oscillations 
3 Hz. G: gAMPA = 0.2 µS from TC to RE cells. Other parameters were the same as in C. Increasing the amplitude of AMPA EPSPs synchronized burst discharges in RE cells, resulting in weakening of GABAB IPSPs in TC cells and diminishing of augmenting responses during the first 3 stimuli.
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FIG. 15.
Effect of intrinsic conductances on the development of augmenting responses. One TC and 1 RE cell from a chain of 27 RE and 27 TC cells is shown during 10 Hz stimulation. Responses of a TC cell to the first 4 stimuli are expanded at right (second column) on a different time scale. A: responses for "basic" values of intrinsic conductances: gTRE = 2 µS/cm2, gTTC = 2.2 µS/cm2, gh = 0.02 µS/cm2. B: gTRE = 1.2 µS/cm2. Other parameters were the same as in A. Decreasing low-threshold Ca2+ conductance in RE cells diminished burst discharges in these cells and resulted in weaker GABAB IPSPs and slow developing augmenting responses. C: gTTC = 1.2 µS/cm2. Other parameters were the same as in A. Weaker low-threshold Ca2+ conductance in TC cells diminished the excitability of these cells and decreased the augmentation of TC responses. D: gh = 0.007 µS/cm2. Other parameters were the same as in A. Decreasing Ih current resulted in faster RE-evoked hyperpolarization of TC cells and augmentation of their responses. Train of shocks was followed by 3-Hz delta oscillations.
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FIG. 16.
Augmenting responses in a 2-dimensional array of 27 × 27 RE and 27 × 27 TC cells. Responses of 9 TC cells located in the different regions of the network are shown. Top left: corresponds to the cell from the top left corner of the network [coordinates (2, 2)]. Bottom right: corresponds to the cell from the center of network [coordinates (14, 14)]. Insets: responses to the first 3 stimuli, on a different time scale. Intensity of stimulation was maximal in the center of the network and decayed exponentially in all directions. Augmenting responses in a 2-dimensional network demonstrated the same features as in a 1-dimensional chain. Cells from the center displayed strong augmentation of responses and fast termination of the poststimulus oscillations. Boundary cells received a low-intensity stimulation and demonstrated delayed augmenting responses followed by prolonged slow oscillations.
) in which each RE cell is connected to all other RE and TC cells within some radius RRE and each TC cell is connected to all RE cells within radius RTC.
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
; Timofeev and Steriade 1998). Augmentation was characterized by a progressive hyperpolarization of TC cells during repetitive stimulation. The model of the thalamic network examined in this paper shows that both synaptic interactions and intrinsic currents contribute to generating augmenting responses. A thalamic stimulus produces an EPSP followed by the RE-induced IPSP in the TC cell, which deinactivates the low-threshold Ca2+ current. The next EPSP then is followed by the LTS. Progressive recruitment of TC cells in the network occurs through GABAB IPSP responses.
) that application of the GABAA agonist clonazepam decreased the GABAB component of the RE-evoked IPSP in TC cells. We have found that this mechanism is especially effective if RE cells are made identical. Even a small variability in the parameters of the neurons leads to the nonsynchronous firing of RE cells and greatly increases GABAB IPSPs in TC cells.
). However, the role of intracellular Ca2+ concentration in the regulation of Ih conductance is uncertain. In one study that used Ca2+-sensitive fluorescent dyes, regulation by intracellular Ca2+ was not observed (Budde et al. 1997), whereas in another study based on the release of caged-Ca2+, regulation of the Ih conductance in TC cells was observed (Lüthi and McCormick 1997). The proposed low-threshold mechanism for augmentation demonstrated here does not depend on the Ca2+ regulation of Ih current. Even after greatly decreasing the Ih conductance, TC cells displayed strong augmenting responses during repetitive stimulation.
; Steriade et al. 1972). This difference can be explained by the fact that the former stimulation does not directly activate RE neurons, whereas the latter form of stimulation does. Based on the computer model, we propose that one of the reasons for this difference is that in the experiments with prethalamic (brachium conjunctivum) shocks there might have been exclusive monosynaptic stimulation of TC cells. We found that weak stimulation of TC cells without stimulating the RE cells resulted in nonaugmented TC responses throughout the train of stimuli. In contrast, the additional stimulation of RE neurons led to augmenting responses in TC cells. For high-intensity stimulation, simultaneous stimulation of dorsal thalamic and RE nuclei increased the duration of the burst discharges in RE cells, which led to the strengthening of GABAB IPSPs and more rapid augmentation of responses in the TC cells. This prediction of the model could be tested by recording from RE cells during repetitive prethalamic stimulation of ascending afferent pathways.
; Leresche et al. 1991; Soltesz et al. 1991; Steriade et al. 1991). Delta oscillations can be generated in a single TC cell that is hyperpolarized as a result of the interplay between low-threshold (IT) and hyperpolarization-activated cation (Ih) currents. However, in the present model, the generation of the slow poststimulus oscillations depended on inhibitory RE neurons. Synchronous burst discharges in RE cells induced a fast hyperpolarization of TC cells that activated the Ih current. This led to the depolarization of TC cells, followed by LTSs and rebound bursts. Finally, burst discharges in TC cells evoked EPSPs and new bursts in RE cells. Progressive desynchronization of the network in the absence of external stimulation decreased the amplitude of the summed IPSPs in the TC cells and led to the termination of poststimulus oscillations.
). However, even a burst of spikes from a single RE cell cannot induce a GABAB IPSP in postsynaptic TC cell (Cox et al. 1997; Sanchez-Vives and McCormick 1997; Sanchez-Vives et al. 1997); rather, bursts from multiple RE cells are needed to induce a GABAB IPSP in a TC cell. During naturally occurring spindles the interaction between dorsal thalamic and RE nuclei is determined mainly by GABAA and AMPA currents. In the present model, the size of the thalamic pool was relatively small, and the effects of strong GABAB inhibition were taken into account by increasing the maximal conductance for GABAB synapses. This gave rapid augmentation of the responses in TC cells during a train of stimuli; however, the spindle oscillations evoked by a single thalamic shock was transformed after a few cycles into slow (3-4 Hz) oscillations.
a decrease of augmentation and an increase in the duration of poststimulus oscillations with distance from the site of stimulationwere found also in the two-dimensional model. However, diminishing the contribution of individual presynaptic cells to the postsynaptic PSP in a two-dimensional network led to faster desynchronization of the network and rapid termination of post-stimulus oscillations.
75 mV, based on in vitro recordings, slightly more negative than in vivo. The low-threshold Ca2+ current in RE cells was deinactivated partially at this level, and the first stimulus in the train elicited a powerful burst discharge (usually ~5-10 spikes). Depolarization of the RE cells inactivated IT channels and the next stimulus evoked weaker responses. However, the buildup of TC-evoked EPSPs led to the slow augmentation of RE responses starting from the third stimulus. These features were especially prominent during low-intensity stimulation. In this case, the burst discharge evoked by the first EPSP in the train was followed by EPSPs without action potential during rest of train. This result is in a good agreement with the in vivo data (Timofeev and Steriade 1998). However, we could not duplicate the experimentally observed augmentation of RE cell responses during the entire train of stimuli for high-intensity stimulation. One possible explanation is that the RE cells in the model were more hyperpolarized than those recorded in vivo. To test this possibility, we injected positive DC current and found that depolarization of RE cells led to weaker but monotonically increasing responses, which were more similar to in vivo responses. Another result of depolarization was weaker IPSPs in TC cells and delayed augmentation. These results may depend on our use of a one-compartment model for the RE cell. There is experimental evidence and corroborating models showing that the low-threshold Ca2+ currents are located in the distal dendrites of RE cells (Destexhe et al. 1996b). Hyperpolarization of the distal dendrites would lead to the deinactivation of the IT current despite more elevated membrane potentials in the somas of RE cells.
; Ulrich and Huguenard 1996). Including intrareticular GABAB conductances in the model would result in weak augmentation of the responses of RE cells in the isolated reticular nucleus during repetitive stimulation. The low-threshold mechanism for augmentation of RE responses is especially effective during high-intensity stimulation. In this case, the powerful burst discharges in the RE cells lead to exalted activation of GABAB receptors and deinactivation of IT channels.
; Ulrich and Huguenard 1996), which leads to their hyperpolarization and LTSs. One of the consequences intrareticular augmentation is to reinforce GABAB IPSPs in TC cells.
; Contreras et al. 1997). The contribution of cortical EPSPs to intrathalamic augmenting responses may be increased by intracortical short term plasticity such as paired-pulse facilitation (Castro-Alamancos and Connors 1996b; Metherate and Ashe 1994).
; Kandel and Buzsáki 1997) and with our recent experimental and modeling results, which will be presented in forthcoming papers.
ACKNOWLEDGEMENTS
APPENDIX
The passive parameters are Cm = 1 µF/cm2, gL = 0.01 mS/cm2, EL =
(A1)
70 mV for TC cell (McCormick and Huguenard 1992) and Cm = 1 µF/cm2, gL = 0.05 mS/cm2, EL = 77 mV for RE cell (Destexhe et al. 1994a). The area of RE cell was SRE = 1.43·10
4 cm2, and the area of TC cell was STC = 2.9·104 cm2.
where the maximal conductances and reverse potentials are gT = 2.0 mS/cm2, gNa = 100 mS/cm2, gK = 10 mS/cm2 for RE cell and gT = 2.2 mS/cm2, gNa = 90 mS/cm2, gK = 10 mS/cm2, gh = 0.02 mS/cm2, gA = 1.0 mS/cm2 for TC cell. For all cells, ENa = 50 mV, EK =
(A2)
95 mV. The reversal potential for low-threshold Ca2+ current was calculated according to the Nerst equation ET = (RT/2F) log([Ca]/[Ca]0), where R = 8.31441 J/(mol °K), T = 309.15°K, F = 96,489 C/mol, and [Ca]0 = 2 mM.
m(t), h(t) 1 satisfy
where m
![<IT><A><AC>m</AC><AC>˙</AC></A></IT>= [<IT>m</IT><SUB>∞</SUB>(<IT>V</IT>) − <IT>m</IT>]/τ<SUB>m</SUB>(<IT>V</IT>),
<IT><A><AC>h</AC><AC>˙</AC></A></IT>= [<IT>h</IT><SUB>∞</SUB>(<IT>V</IT>) − <IT>h</IT>]/τ<SUB>h</SUB>(<IT>V</IT>)](/content/vol79/issue5/fulltext/2730/img013.gif)
(A3)
(V), h(V), 
m(V), and h(V) are nonlinear functions of V extracted from experimental recordings of ionic currents. Gating kinetics was adjusted to 36°C.
;Huguenard and Prince 1992) M = 2, N = 1, m = 1/{1 +exp[(V + 52)/7.4]}, m = (1 + 0.33/{exp[(V + 27)/10] + exp[(V + 102)/15]}), h = 1/{1 + exp[(V + 80)/5]}, h = (22.7 + 0.27/{exp[(V + 48)/4] + exp[(V + 407)/50]}).
; Huguenard and McCormick 1992) M = 2, N = 1, m = 1/{1 +exp[(V + 59)/6.2]}, m = (0.22/{exp[(V + 132)/16.7] +exp[(V + 16.8)/18.2]} + 0.13), h = 1/{1 + exp[(V + 83)4]}, h = (8.2 + {56.6 + 0.27 exp[(V + 115.2)/5]}/{1 + exp[(V + 86)/3.2]}).
) M = 4, N = 1, m = 1/{1 + exp[(V + 60)/8.5]};m = (0.27/{exp[(V + 35.8)/19.7] + exp[(V + 79.7)/12.7]} + 0.1); h = 1.0/{1 + exp[(V + 78)/6]}; h = 0.27/{exp[(V + 46)/5] + exp[(V + 238)/37.5]} if V < 63 mV and h = 5.1 if V > 63 mV.
)
where k = 2 and Eh =
![<IT>I</IT><SUB>h</SUB><IT>= g</IT><SUB>max</SUB>([<IT>O</IT>] + k[<IT>O</IT><SUB>L</SUB>])(<IT>V − E</IT><SUB>h</SUB>)](/content/vol79/issue5/fulltext/2730/img014.gif)
(A4)
40 mV. The fraction of the channels in the opened [O] and locked [OL] forms were calculated according to the Eqs. 3 and 4 where k1 = 2.5 × 107 mM4 ms1, k2 = 4 × 104 ms1, k3 = 0.1 ms1, and k4 = 0.001 ms1 are the constant rates and (V) and (V) are the voltage-dependent transition rates (Huguenard and McCormick 1992; McCormick and Pape 1990): = m/m, = (1 m)/m, m = 1/{1 + exp[(V + 75)/5.5]}; m = (5.3 + 267/{exp[(V + 71.5)/14.2] + exp[(V + 89)/11.6]}).
EKL) (McCormick and Huguenard 1992), where gKL = 0.005 mS/cm2 for RE cell and gKL = 0.012 mS/cm2 for TC cell.
)
where [Ca]
![<FR><NU>d[Ca]</NU><DE>d<IT>t</IT></DE></FR>= − <IT>AI</IT><SUB>T</SUB>− ([Ca] − [Ca]<SUB>∞</SUB>)/τ](/content/vol79/issue5/fulltext/2730/img015.gif)
(A5)
= 2.4·104 mM is equilibrium Ca2+ concentration, A = 5.18·105 mM·cm2/(ms·µA) and = 5 ms.
where the reversal potential is EAMPA = 0 mV for AMPA receptors and EGABAA =
](/content/vol79/issue5/fulltext/2730/img016.gif)
(A6)
70 mV for GABAA receptors in RE cells and EGABAA = 80 mV for GABAA receptors in TC cells (Ulrich and Huguenard 1997). The fraction of open channels [O] is calculated according to Eq. 7
![<FR><NU>d[<IT>O</IT>]</NU><DE>d<IT>t</IT></DE></FR>= α(1 − [<IT>O</IT>])[<IT>T</IT>] − β[<IT>O</IT>],](/content/vol79/issue5/fulltext/2730/img017.gif)
where
![[<IT>T</IT>] = <IT>A</IT>θ(<IT>t</IT><SUB>0</SUB><IT>+ t</IT><SUB>max</SUB><IT>− t</IT>)θ(<IT>t − t</IT><SUB>0</SUB>)](/content/vol79/issue5/fulltext/2730/img018.gif)
(A7)
(x) is the Heaviside function and t0 is the time instant of receptor activation. The parameters for the neurotransmitter pulse were amplitude A = 0.5 and duration tmax = 0.3 ms. The rate constants, and , were = 20 ms and = 0.16 ms for GABAA synapses and = 0.94 ms and = 0.18 ms for AMPA synapses.
)
![<IT>I</IT><SUB>GABA<SUB>B</SUB></SUB>= <IT>g</IT><SUB>GABA<SUB>B</SUB></SUB><FR><NU>[<IT>G</IT>]<SUP>4</SUP></NU><DE>[<IT>G</IT>]<SUP>4</SUP><IT>+ K</IT></DE></FR>(<IT>V − E</IT><SUB>K</SUB>)](/content/vol79/issue5/fulltext/2730/img019.gif)
(A8)
![<FR><NU>d[<IT>R</IT>]</NU><DE>d<IT>t</IT></DE></FR> = <IT>r</IT><SUB>1</SUB>(1 − [<IT>R</IT>])[<IT>T</IT>] − <IT>r</IT><SUB>2</SUB>[<IT>R</IT>]](/content/vol79/issue5/fulltext/2730/img020.gif)
where [R](t) is the fraction of activated receptors, [G](t) is the concentration of G proteins, and EK =
![<FR><NU>d[<IT>G</IT>]</NU><DE>d<IT>t</IT></DE></FR> = <IT>r</IT><SUB>3</SUB>[<IT>R</IT>] − <IT>r</IT><SUB>4</SUB>[<IT>G</IT>]](/content/vol79/issue5/fulltext/2730/img021.gif)
95 mV is potassium reverse potential. The rate constants were r1 = 0.5 mM1 ms1, r2 = 0.0012 ms1, r3 = 0.1 ms1, r4 = 0.034 ms1, and K = 100 µM4.
FOOTNOTES
REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References
and K+-dependent inhibitory postsynaptic potentials evoked by interneurones of the rat lateral geniculate nucleus.
J. Physiol. (Lond.)
399: 153-176, 1988.
0022-3077/98 $5.00 Copyright ©1998 The American Physiological Society
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