The Journal of Neurophysiology Vol. 79 No. 5 May 1998, pp. 2730-2748
Copyright ©1998 by the American Physiological Society

Cellular and Network Models for Intrathalamic Augmenting Responses During 10-Hz Stimulation

Maxim Bazhenov¹, Igor Timofeev², Mircea Steriade², and Terrence J. Sejnowski^{1, 3}

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

	ABSTRACT

Abstract Introduction Methods Results Discussion References

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 (GABA_B) IPSPs. Lateral GABA_A inhibition between identical RE cells, which weakened bursts in these cells, diminished GABA_B 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.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

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). 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).

Two types of cortical mechanisms have been proposed to explain augmenting responses, one based on synaptic mechanismsan 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).

Intrathalamic augmenting responses have been investigated in decorticated animals (Steriade and Timofeev 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 GABA_A- and GABA_B-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).

In the present study, we investigated the mechanisms underlying the low-threshold augmenting responses found in the thalamus in vivo. Because the properties of thalamic cells are quite complex and the interactions between them produce a wide range of dynamical behaviors, we used compartmental models of interacting TC and thalamic reticular (RE) cells to explore the main features of augmenting responses. The minimal intrathalamic network model capable of generating augmenting responses consisted of one RE-TC pair. In larger thalamic networks, additional mechanisms became prominent and the low-threshold Ca²⁺ currents together with GABA_B IPSPs were the principal mechanisms that generated incremental responses in these models.

	METHODS

Abstract Introduction Methods Results Discussion References

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)

(1)

where C_m is the membrane capacitance, g_L is the leakage conductance, E_L is the reversal potential, I^int is a sum of active intrinsic currents (I^int_j), and I^syn is a sum of synaptic currents (I^syn_j).

View larger version (26K): [in this window] [in a new window]   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.

For both RE and TC cells. we included a fast sodium current I_Na, a fast potassium current I_K (Traub and Miles 1991), a low-threshold Ca²⁺ dependent current I_T (Huguenard and McCormick 1992; Huguenard and Prince 1992), and a potassium leak current I_KL (McCormick and Huguenard 1992). A hyperpolarization-activated cation current I_h (Destexhe et al. 1996a; McCormick and Pape 1990) and potassium A current I_A (Huguenard et al. 1991) also were included in TC cells.

All the voltage-dependent ionic currents I^int_j(t) had the same general form

(2)

where g_j is the maximal conductance, m(t) is the activation variable, h(t) is the inactivation variable, and (V  E_j) is the difference between membrane potential and reversal potential.

The model of I_h current takes into account both voltage and Ca²⁺ dependencies (Destexhe et al. 1996a). The voltage-dependence is described by the first order kinetics of transitions between closed C and open O states of the channels without inactivation

(3)

where (V), (V) are the voltage-dependent transition rates.

The Ca²⁺-dependence is based on higher-order kinetics involving a regulation factor P. The binding of the Ca²⁺ ions with unbound form of the regulation factor P₀ leads to the bound form P₁. At the next step P₁ binds to the open state of the channel O that produces the locked form O_L

(4)

Both the open and locked states of the channels contribute to the I_h current

(5)

The equations and values of parameters are given in the APPENDIX.

Synaptic currents

All synaptic currents were calculated according to

(6)

where g_syn is the maximal conductivity, E_syn is the reversal potential, and [O](t) is the fraction of open channels.

GABA_A and -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

(7)

The concentration of the released transmitter [T] was modeled by a brief pulse that is triggered when the presynaptic voltage crosses 0 mV.

GABA_B receptors were modeled by a higher-order reaction scheme that takes into account activation of K⁺ channels by G proteins (Destexhe et al. 1994b, 1996a; Dutar and Nicoll 1988)

(8)

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).

View larger version (59K): [in this window] [in a new window]   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).

This model GABA_B synapse yields a strong response for a prolonged burst of spikes in the presynaptic cell. In contrast, a burst with only a few spikes evokes a weak GABA_B IPSP in the postsynaptic cell. The equations and values of parameters are given inthe APPENDIX.

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). 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 g_ext = 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 (g_KL, g_h for TC cells and g_KL for RE cells) were initialized with some random variability (variance  ~ 20% for g_KL and  ~ 10% for g_h) to diminish the effect of lateral inhibition between reticular neurons and to ensure the robustness of the results.

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). 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.

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; 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

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.

At high intensities of stimulation at 10 Hz, responses from RE thalamic cells exhibited robust augmenting responses characterized by an increasing number of spikes and increasingly long depolarizing responses (Fig. 2). In contrast, at lower intensities of stimulation the responses to successive stimuli decremented, with a progressively decreasing number of spikes. The responses of RE cells to synaptic stimulation at low intensity revealed the coupling between the EPSP and the low-threshold spike (LTS) because of delayed LTS initiation. The efficacy of EPSP to LTS coupling is a major factor that determines whether the response is either incrementing or decrementing. At the lowest intensities of synaptic stimulation some of the EPSPs leads to the abortive LTSs while other ones do not. This becomes evident by comparison of the responses to the first shock at 10% of stimulation with responses to second to fifth stimuli at 10 and 20%.

In TC cells, a single thalamic stimulus typically induced an EPSP and a biphasic IPSP followed by a rebound burst, which could lead to one or few cycles of 2- to 4-Hz delta oscillations or 8- to 10-Hz spindle. During a 10-Hz train of stimuli, the membrane potential became progressively hyperpolarized by IPSPs and the low-threshold currents became progressively deinactivated. This led to an increase in the magnitude of the LTSs and an increase in the number of fast spikes in each burst (Fig. 3).

View larger version (13K): [in this window] [in a new window]   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.

To investigate whether or not the site of stimulation influences the augmenting responses, we recorded intracellularly in the thalamic VL nucleus while stimulating the afferent brachium conjunctivum pathway at 10 Hz. This prethalamic stimulation did not produce an augmenting response (not shown) (see also Timofeev et al. 1996). 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.

View larger version (30K): [in this window] [in a new window]   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.

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 GABA_A and GABA_B 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 I_h 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).

View larger version (19K): [in this window] [in a new window]   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.

To simulate the conditions obtained during intrathalamic stimulation, we provided strong external AMPA responses to both the TC and the RE cells. Figure 4B shows the responses in the coupled RE-TC cells during repetitive stimulation of both neurons. In this case, the external stimulus produced simultaneous EPSPs in RE and TC cells that resulted in almost simultaneous burst discharges after the second stimulus in the pulse train. Prolonged bursts in the RE cell evoked stronger GABA_B IPSPs and more complete deinactivation of the low-threshold Ca²⁺ currents in the TC cell. As a consequence, the TC responses augmented faster than when the external stimulus was applied exclusively to TC cell (compare responses to the 3rd and 4th stimuli in Fig. 4, A2 and B2).

Direct RE stimulation barely changed the strength of TC responses after the fifth stimulus in the train because in the absence of the lateral GABA_A inhibition, RE cells displayed powerful burst discharges. However, there are aspects of the augmenting responses that cannot be captured by this simple RE-TC pair, and in the next section, the critical role of RE cells stimulation in a chain of coupled RE-TC cells will be explored.

Augmentation in the RE-TC pair cell model with TC cell stimulation (presented above for a 10-Hz train of stimuli only) occurred over a range of frequencies. The highest frequency was determined by the time required for deinactivation of the low-threshold Ca²⁺ current in TC cell. The lowest frequency depended on the rate of TC cell repolarization: as the frequency decreased, the low-threshold Ca²⁺ current began to inactivate and eventually the low-threshold Ca²⁺ spike failed to occur. The dependence of the TC cell response on the interstimulus intervals during a train of five shocks is shown in Fig. 5.

The sequence of events that occurred between the first stimulus and the second was explored over a range of interstimulus intervals. Figure 5A illustrates the responses of paired-pulse stimulation for three different interstimulus intervals. For high-frequency stimulation (interspike intervals less than ~60 ms), the second stimulation of the TC cell occurred when the low-threshold Ca²⁺ current was still inactivated. A low-threshold Ca²⁺ spike was not elicited, and the response of the TC cell was not augmented. After an interstimulus interval of 140 ms, the I_T current was almost completely deinactivated and the TC cell displayed a powerful response to the second shock. For longer interstimulus intervals, the repolarization and the rebound burst in the TC cell inactivated the low-threshold Ca²⁺ current, and when the second stimulus was delivered just after rebound burst (for interspike intervals between ~240 and ~280 ms), a nonaugmented response was evoked. For very large interstimulus intervals (greater than ~280 ms), the second stimulus arrived when the TC cell was hyperpolarized after the rebound burst. The hyperpolarization evoked a partial deinactivation the low-threshold Ca²⁺ current and the second response was augmented (see Fig. 5B).

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 GABA_A inhibition between identical RE cells weakened the bursts in these cells, which diminished the GABA_B IPSPs and delayed these augmenting responses in the TC cells (cf. Fig. 4A with Fig. 6A).

View larger version (29K): [in this window] [in a new window]   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.

The lateral GABA_A inhibition between RE cells was especially effective in reducing the total RE-evoked IPSPs in the TC cells when the RE cells were identical. However, even small variations in the parameters of the RE cells broke the simultaneity of the action potentials in these cells and enhanced the GABA_B IPSPs in the TC cells. Figure 6B shows the responses of two coupled pairs of RE and TC cells when one of the RE cells was depolarized by 1 mV with positive DC so that the two RE cells were not identical. For a single RE cell or two coupled identical RE cells, this depolarization would diminish burst discharges because of the partial inactivation of the low-threshold Ca²⁺ current. However, when the two RE cells were not identical, each of them displayed a stronger burst after every second shock. On each cycle, only one of the cells bursted strongly and the total IPSP increased more than in the case of two identical RE cells. Thus variability between RE cells resulted in a faster augmenting response in the TC cells.

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.

View larger version (140K): [in this window] [in a new window]   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).

Figure 8 shows expanded traces of three pairs of TC and RE cells located at different distances from the center of stimulation. The first pair of cells (Fig. 8A) is located near the boundary of the chain and received low-intensity stimulation. This RE cell responded with a six-spike burst to the first shock and responded more weakly (0-2 spikes) to the following shocks. The response decremented because the low-threshold Ca²⁺ current in RE cell partially inactivated during the first spike burst. If the RE cell was depolarized by current injection, so that the I_T current was completely inactivated before stimulation, then the RE cell displayed an augmenting response during the whole train of stimuli (not shown; see also Fig. 12A). The corresponding TC cell displayed a weak and delayed augmenting response with the number of spikes per burst increasing from 0 to 2. The second pair of RE-TC cells (Fig. 8B) is closer to the center of the stimulation and received stronger stimulation. This RE cell showed a remarkable diminution of the response after the first stimulus followed by a slow augmentation of the burst. The paired TC cell displayed a strong but delayed augmentation of the responses during the train of stimuli. Finally, in the third pair of RE-TC cells (Fig. 8C) located at the center of stimulation, both of the cells (TC starting from the 1st shock and RE starting from the 2nd shock) demonstrated strongly augmenting responses. The augmenting responses in the TC cell developed completely during the first three to four stimuli.

View larger version (37K): [in this window] [in a new window]   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.

View larger version (35K): [in this window] [in a new window]   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.

After the simulated train of nine shocks to the linear chain of cells, a sequence of slow delta (3-4 Hz) oscillations was elicited by interactions between RE and TC cells. These oscillations terminated as a result of desynchronization in the network and depolarization of TC cells, which resulted from the Ca²⁺ regulation of I_h current (Destexhe et al. 1996a). 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.

Another mechanism for terminating the poststimulus oscillationsdesynchronization of the networkdepends on parameter variability, the spatial extent of the external stimulation and the radii of connections between TC and RE cells. Three parametersg_KL, g_h for TC, and g_KL 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 I_h 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.

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 GABA_B 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 GABA_A 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 GABA_B 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.

View larger version (112K): [in this window] [in a new window]   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).

In in vivo experiments with 10-Hz stimulation of afferent brachium conjunctivum pathway the TC cells from the VL nucleus displayed monosynaptic responses, occasionally leading to fast spikes, but without augmentation (not shown). In the experiments with prethalamic stimulation of ascending afferent pathways, only the excitatory synapses of TC cells were partially activated, which resulted in a weak and quasihomogeneous stimulation of TC cells and an absence of external input to RE cells. Figure 10 shows the responses of a selected TC cell from the network during exclusive TC stimulation (Fig. 10A) and for simultaneous RE-TC stimulation (Fig. 10B). In both cases, the intensity of stimulation decayed slowly throughout the network with a ratio k = 0.02 (that is 5 times smaller than in the previous experiments). Figure 10, A1 and B1, shows TC responses for low-intensity stimulation. In the absence of RE stimulation, the TC cell displayed single spike responses without augmentation during the entire train of stimuli. However, additional RE stimulation reinforced RE-evoked GABA_B IPSPs and produced augmenting responses in the TC cells. For moderate intensity of the input, the additional RE stimulation resulted in strong and rapid augmentation of TC cell responses (from 1 to 4-5 spikes), whereas exclusive TC stimulation led to much weaker (from 1 to 2-3 spikes) augmenting responses (Fig. 10, A2 and B2). Finally, for high-intensity stimulation, strong monosynaptic activation resulted in powerful burst-discharges in TC cells starting from beginning of the pulse train (Fig. 10, A3 and B3).

View larger version (38K): [in this window] [in a new window]   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.

Thus the additional stimulation of RE neurons is a necessary condition for augmentation to occur in response to moderate and low-intensity stimulation. Note that the boundary cells in the experiment presented in Fig. 9 displayed weak augmenting responses (from 0 to 1 spike) in spite of the low-intensity stimulation. In this case (in contrast to the experiment with quasihomogeneous stimulation shown in Fig. 10), the central RE cells displayed strong burst discharges that led to GABA_B IPSPs in the boundary TC cells through lateral RE-RE and RE-TC connections.

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.

Figure 11A shows the responses of one of TC cells depolarized by direct current. The DC prevented deinactivation of the low-threshold current, and the TC cell did not display augmentation of the responses as observed for DC = 0 (compare Fig. 11, A with B). Progressive RE-evoked hyperpolarization of the TC cell during a train of stimuli resulted in the abolition of the spontaneous firing observed before stimulation.

View larger version (27K): [in this window] [in a new window]   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.

Figure 11C shows the same TC cell under negative DC. Strong hyperpolarization resulted in the complete deinactivation of the low-threshold current before stimulation. Therefore the first shock already evoked a powerful response. The partial inactivation of I_T current during stimulus-evoked burst discharges led to the weakening of the responses to the subsequent stimuli.

In the RE-TC simulations, a strong GABA_B component in the RE-evoked IPSPs is a necessary condition for deinactivation of I_T current in TC cells during repetitive stimulation. The kinetic scheme activated by the GABA_B receptors involving G proteins requires prolonged burst discharges in the RE cells to elicit powerful GABA_B IPSPs, and the bursts depend on the low-threshold Ca²⁺ current. Strong depolarization of RE cell by positive DC current injection inactivated the I_T current, and the RE cell responded only weakly during a train of stimuli (not shown). At smaller depolarizing DC levels, an RE cell displayed augmenting responses (Fig. 12A). In this case, augmentation was obtained as a result of augmenting responses in TC cells. In the absence of DC current injection, the same RE cell displayed a powerful burst discharge for the first stimulus and decrementing responses for subsequent stimuli (Fig. 12B). The diminution of the burst discharges in the RE cell despite increasing EPSPs can be explained by the partial inactivation of the low-threshold current in this cell.

We next explored the effect of changing the strength of stimulation in the absence of a DC current injection. For low-intensity stimulation (Fig. 12C), the RE cell displayed an EPSP and a delayed burst discharge only for the first shock and responded with EPSPs without action potentials for subsequent stimuli. The explanation for this "passive" response already has been giventhe 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.

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), 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 bothGABA_A and GABA_B components. However, the GABA_B 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 GABA_B synaptic coupling during repetitive stimulation of the isolated RE nucleus.

The response of an RE cell in a pair of coupled RE cells during repetitive stimulation was studied in the case of pure GABA_A coupling between cells and for mixed GABA_AGABA_B synapses (Fig. 13A). A weak GABA_B component (maximal conductance was only ~25% of the maximal conductance of RE-TC GABA_B coupling) resulted in a slow hyperpolarization of the RE cells during a train of stimuli; this led to the deinactivation of the low-threshold Ca²⁺ current and an augmenting responses of RE cells. The augmentation was absent if the RE-RE GABA_B receptors were blocked.

View larger version (41K): [in this window] [in a new window]   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).

Figure 13B shows the responses of 27 RE cells with mixed GABA_A-GABA_B coupling during repetitive stimulation. The same set of local intra-RE connections were used as before (see earlier text, Fig. 1C). The RE cells located near the center of network displayed slowly augmenting responses (from 2-3 to 4 spikes) during a train of stimuli. In contrast, the neurons near the boundary of the network that received weak stimulation displayed short burst discharges without significant augmentation. Thus the augmenting responses in the isolated RE nucleus demonstrated the same features found in TC cells. The results of these simulations indicate that the low-threshold mechanism for augmentation is not limited to TC cells. In the presence of lateral GABA_B inhibition responsible for deinactivation of the low-threshold Ca²⁺ current, the RE network displayed an augmenting response during repetitive stimulation.

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.

Figure 14, A-C, shows the influence of changing the strength of GABA_B inhibition on augmentation of TC responses during repetitive stimulation. One arbitrarily selected TC cell is shown. Blocking the GABA_B receptors (see Fig. 14A) eliminated the augmentation. Although RE-evoked GABA_A IPSPs hyperpolarized the TC cells after each shock, the magnitude of the hyperpolarization was not enough to deinactivate the low-threshold Ca²⁺ current, and the TC cells displayed similar responses during whole train of stimuli. The absence of the action potential after the first stimulus was a result of the strong GABA_A IPSP evoked by the powerful first spike burst in RE cells. When GABA_B inhibition was included, the TC cells displayed incremental responses during a train of stimuli (see Fig. 14, B and C) by the low-threshold mechanism of augmentation.

View larger version (32K): [in this window] [in a new window]   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.

Figure 14, D-F, shows the effect of varying the GABA_A inhibition between RE cells and from RE cells to TC cells. Increasing the lateral GABA_A inhibition (Fig. 14D) diminished the burst discharges in RE cells, which resulted in the weakening of GABA_B IPSPs and slowing of the augmenting responses in the TC cells (compare Fig. 14, D with C). The GABA_A component of RE-evoked IPSP was also weaker, giving rise to a single action potential in the TC cell after the first stimulus. The main effect of making the GABA_A inhibition stronger from the RE to TC cells (see Fig. 14E) was a faster hyperpolarization of TC cells after the first stimulus. High GABA_A conductance also decreased the input resistance of a TC cells near the level of reverse potential and consequently decreased the maximal hyperpolarization elicited by GABA_B IPSPs during a train of stimuli. Figure 14F shows the responses of a TC cell after blocking both RE-RE and RE-TC GABA_A receptors. In the absence the lateral GABA_A inhibition between RE cells, powerful burst discharges occurred in the RE cells and bursts in the TC cells augmented rapidly.

Figure 14G shows TC cell responses after increasing the AMPA conductance. Powerful AMPA EPSPs delivered to RE cells elicited synchronous burst discharges that were similar to responses that occurred when the RE cells had identical parameters. Under these conditions, the lateralGABA_A inhibition more effectively decreased the duration of the RE bursts. The result was weaker GABA_B IPSPs and delayed augmenting responses in the TC cells (compare Fig. 14, G with C).

All of the evidence presented thus far suggests that a necessary condition for thalamic augmentation is the presence of GABA_B synapses between RE and TC cells. Increasing the GABA_B conductance made the augmenting response develop faster. In comparison, increasing of GABA_A and AMPA conductances diminished the augmentation of TC cell responses.

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.

View larger version (31K): [in this window] [in a new window]   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.

View larger version (48K): [in this window] [in a new window]   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.

Deinactivation of the low-threshold Ca²⁺ current in thalamic relay cells during repetitive stimulation is caused by the RE-evoked IPSPs. Decreasing the maximal conductance of I_T current in RE cells weakened burst discharges in RE cells (by decreasing the amplitude of the LTSs) and diminished the IPSPs in TC cells. As a consequence, the deinactivation of I_T current in TC cells was weakened and the augmenting responses were delayed (compare Fig. 15, A with B).

Figure 15C shows the dependence of the RE-TC responses on the low-threshold Ca²⁺ current in the TC cells. Decreasing the maximal conductance for the I_T current diminished the amplitude of LTSs in TC cells, and weaker augmenting responses were observed during repetitive stimulation (cf.Fig. 15, A with C). Blocking the I_T channels blocked augmentation, and the TC cells responded with similar (nonaugmenting) responses throughout the entire train of stimuli (not shown).

Figure 15D shows the effect of reducing the I_h current on thalamic augmentation. I_h is a depolarizing current activated by hyperpolarization of the TC cell. Decreasing the I_h conductance resulted in greater hyperpolarization of the TC cells and, consequently, more powerful LTSs in the TC cells in response to the stimulation.

Thus the low-threshold Ca²⁺ current is an essential intrinsic current for eliciting augmenting responses during repetitive stimulation. However, the thalamocortical network displayed a robust augmenting response for a wide range of parameters for the synaptic and intrinsic currents. As a consequence, the proposed mechanism for augmentation is not parameter specific.

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) in which each RE cell is connected to all other RE and TC cells within some radius R_RE and each TC cell is connected to all RE cells within radius R_TC.

Figure 16 shows the responses of equidistant TC cells from a network with N = 27 and 27 × 27 = 729 thalamic relay cells. TC cells located close to the center of the network (bottom right) had strong and rapid augmentation of responses (from 1 to 4 spikes) during a train of stimuli and only a few cycles of poststimulus oscillations. In contrast, the TC cells located close to the boundary of the network (top left) displayed a weak augmenting response (from 0 to 2 spikes) followed by prolonged slow oscillations.

The difference between central and boundary neurons was in the intensity of stimulation. The cells located near the center of the network received powerful RE-evoked GABA_B IPSPs and were strongly hyperpolarized after the first 1-2 stimuli. This resulted in the complete deinactivation of the low-threshold Ca²⁺ current and large LTSs. The neurons far from the center of the stimulation received weaker input that resulted in smaller GABA_B IPSPs in TC cells and only partial deinactivation of the low-threshold Ca²⁺ current during stimulation.

In the two-dimensional network, the contribution of the each individual cell to the whole PSP was much smaller than for the one-dimensional chain. Therefore the mechanism of desynchronization based on the variability of parameters was more effective in the two-dimensional network than in one-dimensional chain. The result was a faster desynchronization and termination of the poststimulus oscillations in the two-dimensional network.

In general, the network geometry does not have a critical role in the proposed mechanism for augmentation. Both one- and two-dimensional networks displayed similar augmenting responses during a train of stimuli.

	DISCUSSION

Abstract Introduction Methods Results Discussion References

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 GABA_B 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.

Although the computational analysis of thalamic augmenting responses presented in this paper was motivated by in vivo recordings from the thalamus of anesthetized cats, the model RE-TC network studied here is not species specific. Only the most basic properties of RE and TC cells and synaptic interconnections were included in the model. The robustness of the results were tested over a wide range of i