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The Journal of Neuroscience, May 15, 1998, 18(10):3574-3588

Dendritic Low-Threshold Calcium Currents in Thalamic Relay Cells

Alain Destexhe¹, Mike Neubig¹, Daniel Ulrich², and John Huguenard²

¹ Laboratoire de Neurophysiologie, Faculté de Médecine, Université Laval, Quebec G1K 7P4, Canada, and ² Department of Neurology and Neurological Sciences, Stanford University Medical Center, Stanford, California 94305

	ABSTRACT

Top Abstract Introduction Materials & Methods Results Discussion References

The low-threshold calcium current (I_T) underlies burst generation in thalamocortical (TC) relay cells and plays a central role in the genesis of synchronized oscillations by thalamic circuits. Here we have combined in vitro recordings and computational modeling techniques to investigate the consequences of dendritically located I_T in TC cells. Simulations of a reconstructed TC cell were compared with the recordings obtained in the same cell to constrain the values of its passive parameters. T-current densities in soma and proximal dendrites were then estimated by matching the model to voltage-clamp recordings obtained in dissociated TC cells, which lack most of the dendrites. The distal dendritic T-current density was constrained by recordings in intact TC cells, which show 5-14 times larger peak T-current amplitudes compared with dissociated cells. Comparison of the model with the recordings of the same cell constrained further the T-current density in dendrites, which had to be 4.5-7.6 times higher than in the soma to reproduce all experimental results. Similar conclusions were reached using a simplified three-compartment model. Functionally, the model shows that the same amount of T-channels can lead to different bursting behaviors if they are exclusively somatic or distributed throughout the dendrites. In conclusion, this combination of models and experiments shows that dendritic T-currents are necessary to reproduce low-threshold calcium electrogenesis in TC cells. Dendritic T-current may also have significant functional consequences, such as an efficient modulation of thalamic burst discharges by corticothalamic feedback.

Key words: computational models; voltage clamp; bursting; oscillations; low-threshold spikes; dendritic calcium currents

	INTRODUCTION

Top Abstract Introduction Materials & Methods Results Discussion References

Thalamocortical (TC) relay neurons play an essential role in the genesis of synchronized oscillations in the thalamus and in the thalamocortical system. This role is conveyed through their intrinsic ability to generate bursts of action potentials in rebound to inhibition. The importance of the rebound response of TC cells was first established by Andersen and Eccles (1962), who referred it as "post-anodal exhaltation." It was later characterized by in vivo (Deschênes et al., 1984) and in vitro intracellular recordings (Jahnsen and Llinás, 1984a) and subsequently called the "low-threshold spike" (LTS). It was also demonstrated that a low-threshold calcium current (I_T) underlies LTS genesis in TC cells (Jahnsen and Llinás, 1984b).

Computational models of TC cells were designed in the early work of Andersen and Rutjord (1964), who represented the rebound response of these cells by a qualitative model. Later, the biophysical characterization of the T-current by voltage-clamp methods (Coulter et al., 1989; Huguenard and Prince, 1992) provided precise data to build more detailed models. Like the model introduced by Hodgkin and Huxley (1952) for action potentials, the activation and inactivation properties of the T-current are sufficient to predict rebound burst generation in current clamp, as found by a number of modeling investigators (for review, see Destexhe and Sejnowski, 1997).

Rebound bursts play an essential role at the network level. Andersen and Eccles (1962) initially hypothesized that TC cells are connected reciprocally with local circuit interneurons, making a powerful oscillator through the interplay of inhibition and rebound response. Although the details were incorrect, the principle was essentially right, as shown by in vivo (Steriade et al., 1985, 1990) and slice experiments (von Krosigk et al., 1993; Huguenard and Prince, 1992), which demonstrated that oscillations are generated by the interaction between TC cells and thalamic reticular (RE) neurons. Computational models of thalamic circuits (Destexhe et al., 1993, 1996a; Wang et al., 1995; Golomb et al., 1996; for review, see Destexhe and Sejnowski, 1997) explored oscillatory mechanisms based on an interplay of inhibition and rebound burst. Possible consequences of this mechanism in synchronizing thalamocortical networks were modeled recently (Destexhe et al., 1998).

Interactions involving T-channels may also take place at the subcellular level. A previous study on RE cells suggested evidence for high T-current densities in distal dendrites (Destexhe et al., 1996b). This study showed that dendritic T-current may explain critical electrophysiological features, such as differences in the intrinsic firing properties between RE cells recorded in vivo and in vitro. For TC cells, evidence for dendritic I_T was obtained recently from calcium imaging of proximal dendrites (Munsch et al., 1997; Zhou et al., 1997). Given the considerable number of synaptic terminals that contact the dendrites of TC cells (Jones, 1985; Liu et al., 1995), these data suggest that complex interactions between synaptic inputs and burst generation may take place in the dendrites of TC cells.

To investigate these type of interactions, we have designed a computational model of the dendritic T-current in TC cells based on a combination of in vitro recordings and computational modeling techniques.

	MATERIALS AND METHODS

Top Abstract Introduction Materials & Methods Results Discussion References

In vitro recordings. The present study focuses on neurons from the ventrobasal nucleus of the thalamus of rats. All in vitro recordings were obtained in TC neurons from the ventrobasal nucleus of young rats [postnatal day 8 (P8)-P15], using either intact slice preparation or acutely dissociated TC cells. All current-clamp recordings were at a temperature of 34-36°C, whereas voltage-clamp recordings were done at 24°C. The methods were described in detail by Huguenard and Prince (1992).

The following procedure was used for calcium current recording in intact neurons in slices (modified from the procedure of Ulrich and Huguenard, 1995). Brain slices (200 µm) were transferred into a recording chamber and superfused (2 ml/min at room temperature) with standard artificial CSF containing (in mM): 126 NaCl, 26 NaHCO₃, 2.5 KCl, 1.25 NaH₂PO₄, 2 MgCl₂, 2 CaCl₂, 0.001 tetrodotoxin, and 10 glucose, equilibrated with 95% O₂ and 5% CO₂. Patch pipettes were pulled from borosilicate glass (Garner Glass, Claremont, CA) and filled with a solution containing (in mM): 120 Cs gluconate, 11 CsCl, 1 MgCl₂, 1 CaCl₂, 10 HEPES, and 11 EGTA, pH adjusted to 7.3 with CsOH, osmolality 290 mOsm. Whole-cell recordings were made with a List EPC-7 amplifier. Series resistance was in the range of 2.5-12 M and was electronically compensated by 70%.

Morphology. A TC neuron was recorded in intact slice preparation and stained with biocytin. The cell is shown in Figure 1A (also see Huguenard and Prince, 1992). We reconstructed the morphology of that cell from serial sections of 80 µm, using a computerized tracing system (Eutectic Electronics, Raleigh, NC) kindly provided by Prof. D. Amaral (University of California, Davis, CA). With the 100× objective used and correction for tissue shrinkage, the theoretical accuracy with which dendritic diameters can be measured was 0.1 µm. However, because of biocytin artifacts, the diameters of some distal dendrites could not be traced precisely, although lengths and branching patterns were accurately reconstructed. In those cases, the diameters were artificially rescaled to match the diameter profile of dendritic segments that could be reconstructed accurately. This procedure led to diameter profiles consistent with previous morphological studies of rat ventrobasal TC cells (Ohara and Havton, 1994). The reconstructed TC neuron is shown in Figure 1B.

View larger version (36K): [in this window] [in a new window]   Figure 1.   Recording, staining, reconstruction, and simulation based on of the same cellular geometry. A, Thalamic relay cell from rat ventrobasal nucleus, intracellularly recorded in slices (Huguenard and Prince, 1992). B, Three-dimensional reconstruction of the same cell. The complete dendritic arbor (of which only part appears in A) was reconstructed from thin serial sections. C, Computational model of the same cell. The simulation (continuous line) is compared with passive responses obtained while recording that cell (noisy trace). The adjustment of the model to the experimental response by a simplex fitting procedure provides estimates of passive parameters (see Results).

The reconstructed morphology of the TC cell was incorporated into NEURON, which can simulate the cable geometry from the three-dimensional coordinates provided by the tracing of the neuron (for more details, see Hines and Carnevale, 1997). The two equivalent cable models studied had either 208 or 1214 compartments and gave nearly identical results.

Computational models of dissociated cells. In acutely dissociated TC cells, most of the dendritic arborizations were removed by the dissociation procedure (Fig. 2A1) (also see Huguenard and Prince, 1992). Simulations of acutely dissociated TC cells used a cable geometry obtained by truncating the dendrites of the original cell (Fig. 2B1). The model shown in Figure 2B1 was obtained by keeping the soma and proximal bits of dendrites of the reconstructed cell based on the morphology of dissociated TC cells (Fig. 2B2) (also see Huguenard and Prince, 1992) and the ratio of input capacitance measured experimentally (113 pF for the intact cell and 16.7 pF on average for dissociated TC cells; Huguenard and Prince, 1992), leading to an area of ~3500 µm². Distal dendrites were removed from the reconstructed cell until the model matched this area, leading to a dissociated cell model, which had only the soma and two proximal dendritic branches, with a total membrane area of 3430 µm² (Fig. 2B1).

View larger version (43K): [in this window] [in a new window]   Figure 2.   Low amplitudes of T-current in dissociated TC cells under voltage clamp. A1, Typical structure of dissociated TC cells, where most of the dendrites were removed by the dissociation procedure, leaving soma and proximal dendrites intact. A2, Voltage-clamp recordings of the T-current in a dissociated TC cell. The voltage-clamp protocol consisted in conditioning the cell at various voltage levels (from 125 to 60 mV) for 1 sec and then stepping the voltage to 30 mV, revealing the transient activation of the current. The peak current was ~400 pA (different cell than that shown in A1). B1, Model of a dissociated TC cell, consisting of the soma with proximal bits of dendrites, adjusted from the input capacitance of the model. B2, Same voltage-clamp protocol as in A2, simulated with the dissociated cell model. The model reproduces the peak amplitude of the T-current in dissociated cells with a moderate density of T-channels (permeability of 1.7 × 105 cm/sec). This procedure provides an estimate of the perisomatic T-current density in TC cells. All experiments and simulations at 24°C.

Voltage-dependent currents. Voltage-dependent conductances were modeled using a Hodgkin-Huxley type of kinetic model (Hodgkin and Huxley, 1952). Because no data exist to constrain the localization and kinetics of the Na⁺ and K⁺ currents responsible for fast action potentials, they were inserted in the soma, and their kinetics were taken from a model of hippocampal pyramidal cells (Traub and Miles, 1991), assuming a resting potential of V_T = 52 mV in their equations, maximal conductances of _Na = 100 mS/cm² and _K = 100 mS/cm², and reversal potentials of E_Na = 50 mV and E_K = 100 mV. This model was already shown to be adequate to model the repetitive firing within bursts of action potentials (Traub and Miles, 1991; Destexhe et al., 1996a,b).

The kinetics of activation and inactivation of I_T in TC cells were modified from a previous model (Huguenard and McCormick, 1992). The activation functions were empirically corrected to account for both voltage-clamp and current-clamp data on TC cells, assuming a ±3 mV error on voltage (see below).

The usual Nernst equation describes the near-equilibrium behavior of ion channels in which the current is described by Ohm's law. Because of the nonlinear and far-from-equilibrium behavior of calcium currents, a different formalism must be used (Hille, 1992), such as the constant-field equations:

(1)

where _Ca (in centimeters per second) is the maximum permeability of the membrane to Ca²⁺ ions, and m and h are, respectively, the activation and inactivation variables. G(V,Ca_o,Ca_i) is a nonlinear function of voltage and ionic concentrations:

(2)

where Z = 2 is the valence of calcium ions, F is the Faraday constant, R is the gas constant, and T is the temperature in Kelvins. Ca_i and Ca_o are the intracellular and extracellular Ca²⁺ molar concentrations, respectively.

The expressions for steady-state activation and inactivation functions were first obtained from voltage-clamp experiments on dissociated TC cells (Huguenard and Prince, 1992). The activation function was empirically corrected to account for the contamination of inactivation (Huguenard and McCormick, 1992). An overall hyperpolarizing shift of 2 mV was applied to compensate for screening charge (voltage-clamp experiments on dissociated cells were done using 3 mM extracellular Ca²⁺, whereas physiological conditions are 1.5-2 mM). In addition, an overall depolarizing shift of 3 mV was necessary to reproduce the current-clamp simulations of TC cells in the present paper. The optimal functions that accounted for both voltage-clamp and current-clamp data on TC cells were:

The voltage-dependent time constant for activation was:

(3)

and for inactivation:

(4)

These functions correspond to an external Ca²⁺ concentration of 2 mM and a temperature of 36°C. All voltage-clamp simulations were done at 24°C assuming Q₁₀ values of 2.5 for both m and h, whereas current-clamp behavior was simulated at 34°C.

Calcium handling was modeled by a first-order system representing Ca²⁺ pumps and buffers, as described by McCormick and Huguenard (1992), with a time constant of decay of Ca²⁺ of 5 msec. At equilibrium, the free intracellular Ca²⁺ concentration was 240 nM, and the extracellular Ca²⁺ concentration was 2 mM, corresponding to a reversal potential of approximately +120 mV.

Simplified models. To generate simplified representations of TC cells, a method was used that consisted of collapsing the dendritic arbor into fewer compartments. We have used a reduction method based on the conservation of axial resistance (modified from Bush and Sejnowski, 1993).

The method consists of merging dendritic branches into equivalent cylinders, which preserve the axial resistance of the original branches. If the cross-sectional area of the equivalent cylinder equals the sum of each individual cross-sectional area, this is equivalent to summing parallel resistances, because 1/r = _j1/R(j), where R(j) are the axial resistances of the collapsed branches. The radius (r) of the equivalent cylinder is then given by:

(5)

where r_i are the radii of the collapsed branches.

The length (l) of the equivalent cylinder is taken as an average of the lengths of the collapsed branches (l_i), weighted by their respective diameters (r_i), such as:

(6)

This modification of the Bush-Sejnowski algorithm was added to accommodate the merging of branches of very different length, which is often encountered while reducing dendritic morphologies, such that of the reconstructed TC cell studied here.

Because the total membrane area is not conserved in this method, the reduced model may not have a correct input resistance. This is compensated by introducing in each equivalent cylinder a dendritic correction factor (C_d), which rescales the values of conductances (g_i) and membrane capacitance (C_m) in the dendrites such that:

(7)

C_d is estimated such that the reduced model has the correct input resistance and time constant (Bush and Sejnowski, 1993).

The three compartments of the simplified model had the following lengths (l) and diameters (diam): l = 38.4 µm, and diam = 26 µm for the soma (area, 2624 µm²); l = 12.5 µm, and diam = 10.3 µm for the proximal segment (area, 403 µm²); and l = 84.7 µm, and diam = 8.5 µm for the distal segment (area, 2261 µm²). The total area was 5289 µm². The dendritic correction factor was C_d = 8.02, as calculated from the ratio of the total surface area of the dendritic segments to their equivalent cylinders. A more accurate estimation of C_d = 7.95 was obtained by fitting simulations to voltage-clamp recordings until the three-compartment model had input resistance and other passive properties matching the reconstructed cell perfectly (see Fig. 11A2).

The equations for the three-compartment model were:

(8)

where V_S, V_M, and V_D are the voltage of somatic, middle, and distal compartments, respectively. C_m = 0.878 µF/cm² is the membrane capacitance; g_L = 0.0379 mS/cm² is the leak conductance; E_L = 69.85 mV is the leak reversal potential; I_T is the T-current (according to Eq. 1); g_SM = 5.19 µS and g_MD = 0.70 µS are the axial conductances (derived from axial resistivity and cross-sectional area of the compartments); A₁-A₃ are the areas of each compartment (see above); and C_d = 7.95 is the dendritic correction. These values correspond to the optimal set of passive parameters obtained by fitting the passive responses of the three-compartment model to experimental voltage-clamp responses (see Results).

A single-compartment model was also generated, and its membrane area was adjusted such that this model matches passive voltage-clamp recordings (see Fig. 11B2). The optimal model had a length and diameter of 100 µm and 76.6 µm, respectively.

We used only one anatomically reconstructed TC cell in this study, in addition to morphologically simplified models. The behavior of the detailed and simplified models was nearly identical (see Results), which suggests that the particular details of the morphology of the cell were unimportant in the context of the present study. The behavior reported in this paper was extremely robust to changes in the values of the parameters, as illustrated by the nearly identical behavior obtained in models with different cable geometries.

All simulations were done using NEURON (Hines and Carnevale, 1997) on Sparc-20 and Ultra-1 workstations (Sun Microsystems, Mountain View, CA).

	RESULTS

Top Abstract Introduction Materials & Methods Results Discussion References

We begin by showing how the thalamic relay cell model was successively constrained by the reconstructed dendritic morphology of a cell recorded experimentally, by voltage-clamp recordings to set its passive properties, by dissociated cell recordings to set its perisomatic T-current density, and by intact-cell recordings to set the T-current density in distal dendrites ("distal" will be used in this paper to refer to the dendritic region >11 µm from the soma). The properties of TC cells in voltage clamp and current clamp are then examined in terms of dendritic T-current. Finally, simplified models of the TC cell are generated and studied in the same context.

Morphology and passive properties

A TC cell from rat ventrobasal nucleus (shown in Fig. 1A) (also see Huguenard and Prince, 1992) was reconstructed using a three-dimensional tracing system. The reconstructed TC cell is shown in Fig. 1B (see Materials and Methods for details concerning the tracing of the cell). There were 11 primary dendrites, having a total length of 7095 µm; the total membrane area of the cell was 23,980.5 µm², including 2625 µm² for the soma, which was ~20-25 µm in diameter (assuming that a 0.1 µm error on diameters leads to approximately ±9% error on the total membrane area). The dendritic arborizations tended to be organized in a bush-like structure, similar to previous morphological observations (Jones, 1985).

Voltage-clamp recordings of passive responses obtained in that cell are shown in Fig. 1A. These recordings were used to estimate the passive parameters by fitting the model to the data (Fig. 1C). Because model and data correspond to the exact same cellular geometry, this procedure leads to a unique set of passive parameters if they are uniform (Rall et al., 1992).

To perform passive fitting, leak currents were inserted in all compartments of the reconstructed cell model. The values of the passive parameters [leak conductance (g_L), leak reversal potential (E_L), axial resistivity (R_a), and specific membrane capacitance (C_m)] and the electrode series resistance (R_s) were obtained by fitting the simulations to experimental data using a simplex algorithm (Press et al., 1986). At each iteration of the simplex algorithm, the model was run, and the root mean squared (rms) error between the experimental recording and the model was minimized. This procedure was repeated from different initial conditions to avoid unstable values of parameters. The values of passive parameters were considered uniform and were consistent with the values estimated from the recordings. Approximately 50-300 iterations were required to converge to a minimum error.

The optimal set of values obtained was C_m = 0.878 µF/cm²; R_a = 173 cm; g_L = 0.0379 mS/cm²; E_L = 69.85 mV; and R_s = 8.1 M. This optimal set was obtained from different initial conditions with ranges of values tested of 0.2-2 µF/cm², 50-500 cm, 0.02-0.2 mS/cm², 70 to 80 mV, and 1-40 M, respectively. The ranges of parameter values yielding similar fitting errors (within a 2 pA maximal rms error) were C_m = 0.856-0.899 µF/cm²; R_a = 147-200 cm; g_L = 0.0376-0.0383 mS/cm²; E_L = 69.72-69.97 mV; and R_s = 7.0-9.5 M. These ranges were obtained by varying each parameter individually around the optimal fit. A more detailed analysis, in which the search procedure was based on experimental precision or on experimental confidence intervals of electrophysiological and morphological measurements, yielded correspondingly larger acceptable ranges of values (Neubig and Destexhe, 1997) (M. Neubig and A. Destexhe, unpublished data).

Because the window current of I_T may affect the resting membrane potential of the cell, the same fitting was also performed in the presence of somatic-dendritic distribution of T-current. In this case, the values obtained were very close (within SE) to that of the passive fitting, except for the leak reversal potential that needed to be readjusted to compensate for the window current, leading to more negative values (E_L = 70.1 to 73.4 mV for dendritic T-current densities of 1.7 × 10⁵ to 12.5 × 10⁵ cm/sec; see below).

In these conditions, the electrotonic length of the longest dendrite was 0.34 space constants (as calculated using the optimal set of passive parameters shown above). The attenuation characteristics of the cell were estimated as follows. A current pulse of 10 msec and 0.1 nA was injected in the middle of a representative terminal branch in the intact-cell model with passive currents. The attenuation was calculated by measuring the maximal voltage deflections evoked by this current injection, there and at the soma. The ratio obtained was ~10-fold (0.098). The opposite protocol was also followed (current injected in soma while measuring in dendrites), and the ratio of voltage deflections was close to unity (0.91).

This TC cell is therefore relatively compact electrotonically, contrary to RE cells analyzed with similar methods (see Destexhe et al., 1996b) but similar to the conclusions of previous studies on TC cells (Bloomfield et al., 1987; Crunelli et al., 1987). Further comparison is difficult, however, because these studies were on a different animal, using different types of recording electrodes, different passive parameters, and a different method to estimate the electrotonic length.

Density of T-current in soma and proximal dendrites

Acutely dissociated neurons were used to characterize the T-current in TC cells (Huguenard and Prince, 1992). This preparation is very useful because the dissociation procedure removes most of the dendritic arbor, leaving the soma intact with proximal bits of dendrites (Fig. 2A1). This preparation therefore leads to very compact cells, in which voltage-clamp recordings can be made with minimal space clamp errors. The kinetics of the T-current used in the present paper (see Materials and Methods) were obtained from such recordings (see Huguenard and McCormick, 1992; Huguenard and Prince, 1992).

As illustrated in a previous model (Destexhe et al., 1996b), another advantage of the dissociated cell preparation is that it allows a direct estimate of the T-current density in the perisomatic region of the cell. This estimation was performed by matching a dissociated cell model to voltage-clamp recordings of the T-current in dissociated TC cells. The model used is shown in Figure 2B1 and was obtained by adjusting the geometry of the model to the input capacitance measured in experimental recordings (see Materials and Methods).

Voltage-clamp recordings in dissociated TC cells show peak T-current amplitudes of ~400 pA (Fig. 2A2). Similar T-current peak amplitudes were obtained assuming a uniform density of T-current in the dissociated cell model (1.7 × 10⁵ cm/sec; Fig. 2B2). A range of T-current densities of 0.5-3.0 × 10⁵ cm/sec reproduced the range of T-current amplitudes measured in dissociated TC cells (350 ± 27 pA; n = 49; from Coulter et al., 1989; and 280 ± 23 pA; n = 26; from Huguenard and Prince, 1992).

Increased density of T-current in more distal dendrites

The presence of T-current was demonstrated in the dendrites of TC cells by optical imaging techniques (Munsch et al., 1997; Zhou et al., 1997). Given the fact that intact TC cells have a considerably more extended dendritic area than dissociated TC cells, this would predict a higher T-current amplitude in intact TC cells than shown in Figure 2A2 for dissociated cells. This is indeed the case, as demonstrated by voltage-clamp recordings of intact TC cells (Fig. 3). The maximal T-current amplitude ranged from ~2 to 8.3 nA in different intact cells (5.8 ± 1.7 nA; n = 7), which is on average ~16-21 times larger than in dissociated cells.

View larger version (21K): [in this window] [in a new window]   Figure 3.   High amplitudes of T-current in intact TC cells under voltage clamp. Inactivation protocol in four TC cells (A-D) recorded in thalamic slices of the ventrobasal nucleus. For each cell, the voltage-clamp protocol giving rise to the largest peak current is shown. The inactivation protocol consisted of conditioning the cell at various voltage levels (from 105 to 40 mV) for 1 sec and then stepping the voltage to a fixed voltage value (55 mV in A, 65 mV in B, 60 mV in C, 45 mV in D). For comparison, a similar protocol in a dissociated cell is shown in the bottom at the same calibration. All cells were the same age (P12); recording temperature was 24°C in all cases.

The model of the reconstructed TC cell was used to estimate the range of T-current needed in dendrites to account for these data. As shown in Fig. 4, the density of T-current estimated from dissociated cells (1.5-2.0 × 10⁵ cm/sec) was insufficient to reproduce T-current amplitudes comparable to intact cells (Fig. 4A), even when the same density was extended to the entire dendritic tree (Fig. 4B). To obtain T-current peak amplitudes of ~2 nA and more, an increased density of T-current had to be assumed in distal dendrites (Fig. 4C,D). To reproduce peak amplitude in the range of 2-7 nA of Figure 3, the range of dendritic densities needed in the model were of 1.7-6.5 × 10⁵ cm/sec for low series resistance (R_s = 0.01 M) and 2.5-50 × 10⁵ cm/sec for high series resistances (R_s = 12 M), which is up to 29 times the density in the soma.

View larger version (17K): [in this window] [in a new window]   Figure 4.   High densities of dendritic T-current are needed to match the T-current amplitude recorded in intact TC cells. The model shows the same inactivation protocol using different distributions of T-current. In all cases, the perisomatic IT density was compatible with recordings in dissociated cells (permeability of 1.7 × 105 cm/sec in soma and proximal dendrites), whereas the density of IT in distal dendrites was varied. A, No dendritic T-current. IT was limited to the perisomatic region. B, Uniform T-current. IT had the same density throughout the neuron. C, Twice dendritic. IT density was twice in distal dendrites compared with the perisomatic density. D, Five times dendritic. Distal dendrites had five times as much T-current density as in the perisomatic region. The latter produced peak IT amplitudes comparable to the average value of intact TC cells recorded in slices (Fig. 3). All simulations at 24°C.

Distal dendritic T-currents affect current-voltage relations

A further indication for the presence of higher density of T-current in dendrites is obtained from the properties of the current-voltage (I-V) relations. I-V curves obtained from voltage-clamp recordings of TC cells show a marked difference between dissociated (Fig. 5A) and intact cells (Fig. 5B). Not only the maximum T-current reaches much higher values, as shown in the previous section, but the shape of the I-V curve is different; the peak occurs at approximately 40 to 30 mV in dissociated TC cells, whereas in intact cells, the I-V curve was significantly shifted, peaking at 70 to 60 mV.

View larger version (29K): [in this window] [in a new window]   Figure 5.   Current-voltage relationship in TC cells under voltage clamp. The graphs show the peak amplitude of T-current obtained during activation protocols under voltage clamp; each protocol consisted of conditioning the cell at 105 mV for 1 sec and stepping to various voltage values (shown in abscissa). A, I-V relation for the T-current in a dissociated TC cell. The peak current was of ~0.4 nA and occurred at 40 mV. B, I-V curve in an intact TC cell (same cell as in Fig. 3C). The peak T-current was here of ~2.5 nA and occurred at 60 mV. The steep decline of the I-V curve above 60 mV is probably attributable to incomplete block of outward currents by cesium. C, Dissociated cell model. A similar I-V curve as in A could be reproduced with moderate T-current density (permeability of 1.7 × 105 cm/sec). D, Intact-cell model. In this case, the I-V curve of the intact cell shown in B could be reproduced using a larger T-current density in distal dendrites (2.5 × 105 cm/sec) compared with the perisomatic region (1.7 × 105 cm/sec) and a series resistance of Rs = 12 M (circles). This I-V curve is compared with the same simulation with uniform T-current density of 1.7 × 105 cm/sec (squares). All activation protocols consisted of conditioning the cell at 115 mV for 1 sec and then stepping the voltage to the values indicated. The peak currents shown are leak-subtracted. All experiments and simulations at 24°C.

In the dissociated cell model, simulated I-V curves had a behavior consistent with experimental data (Fig. 5, compare A,C). In intact cells, however, the behavior depended markedly on the density of the T-current. With higher T-current densities in distal dendrites, the I-V curve was comparable to that recorded in intact cells during experiments (Fig. 5, compare B,D, circles). On the other hand, with uniform T-current densities, the I-V curves were not consistent with experimental observations, neither for the peak amplitude, which was too low, nor for the position of the peak current, which was too depolarized (Fig. 5D, squares). By varying parameters (see below), we found that I-V curve shift were consistent with those observed in experiments only when the density of T-current was significantly increased in distal dendrites. Voltage-clamp simulations using the intact-cell model further showed that the I-V curve shift is attributable to poor voltage-clamp of the cell, which could be attributable to space-clamp and/or series resistance artifacts. During a somatic voltage clamp, the dendritic T-channels are not easily controllable, as shown previously in simulated thalamic reticular cells (Destexhe et al., 1996b). The same phenomenon occurs for TC cells as shown in Fig. 6. From a holding potential of 115 mV, stepping the voltage to a hyperpolarized value (65 mV), at which only few T-channels should open, activates ~10% of the total T-current available for a uniform density of 1.7 × 10⁵ cm/sec (Fig. 6A). On the other hand, with high distal dendritic densities of T-current, the same protocol led to activation of almost the totality of the available T-current (Fig. 6B). In this case, a low-threshold spike was elicited in the dendrites and therefore the recorded current showed anomalously large currents at the soma. The inflection of the current trace in Figure 6B is indeed indicative of poor voltage control (see Huguenard et al., 1988). Consequently, the peak of the I-V curve will occur at more hyperpolarized values because of the poor control over dendritic T-channels.

View larger version (14K): [in this window] [in a new window]   Figure 6.   Poor clamp together with distal dendritic T-currents alters current-voltage relations. Voltage-clamp simulation of the intact TC cell model consisting of conditioning the cell at 115 mV for 1 sec and stepping the voltage to 65 mV. The voltage is shown in soma and distal dendrite, as well as the current. The maximal current that could be evoked (peak of the I-V curve) is shown by dotted lines for comparison. A, uniform T-channel density of 1.7 × 105 cm/sec shows little current activation at 65 mV (0.187 nA), representing ~10% of the total T-current. B, same simulation with high densities of T-current in dendrites (1.7 × 105 cm/sec perisomatic and 8 × 105 cm/sec in distal dendrites). In this case, large uncontrolled voltage transients occurred in both soma and dendrites, leading to a large peak current (4.09 nA), representing 98% of the total available T-current. Series resistance was 12 M, and temperature was 24°C in both cases.

The shift of I-V curve caused by poor voltage control was further illustrated by showing the effect of various parameters (Fig. 7). The I-V curve shift was affected by the total amount of T-channels (Fig. 7A) and the series resistance of the voltage-clamp electrode (Fig. 7B). The T-channel distribution also affected the I-V curve shift both for distributions with same peak current (Fig. 7C) and for distributions where the total amount of T-channels was kept constant (Fig. 7D). These properties show that the I-V curve shift is attributable to a poor control over some, possibly dendritic, portion of T-channels in the cell. This is in agreement with a previous modeling study, which also concluded that imperfect space clamp results in alterations of I-V curves (Müller and Lux, 1993).

View larger version (34K): [in this window] [in a new window]   Figure 7.   Poor clamp and dendritic T-current can explain the shift in the current-voltage curves in intact and dissociated TC cells. A, Effect of the total amount of T-channels. At 100%, the perisomatic and dendritic T-current densities were of 1.7 × 105 and 8 × 105 cm/sec, respectively. The total density of T-current was uniformly decreased by a factor of 2 (50%) and 4 (25%). B, Effect of the series resistance. Same simulation as 100% in A, using three different values of the series resistance. C. Effect of the distribution of T-channels. Two different T-channel distributions were adjusted such as to get similar peak currents at the soma (Rs = 5 M). Somatic & dendritic, 1.7 × 105 cm/sec perisomatic and 8 × 105 cm/sec in dendrites at 11 µm and more from the soma (~82% of membrane area). Somatic only, 42.7 × 105 cm/sec in soma and no T-current in dendrites. D, Same graph, but in this case the Somatic only density (53.3 × 105 cm/sec) was adjusted such that the total number of T-channels was the same as for Somatic & dendritic. All simulations at 24°C.

A test for the quality of voltage control over the dendrites

The poor voltage clamp evidenced above should be detectable by appropriate experiments. Tail currents can be used to assess the quality of voltage control (Huguenard, 1998). This protocol is illustrated in Fig. 8. In the dissociated cell model (Fig. 8A), the amplitude of the tail currents follows closely the time course of activation and inactivation of the current, as expected from an experiment with good clamp (Huguenard, 1998). On the other hand, the same protocol applied to the intact-cell model produced significant deviations of tail current amplitudes (Fig. 8B). Such deviations occurred despite the fact that the model of Figure 8B had moderate density of dendritic T-current. The mismatch between tail currents and T-current activation was paralleled with poor clamp in this model. Because tail currents can be easily measured experimentally, this figure therefore provides an important experimentally verifiable prediction to test that poor voltage clamp is responsible for significant alterations of T-current I-V curves in intact TC cells.

View larger version (30K): [in this window] [in a new window]   Figure 8.   Tail currents are indicative of the quality of voltage control over the dendrites. Left panels, Tail currents. The cell was conditioned at 115 mV for 1 sec, and then the voltage was stepped to 30 mV, leading to transient activation of the T-current. Tail currents are obtained when the voltage is stepped back to 115 mV at different instants during this activation. Right panels, Comparison of the time course of the T-current (continuous line) with the peak tail current amplitudes (squares), scaled to each other. A perfect match of these two currents is indicative of perfect clamp in the cell (Huguenard, 1998). A, Dissociated cell model. The tail currents match closely the activation of the T-current. B, Intact-cell model. In this case, the mismatch between tail currents and T-current activation was paralleled with poor clamp (T-current densities were 1.7 × 105 cm/sec perisomatic and 2.5 × 105 cm/sec in distal dendrites). All currents were subtracted from leak and capacitive components (24°C).

Simulations therefore suggest that the voltage-clamp recordings of dissociated TC cells were always in conditions of good space clamp, as indicated by the well clamped voltage in soma and proximal dendrites (data not shown). On the other hand, simulations of intact TC cells clearly indicate poor control (see voltage traces in Fig. 6B), in agreement with the tail current test shown in Figure 8.

Burst generation in TC cells with dendritic T-current

A further argument in favor of dendritic T-current was given by current-clamp simulations. Current-clamp recordings were obtained in the cell shown in Figure 1A and consisted of injecting depolarizing pulses from rest (73 to 74 mV). Current pulses of 50 and 75 pA amplitude gave rise to low-threshold spikes (LTS) with one and two action potentials, respectively (Fig. 9A). In the model, assuming a uniform density of T-current based on voltage-clamp recordings in dissociated TC cells, the same current-clamp protocol could not give rise to LTS (Fig. 9B), despite a large range of parameters explored, such as the resting level of the cell and the kinetics of I_T.

View larger version (27K): [in this window] [in a new window]   Figure 9.   Correct low-threshold spike generation in intact TC cells requires high densities of dendritic T-current. Current-clamp recordings of LTS in the recorded intact TC cell are compared with simulations based on the same cellular geometry. A, Experimental recordings of LTS in the intact TC cell at rest using two different amplitudes of injected depolarizing current: 50 pA (thin trace) and 75 pA (thick trace). B, Simulations of the same current injection did not generate LTS using a uniform density of T-current based on dissociated cells (1.7 × 105 cm/sec). C, Successful LTS generation with increased density of T-current in distal dendrites. In B and C, the gray levels indicate the density of T-current in different regions of the cell: 1.7 × 105 cm/sec (light gray) and 8.5 × 105 cm/sec (black). All experiments and simulations at 34°C.

With high densities of T-current in distal dendrites, LTS generation similar to the intact cell could be produced (Fig. 9C). One- and two-spike bursts were generated by 50 and 75 pA current injection, respectively, whereas the one-spike burst had a longer latency (although not as long as in experiments). The latency could be increased by using more negative resting membrane potential (data not shown), but in this case the resting values were not in agreement with the data. The correct latency of the first burst may therefore depend on the presence of other currents not included here, such as I_h, which is active at rest and therefore likely to affect the resting level of the cell (Pape, 1996).

Taking the number of spikes as the reference behavior, only a narrow range of T-current densities gave rise to burst responses with one and two spikes as in Figure 9A. Too low densities did not produce LTS, as in the case of uniform T-current (Fig. 9B), whereas too high densities gave rise to a correct burst for 50 pA current injection but generated an exceedingly powerful burst at 75 pA (data not shown). Therefore, having access to the current-clamp recordings of the reconstructed TC cell constitutes a very strong constraint for the total amount of T-current in the cell. Correct burst behavior could be obtained using uniform high densities of T-current (~7 × 10⁵ cm/sec), but that model was inconsistent with dissociated cells. Assuming that the perisomatic density of T-current was identical to that estimated from dissociated cells (1.7 × 10⁵ cm/sec), a relatively narrow range of T-current density in distal dendrites gave rise to burst generation consistent with experimental data. This type of T-channel distribution was in agreement with all voltage-clamp and current-clamp data.

Assuming a ±3 mV error on all voltages (the voltage of the experimental data of Fig. 9A as well as the voltage of the kinetics of I_T) gave a possible range of dendritic densities of T-current between 7.6 × 10⁵ and 12.5 × 10⁵ cm/sec, which is ~4.5-7.6 times the density of the soma.

To compare the above dendritic T-current permeabilities with published values, they were converted into conductances by simulating the calcium current using the Nernst relation (Hille, 1992). The range of dendritic T-current conductance obtained was ~0.8-1.4 mS/cm² (8-14 pS/µm²). This estimated conductance range is slightly larger but close to the average T-current densities of 7-10 pS/µm² measured in the dendrites of hippocampal pyramidal cells (Magee and Johnston, 1995).

T-channels can be controlled more efficiently if they are dendritic

An important question is how does dendritic current location shape the burst of TC cells. To answer this question, the reconstructed TC cell was simulated using two different distributions of T-current with same total number of T-channels (Fig. 10, Somatic & dendritic, Somatic only). For increasing intensities of injected current, the cell successively generates passive responses, subthreshold LTS, and full-blown bursts with sodium spikes (Fig. 10A). The generation of these LTS responses shows differences between somatic and somatodendritic distributions of T-current, with LTS evokable by smaller current injections for somatic-only distributions (Fig. 10B). This property was already apparent from I-V curves, in which somatically localized T-channels led to higher peak T-current amplitudes compared with T-channels distributed in dendrites (Fig. 7D, triangles). Therefore, localizing T-channels in the dendrites decreases the excitability of the cell with respect to LTS generation.

View larger version (32K): [in this window] [in a new window]   Figure 10.   Consequence of dendritic T-current in shaping the burst response of thalamic relay cells. A, Three representative types of response to depolarizing current injection from rest: passive (P), subthreshold (S), and burst (B) responses. B, LTS peak amplitude represented as a function of the amplitude of injected current in the soma. For this simulation, fast Na+ and K+ currents underlying action potentials were not included, and the reconstructed TC cell had two different somatodendritic distributions of T-current: Somatic & dendritic (1.7 × 105 cm/sec perisomatic and 8.5 × 105 cm/sec dendritic) and Soma only (density of 56.53 × 105 cm/sec in soma with none in dendrites; adjusted such that the total number of T-channels was the same as for Somatic & Dendritic). The fact that these two curves do not overlap shows the effect of channel segregation on burst generation in normal conditions. C, LTS peak amplitudes in the presence of dendritic shunt conductances. With a dendritic shunt conductance of gL = 0.15 mS/cm2, the burst response becomes significantly different whether the T-current is located in the dendrites or exclusively in the soma.

An equally important question is how these properties can be modulated by other currents in the dendrites. In particular, the dendrites of TC cells are densely covered by synaptic terminals from various excitatory and inhibitory neurons. Under conditions of tonic activity that characterizes active states (Steriade et al., 1990), TC cells are therefore bombarded by mixed excitatory and inhibitory inputs, which should lead to significant dendritic shunt. The effect of dendritic shunt conductances on burst generation is depicted in Figure 10C. In this case, the differences between somatic only and somatic and dendritic T-channel localization are remarkably enhanced (Fig. 10C). In addition, the LTS response was less steep, leading to more "graded" bursting behavior in the presence of shunt conductances. More importantly, dendritic shunt shifted the LTS response curve more efficiently for dendritic T-channels (Fig. 10, compare Somatic & dendritic curves in B,C) than for somatic T-current (Fig. 10, compare Somatic only curves). These simulations therefore show that the same amount of T-channels can be controlled differently if they are exclusively somatic or distributed throughout the dendrites. Possible functional consequences of this property in the behavior of TC cells in vivo will be considered in Discussion.

Simplified models of TC cells

To provide a simplified representation of somatodendritic interactions during low-threshold spike generation in TC cells, we have designed a simplified model by collapsing the dendritic structure into a few compartments based on the conservation of axial resistance, a theme previously proposed by Bush and Sejnowski (1993). A modified version of this method was used here (see Materials and Methods). The reduction was based on a partition of the cell into three regions, as considered previously: (1) the soma, (2) proximal dendrites (corresponding to those of dissociated cells), and (3) the remaining (distal) dendrites. Based on this partition, the collapse algorithm was applied to generate a reduced model with three compartments, each corresponding to the aforementioned regions. The model obtained is shown in Figure 11A1.

View larger version (28K): [in this window] [in a new window]   Figure 11.   Simplified models of TC cells. A1, Three-compartment model obtained by collapsing the dendritic morphology of the intact cell (see Materials and Methods). A2, Adjustment of the dendritic correction of the model to obtain passive properties consistent with experimental recordings. A3, I-V curves in voltage clamp, comparing the intact-cell model (squares) with the simplified model with the same density of T-current (triangles; same densities as in Fig. 9C). A slightly increased dendritic density matched the I-V curve of the intact model (circles; dendritic density of 9.5 × 105 cm/sec). A4, Low-threshold bursts with the simplified model (9.5 × 105 cm/sec). B1, Single-compartment model of the TC cell. B2, Adjustment of the membrane area such that the model fits experimental passive responses. B3, I-V curves in voltage clamp, with intact-cell model (squares) and its best match with the single-compartment model (triangles; density of 6 × 105 cm/sec). The circles indicate the model needed to reproduce current-clamp behavior (density of 8 × 105 cm/sec). B4, Low-threshold bursts with the single-compartment model (density of 8 × 105 cm/sec).

The next step was to obtain passive properties consistent with experimental data. The simplified model was endowed with the same passive parameters as the detailed model, and a dendritic correction factor (C_d) was applied to the dendrites to compensate for their reduced membrane area (see Materials and Methods). The value of dendritic correction was adjusted by fitting the passive responses of the model to that obtained during voltage-clamp recordings (Fig. 11A2). With C_d = 7.95 (range, 7.92-7.97) the model fitted the data remarkably well (Fig. 11A2). This value is close to the reduction ratio of dendritic membrane, which was 8.02 for this model.

When T-channels were inserted using somatic and dendritic densities as described in previous sections, the simplified model generated voltage-clamp behavior very close to the detailed model, with very similar peak amplitudes (Fig. 11A3, compare triangles, squares). With a slightly increased density of T-current in dendrites, the simplified model could match closely the complete I-V curve of the detailed model (Fig. 11A3, compare circles, squares).

Using these T-current densities, the behavior was examined in current clamp. First, the somatodendritic density that matched closely the I-V curve generated low-threshold responses very similar to the data and the detailed model (compare Figs. 11A4, 9). Second, like the detailed model, the genesis of correct low-threshold bursts required increased densities of dendritic currents in the simplified model (Fig. 12A). This latter point suggests that high densities of dendritic calcium currents are needed to be consistent with all data, and that this conclusion is independent of the particular morphological details of the model.

View larger version (27K): [in this window] [in a new window]   Figure 12.   Burst responses in the three-compartment model of TC cells with dendritic T-current. A, Current-clamp simulations of LTS generation in the three-compartment TC cell model using two different amplitudes of injected depolarizing current (50 and 75 pA from rest; Fig. 9B,C). A1, No LTS could be generated with uniform T-current density based on dissociated cell recordings (1.7 × 105 cm/sec, indicated by gray shades in the scheme). A2, Successful LTS generation in the simplified model with high densities of T-current in dendrites (9.5 × 105 cm/sec, indicated by black shades in the scheme). B, LTS peak amplitude represented as a function of the amplitude of injected current in the soma (similar description as in Fig. 10). Somatodendritic T-current distributions were Somatic & dendritic (density of 1.7 × 105 cm/sec perisomatic and 9.5 × 105 cm/sec dendritic) and Somatic only (density of 56.36 × 105 cm/sec exclusively in the soma). Burst responses and the differences attributable to channel segregation in the cell were similar to those of the reconstructed TC cell model (Fig. 10B). C, LTS peak amplitudes in the presence of dendritic shunt conductances (gL = 0.15 mS/cm2). The enhanced differences between the two curves are comparable to those of the reconstructed TC cell model (Fig. 10C).

The effects of the electrical separation of currents in the cell were tested with the three-compartment model (Fig. 12B). As in the detailed model, localizing T-channels in the dendrites diminished the excitability of the cell for LTS generation. These differences are markedly enhanced in the presence of dendritic shunt conductances (Fig. 12C), similar to the detailed model (compare with Fig. 10B,C). This demonstrates that these types of somatodendritic interactions do not need the precise dendritic morphology to be simulated, but they critically need an increased density of T-current in dendrites.

Finally, a single-compartment model of the TC cell was generated for comparison. A first possibility was to remove the dendrites from the detailed model, but in this case, the isolated soma did not generate bursts of action potentials and had an incorrect input resistance. A second possibility was to increase the membrane area until the model matched the input resistance of the intact cell. In this case, with passive properties identical to the detailed model, the total membrane area was adjusted by fitting the one-compartment model until it matched the passive responses of the TC cells under voltage clamp (Fig. 11B2).

The density of T-current was calculated such that the total amount of T-channels was identical to the detailed model. In this case, the peak amplitude of the T-current was similar to the detailed model, but