Regulation of AMPA and NMDA receptor-mediated EPSPs in dendritic trees of thalamocortical cells

Abstract

Two main excitatory synapses are formed at the dendritic arbor of first-order nuclei thalamocortical (TC) neurons. Ascending sensory axons primarily establish contacts at large proximal dendrites, whereas descending corticothalamic fibers form synapses on thin distal dendrites. With the use of a multicomparment computational model based on fully reconstructed TC neurons from the ventroposterolateral nucleus of the cat, we compared local responses at the site of stimulation as well as somatic responses induced by both α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR)- and N-methyl-d-aspartate receptor (NMDAR)-mediated currents. We found that AMPAR-mediated responses, when synapses were located at proximal dendrites, induced a larger depolarization at the level of soma, whereas NMDAR-mediated responses were more efficient for synapses located at distal dendrites. The voltage transfer and transfer impedance were higher for NMDAR than for AMPAR activation at any location. For both types of synaptic current and for both input locations at the dendritic arbor, somatic responses were characterized by a low variability despite the large variability found in local responses in dendrites. The large neurons had overall smaller somatic responses than small neurons, but this relation was not found in local dendritic responses. We conclude that in TC cells, the dendritic location of small synaptic inputs does not play a major role in the amplitude of a somatic response, but the size of the neuron does. The variability of response amplitude between cells was much larger than the variability within cells. This suggests possible functional segregation of TC neurons of different size.

early investigations have shown that local synaptic responses dramatically depend on the amount of neurotransmitters released and on the location of the neurotransmitter-release sites at the dendritic arbor of the postsynaptic cell (Katz 1969; Komendantov and Ascoli 2009; Magee and Cook 2000; Redman 1990; Rinzel and Rall 1974). Despite some variability in the amplitude of somatic responses, this variability is rather small compared with the variability of local responses in dendrites, except for neurons lacking an electrotonically compact structure (i.e., apical dendrite of pyramidal cells) (Chitwood et al. 1999; Jaffe and Carnevale 1999).

Thalamocortical (TC) cells are characterized by a complex morphology, with dendrites organizing themselves in a way that each TC neuron occupies a rather spherical region in the dorsal thalamus (Crunelli et al. 1987; Friedlander et al. 1981; Turner et al. 1997; Zomorrodi et al. 2010). TC neurons of the ventroposterior complex of the thalamus receive excitatory inputs from somatosensory afferents at thick proximal dendrites (Liu et al. 1995; Williams et al. 1994), but excitatory synapses are also established at thin distal dendrites by corticothalamic (CT) fibers (Hoogland et al. 1991; Liu et al. 1995). At lemniscal (LM) synapses, the main contribution to the postsynaptic responses comes from α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) activation, whereas at CT synapses, N-methyl-d-aspartate receptor (NMDAR) activation contributes more than AMPARs to the postsynaptic responses (Golshani et al. 1998; Miyata and Imoto 2006). A higher contribution of NMDARs to the postsynaptic response is found at early stages of life for both LM and CT synapses (Arsenault and Zhang 2006; Golshani et al. 1998). Previous studies demonstrated that the activation of CT synapses on TC neurons elicits low-amplitude, long-lasting responses, but the activation of ascending sensory fibers induces large-amplitude, short-lasting responses (Timofeev et al. 1996; Turner and Salt 1998). This difference can be explained by a large number of release sites formed at each LM synaptic bouton and a single release site formed at each CT terminal on ventroposterolateral (VPL) nucleus neurons (Liu et al. 1995). The question that we asked was whether identical synaptic stimulation (AMPA or NMDA) applied to proximal vs. distal dendrites of TC neurons from the VPL nucleus would result in comparable amplitude of somatic responses.

To answer this question, we used a multicompartment computational model based on eight reconstructed TC neurons from the VPL nucleus of the cat's thalamus. Major morphological features of those cells have been analyzed and reported in a previous study (Zomorrodi et al. 2010), and the exact morphological data can be downloaded from our website (see endnote). Out of these eight neurons, seven were retrogradely stained by Fluoro-Ruby injection into the somatosensory cortex, and one neuron was stained intracellularly with neurobiotin. The objective was to investigate how the morphological features of VPL neurons affect signal propagation in these neurons.

We investigated the variability of responses depending on cell size, type of receptors (AMPA vs. NMDA), and specific location of synaptic inputs. We found that despite major differences in the local amplitude of excitatory postsynaptic potentials (EPSPs) elicited in various parts of the dendritic tree, their somatic amplitude was similar.

MATERIALS AND METHODS

Multicompartment model.

To compare the somatic responses with excitatory synapses innervating different dendrites or different branches of the same dendritic tree, we used a multicompartment model based on three-dimensional reconstructions of eight real TC neurons from the VPL nucleus of the cat that was processed with minimal shrinkage. The detailed morphological description of these cells was given previously (Zomorrodi et al. 2010). Simulations were carried out on the NEURON simulation environment (Hines and Carnevale 1997). The minimal number of compartments assigned to each cell was initially evaluated using the d_lambda rule (Hines and Carnevale 2001) but could be increased in some sections (see below). Somatic EPSPs were not altered by this local increase in the number of compartments.

The model was conductance based, and each compartment could be described by the Hodgkin-Huxley equations (Hodgkin and Huxley 1952). Passive properties were assumed constant over all compartments and cells. The membrane capacitance (C_m = 0.878 μF/cm²), the leak conductance (g_leak = 0.0379 mS/cm²), its associated reversal potential (E_leak = −69.85 mV), and the axial resistivity (R_a = 173 Ω·cm) were assigned according to Destexhe and colleagues (1998), who fitted the model outcome to experimental data using a simplex algorithm. These values are very similar to those obtained in other studies of TC neurons (Briska et al. 2003; Perreault and Raastad 2006). In all performed simulations, Na⁺ and K⁺ channels were included in the somatic compartment, with the kinetics of fast-action potentials taken from a model of hippocampal pyramidal cells (Traub and Miles 1991). The corresponding peak conductance and reversal potential for both Na⁺ and K⁺ currents were, respectively, set to ḡ_Na = 200 mS/cm², E_Na = 50 mV, ḡ_K = 200 mS/cm², and E_K = −100 mV.

Active conductance for the low-threshold Ca²⁺ current (I_T) was included in the model. This typical current of the TC neuron was modeled via Hodgkin-Huxley-like equations based on Huguenard and McCormick (1992). However, the kinetics of I_T were taken from a more recent study (Destexhe et al. 1998). T-channels mediating I_T were inserted in all sections. However, based on previous experimental and computational studies (Destexhe and Sejnowski 2002; Williams and Stuart 2000; Zhou et al. 1997; Zomorrodi et al. 2008), a higher density of T-channels was assigned to the proximal part of dendrites through the adjustment of the maximal permeability (P̄_Ca)

$${\overline{P}}_{\text{Ca}}=\{\begin{array}{lll}20.6\times {10}^{-5}\text{cm}/\text{s}\hfill & \hfill & \text{in}\text{soma}\hfill \\ 41.2\times {10}^{-5}\text{cm}/\text{s}\hfill & \text{if}\hfill & x<40\mu \text{m}\hfill \\ 5\times {10}^{-5}\text{cm}/\text{s}\hfill & \hfill & \text{otherwise},\hfill \end{array}$$ (1)

where x is the distance to the cell body. Ca²⁺ extrusion and buffering within a shell of 0.1 μm of thickness beneath the membrane were modeled with a first-order differential equation (McCormick and Huguenard 1992). The intracellular Ca²⁺ concentration at equilibrium was set to 240 nM, and for fast Ca²⁺ handling, a time constant τ_Ca = 5 ms was used (Destexhe et al. 1998).

Given that model, the resting membrane potential (V_m) was approximately −67 mV for all cells. In all simulations, a small hyperpolarizing current was injected at the cell body of the neuron to set the membrane potential to −70 mV prior to stimulation, unless otherwise indicated. All simulations were carried out assuming a temperature of 34°C. To control for a larger range of parameters, we also investigated effects of I_T at a membrane potential of −75 mV. In these experiments, the maximal permeability was set to 0, 1, or 1.5 × P̄_Ca.

AMPAR- and NMDAR-mediated synaptic currents.

For all reconstructed TC cells, we stimulated with an excitatory synaptic current I_syn all possible dendritic branches at distances of 60 μm (47–78 branches in different cells) and 150 μm (59–131 branches in different cells) to the cell body to compare somatic responses with proximal and distal inputs. To increase the spatial resolution at proposed locations of synapses, we divided stimulated dendritic sections to form compartments of ∼1 μm length. A realistic, fast excitatory and voltage-independent conductance (g_AMPA) and a slower voltage-dependent conductance (g_NMDA) were modeled to represent, respectively, AMPAR- and NMDAR-mediated currents. Standard equations (Baker et al. 2010; Jahr and Stevens 1990) described the synaptic conductance

$${\text{g}}_{\text{AMPA}}=a\left[\exp \left(-\frac{t}{{\tau }_2^{\text{AMPA}}}\right)-\exp \left(-\frac{t}{{\tau }_1^{\text{AMPA}}}\right)\right]$$ (2)

$${\text{g}}_{\text{NMDA}}=b\frac{\exp \left(-\frac{t}{{\tau }_2^{\text{NMDA}}}\right)-\exp \left(-\frac{t}{{\tau }_1^{\text{NMDA}}}\right)}{1+\frac{{\left[{\text{Mg}}^{2+}\right]}_{\text{ext}}}{3.57}\exp \left[-0.062V_{\text{m}}\left(t\right)\right]}$$ (3)

where t refers to the time after the onset of the excitatory postsynaptic current; τ₁^AMPA = 0.1 ms, τ₂^AMPA = 1.4 ms, τ₁^NMDA = 0.5 ms, and τ₂^NMDA = 13 ms are time constants; a = 2.5 nS and b = 6.1 nS are coefficients used to set the maximal conductance at the synapse; and [Mg²⁺]_ext = 1 mM is the extracellular concentration of Mg²⁺. The intensity of the synaptic current is given by Ohm's law: I_syn = g_syn(V_m − E_syn) where g_syn is the synaptic conductance. The reversal potential of the synaptic current E_syn was set to 0 mV for both AMPA and NMDA synapses. These parameters of synaptic currents yielded peak conductances of 1.9 nS for AMPAR- and 0.23 nS (at −70 mV) for NMDAR-mediated currents. The somatic responses obtained from those stimuli were of the order of 0.4 mV, which roughly corresponds to the amplitude of somatic EPSPs induced by the activation of a single vesicle release site (CT synapse) at TC neurons (Golshani et al. 2001). Unless indicated, the parameters for the synaptic currents were as indicated above. To explore a larger range of parameters, we also used peak AMPAR- or NMDAR-mediated conductances of 0.128 nS and 0.5 nS. Finally, in one experiment, we simultaneously activated both AMPARs and NMDARs. Here, the target amplitude of somatic EPSP was also 0.4 mV. To achieve that for proximal (LM) stimuli, we simply changed parameters a and b of Eqs. 2 and 3 to 1.9 nS and 2.6 nS, respectively. For distal (CT) stimuli, we set a = 0.46 nS and b = 5 nS. Based on Miyata and Imoto (2006), the ratios of the NMDAR-mediated component to the non-NMDAR-mediated component were in the mean 60% and 192% for LM and CT, respectively.

Mean dendritic diameter.

To estimate how the diameter of dendrites changes with the distance to soma, we measured the dendritic diameter D as a function of the distance x to the cell body for every possible path from the soma to a dendritic tip. Dendritic sections were compartmentalized in bins of 1 μm. The mean diameter at a point x was given by the following equation

$$\langle D\left(x\right)\rangle =\frac{1}{n\left(x\right)}{\displaystyle {\sum }_{k=1}^{N\left(x\right)}D\left(x\right)}$$ (4)

where N(x) is the number of paths reaching the point x. Therefore, the dendrites with multiple branches had a higher weight in the calculation as opposed to dendritic trees with a few branches.

The mean dendritic diameter is given for each distance x to the soma. Later in the study, we will refer to the average path diameter. We define this quantity as the averaged diameter of the path joining the soma and a site of stimulation.

Input impedance, voltage transfer, and transfer impedance.

To describe the excitability of cells or of dendritic sites, we calculated the input impedance R_in by applying in the model (passive membrane) a 20-pA hyperpolarizing current pulse of 200 ms duration and by measuring the amplitude of the voltage deflection induced. To quantify the degree of attenuation of EPSPs propagating from the site of stimulation to the soma, we calculated the voltage transfer V_T, defined as the ratio of the amplitude of the somatic response to the amplitude of the local response. Voltage transfer has values between zero and one. Low values indicate a strong attenuation of the EPSP, whereas values close to one indicate a small attenuation. To additionally quantify the efficiency of the transfer of synaptic signals, we calculated the transfer impedance Z_T (Jaffe and Carnevale 1999; Norenberg et al. 2010), defined as the ratio of the amplitude of the voltage somatic response to the amplitude of the synaptic current at the site of stimulation. Large values of Z_T indicate an efficient transfer of the synaptic signal, whereas small values indicate a weak signal transfer.

Analysis.

Analysis was done on the MATLAB environment (MathWorks, Natick, MA). The normality of the data obtained for each cell was estimated with a one-sample Kolmogorov-Smirnov test. To compare responses obtained for proximal vs. distal inputs for each cell (n ≥ 47), we used a two-sample t-test (two-tailed, unequal variances). To compare responses with the activation of different receptors (AMPA vs. NMDA), we used a paired t-test. Small samples (n = 8) were compared with a Mann-Whitney U-test. To estimate the dependence between two variables, Spearman's rank correlation coefficient was used when linear correlation could not be assumed [nonlinear dependence and/or small sample (n < 15)]. Otherwise, Pearson's correlation coefficient was computed. Correlation coefficients are denoted r. For plots that display fittings, the coefficient of determination R² that describes the goodness of fit is calculated when needed. To measure the dispersion of the data, the coefficient of variation was calculated as the SD of the sample divided by its mean. To obtain standardized samples (see Fig. 6), the data were processed by applying the z score function of MATLAB (statistics toolbox), where the mean was subtracted from each sample, and the result was divided by the SD of the sample. Statistical significance was assumed when P < 0.05. In all figures that follow, *P < 0.05; **P < 0.01; ***P < 0.0005; NS, nonsignificant.

Fig. 6.

Dependence of somatic responses on the average path diameter. A: amplitude of somatic responses to a proximal (60 μm; circles; n = 74) or a distal (150 μm; diamonds; n = 110) stimulus vs. the average path diameter measured from the site of stimulation to the soma in cell 1 for both AMPAR (A1)- and NMDAR (A2)-mediated currents. B, C, and D: same as A but for cells 2, 4, and 6, respectively.

RESULTS

Variability of synaptic signals in modeled TC neurons.

In the first experiment, we stimulated independently two dendritic trees from two different cells: one cell of median size [cell 2; see Fig. 2C in Zomorrodi et al. (2010)] and the cell with the largest total membrane area from our sample [cell 6; see Fig. 2C in Zomorrodi et al. (2010)]. In each cell, the stimuli were applied to one proximal branch (15 μm from the soma; Fig. 1, A and B) and to one distal branch (150 μm from the soma; Fig. 1, A and B). Responses of the neuron to a single excitatory stimulus were recorded at different locations on the path of propagation, as indicated in Fig. 1C.

Fig. 2.

Geometrical and electrotonic properties of reconstructed neurons. A: mean dendritic diameter vs. distance to the cell body in 4 thalamocortical (TC) cells. The investigated neurons revealed a similar profile in their dendritic diameters as a function of the distance to soma. The diameter decreased in a steep fashion with distance to soma at the perisomatic region, but this decrease in diameter was moderate at distal dendrites. The mean curve was properly fitted by a decaying exponential function. The vertical, dashed line defines the respective domains of the proximal (≤60 μm) and the distal (>60 μm) parts. B: relationship of neuronal input impedance to total membrane area in 8 reconstructed TC neurons. C: dependence of the local amplitude of responses in 1 neuron (cell 1) to the local input impedance (C1 for AMPARs; C2 for NMDARs). D: the rate of increase in local input impedance with the dendritic diameter depends on the location in dendrites. a exp[bx] + c, Equation used for the fitting; a, b, and c, parameters of fitting; x, independent variable; A, total membrane area; a x^−3/2, equation used for the fitting; τ_m, membrane time constant; L, electrotonic length; C_m, membrane capacitance; R_in, input impedance; R², coefficient of determination.

Fig. 1.

Variability of synaptic responses. A and B: reconstructed dendritic trees from cell 2 (A) and cell 6 (B). A synaptic current was applied at the proximal or the distal part of dendritic trees as indicated (pipette 1, 15 μm from soma; pipette 2, 150 μm from soma). C: attenuation of voltage signals in their propagation toward the soma for both α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR; C1)- and N-methyl-d-aspartate receptor (NMDAR; C2)-mediated currents. Voltage responses were induced by the synaptic current application at proximal (left columns) and distal (right columns) locations depicted in A and B. Voltage responses are shown at different locations: 15, 10, and 5 μm and at the soma for the proximal stimulus (1) and at 150, 100, and 50 μm and at the soma for the distal stimulus (2). Arrow in C1 points to the fast prepotential-like response. Color traces in C correspond to depicted dendrites in A and B.

For both cells, the activation of AMPARs at a thin distal branch (150 μm) induced a large and fast depolarization of the membrane at the site of stimulation (Fig. 1C1). The application of the same conductance at a thick proximal branch (15 μm) generated a much smaller EPSP (Fig. 1C1). The EPSPs evoked at the distal part of dendritic arbors were dramatically attenuated during their propagation toward the soma (Fig. 1C1), whereas the EPSPs generated near the soma were weakly attenuated (Fig. 1C1). As a result, the somatic responses to proximal stimuli had higher amplitude (Fig. 1C1) than responses to distal stimuli (Fig. 1C1).

The activation of NMDARs also induced EPSPs of larger amplitude at distal dendrites (150 μm; Fig. 1C2) than at proximal dendrites (15 μm, Fig. 1C2). However, the attenuation for NMDAR-mediated responses propagating toward the soma was smaller than for AMPAR-mediated responses. As a consequence, somatic responses to the activation of distally located NMDARs were higher in amplitude than somatic responses to the activation of the same receptors located proximally. Despite the small amplitude of NMDAR-mediated EPSPs evoked at proximal dendrites, their amplitude attenuated only to a minor extent in their propagation toward the soma.

As expected, responses evoked by stimulation with a NMDAR-mediated current (Fig. 1C2) had a slower time course compared with responses to stimulation with an AMPAR-mediated current. This slow time course is likely the explanation for a lower attenuation of NMDAR-mediated EPSPs (Magee 2000). Thus only a low-intensity, NMDAR-mediated synaptic current (see materials and methods) was sufficient to generate somatic responses of the same order of magnitude as the ones obtained for AMPARs (Fig. 1, compare C1 and C2).

The somatic responses evoked in the largest cell had a faster time course than those obtained in the smaller cell. The fast responses of the largest cell to the activation of proximal AMPARs (Fig. 1C) exhibited a shape similar to a fast prepotential (FPP), a voltage deflection observed at the soma and usually associated with attenuated dendritic spikes (Crochet et al. 2004; Maekawa and Purpura 1967; Spencer and Kandel 1961; Timofeev and Steriade 1997).

Geometrical and electrotonic properties of reconstructed neurons.

Primary dendrites of VPL neurons are thick and frequently end in tufts of multiple secondary branches, and these second-order dendritic collaterals are fine in caliber (Sawyer et al. 1994; Spreafico et al. 1983; Turner et al. 1997; Yamamoto et al. 1985, 1991; Yen et al. 1985; Zomorrodi et al. 2010). With the use of Eq. 4, we quantified the mean dendritic diameter as a function of the distance to the soma for four cells: the smallest (cell 4), the largest (cell 6), and the two cells of median size (cells 1 and 2; Fig. 2A). We found a steep initial drop in the mean diameter at the perisomatic region of dendrites (up to ≈60 μm) but a moderate decrease in diameter at remote dendritic branches. The overall change in the mean diameter of dendrites could be appropriately fitted by a decaying exponential function (Fig. 2A). We defined the initial 60 μm of dendrites as the proximal part of the dendritic arbor and the remaining part as the distal part.

Despite a similar profile of dendritic diameters, the cells had a different size and therefore, different input impedance that showed a highly significant (P < 0.0001) relationship (Fig. 2B). By fitting our data with an equation derived from Rall's work (1977; see Fig. 2B), we estimated the electrotonic length L of investigated TC neurons, which was L = 1.15, a value similar to that of the dorsal lateral geniculate nucleus X and Y neurons (Bloomfield et al. 1987). The small value of L suggests that distal dendritic inputs provide an important contribution to somatic responses. The estimated membrane time constant was τ_m = 20 ms.

We also calculated the local input impedance at dendritic sites stimulated with the synaptic currents. The amplitude of local responses to the activation of both AMPAR (Fig. 2C1)- and NMDAR (Fig. 2C2)-mediated conductances depended on the local input impedance for both proximal (60 μm) and distal (150 μm) inputs.

According to the cable theory, the input impedance depends on both the diameter of the innervated cable and on its extent in space (see appendix). Here, we show that indeed, the local input impedance was highly correlated with the local diameter of dendritic branches stimulated in TC neurons for both proximal and distal sites (r = −0.68, P = 6 × 10⁻¹² for proximal inputs; r = −0.60, P = 4 × 10⁻¹¹ for distal inputs; Fig. 2D). This relationship was well fitted by a power law (∝D^−3/2), such as found for cables (Fig. 2D; see also appendix). The number of dendritic tips and the dendritic path length in forward and backward directions also correlated with the local input impedance but to a lesser extent (not shown). Therefore, the local diameter is the main morphological parameter determining the input impedance at dendritic sites.

Dendritic diameters modulate local and propagating EPSPs.

We investigated the impact of both the local diameter and the average path diameter on local dendritic and somatic responses, respectively. The stimuli were applied to proximal (60 μm from soma) and distal (150 μm from soma) branches in four investigated cells. Because the dendritic diameter determines the local input impedance, and the local input impedance determines the amplitude of local response (Fig. 2, C and D), we found a clear relation between the local amplitude of responses and the local dendritic diameter (Fig. 3). The local amplitude of EPSPs was smaller at thick branches than at thin ones for both AMPARs and NMDARs (Fig. 3; r < −0.55; P < 1 × 10⁻⁴). The results obtained with the activation of distally located AMPARs could be fitted properly by the theoretical function obtained by Softky (1994) for fast synaptic currents (Fig. 3, A1, B1, C1, and D1; see appendix). In contrast, the activation of proximally located AMPARs generally evoked weaker local responses than predicted by the theoretical function (Fig. 3, A1, B1, C1, and D1), due to their proximity to the somatic expanse that reduces the local input impedance in the perisomatic region (Fig. 2D). Local responses obtained with the activation of NMDARs were also generally smaller for proximal inputs (Fig. 3, A2, B2, C2, and D2) than for distal inputs. The local amplitude of responses steeply decreased with an increase in the dendritic diameter. This relation could not be approximated by Softky's expression (1994) but remained highly significant in all cases (r < −0.55; P < 1 × 10⁻⁴). Due to the voltage dependence of NMDAR-mediated conductance, the intensity of the synaptic current also varied with the local diameter. For large diameter branches, local NMDAR-mediated EPSPs were very small in amplitude, because the weak depolarization at the point of stimulation was not efficient in removing the Mg²⁺ block. To control for a larger range of synaptic conductances, we also used peak AMPAR-mediated conductances of 0.128 nS, 0.5 nS, and 1.9 nS and peak NMDAR-mediated conductances of 0.128 nS, 0.23 nS, and 0.5 nS. The use of smaller or higher conductances did not alter the dependence of local responses on the dendritic diameter, but as expected, it changed the magnitude of responses (not shown).

Fig. 3.

Dependence of local responses on the local dendritic diameter. A: amplitude of local responses to a proximal (60 μm; circles; n = 74) or a distal (150 μm; diamonds; n = 110) stimulus vs. the diameter at the site of stimulation in cell 1 for both AMPAR (A1)- and NMDAR (A2)-mediated currents. Curves correspond to a theoretical function obtained by Softky (1994) that fits to distal AMPAR-mediated excitatory postsynaptic potentials (EPSPs) only (see appendix). B–D: same as A but for cell 2 (B; proximal, n = 70; distal, n = 120), cell 4 (C; proximal, n = 47; distal, n = 59), and cell 6 (D; proximal, n = 56; distal, n = 131).

Next, we estimated in detail the propagation of AMPAR- and NMDAR-induced EPSPs in a single dendritic branch (cell 1, 150 μm from the soma; Fig. 4, A and B). In control conditions, at the site of stimulation, the AMPAR-mediated EPSP was higher in amplitude than the NMDAR-mediated EPSP, but it was lower at the level of soma (Fig. 4B). The steeper decrease in the depolarization from the site of stimulation to the soma for the AMPAR-mediated EPSP reveals a stronger attenuation than for the NMDAR-mediated EPSP, as confirmed by voltage transfer values (Fig. 4B). The larger attenuation rate of EPSPs induced by AMPAR activation could be the result of higher local amplitude. Therefore, we reduced the synaptic conductance to obtain the same local amplitude as the one obtained for NMDARs (Fig. 4B). In this case too, the somatic response induced by AMPAR activation was lower than the NMDAR-mediated response, indicating a larger attenuation of AMPAR-mediated EPSPs than NMDAR-mediated EPSPs. NMDAR-mediated responses have a slower time course, and they are enhanced by membrane depolarization. To ensure that indeed, the time course of NMDAR-mediated EPSPs was responsible for its better transmission to the soma, we removed the voltage dependence of NMDARs by fixing V_m to −70 mV in Eq. 3. The NMDAR-mediated EPSP reached the soma with higher amplitude than the EPSP mediated by AMPARs, with matched amplitude at the site of stimulation, but lower than for control AMPARs and NMDARs. The voltage transfer associated with NMDARs with a fixed conductance remained higher than for AMPARs (control and reduced conductance; Fig. 4B). The voltage dependence of the NMDAR-mediated conductance was therefore not necessary to transmit efficiently the dendritic EPSPs to the soma. The calculation of voltage transfers (Fig. 4C) and transfer impedances (Fig. 4D) for all possible proximal and distal positions on cell 1 confirmed that NMDAR-mediated responses ensure a better transfer of synaptic signals than AMPAR-mediated responses. Note that the strongest attenuation occurs before distal EPSPs reach the proximal part of dendrites (Fig. 4B).

Fig. 4.

Attenuation of EPSPs, voltage transfer, and transfer impedance. A: dendritic tree of a reconstructed TC neuron indicating the position of a stimulating electrode (pipette; 150 μm from soma). B: peak amplitude of EPSP in a dendrite at different distances from soma. Black curves, AMPAR-mediated responses; gray curves, NMDAR-mediated responses. To fit the local amplitude of the NMDAR-mediated EPSP at the site of stimulation, the AMPAR-mediated conductance was reduced (dashed, black curve). To probe voltage dependency of NMDAR-mediate EPSPs, the Mg²⁺ block mechanism was inactivated (dashed, gray curve). Inset shows peak amplitude of responses at the perisomatic region. Voltage transfer values (V_T) are indicated for each case. C: mean voltage transfer values for cell 1; D: mean transfer impedance values for cell 1 (***P < 0.0005).

To probe attenuation rates of EPSPs propagating toward the soma, we systematically investigated the voltage transfer as a function of the average path diameter of dendrites for all dendritic branches at studied locations in four neurons (Fig. 5). We found that the voltage transfer was positively correlated (r ≥ 0.3947; P ≤ 0.002) with the average path diameter for both proximal and distal synapses and for both AMPARs and NMDARs, indicating that in a larger dendritic path, the EPSPs propagate with lower attenuation.

Fig. 5.

Voltage transfer values vs. the average path diameter for each dendritic branch at each investigated location [proximal (60 μm; circles) vs. distal (150 μm; diamonds) dendrites] for 4 studied neurons (A–D). AMPAR-mediated stimuli (left column); NMDAR-mediated stimuli (right column). Voltage transfer values increase with the thickness of the path and are larger for proximal stimuli than for distal stimuli.

Accordingly, following the activation of AMPARs, the somatic responses were generally higher in amplitude for dendrites with a thick dendritic path than for dendrites with a thin dendritic path (Fig. 6, A1, B1, C1, and D1). For the four cells investigated and for both proximal and distal AMPAR activation, the somatic amplitude positively correlated with the average path diameter (r > 0.45; P ≤ 3 × 10⁻⁴). In thin dendrites, the local responses were of high amplitude, but they attenuated dramatically in their propagation toward the soma; in thick dendrites, the local responses were small, but the attenuation rate was low, and overall, the somatic responses were higher in amplitude than for small dendritic-averaged path diameters. In contrast, the activation of NMDARs induced a larger depolarization at the cell body when the stimulus was applied to thin dendrites compared with the depolarization induced at thick dendrites (Fig. 6, A2, B2, C2, and D2). In all cases but one (proximal stimuli at cell 6), the somatic amplitude was negatively and significantly correlated with the average path diameter (r < 0.42; P ≤ 2 × 10⁻⁶). Due to the voltage dependence of NMDAR-mediated conductance and to high local input impedance (Fig. 2C2), the local responses induced by the activation of NMDARs on thin (mainly distal) dendrites were of higher amplitude (Fig. 3, A2, B2, C2, and D2). Owing to a much slower time course, the amplitude of NMDAR-induced propagating EPSPs was attenuated less by low-pass filtering properties of dendrites than AMPAR-mediated EPSPs and resulted in higher amplitude somatic responses when thin or distal dendrites were stimulated, despite low-voltage transfer values (Fig. 5, A2, B2, C2, and D2).

The use of peak AMPAR-mediated conductances of 0.5 nS yielded to similar patterns of the amplitude of somatic responses vs. dendritic diameter but of different magnitude (not shown). When the AMPA conductance was decreased to 0.128 nS, the somatic responses were at the noise level (0.03–0.0335 mV; not shown). The variation in peak NMDAR-mediated conductances (see materials and methods) did not alter the dependence of somatic amplitudes on the dendritic diameter, but it was scaled in relation to the stimulation strength (not shown).

In all eight investigated TC neurons, the mean local amplitude induced by the stimulation of distal dendrites was significantly higher than that produced by the stimulation of proximal dendrites, and it was true for both AMPAR- and NMDAR-mediated EPSPs (Fig. 7A). The absolute difference in the somatic amplitude of EPSPs induced by proximal vs. distal stimuli was smaller than for the local amplitude. However, the somatic amplitude was significantly higher when an AMPAR-mediated current was applied at proximal dendrites (Fig. 7B1). This relation was opposite for NMDAR-dependent responses. The activation of NMDAR-dependent currents in distal dendrites resulted in significantly larger somatic responses compared with the activation of the same receptors located on proximal dendrites (Fig. 7B2).

Fig. 7.

Amplitude and time-to-peak of synaptic responses elicited by proximal and distal stimuli. A: amplitude of AMPAR (A1)- and NMDAR (A2)-mediated local responses for proximal (60 μm; white bars) and distal (150 μm; gray bars) stimuli. B: same as A but for somatic responses. C: time-to-peak of AMPAR (C1)- and NMDAR (D2)-mediated somatic responses for proximal (60 μm; white bars) and distal (150 μm; gray bars) stimuli (***P < 0.0005; NS, nonsignificant).

In the same data set, we investigated the time-to-peak of somatic responses evoked by an AMPAR-mediated current. It was significantly longer for distal inputs than for proximal inputs (Fig. 7C1). However, when an NMDAR-mediated current was applied, the time-to-peak was smaller for distal inputs than for proximal inputs in most cells (Fig. 7C2).

Dendritic arbor complexity vs. EPSP amplitude in TC neurons.

Above, we demonstrated that despite the fact that we applied stimuli to fixed distances from the soma (60 μm or 150 μm), both local and somatic responses were of variable amplitude due to different diameters of dendrites. At this point, we hypothesized that the complexity of dendritic trees may affect the amplitude of responses. We observed that bushy dendritic subtrees tend to emerge from large dendritic sections, whereas only a few branches are typically formed at thin dendrites. The analysis of the dendritic complexity of cell 1 (Fig. 8A) shows that when the first order dendritic sections (primary branches) were relatively thin (up to 1.6 μm), the total number of subsections formed by this primary branch was smaller or equal to eight (Fig. 8A1). In contrast, when the primary branches were thicker, the number of formed subsections was higher (Fig. 8A1). Such a significant correlation was observed for the shown neuron (cell 1) and for the whole analyzed population of eight neurons. That stands in agreement with results published for X and Y cells from the dorsal lateral geniculate nucleus (Bloomfield et al. 1987). The same principle remained true for the second, third, and fourth orders of dendritic branches, as demonstrated by a high and significant coefficient of correlation (Fig. 8, A2–A4).

Fig. 8.

Correlation between dendritic diameter and amplitude of voltage responses with the complexity of dendritic arbors. A: number of dendritic subsections emerging from a given dendritic section vs. the mean diameter of that section. Data are shown and linearly fitted (dots and black lines, respectively) for the 1st 4 orders of branching of cell 1 (A1–A4, respectively). The mean fit obtained for all investigated cells is also shown (dashed lines). B: z-scored (see materials and methods) mean local amplitude of responses to proximal (r_prox; 60 μm; circles) and to distal (r_dist; 150 μm; diamonds) stimuli obtained for each tree of all investigated cells vs. the total number of dendritic sections in the stimulated dendritic tree. Data are shown for both AMPAR (B1) and NMDAR (B2). Mean amplitudes were z-scored to pool the results obtained in all cells together. C: same as B but for the somatic amplitudes (*P < 0.05; **P < 0.01; ***P < 0.0005; NS, nonsignificant).

Earlier, we showed that dendritic diameters modulate local and somatic EPSPs, and here, we show that dendritic diameters vary with the complexity of dendritic trees. Therefore, we analyzed the relation between the amplitude of local (Fig. 8, B1 and B2) and somatic (Fig. 8, C1 and C2) responses and the complexity of dendritic trees. We found that the local responses evoked both at proximal and distal locations and induced by the activation of both AMPARs and NMDARs were negatively correlated with the complexity of dendritic trees (Fig. 8, B1 and B2). The picture was different for AMPAR-mediated somatic responses. The activation of proximally located AMPARs induced responses that fail to show a significant correlation with the total number of sections of the stimulated tree. However, the smallest somatic responses were observed when simple dendritic trees (small number of sections) were stimulated (Fig. 8C1). On the other hand, the activation of the same receptors at distal dendritic branches induced somatic responses that were significantly correlated with the total number of sections. Complex dendritic trees gave higher somatic responses than simple dendritic trees (Fig. 8C1). When NMDARs were activated, the stimuli applied to simple dendritic trees induced larger somatic responses than the stimuli applied to complex dendritic trees, independently of the distance to soma (proximal or distal input; Fig. 8C2).

Between-cell/within-cell variability of synaptic responses.

Results shown in Figs. 3, 6, and 7 suggest that the mean amplitudes of responses differ across neurons. Because the metric properties of analyzed TC neurons were different (Zomorrodi et al. 2010), we investigated the relation between the amplitude of synaptic responses and the size of stimulated cells, as quantified by the total membrane area (Fig. 9, A and B). We found that in general, the amplitude of somatic voltage responses was higher for cells with a small total membrane area than for cells with a larger membrane area. Cells with a similar membrane area had similar amplitudes of somatic responses (Fig. 9B). The amplitude of somatic responses showed a clear, monotonic relation to the total membrane area in all tested conditions (proximal and distal inputs, AMPARs and NMDARs; Fig. 9B; P < 0.0005). However, this dependence of the amplitude of voltage responses on the size of the cell was less pronounced for local responses (Fig. 9A). Generally, the relation was not monotonic, and for responses induced by the activation of NMDARs at proximal dendrites, the relation was not significant.

Fig. 9.

Dependence of the amplitude of voltage responses to the cell size. A: amplitude of local responses to the activation of proximal (60 μm; open symbols) or distal (150 μm; filled symbols) AMPAR (A1) and NMDAR (A2) vs. the total surface area of stimulated cells. B: same as A but for somatic responses. C: mean coefficient of variation (n = 8) of the amplitude of both local (gray bars) and somatic (white bars) responses to the activation of AMPARs (C1) and NMDARs (C2). D: coefficient of variation of somatic responses in cell 1 was only slightly affected by the presence of the low-threshold Ca²⁺ current (I_T) in TC neurons. In each column (proximal or distal input), the left symbols stand for passive dendrites, and right symbols stand for dendrites containing I_T (*P < 0.05; ***P < 0.0005; NS, nonsignificant).

The results shown in the Fig. 9, A and B, indicate that the variability in the amplitude of local responses was much higher than the variability in the amplitude of somatic responses. We computed the coefficient of variation of all responses (proximal and distal inputs, AMPARs and NMDARs, all cells). We found that indeed, the variability of local responses was three to 10 times higher than the variability of somatic responses (Fig. 9C), suggesting that the morphological properties of dendritic trees are tuned to normalize the impact on the soma of synaptic inputs coming to different dendrites.

In one middle-size neuron (cell 1), we investigated whether I_T was responsible for the normalization of somatic responses. Removal of I_T slightly reduced the mean amplitude of local and somatic responses for all tested stimuli (proximal and distal stimuli) by <0.02 mV when AMPARs were activated. When NMDARs were activated, the mean amplitude of somatic responses was decreased by <0.1 mV, but the mean amplitude of local responses in distal dendrites was decreased by 0.21 mV (2% of amplitude). We used the coefficient of variation to describe the variability of responses. For all AMPAR-mediated EPSPs (local and somatic EPSPs, proximal and distal stimuli), the coefficient of variation remained rather stable (Fig. 9D1). The highest reduction in the coefficient of variation (2%) was observed for local responses to the activation of proximal NMDARs (Fig. 9D2). We also tested the effects of I_T on local and somatic responses when the neuron was hyperpolarized to −75 mV and for various values of maximal Ca²⁺ permeability (0, 1, and 1.5 × P̄_Ca). Changes in the Ca²⁺ permeability in this range of parameters did not influence the amplitude of local responses and the dependence of somatic responses on the dendritic diameter. However, the somatic responses without Ca²⁺ permeability (0 × P̄_Ca) were, on average, 11% (AMPARs) or 35% (NMDARs) smaller than the responses obtained with a peak Ca²⁺ permeability of 1.5 × P̄_Ca (not shown). These results indicate that I_T does play a role in controlling the amplitude of somatic responses but does not play a major role in the normalization of somatic responses.

Validation of the computational model.

The results shown in the Fig. 1C1 indicate that the time course of voltage responses may differ for identical stimuli applied to different locations on dendrites or to distinct cells. For example, the response to the application of an AMPAR-mediated current at proximal dendrites of cell 6 often showed a sharp FPP-like shape (Fig. 1C1). This type of response was not observed when distal synapses were activated or when other neurons from our sample were stimulated. As mentioned in introduction, one of the neurons investigated in this study (cell 6) was recorded intracellularly. To validate our model, we compared the somatic responses of that modeled neuron with the activation of AMPARs at proximal dendrites with electrophysiological responses of the same neuron recorded in vivo to medial lemniscus stimulation. The model's response was much smaller in amplitude than the responses to medial lemniscus stimulation (Fig. 10, A–C). It is known that LM synaptic terminals establish several release sites on proximal dendrites and that a single LM axon forms several synaptic knobs in proximity (Jones 2007). Therefore, we simulated the activation of AMPARs on three different branches to mimic the synaptic contacts formed by three LM terminals, and at each terminal, we modeled the release of eight vesicles through eight release sites. The membrane potential prior to stimulation of both the modeled neurons and the neuron recorded in vivo was −65 mV. In these conditions, the response generated by the model was identical to the response recorded in vivo (Fig. 10, B and D).

Fig. 10.

Validation of the computational results. A: morphology of reconstructed cell 6. The same neuron was used to investigate effects of T-channel distribution in TC neurons (Zomorrodi et al. 2008). B: intracellular responses of that cell to the stimulation of the medial lemniscus in an in vivo experiment. C: response of a modeled neuron to the activation of AMPARs at an individual site located on a proximal dendrite. D: response of a modeled neuron to the activation of AMPAR at 24 sites located on a proximal dendrite. Note the similarity between the response of a modeled neuron to the stimulation of 24 release sites and the response recorded in vivo to the stimulation of the medial lemniscus. E: active conductances do not affect peak amplitude of EPSP and its early part of the decaying phase that gives rise to the fast prepotential (FPP)-like shape. F: cutting dendritic branches to the indicated maximal path lengths reduced the total membrane area (A_m) and progressively abolished the FPP-like shape.

To investigate the nature of FPPs observed in the largest cell from our sample (cell 6; Fig. 10A), we first removed the channels underlying the different intrinsic currents that were present in the model. Blocking Na⁺ and K⁺ channels inserted in the soma had no effect on the shape of EPSPs (Fig. 10E). Removing the T-channels from our model affected the latter part of the repolarizing phase of EPSPs (Fig. 10E). However, the absence of I_T had no effect on the initial part of the repolarizing phase of EPSPs, suggesting that I_T does not mediate the FPPs. Finally, simulations made on a purely passive cell showed the same EPSP shape as observed without I_T but with Na⁺ and K⁺ channels present in the model (Fig. 10E).

Because the FPPs were only observed in the largest cell of our sample, we hypothesized that the size of the cell modulates the time course of EPSPs and is responsible for the generation of FPPs by providing current sinks toward extensive dendrites. To investigate this issue, we modified in a progressive fashion the total surface area of cell 6 by cutting dendrites to a maximal path length of 250, 200, and 150 μm. As the majority of branching points in this cell was located within the first 120 μm from soma (Zomorrodi et al. 2010), the topological structure of the neuron was preserved. A slight decrease in the total surface area (maximal path length of 250 μm) did not affect the shape of EPSPs (Fig. 10F). Any further reduction of the total surface area progressively removed the FPPs and smoothened the peak of EPSPs (Fig. 10F). These results indicate that the large dendritic expense was sufficient to generate somatic FPPs.

Finally, we investigated the effects of a simultaneous activation of AMPAR and NMDAR, as found in LM and CT synapses. For the LM synapse, the response to the coactivation of AMPAR and NMDAR was indistinguishable from the arithmetic sum of their individual responses (Fig. 11A). For the CT synapse, the coactivation of AMPAR and NMDAR induced a response that was slightly larger than the arithmetic sum of individual responses (Fig. 11A). To examine the role of the NMDAR-mediated component in the transfer of EPSPs from dendrites to soma, we performed simulations on cell 1 for both LM (all possible locations at 60 μm from soma) and CT (all possible locations at 150 μm from soma) synaptic currents and calculated the voltage transfer and the transfer impedance. For both LM and CT synaptic currents, the voltage transfer and the transfer impedance were significantly reduced when the NMDAR-mediated component was blocked (Fig. 11B). This reduction was much larger for CT synapses than for LM synapses [62% (voltage transfer) and 72% (transfer impedance) reductions for CT synapses compared with 18% (voltage transfer) and 20% (transfer impedance) reductions for LM synapses]. These results show that the use of synaptic stimuli with a previously estimated ratio of NMDAR-mediated currents to AMPAR-mediated currents, as found at LM and CT synapses (Miyata and Imoto 2006), was sufficient to enhance the transfer of synaptic signals.

Fig. 11.

Effects of coactivation of AMPAR and NMDAR in lemniscal (LM) and corticothalamic (CT) synapses. A: amplitude of excitatory postsynaptic currents and EPSPs induced by activation of AMPAR, NMDAR, their arithmetic sum, and their coactivation in LM and CT synapses. Voltage transfer (B) and transfer impedance (C) induced by activation of AMPARs and coactivation of AMPAR and NMDAR at LM and CT synapses (***P < 0.0005).

DISCUSSION

In this modeling study conducted on morphologically reconstructed TC neurons, we show that 1) the activation of either AMPARs or NMDARs induced large, depolarizing responses in distal dendrites that were reduced dramatically in amplitude at the level of soma; 2) despite the large variability of responses in dendrites, which depends on the dendritic diameter and as follows on the complexity of the dendritic tree, their variability at the level of soma was small; 3) in contrast, the overall cell size played a major role in the amplitude of somatic EPSPs—the smallest neurons generated large EPSPs, and the largest neurons generated small EPSPs; and 4) the activation of AMPARs at proximal dendrites had a slightly larger but highly significant impact on the soma than the activation of those receptors at distal dendrites, whereas the somatic impact of the activation of NMDARs was significantly larger when these receptors were located on distal dendrites.

Amplitude of local responses in dendrites.

The stimulation of dendrites with excitatory conductances of 1.9 nS (for AMPARs) and 0.23 nS (for NMDARs) evoked somatic postsynaptic voltage responses similar to the one expected from the release of a single vesicle at the CT synapse (Golshani et al. 2001), but it induced dendritic responses spanning from several up to 50 mV. The largest responses were elicited at thin dendrites, and the smallest responses were found at thick (usually more proximal) dendrites. This result was expected from Ohm's law, and it was demonstrated previously for other types of neurons (Komendantov and Ascoli 2009; Magee and Cook 2000; Rinzel and Rall 1974). However, there are possibly some details specific to TC neurons. We found that only the relation between the local amplitude of distal AMPAR-mediated EPSPs and the diameter follows the mathematical expression obtained by Softky (1994) for fast synaptic currents. The amplitude of AMPAR-mediated EPSPs at proximal dendrites was smaller than what was predicted from that expression. It likely occurred because the proximity to the large somatic compartment reduced the impedance at the perisomatic region (Fig. 2D).

Regulation of somatic responses.

There are three important aspects to mention. For a given neuron, we found that despite the high variability in the amplitude of local responses in dendrites stimulated at the same distance from the soma, the amplitude of somatic responses for the same neuron was much less variable (Fig. 9C). These results are consistent with other studies of fast synaptic events in TC neurons (Briska et al. 2003; Perreault and Raastad 2006), but we demonstrated that this normalization also stands for NMDAR-mediated EPSPs. A similar phenomenon of normalization was found in other neurons that lack extended apical dendrites (Chitwood et al. 1999; Jaffe and Carnevale 1999; Schmidt-Hieber et al. 2007). Second, we found that stimulation of proximal vs. distal dendrites of the same neuron induced somatic responses comparable in amplitude (Figs. 6 and 7B). Small-amplitude local responses elicited at proximal dendrites attenuated to a minor extent in their propagation to soma, whereas large-amplitude responses elicited at distal dendrites attenuated to a major extent, mainly before reaching the proximal part of dendrites. This is consistent with the pronounced tapering of proximal dendrites and with higher geometrical ratios (see appendix) at the perisomatic region of VPL neurons (Zomorrodi et al. 2010). Such attenuation ensures that large dendritic distal EPSPs do not interfere dramatically with small dendritic proximal EPSPs. The mechanisms described previously for the so-called dendritic democracy were limited to amplification of distal inputs by a dendritic intrinsic current, scaling of synaptic strength, and increased sensitivity of postsynaptic sites (Häusser 2001). Our current study on TC neurons combined with previous computational investigations (Chitwood et al. 1999; Jaffe and Carnevale 1999) demonstrates that morphological properties of neurons by themselves can ensure the regulation of dendritic signals evoked at the different parts of dendritic trees by a progressive increase of input impedance with distance to soma. Therefore, our model predicts that in any electrotonically compact neuron, the somatic responses to a small synaptic current will depend, to a minor extent, on the location where this current is applied. This mechanism might ensure the linear integration of inputs to TC neurons at the level of soma. Third, we found that due to input impedance differences, a synaptic input to small neurons induced larger responses at the soma than the same input to large neurons. We found this variability across cells to be more pronounced than the variability within each cell. This implies a functional segregation of TC neurons. Large neurons possess more membrane surface and are likely innervated by more synapses, as in the case of cortical pyramidal neurons (DeFelipe and Farinas 1992). They will respond (generate spikes) to multiple inputs compared with small neurons, in which a few simultaneously activated synapses will elicit an action potential. We found that the clear monotonic relation of somatic responses to the cell size could not be validated for dendritic sites. This suggests that dendritic branches are rather independent processing units and constitute a first stage of integration, as supported by previous studies (Branco et al. 2010; Losonczy and Magee 2006; Poirazi et al. 2003; Williams 2004).

Difference between AMPAR- and NMDAR-mediated responses.

We found that despite a dendritic normalization of EPSPs, the activation of AMPARs had a stronger impact on the soma when the receptors were found at proximal dendrites rather than at distal dendrites (Fig. 5B1). In contrast, the activation of NMDARs had a stronger impact on soma when distal dendrites were stimulated (Fig. 5B2). There are at least two factors that explain this difference. It is well known that NMDARs are voltage dependent (Mayer et al. 1984; Nowak et al. 1984). Then, due to a high-input resistance at distal dendrites, a relatively small current will depolarize them to the voltages at which NMDAR-mediated conductances progressively reinforce the voltage response. The second aspect is a lower attenuation rate for propagating NMDAR-mediated EPSPs than for AMPAR-mediated responses. The reduced attenuation rate depends on the slow time course of NMDAR-mediated EPSPs. Our model predicts that large somatic effects induced by the activation of NMDARs at distal (CT) synapses (Golshani et al. 1998) could be mediated by a relatively small number of NMDARs. In contrast, the effects of NMDAR activation would be smaller if they would be localized on proximal dendrites. This might have an important role for TC neuron physiology, because NMDARs are present in higher proportions at distal CT synapses than at proximal LM synapses. A similar distribution of NMDARs with distance to soma has also been found for pyramidal cells (Branco and Häusser 2011; Otmakhova et al. 2002). Our results suggest that coactivation of AMPAR and NMDAR on distal dendrites ensures a reliable transfer of CT excitation to the soma of VPL TC neurons.

One of the objectives of our study was to investigate why experimentally recorded CT EPSPs had a longer time course than LM EPSP responses (see introduction). Here, we show that the activation of AMPARs on distal dendrites induced slower responses at soma compared with their activation at proximal dendrites (Fig. 7C1). In the majority of investigated neurons, the activation of NMDARs on distal dendrites induced faster somatic responses compared with proximal activation of the same receptors (Fig. 7C2). These results predict that distally located synapses with AMPARs could be a factor of the slower time course of somatic responses induced by the stimulation of CT fibers. However, we found in somatic recordings that the time-to-peak of NMDAR-mediated EPSPs was approximately four times slower than for AMPAR-mediated EPSPs. Our data suggest that the activation of NMDAR-dependent currents in distal dendrites could be primarily responsible for the longer time course of somatic EPSPs induced by the activation of CT synapses.

Generation of FPPs in TC neurons.

Multiple studies reported the presence of FPPs in TC (Deschênes et al. 1984; Maekawa and Purpura 1967; Timofeev and Steriade 1997), hippocampal (Spencer and Kandel 1961), and neocortical (Crochet et al. 2004) neurons. FPPs are characterized by fast-rising and fast-decaying initial components of the depolarizing response. Because of their voltage dependence in pyramidal neurons (Crochet et al. 2004; Spencer and Kandel 1961), it was proposed that FPPs are the result of the activation of dendritic-active conductances (dendritic spikes). In TC neurons, FPPs were recorded in a large range of voltages (Timofeev and Steriade 1997). Here, we show that without the implication of any active conductance, the shapes that resemble FPPs could be recorded in large neurons when proximal AMPARs were activated (Figs. 1C1 and 10). We did not observe this type of response in either smaller neurons or when distal synapses or NMDARs were activated. Fast-rising and decaying phases of EPSPs are explained purely by the morphological properties of dendrites; larger cells promote faster voltage responses due to the current outflow in other parts of the neuron.

Limitations and validation of our study.

Here, we did not consider multiple active conductances that are present in TC neurons. They can have a significant impact on the expression of both local and somatic responses. The major difficulty of implementing active conductances is that for many of them, the density of their channel distribution on different neuronal compartments is unknown. We have shown recently that a change in the distribution of T-channels can lower the threshold of the low-threshold spike generation by up to 64% (Zomorrodi et al. 2008). The addition of other conductances to dendritic locations might affect neuronal output, as was demonstrated for pyramidal neurons (Cook et al. 2007; Hu et al. 2009; Ulrich 2002). However, the low-threshold spike response appears to be identical in TC neurons, with or without H-current, when the stimuli were applied at similar levels of the membrane potential (Meuth et al. 2006). This is also true for pyramidal neurons in which when electrotonically more compact basal dendrites were investigated, the H-current blockage affected only slightly the attenuation of synaptic responses (Golding et al. 2005). Another limitation is that we investigated the effects of a very small (presumably, single vesicle-dependent) synaptic conductance. However, it is known that LM synapses in VPL TC neurons contain multiple release sites (Liu et al. 1995). The activation of multiple release sites in dendrites may lead to nonlinear summation of EPSPs, which would affect the neuronal output.

The choice of parameters describing passive cell properties (C_m, R_a, and g_leak) could influence the obtained results. We did not investigate the dependence of EPSPs on C_m. It has been shown that C_m is rather constant across cell types and does not depend on proteins embedded in the membrane (Gentet et al. 2000). We tested effects of modulation of R_a and g_leak on neuronal responsiveness. An increase or a decrease of R_a by 25% affected local but not somatic responses. An increase or a decrease of g_leak by 25% slightly affected the maximal amplitude of somatic but not local responses. This was true for both AMPAR- and NMDAR-mediated responses (not shown). Our main conclusions remain unchanged: AMPARs were more efficient in depolarizing the soma when they were located at proximal dendrites, whereas the opposite was true for NMDARs, and somatic responses remained relatively constant in amplitude.

Despite the limitations described above, we believe that our modeling study provides reliable physiological information, because the activation of several synapses on proximal dendrites in the model perfectly reproduced the shape of the EPSP induced by the medial lemniscus stimulation as recorded in vivo (Fig. 10, B and D).

ENDNOTE

At the request of the authors, readers are herein alerted to the fact that additional materials related to this manuscript may be found at the institutional website of one of the authors, which at the time of publication, they indicate is: [http://www.crulrg.ulaval.ca/pages_perso_chercheurs/timofeev_i/shared.html]. These materials are not a part of this manuscript and have not undergone peer review by the American Physiological Society (APS). APS and the journal editors take no responsibility for these materials, for the website address, or for any links to or from it.

GRANTS

Support for this study was provided by National Science and Engineering Research Council of Canada (Grant 298475), Canadian Institutes of Health Research (MOP-37862, MOP-67175), and National Institute of Neurological Disorders and Stroke (1R01NS060870). I. Timofeev is a Fonds de la Recherche en Santé du Québec Research Scholar.

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

Author contributions: F.L., H.K., and I.T. conception and design of research; F.L. and I.T. performed experiments; F.L. and I.T. analyzed data; F.L. and I.T. interpreted results of experiments; F.L. and I.T. prepared figures; F.L. drafted manuscript; F.L. and I.T. edited and revised manuscript; F.L. and I.T. approved final version of manuscript.

APPENDIX

Dendritic morphology determines the attenuation of synaptic signals.

In their propagation toward the soma, EPSPs are subject to attenuation, which is mainly governed by two physical processes. First, the thickness of the path determines axial and membrane resistances and therefore, the electrotonic attenuation in dendritic cables defining that path. In uniform, semi-infinite cables, this is described properly by the length constant, generally denoted λ (Rall 1959)

$$\lambda ={\left[\frac{D}{4}\frac{R_{\text{m}}}{R_{\text{a}}}\right]}^{1/2}.$$

D, R_m, and R_a are, respectively, the diameter of the cable (in units of length), the passive membrane resistance (in units of resistance × units of surface), and the axial resistivity (in units of resistance × units of length). A steady-state voltage deflection, initiated by constant current injection at the extremity of a semi-infinite cable, will be attenuated to 1/e ≈ 37% of its amplitude at a distance λ from the extremity. The thinner the path is, the smaller the λ and the stronger the electrotonic voltage attenuation are.

Second, the particular geometrical and topological features of dendritic trees impose specific input impedances at branching points. For branches of several λ in length connected together, the behavior of signals approaching the branching point can be described properly by Rall's geometrical ratio (Goldstein and Rall 1974)

$$GR=\frac{{\displaystyle {\sum }_j{D}_j^{3/2}}}{D_{\text{p}}}.$$

where D_p is the diameter of the section along which the signal propagates to the branching point, and D_j is the diameter of each section j emerging from that branching point. This relation also stands when only two segments of different diameters are connected together. For a thin segment receiving a synaptic input and connecting to a much thicker one, which is generally the case in forward propagation of dendritic signals toward the soma, there is low input impedance at the branching point, causing the voltage transient to attenuate when spreading from the thin segment to the thick one, despite a high current flow toward the thick segment. Therefore, the EPSPs evoked at dendrites are largely attenuated during their propagation toward the cell body. The relatively thin dendritic trunks connecting the large somatic expanse can account for a considerable amount of that attenuation.

Local responses depend on the dendritic diameter.

For a semi-infinite cable, the input impedance at the origin was given by Rall (1959, 1977)

$$R_{\infty }={\left(R_{\text{m}}{R}_{\text{a}}\right)}^{1/2}\frac{2}{\pi D^{3/2}}$$

When the membrane resistance and the axial resistivity remain fixed all along the cable, the input impedance depends only on the diameter of the cable. For a finite cable with a sealed end at a distance L (normalized to λ) from the origin, the input impedance at the origin is given by

$$R_{\text{in}}=R_{\infty }\text{coth}L.$$

If the end of the cable at a distance L from the origin is rather an open end, R_in is described as

$$R_{\text{in}}=R_{\infty }\text{tanh}L.$$

Those equations reveal that the input impedance is a function of both the thickness of the cable and its extent in space.

Based on the cable theory, Softky (1994) previously obtained an expression that allows the estimation of the amplitude V_peak (voltage peak value) of an EPSP evoked by a fast current input

$$V_{\text{peak}}=1.5\frac{R_{\text{a}}^{1/2}{I}_{\text{peak}}}{{\left(\pi D\right)}^{3/2}{C}_{\text{m}}^{1/2}}\sqrt{t_{\text{peak}}}$$

where I_peak is the peak value of the current applied, and t_peak is the time taken by the current to reach this peak, starting from its onset. C_m is the membrane capacitance in units of capacitance/units of area. This expression predicts that the amplitude of an EPSP increases considerably as the diameter of the targeted branch decreases. Note that here, V_peak does not depend on R_m. This equation is only an approximation, because it does not take into account the reversal potential of the excitatory synaptic current, which is ∼0 mV for glutamatergic receptors, and may not be valid for slower synaptic currents.