1 INTRODUCTION

Neurons within the nuclei of the thalamus present regional specializations overlaid onto a functional architecture of shared connectivity and cellular intrinsic properties (Bickford, 2015; Guillery & Sherman, 2002; Halassa & Acsády, 2016; Halassa & Sherman, 2019; Jones, 1998; Phillips et al., 2019). One of the shared properties of thalamic neurons is that they fire in two fundamentally different modes, tonic mode when they are depolarized, and burst mode, when hyperpolarized (Gutierrez et al., 2001; Huguenard, 1996; Jahnsen & Llinás, 1984a, 1984b; Perez-Reyes, 2003). Bursts across the thalamus are considered fairly stereotyped signals that provide enhanced detectability of sensory stimuli during wakefulness and contribute to the generation of rhythms during sleep (Crunelli et al., 2018; Guido et al., 1992; Guido & Weyand, 1995; Llinás & Steriade, 2006; Nicolelis, 2005; Reinagel et al., 1999; X. Wang et al., 2007; Whitmire et al., 2016). However, it is unclear whether burst properties vary in different thalamic regions according to their connectivity with cortex, to the sensory modality they process or to both.

Burst firing requires a relatively prolonged hyperpolarization of the cell to deinactivate low-threshold, T-type, calcium channels, which can then be activated through depolarization to produce a rapid succession of sodium-potassium action potentials (Jahnsen & Llinás, 1984a, 1984b; Suzuki & Rogawski, 1989). The same time course that deinactivates the T-channels helps replenish neurotransmitter in the presynaptic terminals of thalamocortical driver synapses, which contributes to increase the effectiveness of burst spikes, compared to tonic firing, at activating postsynaptic cortical cells (Gil et al., 1997; Hu & Agmon, 2016; Krahe & Gabbiani, 2004; S. M. Sherman, 2001; Swadlow & Gusev, 2001; Viaene et al., 2011a, 2011b, 2011c). The number of spikes in the burst also determines thalamocortical transmission; thalamic bursts with more than one spike were more effective at activating pyramidal cells and somatostatin interneurons in the somatosensory cortex (Hu & Agmon, 2016). Therefore, if cells in different parts of the thalamus produce bursts with different delays after removal from hyperpolarization, or with different numbers of spikes, it will have implications for the effective transmission of information to cortex.

In addition, thalamic cells burst at higher rates during sleep (Fourment et al., 1984; Llinás & Steriade, 2006; Varela & Wilson, 2020; Weyand et al., 2001), when they contribute to the generation of sleep spindles, hallmark oscillations of non-rapid eye movement (NREM) sleep that provide temporal windows for coordination of thalamocortical and hippocampal networks (Astori et al., 2011; Bal et al., 1995; Sirota et al., 2003; Staresina et al., 2015; Steriade et al., 1985, 1987; Varela & Wilson, 2020). Bursts with different properties (latency to burst, number of spikes/burst, and intraburst spike frequency) could thus influence thalamic function across behavioral states, the detection of sensory stimuli during wakefulness and the oscillatory coupling of thalamocortical networks during sleep.

There are reports of a larger T-current in cells of the lateral posterior (LP) nucleus compared to cells in the lateral geniculate (Li et al., 2003; Wei et al., 2011) and of bursts with more spikes in cells of the ventral posterior (VP) compared to the posterior medial nucleus (Landisman & Connors, 2007; Slézia et al., 2011). Cells in higher order were more likely to fire spikes in bursts compared to cells in first-order (FO) nuclei (Ramcharan et al., 2005), and the propensity to burst was also higher in thalamic reticular nucleus (TRN) cells connected to sensory nuclei compared to TRN cells connected to higher-order (HO) dorsal thalamus (Clemente-Perez et al., 2017; Fernandez et al., 2018; Li et al., 2020; Martinez-Garcia et al., 2020). These results suggest that burst properties vary according to the functional organization of the thalamus. One hypothesis is that burst properties will be congruent with the hierarchical level of the network in which a thalamic nucleus is embedded (FO or HO, core or matrix; Guillery & Sherman, 2002; Jones, 1998). It is also possible that the type of information processed by a given nucleus determines the firing properties of its thalamocortical cells, in which case burst properties may be different in nuclei processing different sensory input. To shed light on these hypotheses, we studied the properties of bursts recorded intracellularly (whole-cell patch clamp; rat brain slices) in six thalamic nuclei, one FO and one HO nucleus in each of three sensory systems (somatosensory, visual, and auditory). We then used compartmental models to gain insight on the underlying molecular mechanisms and functional implications of the burst diversity we observed in the in vitro data.

2 MATERIALS AND METHODS 2.1 Animal subjects

We used P11 to 18 days old Sprague–Dawley rats of both sexes (Harlan Sprague–Dawley, Indianapolis, IN). The animals were euthanized via decapitation as part of the procedure of slice preparation. All the experimental procedures were approved according to the animal care guidelines of The University of Chicago.

2.2 In vitro data collection

Intracellular whole-cell patch clamp recordings were performed in current clamp configuration in six thalamic nuclei (Varela & Sherman, 2009, 2007): three FO nuclei (lateral geniculate nucleus, ventral posterior nucleus [VP], and ventral medial geniculate body [vMGB]) and three HO nuclei (lateral posterior nucleus [LP], posterior medial nucleus [POm], and dorsal medial geniculate body [dMGB]). Briefly, 400 μm coronal slices, which are unlikely to preserve connections with the TRN, were prepared from the brains of P11-18 rats and were maintained in a beaker with artificial cerebrospinal fluid (ACSF composed of, in mM: 125 NaCl, 25 NaHCO3, 3 KCl, 1.25 NaH2PO4, 1 MgCl2, 2 CaCl2, and 25 glucose) supplemented with 95% O2–5% CO2. We prepared coronal slices at anteroposterior coordinates that contained the nuclei of interest; the slices were maintained at 30°C for ∼30 min after sectioning, then kept at room temperature for the duration of the experiment. Recordings were performed in a standard patch clamp rig under microscope observation and cells were selected with the aid of the microscope. The inflow rate of ACSF (warmed to 30 ± 2°C before entering the chamber holding the slice) was kept at ∼2 ml/min. The micropipette solution contained (in mM): 117 KGluconate, 13 KCl, 10 (4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid) (HEPES), 2 Na2ATP, 0.4 Na3GTP, 1 MgCl2, 0.07 CaCl2, and 0.1 ethylene glycol tetra-acetic acid (EGTA). Signals were amplified and filtered (30 kHz) with an Axoclamp 2A amplifier, digitized with the Digidata 1200B converter and sampled at 10 kHz (Axon Instruments, Union City, CA). Cells with input resistance below 100 MOhms or access resistance above 30 MOhms were discarded. Square current pulses (median number of pulses per cell = 7, inter-quartile-range [IQR] = 5–8 pulses) of decreasing negative current (average starting pulse −0.41 ± 0.13 nA, subsequent pulses increased by −0.05 ± 0.01 nA) and ≥ 400 ms duration were used to hyperpolarize each cell through a range of physiological voltages from −62.44 to −128 mV from an initial resting potential of −61.41 ± 4.98 mV to induce rebound bursts upon release from hyperpolarization. The burst data resulting from the current injection protocol were collected before the cells were tested as part of the experiments by Varela and Sherman (2007, 2009), and so no modulators or drugs were applied to the cell before or during the current injection protocols used for burst induction used for this manuscript. Only one cell was recorded in each brain slice.

2.3 In vitro burst analysis For every current injection applied to a cell, the recorded voltage trace was analyzed to quantify the features discussed in Section 3. Resting potential was calculated as the average membrane potential in the first 200 ms of the voltage trace, before the negative current pulse started. We estimated the hyperpolarization level preceding burst induction for each current injection pulse as the average membrane potential in the 100 ms immediately before the end of the negative current injection pulse. A burst was identified as a rebound low-threshold spike (LTS) with at least one Na+-K+ spike. For each burst produced after current injection, we quantified several features: number of spikes in the burst, interspike interval (ISI), latency to the first spike, and decay time constant. The spikes were detected in the voltage traces using the findpeaks function in Matlab, followed by visual inspection. We defined a pulse as producing no burst when no Na+-K+ spikes were observed after the hyperpolarization; in most cases, pulses that did not induce a burst were ohmic responses and had no LTS associated with them. Only seven pulses of current injection, one in each of seven different cells evoked an LTS with no Na+-K+ spikes). We never observed tonic firing when cells were released from hyperpolarization. We used the ISIs to estimate the first ISI frequency in spikes/s. Bursts with only one spike were excluded from within-burst spike frequency calculations. Spike frequency adaptation within the burst was calculated as the percent change from first to last ISI frequency for cells with at least four spikes. The latency was calculated as the time from the end of the negative current pulse to the peak of the first spike in the burst. We estimated the decay time constant by fitting the sum of two exponential curves to the voltage trace after the last spike in the burst (Equation (1)). There were two components to the decay, the slower decay time constant was too long (average = 34,662 ms) to explain the drop in voltage following the transient T current. Therefore, we considered the faster component as the estimate for the decay time constant for the T-current dynamics. (1)where V is the membrane potential and t is the time. 2.4 Compartmental models We used the DynaSim toolbox in Matlab (Sherfey et al., 2018) to implement a single compartment model (Equations (2) and (3)) that includes the most relevant voltage-dependent currents of thalamic cells and reproduces the essential features of burst and tonic firing of thalamocortical cells. The membrane potential in the compartment was described by: (2)where V is the membrane potential, Cm is the membrane capacitance (1 μF/cm2), INa and IK are the sodium and potassium currents responsible for the action potential, IT is the low-threshold calcium current responsible for burst firing. Iapp (in μA/cm2) was used to simulate current injection into the cell. In this model, the voltage-dependent currents are variants of the same generic Hodgkin–Huxley (HH) equation (Hodgkin & Huxley, 1952): (3)which expresses each current, Ij, as the product of the maximum conductance, gj, activation, m, and inactivation, h, variables, and the difference between the membrane and reversal potentials (V – Ej). We chose parameters as in the study by Benita et al. (2012), Destexhe et al. (1996), and Soplata et al. (2017), with modifications to ILeak and IKLeak. Here, we opted for a more depolarized model, which may be more similar to wakefulness conditions. We used gKLeak = 0.014 mS/cm2, EKLeak = ELeak = −60 mV. gT was varied between 0.15 and 1 mS/cm2 in simulations where we shifted the activation and inactivation curves. For simulations for burst oscillatory frequency (Section 3.8), gT was kept at 1 mS/cm2.

In one of our models, we also implement a neurotransmitter release probability variable (Benita et al., 2012). This variable remains at a steady-state probability of release, until a presynaptic spike reduces the release probability by a fraction of 0.1 and then it recovers with a time constant of 400 ms. To test the implications of different synaptic release probabilities for thalamocortical transmission, we connected the single compartment model of the thalamic cell with a compartmental model of either one pyramidal cell or an interneuron, with the same currents and parameters used in the network model of Benita et al. (2012), except we lowered the equilibrium potential for the leak current in the Pyramidal cell to −70 mV (Benita et al., 2012 used −60.95 mV) to increase the dynamic range of excitatory postsynaptic potential (EPSP) amplitudes evoked by the thalamic cell. The pyramidal cell model was a two-compartment model with soma (including leak, A-type, and slow potassium currents, as well as sodium and potassium action potential generating currents) and one dendrite (including inwardly rectifying potassium current, persistent sodium current, slow calcium-dependent potassium current, and high-threshold calcium current). The interneuron had a single compartment with potassium leak current and the sodium and potassium action potential generating currents; the thalamic cell model was connected either to the pyramidal cell dendrite or to the interneuron through an α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) current. The scripts for the models used in this article are available at https://github.com/nidhi-desai/thalamic-distinct-burst. The code implementing the individual currents and model specifications is available at https://github.com/asoplata/dynasim-extended-benita-model.

2.5 Statistical analyses

For population results, we report the mean and SD in the text and display the population distribution of the calculated metrics in figures in box and whisker plots. Because the distributions of the metrics we calculated were non-Gaussian and the samples sizes small, we opted for nonparametric statistical tests. We used the Kruskal–Wallis test for group comparisons. We used Kruskal–Wallis test with post hoc analysis using Tukey–Kramer correction for multiple comparison tests to test for differences in burst properties across cells. Also, we used the Wilcoxon signed-rank test to compare paired data under difference conditions.

To estimate the change in spikes per burst and within-burst spike frequency (spikes/s) as a function of hyperpolarization, we used a generalized linear model (GLM; Equations (4) and (5); Kramer & Eden, 2016; https://github.com/Mark-Kramer/Case-Studies-Kramer-Eden) to estimate the spikes/burst or their frequency (μ) as a linear function of the hyperpolarization level (X) induced by the negative current pulses, assuming a Poisson distribution of errors (Equation (4)). The model included two parameters, β0, representing the expected value of the dependent variable at baseline membrane potential, and β1, representing the expected change in the dependent variable for each unit of change in the covariate. The model was fit using a maximum likelihood approach to estimate the values of the parameters that best predict the data. Parameter estimates based on this method are often normally distributed, which allowed us to define 95% confidence intervals at ±2 times the standard error for each parameter (obtained from Matlab's maximum likelihood estimation). From the fitted model, we estimated the change in the response variable (spikes/burst, spike frequency) per mV change in membrane potential from the equivalent equation (5). The Wald test was used to test the significance of the hyperpolarization level parameter (β1). The Wald test assesses whether a parameter is significantly different from 0, in which case it is considered to have a significant contribution to the model (Kramer & Eden, 2016). We used the GLM to characterize the relation between burst properties and hyperpolarization in each individual cell; because we did not attempt to develop general predictive models, we did not include regularization parameters. (4) (5)In the analyses in which we systematically shifted the levels of T-channel conductance and its voltage dependence, we used the distributions of burst properties in each nucleus from our in vitro data (Figures 1(d) and 4(b)) to determine whether the burst properties obtained from model simulations more closely resembled bursts from FO or from HO nuclei. First, we calculated the probability density functions for the distribution of spikes per burst and latency for each of the six nuclei; for each of the simulated bursts, we then calculated the probability of seeing a burst with the same number of spikes per burst and latency in each of the six nuclei (by multiplying the probability of observing a burst with the same number of spikes in each nucleus by the probability of observing a burst with the same latency). We used the nucleus with the highest combined probability to determine whether FO or HO nuclei most closely resembled the burst properties produced in the model by a particular combination of T-channel conductance and voltage dependence. Number of spikes in bursts evoked by hyperpolarization of TC cells in different nuclei. (a) Cells were recorded in current clamp and injected with step pulses to evoke rebound bursts. (b) For each burst, we quantified the number of spikes and time-dependent features like latency to spike and inter-spike interval (see Section 2 for details). (c) Examples of bursts from six thalamic cells from different nuclei show different number of spikes/burst at similar hyperpolarization level prior to the burst across the cells (average − 90.92 ± 0.90 mV sd). (d) Distributions of number of spikes/burst (jittered to help visualization of individual data points) for all bursts across the population of thalamic cells in first-order (blue) and higher-order (red) nuclei. Boxes indicate the median and 25%–75% quartiles. dLGN, dorsal lateral geniculate nucleus; dMGB, dorsal medial geniculate body; LP, lateral posterior nucleus; POm, posterior medial nucleus; vMGB, ventral medial geniculate body; VP, ventral posterior nucleus [Color figure can be viewed at wileyonlinelibrary.com] 3 RESULTS

We recorded intracellularly in current clamp mode from 91 cells in six nuclei of the dorsal thalamus (sample size per nucleus in Table 1). All of the nuclei are sensory regions of the thalamus; three of the nuclei (dorsal lateral geniculate nucleus [dLGN], VP, vMGB) are FO in the visual, somatosensory, and auditory systems, whereas the other three (LP, POm, and dMGB) are HO functionally associated with the same sensory systems (Guillery & Sherman, 2002; Prasad et al., 2020). Thus, this sample allowed us to investigate how the properties of bursts resulting from rebound after hyperpolarization relate to thalamocortical connectivity and to sensory modality. We applied steps of negative current to induce a rebound burst at the end of the current step (Figure 1(a)). For each burst, we quantified several features to characterize its dynamics, such as the number of spikes, within-burst frequency of ISIs, latency to the first spike (Figure 1(b)) and the decay time from the last spike in the burst to the baseline membrane potential (see Section 2 for details).

TABLE 1. Descriptive statistics across recorded nuclei: Spikes per burst—median, (inter-quartile range), (minimum and maximum); hyperpolarization voltage—mean ± standard deviation for all traces for all cells in each nucleus Nucleus Sensory modality Functional order Number of cells (pulses) Percent of pulses with no burst Spikes per burst median, iqr, range Hyperpol-arization (mV) LGN Visual First 13 (87) 39 1, (1–1), (1–3) −90 ± 14 LP Visual Higher 15 (107) 24 4, (2–5), (1–7) −93 ± 14 vMGB Auditory First 9 (50) 14 1, (1–1), (1–2) −83 ± 15 dMGB Auditory Higher 20 (128) 30 3, (2–4), (1–6) −90 ± 14 VP Somato-sensory First 16 (99) 2 5, (3–5), (1–7) −78 ± 7 POm Somato-sensory Higher 18 (130) 38 3, (2–4), (1–6) −87 ± 12 Abbreviations: dLGN, dorsal lateral geniculate nucleus; dMGB, dorsal medial geniculate body; LP, lateral posterior nucleus; POm, posterior medial nucleus; vMGB, ventral medial geniculate body; VP, ventral posterior nucleus. 3.1 Visual and auditory thalamic neurons in FO nuclei produce bursts with less spikes than in HO nuclei

Some cells were more likely to produce a burst when released from hyperpolarization. We found that 26% of the negative current pulses did not induce a rebound burst (defined as a LTS—with at least one Na+-K+ spike), even though the average hyperpolarization level during those pulses was −89.5 ± 15.17 mV. The percentage of pulses that did not induce a burst was different across thalamic nuclei, ranging from 2% in VP to 39% in dLGN (see Table 1 for all nuclei). The “no-burst” percentages include a few current pulses that evoked an LTS but no Na+-K+ action potentials, something that was rare in our sample (seven cells from vMGB, dMGB, dLGN, and VP produced an LTS with no Na+-K+ spikes after one pulse of current injection, all the other hyperpolarizing pulses induce bursts with Na+-K+ spikes in these cells).

When a burst occurred, it had between one and seven spikes. Figure 1(c) shows representative examples of bursts evoked in six different cells recorded in each of the six nuclei after a negative current pulse that brought the six cells to a similar hyperpolarization level. These examples show that even at similar hyperpolarization levels, cells in different nuclei produced bursts with different number of spikes. The population results (Figure 1(d); median values per nucleus in Table 1), showed that in FO nuclei, cells in the visual and auditory nuclei mostly had one spike/burst, which was significantly different from somatosensory FO cells, which had five spikes/burst on average (p < .001, Kruskal–Wallis test); in contrast, we did not find significant differences among the HO nuclei of different sensory systems (average LP = 4, dMGB = 3, POm = 3; p > .27, Kruskal–Wallis test). When comparing FO with HO nuclei in individual sensory systems, the HO nucleus in the visual and auditory systems had more spikes/burst compared to their FO counterparts, while the FO nucleus had more spikes/burst in the somatosensory system (p < .001, Kruskal–Wallis test).

These results suggest that sensory HO nuclei and VP consist of cell populations that produce a broad range of spikes/burst, higher on average than in the other nuclei, and with similar distributions in HO areas (Figure 1(d)). In addition, we found that in FO nuclei the number of spikes within bursts are determined by the specific sensory system. Specifically, FO cells of the visual and auditory system produced bursts that were often limited to one spike, whereas the VP nucleus stood out from the others as having the highest proportion of bursting cells, which also produced the bursts with the highest number of spikes.

3.2 The number of spikes per burst remains stable with hyperpolarization

Because the number of spikes in a burst may depend on the hyperpolarization level of the cell before the burst, we analyzed how the number of spikes per burst changed depending on the average membrane potential in a 100 ms window before the end of the current injection to the cell. Figure 2 shows the number of spikes per burst at different hyperpolarization levels for each cell in the six nuclei starting with zero referring to the least hyperpolarized trace which lead the cell to burst (yellow lines—cells with constant number of spikes and green lines—cells with varying number of spikes with hyperpolarization). For the population, we found that 38% (n = 29) of the cells that produced rebound bursts (n = 77) had a constant number of spikes regardless of the hyperpolarization level, and 62% (n = 48) showed changes in number of spikes with increased hyperpolarization. The fraction varied across nuclei, with both dLGN and vMGB being the most stable with hyperpolarization; in both dLGN and vMGB, 67% (12 out of 18 cells; Figure 2(a,b)) showed a constant number of spikes with hyperpolarization, while only 6% of cells from VP (1 out of 16 cells; Figure 2(c)) followed this trend. In the HO group (LP, dMGB, POm), a minority of cells (37%,16 out of 43 cells; Figure 2(d,e,f)) showed no change in the number of spikes with increasing hyperpolarization.

Number of spikes per burst at increasing hyperpolarization levels. Each line represents data from one cell (jittered in y-axis); zero in the x-axis corresponds to the least hyperpolarized pulse that led to a burst, and subsequent points indicate more hyperpolarized pulses with respect to this zero level. Each panel contains cells from six different nuclei (first order—(a) dLGN, (b) vMGB, (c) VP and higher order—(d) LP, (e) dMGB, (f) POm). Yellow lines represent cells for which the number of spikes per burst were constant irrespective of the hyperpolarization level, and green lines represent cells for which the number of spikes per burst varied with hyperpolarization. The number of cells in each nucleus belonging to one of the two types is included in the textbox on the top-right corner of each panel. Note that the range of the x- and y-axes was adjusted for each nucleus and is not same in all panels. dLGN, dorsal lateral geniculate nucleus; dMGB, dorsal medial geniculate body; LP, lateral posterior nucleus; POm, posterior medial nucleus; vMGB, ventral medial geniculate body; VP, ventral posterior nucleus [Color figure can be viewed at wileyonlinelibrary.com]

We then looked specifically at cells which showed a change in the number of spikes per burst with increasing hyperpolarization (n = 49). We compared the number of spikes produced by the first current pulse which evoked a burst in a cell, to the number of spikes produced at a higher hyperpolarization level. We found that 34 cells showed an increase in number of spikes by an average of one spike, with an average increase in hyperpolarization of 12.5 mV (from −72.83 to −85.32 mV). The remaining 15 cells did not show a consistent relationship between number of spikes and hyperpolarization, meaning that the spikes per burst went up and down with subsequent current pulses. Even in VP cells, which had the largest number of cells in which the number of spikes/burst changed with hyperpolarization, the observed changes were small (one spike on average for a hyperpolarization difference of 11.77 mV). In a subset of cells with stronger hyperpolarization (average = 22.43 mV from −73.22 to −95.65 mV, n = 22), we still found that the increase in number of spikes was one spike on average.

Lastly, to estimate the relation between spikes per burst and hyperpolarization more precisely, we used a GLM of the spikes per burst with the hyperpolarization potential as covariate; this model showed narrow and nonsignificant changes in the number of spikes with hyperpolarization (average increase in number of spikes per millivolt of hyperpolarization = 1.3% C.I. = [−8.67, 6.21], n = 49; p value = .67 Wald test). Although the confidence intervals of the GLM estimates were broad, altogether this set of results showed little change in the number of spikes with hyperpolarization in the thalamic cells we sampled. Therefore, regardless of the order or the sensory modality, the number of spikes/burst remained fairly stable for a given cell within the range of physiological membrane potential.

3.3 Increase in within-burst spike frequency with hyperpolarization

Even if the number of spikes remains similar, the level of hyperpolarization before the pulse may influence the frequency (spike rate per second) at which the spikes in the burst occur. Figure 3(a) displays raw traces of the bursts of two sample cells at increasingly hyperpolarized membrane potentials; in one cell, the number of spikes increases with hyperpolarization and, in the other one it remains constant, but both cells show an increase in the spike rate of the first two burst spikes with hyperpolarization (Figure 3(b–e) shows all cells in LP, dMGB, VP and POm, respectively). dLGN and vMGB neurons were not included in this analysis since they mostly had one spike per burst. We compared the spike frequency of the first two spikes in the burst produced by the least hyperpolarizing current pulse, which evoked a burst in a cell (0 in panels 3(b–e)), to the spike frequency produced by at least 10 mV of additional hyperpolarization from that level for the 46 cells which had at least two spikes per burst. In this sample, 84.78% of the cells (n = 39) showed an increase in frequency by 46.4 ± 34.46 spikes/s (19.1% increase on average) from an initial frequency of 242.48 ± 64.69 spikes/s (p < .001, Wilcoxon signed-rank test) with an average increase in hyperpolarization of 12.19 mV, from −73.64 to −85.83 mV. In a subset of cells (n = 19), in which the hyperpolarization was increased further by an additional 10.44 mV, from −84.76 to −95.21 mV, the average percent increase in frequency was just 2.17% (p = .56, Wilcoxon signed-rank test). This showed that the initial increase in hyperpolarization has the largest effect on within-burst spike frequency and this effect saturates as the cell is hyperpolarized further.

Increase in within-burst spike frequency with hyperpolarization. (a) Example bursts (from two VP cells) showing an increase in the spike rate with hyperpolarization (dotted lines), irrespective of the number of spikes per burst increasing (cell in green) or remaining constant (cell in yellow) with hyperpolarization. (b–e) Each line represents the frequency of the first intra-burst spike interval for one cell, at increasing hyperpolarization levels from the first level that produced a burst. Panels contain data for cells from four different nuclei—(b) LP, (c) dMGB, (d) POm, (e) VP. Note that the range of the x-axis is not same in all panels. (f) We found no statistical difference in the frequency across nuclei (LP, dMGB, VP and POm; dLGN and vMGB were not included in this analysis because of low number of spikes per bursts). Blue = FO; red = HO. (g) Distributions of spike frequency adaptation between last and first intra-burst intervals for cells with at least four spikes/burst show POm having lower adaptation compared to other two HO nuclei. dLGN, dorsal lateral geniculate nucleus; dMGB, dorsal medial geniculate body; LP, lateral posterior nucleus; POm, posterior medial nucleus; vMGB, ventral medial geniculate body; VP, ventral posterior nucleus [Color figure can be viewed at wileyonlinelibrary.com]

Even in the group of cells which had a constant number of spikes (n = 18; yellow lines in Figure 3(a–e)) with hyperpolarization, we observed the same trend of an increase in frequency with hyperpolarization in 17 out of 18 cells; these cells showed an increase in frequency of 41.34 ± 37.17 spikes/s with an average increase in hyperpolarization of 12.85 mV (p < .001, Wilcoxon signed-rank test). Applying the GLM approach (to all cells with at least two spikes per burst; n = 46) to estimate the within-burst spike frequency with the hyperpolarization voltage as covariate, showed that the changes in spike frequency with hyperpolarization were small (average increase in frequency per millivolt of 0.75% with C.I. = [−0.2, 1.67], n = 53), but the trend was significant in 38% of the cells, with an average increase of 1.27% (p < .05, Wald test). When we looked at the within-burst spike frequency in different nuclei across all bursts with at least two spikes per burst (n = 46 cells), we did not find significant differences among any of the nuclei (p = .22, Kruskal–Wallis test; Figure 3(f)).

Lastly, for cells with at least four spikes/burst (n = 34), we quantified within-burst spike frequency adaptation as the percent change in the frequency at the last spike interval in the burst compared to the frequency at the first interval; the average within-burst spike frequency adaptation was 58.06 ± 12.46% (n = 34). When we compared the within-burst adaptation at two different hyperpolarization levels (average = −75.11 and − 85.01 mV; average difference between levels = 10.09 mV), the cells showed no significant difference in their within-burst spike frequency adaptation (p = .19, Kruskal–Wallis test). Among HO, cells in POm had significantly lower within-burst adaptation (POm = 50.98 ± 13.6%) compared to the other two HO nuclei (Figure 3(g); LP = 59.4 ± 14.88%, dMGB = 64.16 ± 7.9%; p < .027, Kruskal–Wallis test).

This set of results suggests that, irrespective of the number of spikes per burst remaining constant or changing with hyperpolarization level, the spike frequency of the first ISI in a burst increases with more hyperpolarization but not the spike frequency adaptation within the burst.

3.4 Longer latencies to burst in HO nuclei and dLGN neurons

The latency with which bursts are produced after hyperpolarization could influence the band-pass filter and oscillatory properties of thalamic neurons. We quantified latency as the time (in milliseconds) from the end of the current injection pulse to the peak of the first spike in the burst. Figure 4(a) shows bursts from four cells that are hyperpolarized to a similar membrane potential level (−89.25 ± 0.96 mV), and yet the vMGB and VP cells (blue traces) produced a rebound burst with much shorter latency than the dMGB and POm cells (red traces). The population data (Figure 4(b)) showed that the HO cells have significantly longer latencies than FO cells in the auditory (vMGB = 49.42 ± 21.83 ms and dMGB = 135.96 ± 64.90 ms) and somatosensory systems (VP = 48.96 ± 31.96 ms and POm = 135.96 ± 64.90 ms; p < .001, Kruskal–Wallis test). In the visual system, the latencies were not significantly different between the FO and HO nuclei (dLGN = 85.96 ± 39.96 ms and LP = 101.51 ± 79.35 ms; p = .99, Kruskal–Wallis test). Among FO nuclei, latencies in dLGN were significantly longer than vMGB and VP (p < .001, Kruskal–Wallis test). dMGB had the longest latencies among all nuclei (p < .001, Kruskal–Wallis test). The FO cells also covered a narrower range of latencies compared to HO or dLGN cells (Figure 4(b)). Even when we compared the latencies at a particular hyperpolarization (−84.83 ± 3.49 mV), we still found that FO cells in the auditory and somatosensory system had lower latencies compared to their HO counterparts (vMGB = 44.56 ± 22.37 ms and dMGB = 131.04 ± 47.88 ms; VP = 38.17 ± 22.83 ms and POm = 94.98 ± 60.97 ms, p < .014, Kruskal–Wallis test).

Latencies to burst reach higher values in higher-order (HO) nuclei and dorsal lateral geniculate nucleus (dLGN). (a) Bursts evoked from similar hyperpolarization levels in two cells of the auditory (left) and somatosensory (right) systems display short latency in first-order (FO) nuclei and longer latency in the corresponding HO. (b) Population distribution of the latency values for all evoked bursts. (c) Lines represent burst latencies at different hyperpolarization levels for each cell in FO (blue) and HO (red) nuclei in visual (i), auditory (ii) and somatosensory (iii) systems and show a decrease in latency with increased hyperpolarization. Insets show exponential fits for each of the cells in the raw data plots, with the average of the fits shown by darker blue and red lines (average R2 for fits in the insets: (i) .97 ± .04, (ii) .99 ± .01, (iii) .98 ± .05). Note the difference in latencies between FO and HO at every level of hyperpolarization in auditory and somatosensory systems. (d) A negative correlation was observed in the plots of latency against number of spikes per burst for FO and HO nuclei (R2 indicates goodness-of-fit for a linear model). Blue = FO; red = HO [Color figure can be viewed at wileyonlinelibrary.com]

We then studied the effect of hyperpolarization on latency (Figure 4(c)). For 97% (n = 69) of cells, the latency decreased on average 40.72 ± 33.7 ms (from an initial value of 124.72 ± 75.74 ms) when hyperpolarized by an additional 12.63 mV from −74.02 mV (p < .001, Wilcoxon signed rank test). The pulses with lower hyperpolarization produced bursts with longer latency, and as the hyperpolarization increased, most cells settled into characteristic latencies. We found that the relation between hyperpolarization and latency was fitted well by a sum of two exponential functions (average goodness-of-fit R2 = .98 ± .04; exponential fits for all cells in the insets of Figure 4(c)). To test whether the latencies settle into similar values, for each cell, we used the fitted model to estimate the fastest latencies to produce a rebound burst between −70 and −100 mV of hyperpolarization. This analysis found that the shortest latency for FO cells (45.25 ± 26.84 ms) was significantly lower than the shortest latency estimated for HO cells (88.65 ± 57.72 ms, p < .001, Kruskal–Wallis test). These results suggest that FO and HO cells in the auditory and somatosensory thalamus differ in their rebound oscillatory properties, such that the FO cells will be able to produce rebound bursts at faster frequencies (up to about 20 Hz based on the fastest latencies estimated from the exponential model fits), whereas many HO cells may have an upper limit for rebound burst firing at about 10 Hz. Instead, the latencies we observed in the visual thalamus suggest that these cells can follow similar frequencies of bursting regardless of the order of the nucleus. We performed an additional analysis to look at the correlation between latency and the number of spikes and found a small tendency for shorter latencies to occur with more spikes per burst, and the trend was similar in FO and HO nuclei (Figure 4(d)).

Another factor that can determine the frequency of bursts in thalamocortical cells is the time that it takes for the membrane potential to decay back or recover to baseline levels after a burst. To find out whether the latency to burst was associated with different recovery times, we studied the correlation of latency with the time it took for the cell to decay back to resting membrane potential after the burst. For this analysis, we quantified the decay time constant by fitting the sum of two exponential curves to the voltage trace after the last spike in the burst ended (goodness-of-fit R2 = .98 ± .02 for all bursts). The initial voltage drop was largely explained by the exponential function with the shortest time constant (78.82 ± 53.49 ms). When comparing cells across nuclei (Figure 5(a)), we did not find a clear association between the decay time constant and the order or sensory modality of the nucleus, and the results were more variable than the spikes/burst and latency results reported above. We found that the decay time constant was fastest for dLGN (57.08 ± 23.35 ms) and POm cells (56.76 ± 24.51 ms), followed by dMGB (72.5 ± 33.6 ms), vMGB (74.54 ± 25.44 ms), LP (92.6 ± 69.17 ms), and VP (106.16 ± 74.51 ms). In the visual system, FO cells on average had shorter decay time than HO cells (p < .01), while in the somatosensory system FO cells had longer decay time compared to HO cells (p < .001), and for auditory no significant difference was found between FO and HO cells (p = .86, all Kruskal–Wallis tests). We did not find a significant correlation between latency to burst and the decay time constant after the burst (r = −.18, Figure